POWDER PROCESSING AND MECHANICAL PROPERTIES OF Ag0.86Pb19SbTe20 (LAST)
AND Pb0.95Sn0.05Te – PbS 8% (PbTe-PbS) THERMOELECTRIC MATERIALS
By
Jennifer Elisabeth Ni

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTORATE OF PHILOSOPHY
Materials Science Engineering
2012

ABSTRACT
POWDER PROCESSING AND MECHANICAL PROPERTIES OF Ag0.86Pb19SbTe20 (LAST)
AND Pb0.95Sn0.05Te – PbS 8% (PbTe-PbS) THERMOELECTRIC MATERIALS
By
Jennifer Elisabeth Ni
Thermoelectric (TE) materials convert between thermal and electrical energy and when
used with existing processes will increase the efficiency via waste heat recovery.
Ag0.86Pb19SbTe20 (LAST) and Pb0.95Sn0.05Te – PbS 8% (PbTe-PbS) materials exhibit good
thermoelectric (TE) properties and have potential applications as thermoelectric generators in
waste heat recovery. However, to fully characterize the thermo-mechanical behavior of LAST
and PbTe-PbS materials under in-service conditions, knowledge is needed of the mechanical and
thermal properties at room and high temperature.
As fracture strength is inversely proportional to the square root of grain size, cast ingots
were powder processed to reduce powder particle size. Three different powder processing
methods were used (1) dry milling only, (2) wet milling only, or (3) dry milling and wet milling
The specimens were fabricated using hot pressing or pulsed electric current sintering (PECS)
from planetary ball milled powders.
In this study, elastic moduli, including Young's modulus, shear modulus, and Poisson's
ratio, were measured dynamically using resonant ultrasound spectroscopy (RUS) at room
temperature and as a function of temperature up to 663 K. The room temperature porosity
dependence for Young’s modulus followed the empirical exponential relationships common for
brittle materials, with a material dependent constant bPE of 3.5 and 1.3 for LAST and PbTe-PbS,

respectively. The room temperature Young’s modulus for a theoretically dense specimen was
58.4 ± 0.6 GPa and 56.2 ± 0.4 GPa for for LAST and PbTe-PbS, respectively. For hot pressed
PbTe-PbS specimens, the Vickers indentations mean hardness and fracture toughness was 1.18 +
1/2

0.09 GPa and 0.35 ± 0.04 MPa·m

.

The coefficient of thermal expansion is important for understanding the mechanical
response of a material to a thermal gradient or a thermal transient. For PbTe-PbS the coefficient
of thermal expansion measured using dilatometry and high temperature x-ray diffraction was
-6

-1

21.5 x 10 K .
Bloating during post-densification annealing was measured indirectly using resonant
ultrasound spectroscopy and dilatometry and directly using scanning electron microscopy. Dry
milled only PECS-processed PbTe-PbS specimens did not bloat during post-densification
anneals up to 936 K. Hot pressed and PECS-processed specimens processed from wet milled
and dry and wet milled powder bloated during densification anneals at temperatures over 603 K.

DEDICATION

For my brother,
David Randolph Ni

iv

ACKNOWLEDGMENTS

It is a pleasure to thank the many people who made this thesis possible.

It is difficult to overstate my gratitude to my Ph.D. supervisor, Professor Eldon Case. With
his enthusiasm, his inspiration, and his great efforts to explain things clearly and simply, he
helped to make Materials Science fun for me. Throughout my thesis-writing period, he provided
encouragement, sound advice, good teaching, and extensive editing. I would have been lost
without him.

I would like to acknowledge the help of my lab colleagues, Dr. Fei Ren, for his guidance in
learning the equipment in lab, especially teaching me the RUS analysis, Robert Schmidt, Ryan
Stewart, and Daniel Kleinow for powder processing, Kristen Khabir for help with laser particle
size analysis, Edward Timm for hot pressing and Karl Dresch for PECS-processing.

Thank you to the Center for Advanced Microscopy at Michigan State University. They
carefully maintained each of the scanning electron microscopes that were used in this
dissertation, as well as provided advice and encouragement.

Thank you to the High Temperature Materials Laboratory at Oak Ridge National Laboratory.
The temperature dependent elastic moduli and thermal expansion measurements were performed
using the equipment at the High Temperature Materials Laboratory. I would like to offer thanks
to both Edgar Lara-Curzio and Rosa Trejo for their advice, training and guidance during my
visits to Oak Ridge National Laboratory.

v

TABLE OF CONTENTS
List of Tables .............................................................................................................................. xi
List of Figures ............................................................................................................................ xvi
1.0 Introduction .......................................................................................................................... 1
1.1 Thermoelectrics for use in waste heat recovery ................................................................... 1
1.2.0 Figure of merit as a measure of efficiency for thermoelectrics ............................ 2
1.3.0 Importance of mechanical properties for thermoelectric materials ...................... 4
1.3.1 Thermal shock/thermal fatigue resistance ................................................ 5
1.3.2 Elastic moduli .......................................................................................... 6
1.3.3 Coefficient of thermal expansion .............................................................. 9
1.3.4 Bloating at elevated temperatures ............................................................. 10
1.3.5 Effect of porosity in brittle materials ........................................................ 11
1.3.6 Effect of porosity in thermoelectrics ......................................................... 12
1.4.0 Fabrication and mechanical testing of thermoelectric materials ........................... 14
1.5.0 References ............................................................................................................. 17
2.0 Experimental Procedure .................................................................................................... 23
2.1.0 Ingot Fabrication ................................................................................................... 23
2.2.0 Powder processing ................................................................................................ 23
2.2.1 CGSR (Crushed, Ground, Sieved, Reground) .......................................... 23
2.2.2 Milling jar and Media for milling ............................................................. 25
2.2.3 Milling....................................................................................................... 26
2.2.3.1 Dry milling ................................................................................. 26
2.2.3.2 LAST milling – Wet milling with D = 10 mm media
and hexane ................................................................................. 27
2.2.3.3 LAST and PbTe-PbS wet milling with D= 20 mm
and D = 3 mm alumina media with hexane ............................... 27
2.2.3.4 PbTe-PbS Wet milling D= 20 mm and 3 mm with ethanol
– No Dry milling ........................................................................ 28
2.2.3.5 Mixing nanoparticle additions with PbTe-PbS powders ............ 29
2.2.4 Removing media and powder from milling jar after wet milling. ............ 29
2.3.0 Cleaning the media, jar, and sieves ....................................................................... 30
2.3.1 Cleaning the alumina milling media ......................................................... 30
2.3.2 Cleaning the alumina lined milling jar...................................................... 30
2.3.3 Cleaning the sieves .................................................................................. 31
2.4.0 Powder particle size determination using SEM ................................................... 32
2.5.0 Powder particle size determination using laser particle analysis .......................... 32
2.5.1 Analysis liquid for laser particle analysis ................................................. 33
2.5.2 Batch runs for laser particle analysis ........................................................ 34
2.6.0 Densification via Hot pressing (HP) ..................................................................... 35
2.7.0 Densification via Pulsed Electric Current Sintering (PECS) ................................ 36
2.8.0 Specimen Cutting and polishing ........................................................................... 40
vi

2.8.1 Mounting in epoxy .................................................................................... 40
2.8.2 Mounting on an aluminum stub. ............................................................... 41
2.8.3 Polishing specimens .................................................................................. 42
2.8.4 Washing the polishing wheel by hand ....................................................... 42
2.8.5 Washing the polishing wheel using an ultrasonic cleaner ....................... 44
2.9.0 Index of refraction and extinction coefficient measured via ellipsometry............ 45
2.10.0 X-ray diffraction ................................................................................................. 45
2.11.0 Hardness measured via Vickers indentations ...................................................... 46
2.11.1 Calibration of indenters at each load ....................................................... 46
2.11.2 Vickers Hardness ..................................................................................... 46
2.13.0 Fracturing specimens .......................................................................................... 47
2.14.0 Thermal annealing to determine grain size and generate bloating ..................... 47
2.15.0 Grain size measured by linear intercept method ................................................. 48
2.16.0 Room temperature elastic moduli measured via Resonant Ultrasound
Spectroscopy (RUS)........................................................................................... 51
2.17.0 High temperature elastic moduli measured via RUS ......................................... 53
2.18 Calculating the acoustic Debye temperature.......................................................... 55
2.19 Thermal Expansion Measurements ........................................................................ 56
2.19.1 Maximum temperature of the thermal cycle during thermal
expansion measurements was 603 K in each experiment ...................... 56
2.19.2 Thermal expansion measured using two different maximum
Temperatures .......................................................................................... 56
2.20.0 References ........................................................................................................... 57

3.0 Porosity dependence of elastic moduli in LAST Lead-antimony-silver-tellurium)
thermoelectric materials ............................................................................................................. 59
3.1. Introduction ............................................................................................................. 60
3.2. Background ............................................................................................................. 61
3.2.1 Effect of porosity on physical properties .................................................. 61
3.2.2 Effect of porosity on thermoelectric properties ........................................ 62
3.3. Experimental procedure ......................................................................................... 66
3.3.1 Specimen preparation................................................................................ 66
3.3.2 Specimen Preparation and Microstructural Examination ......................... 69
3.3.3 Resonant Ultrasound Spectroscopy (RUS) measurements ....................... 69
3.4. Results and Discussion ........................................................................................... 69
3.4.1 Microstructural analysis ........................................................................... 69
3.4.2. Room temperature elastic moduli as a function of porosity .................... 70
3.4.2.1. Young’s modulus and shear modulus as a
function of porosity .................................................................... 72
3.4.2.2. Simulation of errors in modulus-porosity
parameters as a function of the uncertainty in mass
density measurement. ................................................................. 81
3.4.2.3. Poisson’s ratio as a function of porosity ................................... 83
3.5. Summary and Conclusions ..................................................................................... 87
vii

3.6 References ................................................................................................................ 90
4.0 Room temperature Young’s modulus, shear modulus, Poisson’s ratio and hardness of
PbTe-PbS thermoelectric materials...................................................................................... 94
4.1 Introduction ............................................................................................................ 95
4.2 Experimental Procedure ......................................................................................... 96
4.3 Results and Discussion ............................................................................................ 101
4.4. Summary and Conclusions ..................................................................................... 120
4.5 References ................................................................................................................ 122
5.0 Bloating in (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 thermoelectric specimens
as a result of processing conditions ..................................................................................... 128
5.1 Introduction ............................................................................................................. 129
5.2 Experimental Procedure ......................................................................................... 131
5.3 Results and Discussion ............................................................................................ 133
5.4 Summary and Conclusions ...................................................................................... 139
5.5 References ................................................................................................................ 142
6.0 Fracture mode, microstructure, and temperature-dependent elastic moduli for
thermoelectric composites of PbTe-PbS with SiC nanoparticle additions .......................... 144
6.1.0 Introduction ........................................................................................................... 145
6.2.0 Background: Nanostructures in thermoelectric materials ..................................... 147
6.3.0 Experimental Procedure ........................................................................................ 148
6.4.0 Results and Discussion ......................................................................................... 154
6.4.1 Measurements on as-densified specimen .................................................. 154
6.4.1.1 Room temperature elasticity measurements of as-densified
specimens .............................................................................................. 158
6.4.1.2 Microstructure of as-densified fracture surfaces........................ 158
6.4.1.3 Mechanical property implications of SiCnp additions .............. 162
6.4.2 Room temperature microstructure and elastic moduli analysis following
post-densification annealing ..................................................................... 163
6.4.2.1 Volume change after post-densification annealing ................... 163
6.4.2.2 Bloating-induced porosity generated by post-densification
annealing ............................................................................................... 166
6.4.2.3 Effect of SiCnp additions on bloating and grain growth .......... 166
6.4.2.4 Cleaning of powder surfaces by PECS ...................................... 170
6.4.3 High Temperature elasticity measurements .............................................. 171
6.4.3.1 Temperature behavior of Poisson’s ratio as a function of
SiCnp addition ............................................................................ 180
6.4.3.2 Hysteresis in elastic moduli measurements for hot pressed
specimens ................................................................................... 181
6.4.3.3 Observations in the literature of elasticity changes due to
bloating during post-densification annealing of other
viii

materials ..................................................................................... 182
6.5.0 Summary and Conclusions ................................................................................... 184
6.7.0 References ............................................................................................................ 187
7.0 The effect of processing on strain during thermal expansion measurements for
(Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 thermoelectric material .................................. 195
7.1.0 Introduction .......................................................................................................... 196
7.2.0 Experimental procedure ........................................................................................ 198
7.2.2 Microstructural analysis via scanning electron microscopy ..................... 198
7.2.3 Thermal expansion experimental procedure ............................................. 201
7.2.3.1 Dilatometery measurements....................................................... 201
7.2.3.2 High-temperature x-ray diffraction measurements .................... 202
7.3.0 Results and discussion ....................................................................................... 202
7.3.1 Possible bloating monitored via SEM....................................................... 202
7.3.2 Thermal Expansion Results ................................................................... 204
7.3.2.1 CTE measurements via dilatometer (TMA) ............................. 204
7.3.2.2 CTE measurements via x-ray diffraction .................................. 210
7.3.2.3 Comparison of the CTE results to the literature ........................ 210
7.3.3 Hysteresis in thermal expansion measured by dilatometery ..................... 216
7.3.3.1 Hysteresis in thermal expansion caused by bloating ................. 216
7.3.3.2 Comparison to bloating monitored by elastic moduli
measurements ............................................................................. 219
7.4.0 Summary and Conclusions ....................................................................... 220
7.5.0 References ................................................................................................. 222
8.0 Summary and Conclusions .................................................................................................. 227
8.1.0 Porosity dependence of the elastic moduli for LAST ........................................... 227
8.2.0 Room temperature mechanical properties for PbTe-PbS ...................................... 227
8.2.1 Hardness measured via Vickers indentation ............................................. 228
8.2.2 Fracture toughness measured via Vickers indentation .............................. 228
8.2.3 Elastic moduli measured via resonant ultrasound spectroscopy .............. 229
8.3.0 Bloating monitored via SEM for PbTe-PbS specimens ........................................ 230
8.4.0 Temperature-dependent elastic moduli and CTE for PbTe-PbS ........................... 230
8.4.1 Temperature dependent elastic moduli measured via RUS ...................... 230
8.4.2 Temperature dependent coefficient of thermal expansion
measured via dilatometry and high-temperature x-ray diffraction ........... 231
8.4.3 Bloating monitored using HT-RUS and dilatometry ................................ 231
8.5.0 Room temperature elastic moduli for LLZO ........................................................ 232
8.6.0 Future Work .......................................................................................................... 233
8.6.1 Higher purity SiCnp .................................................................................. 233
8.6.2 SiCnp fracture toughness ......................................................................... 233
8.6.3 Fracture strength and Weibull analysis of PbTe-PbS specimens with and
without SiCnp ................................................................................................. 234
8.7.0 References ............................................................................................................. 235
ix

Appendices ................................................................................................................................. 238
Appendix A: Room temperature elastic moduli and Vickers hardness of hot pressed
LLZO cubic garnet ............................................................................................. 240
A.1.0 Introduction ......................................................................................................... 241
A.2.0 Experimental Procedure ....................................................................................... 241
A.2.1 Specimen Preparation ............................................................................. 241
A.2.2 X-ray diffraction and scanning electron microscopy ............................... 241
A.2.3 Vickers indentation measurements ........................................................... 244
A.2.4 Resonant ultrasound spectroscopy (RUS) measurements ....................... 244
A.3.0 Results and Discussion......................................................................................... 245
A.3.1 Microstructure and lattice parameter of LLZO specimens ...................... 245
A.3.2 Elastic moduli measured via RUS ........................................................... 248
A.3.3 Hardness measured via Vickers indentation testing ................................. 248
A.3.4 Comparison of LLZO elastic moduli and hardness with literature
data for other garnets .............................................................................. 250
A.4.0 Summary and Conclusions................................................................................... 254
A.5.0 References ............................................................................................................ 256
Appendix B: Milling parameters and processing conditions for PbTe-PbS PECS specimens .. 261

x

LIST OF TABLES
Table 2.1 ......................................................................................................................................37
The maximum temperatures, pressures and times used for sintering via pulsed electric
current sintering (PECS) PbTe-PbS specimens in this study.
Table 2.2 ......................................................................................................................................43
Diamond Polish Table. Each diamond grit was used in succession to polish a specimen
until reaching the desired polished surface on the specimen. The last polish used was
either the 1 μm or 0.5 μm polishing grit compound.
Table 3.1 ........................................................................................................................................67
Processing method, chemical composition, dimensions, and mass for the specimens
included in this study. All specimens were rectangular parallelepipeds.
Table 3.2 .......................................................................................................................................68
Processing conditions, including maximum temperature, maximum pressure and total
time at maximum temperature for the hot pressed specimens used in this study.
Table 3.3 .......................................................................................................................................80
Parameters bPE, ED, bPG, and GD obtained from the least-squares fit to the linear (Eqs.
3.4 and 3.5) and exponential (Eqs. 3.1 and 3.2) empirical relationships for the Young’s
2
and shear moduli. N is the number of specimens included in each analysis and r is the
coefficient of determination
Table 3.4 ........................................................................................................................................83
Using perturbed density data (Section 3.4.2.2), a least-squares analysis was used to
simulate the effect of the uncertainty in density measurement. This table lists maximum,
2
minimum and standard deviations (std) of parameters bPE, ED, bPG, and GD and r
(coefficient of determination) obtained from the least-squares fit to the linear (Eqs. 3.4
and 3.5) and exponential (Eqs. 3.1 and 3.2) empirical relationships for the Young’s and
shear moduli using the perturbed density data.

Table 4.1 .......................................................................................................................................104
Comparison of Vickers indentation hardness for the polycrystalline (PC) specimens
included in this study (Pb0.95Sn0.05Te–8% PbS) with hardness data from the literature for
PbTe-PbS, PbTe and PbS polycrystalline (PC) and single-crystal (SC) specimens for N
indentations per specimen.
Table 4.2a ....................................................................................................................................112
Fracture toughness, Kc, determined using Vickers indentation for the hot pressed
polycrystalline (PC) Pb0.95Sn0.05Te–8% PbS specimens included in this study.

xi

Table 4.2b .....................................................................................................................................113
The fracture toughness (Kc) for polycrystalline (PC) or glasses (G) from literature for
various thermoelectrics, semiconductors, and chalcogenides using Vickers indentation
(VI), single edged notched beam (SENB), or double-torsion and double-cantilever-beam
(DTDCB) methods.
Table 4.3 ......................................................................................................................................117
Room temperature Young’s modulus, E, shear modulus, G, and Poisson’s ratio,
measured by Resonant Ultrasound Spectroscopy (RUS) for the PbTe-PbS
(Pb0.95Sn0.05Te–8% PbS) polycrystalline (PC) specimens included in this study
compared to doped and un-doped polycrystalline (PC) and single-crystal (SC) roomtemperature modulus data from the literature.
Table 5.1 ......................................................................................................................................132
The powder processing conditions and sintering parameters for the hot pressed (HP) and
pulsed electric current sintering (PECS) densified specimens processed using powders that
were crushed, ground, sieved, and re-ground (CGSR) powder was either (1) set aside for
densification, (2) dry milled (DM), (3) dry milled and then wet milled (D/WM), or (4) wet
milled (WM). For the post-densification anneals, the heating and cooling rates were 5
K/min and 2 K/min for specimens prepared for SEM observation and RUS elasticity
measurements, respectively.
Table 6.1 ......................................................................................................................................149
The processing conditions for twenty-six ((Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2)
specimen included in this study. Using resonant ultrasound spectroscopy, the
temperature-dependent elastic moduli (E(T)) were measured for twelve specimens and
the room-temperature elastic moduli as a function of porosity (E(P)) were measured for
four specimens. The microstructure (M) was examined using scanning electron
microscopy for 15 specimens.
Table 6.2a ...................................................................................................................................152
A comparison of the as-densified specimens mean grain sizes, GSDNS, for different
powder processing (dry milling (DM), wet milling (WM), and dry and wet milling
(D/WM)) and sintering techniques (hot pressed (HP) and PECS-processed). The
difference in powder processing is the likely cause of the factor of two difference
between the four wet milled hot pressed and PECS processed specimens and six dry
milled PECS-processed specimens. The PECS specimens were sintered at the stated
temperature for 20 minutes. For the as-densified dry milled PECS-processed specimens,
the mode-mixity was calculated as the areal fraction of the transgranular grains appearing
on a specimen’s fracture surface. In general, as the mode mixity increased to 1.0,
transgranular fracture dominates and the fracture toughness increases.

xii

Table 6.2b ...................................................................................................................................153
Mean grain sizes of the as-densified and the annealed specimens are designated by
GSDNS and GSANN, respectively. For dry milled PECS-processed specimens with 0.0
vol% SiCnp, the GSANN increased in three specimens after post-densification anneals up
to 936 K. However, the inclusion of SiCnp limited grain growth in three specimens
during post-densification anneals up to 873 K.
Table 6.3 ......................................................................................................................................155
The least-squares fitting parameters EP=0 and bPE (Eq. (6.4a)) and GP=0 and bPG (Eq.
(6.4b)) to the Young’s modulus and shear modulus to the four as-densified and four postdensified specimens in Figure 6.1.
Table 6.4 ......................................................................................................................................165
The relative volume change twelve specimens for each HT-RUS heating/cooling cycle.
Table 6.5 ......................................................................................................................................168
In this study, the inclusion of SiCnp inhibited porosity (bloating) for PECS-processed
PbTe-PbS specimens. After a post-densification anneal at 693 K for two hours, for the
PbTe-PbS specimen without SiCnp, PECS-01, the volume fraction porosity, P, however,
for two specimens with SiCnp, P increased only by 20%. E is the Young’s modulus
measured at room temperature using resonant ultrasound spectroscopy.
Table 6.6 .....................................................................................................................................174
The least-squares fitting parameters, ERT and bTE, equation (6.6a) for the seven hot
pressed and five PECS-processed PbTe-PbS thermoelectrics included in this study. P is
the volume fraction porosity before thermal cycling, N is the number of E versus
2
temperature data points in the least-squares fit and r is the coefficient of determination
for the least-squares fit to equation (6.6a). For specimens where there was no observable
hysteresis, a single entry is given. Specimens HP-53 #A, HP -53 #C-TC2, HP -54 #2,
and HP -55 #1 have an observable hysteresis in E versus T, thus there are two entries, one
for heating and one for cooling.
Table 6.7 .......................................................................................................................................175
In the open literature for doped PbTe-based thermoelectrics, ERT and bTE, the leastsquares fitting parameters from equation (6.6a), are similar to the least-squares fitting
parameters in this study (Table 6.2). P is volume fraction porosity, N is the number of
2
data points in the least-squares fit and r is the coefficient of determination.

xiii

Table 7.1a ....................................................................................................................................199
The processing conditions for specimens included in this study that were measured using
dilatometery (TMA), high-temperature x-ray diffraction (HT-XRD) and scanning
electron microscopy (SEM) All PbTe-PbS powder and bulk specimens have the same
composition, (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2
Table 7.1b ....................................................................................................................................200
The powder processing, measurement technique, ramp rate and temperature ranges for
the CTE measurements included in this study. For each dilatometer test, the atmosphere
was flowing 96 % Ar-4% H2, whereas for the HT-XRD measurements the atmosphere
was 96 % N2-4% H2.
Table 7.2. ......................................................................................................................................205
The mean CTE, calculated from the TMA thermal expansion data for 4 hot pressed (HPspecimens), 1 PECS pressed (PECS- specimens) and two cast ingot (CIW) processed
(Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 specimens. For each specimen, the thermal
expansion measurements were performed on six to twelve half thermal cycles, where a
heating and a cooling half cycle comprises a full thermal cycle. The full temperature
range over which the measurements were performed are indicated. The temperature
range over which the data was analyzed was 325 K – 595 K. Note that the average CTE
values are very similar for both the hot pressed and PECS specimens and CTE values are
relatively constant for each half cycle during the TMA measurement process on a given
specimen.
Table 7.3 .......................................................................................................................................209
The average CTE for the powder and bulk specimens measured using HT-XRD. The
2
coefficient of determination, r , is for the slope upon cooling for the temperature
dependent lattice parameter.
Table 7.4 ......................................................................................................................................215
The average CTE for thermoelectrics in the literature. The fabrication technique, density,
temperature range, and measurement method for each composition.
Table A.1 ......................................................................................................................................235
The specimen geometry, dimensions, density, volume fraction porosity, P and
measurement techniques for the LLZO rectangular parallelepiped, RP, and crescentshaped, CR, specimens included in this study. The specimens were powder processed
from ingot and densified by hot pressing. The elastic moduli were measured using
resonant ultrasound spectroscopy (RUS) and the hardness was measured via Vickers
indentations.

xiv

Table A.2. .....................................................................................................................................249
The density, volume fraction porosity, P, Young’s modulus, E, bulk modulus, B, shear
modulus, G, and Poisson’s ratio, , for the hot pressed rectangular parallelepiped
specimens included in this study as well as for polycrystalline garnet specimens from the
literature.
Table A.3 ......................................................................................................................................251
The exponents mB, mG, and mH obtained by a least-squares fit to equation (2) for bulk
modulus, B, shear modulus, G, and hardness, H data, respectively from the literature for
2
various cubic crystalline structures. The coefficient of determination, r , along with the
number of particular compositions of a given crystal structure included in the leastsquares fit, N, are listed within the parentheses given below each of the numerical values
of the fitted exponents.
Table B.1 .................................................................................................................................... 263
The powder processing for each PECS-processed specimen. All milling was performed
using a planetary mill in an argon-atmosphere glove box. The specimens were fabricated
using powders that were (1) dry milled, (2) wet milled, or (3) dry and wet milled. The
media referenced in this table were alumina spheres. The mix mill refers to the planetary
milling of PbTe-PbS powders with SiC nanoparticles (SiC).

xv

LIST OF FIGURES
Figure 1.1 .................................................................................................................................. 3
Diagram of a thermoelectric module. The application of a temperature differential causes
an electric current to run through the specimen. After from Riffat et al, Thermoelectrics:
a review or present and potential applications, Applied thermal engineering 23 (2003).
Figure 1.2 ................................................................................................................................. 8
Schematic of elastic moduli change with temperature. The elastic moduli decrease with
temperature in each regions. Region I is from 0 K to approximately 0.3θD and 0.5θD.
Region II is a linear region. Region III is the viscoelastic or anelastic region, beginning
at the onset temperature of grain boundary sliding, TONSET.
Figure 2.1 ................................................................................................................................... 24
Schematic of powder processing procedure for PbTe-chalcogenides in this study. Both
the powder particles and the bulk specimens were characterized using scanning electron
microscopy.
Figure 2.2 .................................................................................................................................. 38
Temperature-Pressure versus time for pressing specimens C-PTS-P-09. The maximum
temperature and pressure was 823 K and 60 MPa, respectively. The heating rate was 50
K/minute and the cooling rate was 5 K/minute. The pressure reached a maximum of 60
MPa 60 seconds after the temperature reached a maximum of 823 K.
Figure 2.3 .................................................................................................................................. 39
Temperature-Pressure versus time for pressing specimens C-PTS-P-11 and C-PTS-P-12.
The maximum temperature and pressure was 823 K and 60 MPa, respectively. The
heating rate was 50 K/minute and the cooling rate was 5 K/minute. During cooling, the
specimen was thermally annealed at 573 K for 200 minutes to reduce residual stresses.
Figure 2.4 ................................................................................................................................... 52
Schematic of the Resonant Ultrasound Spectroscopy (RUS) apparatus used for Young’s
modulus measurements. The specimen was balanced on the three transducers.
Figure 2.5 ................................................................................................................................... 52
An example of an acoustic vibrational spectrum induced in a mechanically driven
specimen. The resonant peak positions were functions of the elastic moduli, geometry,
dimensions and mass density of the specimen This spectrum is from C-PTS-P-07 at 363
K.
Figure 3.1 .................................................................................................................................. 68
Time-temperature profile for the fabrication of the five ingots specimens included in this
study. N138 (Ag0.43Pb18Sb1.2Te20), N155, and N160-4,-5 and -9 (Ag0.86Pb19Sb1.0Te20)
(Table 3.2a). Specimens N160-4, -5 and -9 were cut from a single ingot.

xvi

Figure 3.2 ................................................................................................................................... 71
SEM micrographs of the as polished surfaces of specimens (a) HP3 (P = 0.01) (b) HP30
(P = 0.01) (c) HP7 (P = 0.10), as well as the thermally etched surfaces (d) HP3 (P =
0.01, thermally etched at 598 K for 2 hrs) (e) HP30 (P = 0.01, thermally etched at 673 K
for 2 hrs) (f) HP7 (P = 0.10, thermally etched at 698 K for 2 hrs)
Figure 3.3a ................................................................................................................................ 73
For the hot pressed specimens only (compositions Ag0.43Pb18Sb1.2Te20 and
Ag0.86Pb19Sb1.0Te20), the solid line indicates the least-squares fit to linear relationship
(Eq. 3.4) for Young’s modulus (determined by room temperature RUS) as a function of
porosity.
Figure 3.3b ................................................................................................................................. 74
For the combined data set (12 hot pressed specimens and 5 cast specimens), the solid
line indicates the least-squares fit to linear relationship (Eq. 3.4) for Young’s modulus
(determined by room temperature RUS) as a function of porosity.
Figure 3.3c ................................................................................................................................ 75
For the hot pressed specimens only, the solid line indicates the least-squares fit to linear
relationship (Eq. 3.5) for shear modulus (determined by room temperature RUS) as a
function of porosity.
Figure 3.3d ................................................................................................................................ 76
For the combined data set (12 hot pressed specimens and 5 cast specimens), the solid line
indicates the least-squares fit to linear relationship (Eq. 3.5) for shear modulus
(determined by room temperature RUS) as a function of porosity.
Figure 3.3e ................................................................................................................................ 77
For the combined data set (12 hot pressed specimens and 5 cast specimens), the solid line
indicates the least-squares fit to the exponential relationship (Eq. 3.2) for shear modulus
(determined by room temperature RUS) as a function of porosity.
Figure 3.3f ................................................................................................................................. 78
For the hot pressed specimens only, the Poisson’s ratio determined by room temperature
RUS measurements versus volume fraction porosity.
Figure 3.3g ................................................................................................................................ 79
For the combined data set (12 hot pressed specimens and 5 cast specimens), Poisson’s
ratio determined by room temperature RUS measurements versus volume fraction
porosity of the combined data (hot pressed and cast ingot specimens.

xvii

Figure 4.1 .................................................................................................................................. 98
Particle size distribution obtained from laser light scattering apparatus.
Figure 4.2 ................................................................................................................................... .103
SEM micrographs of the as-polished surfaces of Pb0.95Sn0.05Te – PbS 8% specimens
fabricated by (a) casting from the melt and (b and c) hot pressing.
Figure 4.3 .................................................................................................................................. .105
SEM micrographs of annealed fractured surfaces of hot pressed Pb0.95Sn0.05Te–8% PbS
specimens cut from hot pressed billets (a) MSUHP-53 and (b) MSUHP-54. MSUHP-53
was annealed for 5 hours at 573 K and MSUHP-54 was annealed for 5 hours at 693 K,
both in a 96% Ar + 4% H2 atmosphere.
Figure 4.4 ................................................................................................................................... .106
SEM micrograph of wet milled powders used to fabricate billet MSUHP-54. Note that a
significant factor of the powders particles have a diameter less than about 100 nm, which
is below the effective measurement threshold of the laser scattering apparatus. A fracture
surface of a specimen hot pressed from this powder is shown in Figure 4.3b.
Figure 4.5 ................................................................................................................................... .110
The mean hardness as a function of the applied Vickers indentation load for hot pressed
(open symbols) and cast (filled symbols) specimens in the PbTe-PbS system. The mean
hardness values, averaged over all loads for the Pb0.95Sn0.05Te–8% PbS hot pressed
MSUHP-53 and MSUHP-54 specimens are shown by the dotted and dashed lines,
respectively. The mean hardness values averaged over all loads for the Pb0.95Sn0.05Te–
8% PbS cast NW-Ingot G and MSU-Ingot 7A specimens are indicated by the dot-dashed
and dot-dot-dashed lines, respectively. The hardness data from Darrow et al. [36] for cast
PbTe-PbS 5% and PbTe-PbS 10% specimens is shown for comparison (half-filled
symbols).
Figure 4.6 .................................................................................................................................. 114
SEM micrographs of Vickers indentations at a) 0.25 N, b) 2.0 N, and c) 4.9 N for MSUIn #7A, and d) 0.25 N for MSUHP-54 #C, e) 2 N for MSUHP-53 #3, and f) 4.9 N for
MSUHP-54 #C.
Figure 5.1 .................................................................................................................................. 134
The as-densified fracture surfaces of (a) HP-DM-01 and (c) HP-CGSR-01 do not show
bloating. Annealing (b) HP-DM-01 at 723 K for 4 hours and (d) HP-CGSR-01 at 973 K
for 6 hours resulted in bloating as evidenced by the increased porosity of the internal
fracture surfaces. All annealing was performed in flowing Ar.

xviii

Figure 5.2 .................................................................................................................................. 135
The as-densified fracture surfaces of (a) HP-D/WM-01 and (c) PECS-WM-01 do not
show bloating. Annealing (b) HP-D/WM-01 at 693 K for 2 hours and (d) PECS-WM-01
at 823 K for 2 hours resulted in bloating as evidenced by the increased porosity of the
internal fracture surfaces. All annealing was performed in flowing Ar or Ar (96%)-H2
(4%).
Figure 5.3 ................................................................................................................................... 136
In contrast to the annealing behavior depicted in Figures 5.1 and 5.2, the (a) as-densified
PECS-DM-02 did not bloat after annealing at (b) 663 K for 2 hours, (c) 823 K for 2
hours, and (d) 936 K for 2 hours. All annealing was performed in flowing Ar (96%)-H2
(4%).
Figure 5.4 .................................................................................................................................. 138
The bloating (Figures 5.1 and 5.2) or lack of bloating (Figure 5.3) observed in the SEM
study is also evident in the RUS measurements of Young’s modulus, E, versus volume
fraction porosity, P. For the nine as-densified HP and PECS specimens along with the 32
annealing measurements on the same nine specimens (Table 1), as P increased, E
decreased. The filled symbols and open symbols represent the E values for the asdensified and annealed specimens, respectively. Equation (5.1), widely used to describe
the E versus P behavior for brittle materials [10, 11], also fits the E versus P behavior
2
well (r = 0.990) for the 41 RUS measurements included in this study. The dashed line
represents the least-squares fit to equation (5.1).
Figure 6.1 .................................................................................................................................. 156
The porosity dependence of the (a) Young’s modulus, E, shear modulus, G, and (b)
Poisson’s ratio for four as-densified PECS-processed specimens (filled symbols) and four
thermally annealed hot pressed and PECS-processed specimens with 0.0 vol% SiCnp.
Each individual specimen is represented by the same symbol in figure (a) and (b). The
least-squares fit to Eq. (6.4a) to these 8 specimens is represented by the dashed line. The
solid line and dotted lines represent the average and standard deviation in Poisson’s ratio,
respectively.
Figure 6.2 ................................................................................................................................... 159
The as-densified and post-densification fracture surfaces of (a, b) D/WM PECS-10, (c, d)
DM PECS-20 and (e, f) DM PECS -18 (with 2.0 vol% SiCnp). Few pores are evident in
the SEM micrographs of the as-densified fracture surfaces. Annealing at 936 K for 2
hours resulted in bloating for (b) D/WM PECS-10 and (f) DM PECS -18 (with 2.0 vol%
SiCnp) specimens as evidenced by the increased porosity of the internal fracture surface
while, in contrast, the (d) DM PECS-20 specimen did not bloat after annealing under
identical conditions.

xix

Figure 6.3 .................................................................................................................................. 160
The (a) as-densified and (b) post-densification fracture surfaces of PECS-10. After postdensification annealing to 936 K for 2 hours, long lenticular pores were observable on the
fresh fracture surface of D/WM PECS-10.
Figure 6.4 .................................................................................................................................. 161
The (a) fracture surfaces of the specimen without added SiCnp, PECS-15, exhibits a
much higher fraction of intergranular fracture than (b) the specimen with 2.5 vol% SiCnp,
PECS-16 (Table 6.2a). Both specimens were PECS-processed at 673 K for 20 minutes
using a pressure of 60 MPa.
Figure 6.5 .................................................................................................................................. 172
Schematics of hysteresis between heating and cooling in Young’s modulus due to (a – c)
microcracking and (d) due to bloating. In this study, the specimen HP-54#2 bloated when
thermally cycled to 663 K (d). The dashed and dashed-dot lines represent the leastsquares fit to Eq. (6.6a) to heating and cooling, respectively.
Figure 6.6 .................................................................................................................................. 176
Temperature dependence of the (a - d) Young’s modulus, E, (d) shear modulus, G, and (ef) Poisson’s ratio, , for hot pressed (HP) and PECS-processed PbTe-PbS specimens upon
heating (filled symbols) and cooling (open symbols). For E and G, the symbol size is
greater than the error bars. In parentheses, next to the specimen label, is the maximum
temperature for each thermal cycle. The least-squares fit to Eq. (6.6a) to the Young’s
modulus during heating, cooling, and heating/cooling is represented by the dashed,
dotted, and solid lines, respectively. A least-squares fit to Eq. (6.7) to the temperaturedependent Poisson’s ratio is represented by the dashed-dot line. The hysteresis in E
versus T for specimens HP-53 #A, HP-53 #C-TC2, HP -54 #2, and HP -55 #1 is not
apparent in the figures because of the number of temperature-dependent Young’s moduli
data points.
Figure 6.7 .................................................................................................................................. 183
The Young’s modulus as a function of volume fraction porosity, P, for Ti-6Al-4V
specimens after post-densification anneals up to 1303 K [Oppenheimer 2010]. This
behavior is consistent with the empirical exponential decrease common to brittle
materials (Eq. (6.4a)). The solid line represents a least-squares fit to Eq. (6.4a) of the
Oppenheimer et al. Young’s modulus versus P data [Oppenheimer 2010].
Figure 7.1 .................................................................................................................................. 203
The dimension change as a function of temperature for (a) a cast ingot (CIW040S), (b) a
PECS-processed specimen (PECS-15) and (c) a hot pressed specimen (HP-55). There
were a total of 6 or 8 half cycles, where HT1, 2, 3, and 4, are the first, second, third and
fourth heating cycles, and CL1, 2, 3, and 4 are the first, second, third and fourth cooling
cycles. For the hot pressed specimen (c), half cycles 1 to 6 are from 297 K to 603 K and
the half cycles 7 – 12 are from 297 K to 663 K. The heating/cooling rates were 2.0
K/min for all runs. Notice that for MSUHP-55 #1 the hysteresis between heating and
cooling increased when the maximum temperature increased
xx

Figure 7.2 .................................................................................................................................. 207
The lattice parameter as a function of temperature for powder that was powder that was
dry milled only (a) CIW064S and wet and dry milled (b) CIW041S, (c) PbTe-PbS 9, (d)
CIW036S, (e) CIW040S and (f) CIW063S. The dash-dotted line is an extrapolation of
the least-squares fit to the lattice parameters between 303 K and 483 K using equation
(7.3b) The dotted line is a least-squares fit to the cooling data.
Figure 7.3 .................................................................................................................................. 211
The micrographs for the as-pressed fractured surfaces for (a) HP-53, (c) PECS-02, and
(e) PECS-10S. The fractured pieces were annealed at 773 K, for MSUHP-53, and 823 K,
for PECS-02, and PECS-10S, for 2 hours in flowing 96% Ar + 4% H2 gas and then refractured upon cooling. The new fractured surfaces for (b) HP-53, (d) PECS-02, and (f)
PECS-10S were examined for bloating. The annealed fractured surfaces for HP-53 and
PECS-02 surfaces showed evidence of bloating, where as PECS-10S did not show
evidence of bloating.

Figure A.1 .................................................................................................................................. 246
The fracture surfaces for the hot pressed specimens (a) LLZO-01 and (c – d) LLZO-02.
The fracture surface of LLZO-02 was examined at (e) five different sites along the
diametral fracture. Each site was roughly 3 mm apart and sites 1 and 5 were
approximately 0.5 mm from the specimen edge. For each micrograph the grain size was
measured using the linear intercept method and a stereographic projection factor of 1.5
[15].
Figure A.2 .................................................................................................................................. 252
The (a) Young’s modulus, (b) shear modulus, and (c) hardness as a function of lattice
parameter for the aggregate average values for single crystal garnet data in the literature
(open symbols) and the LLZO garnet specimens in this study (filled symbol). In (a), (b),
and (c) the dashed line represents the least-squares fit of equation (A.2) to the data in this
study and single crystal garnet in the literature [27, 33 - 38]. The scatter in hardness, H,
is likely due to the different mechanisms that can affect H (Section A.3.3).
Figure B.1 ................................................................................................................................. 268
The temperature-pressure-time profile for PECS-processed specimens, C-PTS-P-01, CPTS-P-02, C-PTS-P-03, and C-PTS-P-04. The heating rate and cooling rate was 50
K/minute and 5 K/minute, respectively. The ramp rate for pressure during heating was 5
MPa/min and 0.5 MPa/min during cooling. The specimens were sintered at the
maximum temperature and pressure for 20 minutes

xxi

Figure B.2 ................................................................................................................................. 268
The temperature-pressure-time profile for PECS-processed specimens, C-PTS-P-05, CPTS-P-06, and C-PTS-P-07. The heating rate and cooling rate was 50 K/minute and 5
K/minute, respectively. The maximum temperature was held for 20 minutes. The
pressure was held at 20 MPa during heating until the specimen reached the maximum
temperature. Once the specimen reached 823 K, the pressure was increased to 60 MPa.
Figure B.3 ................................................................................................................................. 269
The temperature-pressure-time profile for PECS-processed specimen, C-PTS-P-08. The
heating rate and cooling rate was 50 K/minute and 5 K/minute, respectively. The
maximum temperature was held for 20 minutes. The pressure was held at 20 MPa during
heating until the specimen reached the maximum temperature, 873 K. Once the
specimen reached 873 K, the pressure was increased to 60 MPa.

Figure B.4 ................................................................................................................................. 269
The temperature-pressure-time profile for PECS-processed specimen, C-PTS-P-09. The
heating rate and cooling rate was 50 K/minute and 5 K/minute, respectively. The
maximum temperature was held for 30 minutes. The pressure was held at 20 MPa during
heating until the specimen reached the maximum temperature, 873 K. Once the
specimen reached 823 K, the pressure was increased to 60 MPa. The longer sintering
time was due to a miscommunication with Karl Dresch.
Figure B.5 ................................................................................................................................. 270
The temperature-pressure-time profile for PECS-processed specimens, C-PTS-P-10, CPTS-P-11, and C-PTS-P-12. The heating rate and cooling rate was 50 K/minute and 5
K/minute, respectively. The maximum temperature was held for 20 minutes. The
pressure was held at 20 MPa during heating until the specimen reached the maximum
temperature. Once the specimen reached 823 K, the pressure was increased to 60 MPa.
To reduce possible residual stresses, the specimen was cooled to 573 K and thermally
annealed for 120 minutes. The pressure was slowly reduced in steps during cooling.
Figure B.6 ................................................................................................................................ 271
The temperature-pressure-time profile for PECS-processed specimens, C-PTS-P-13, CPTS-P-14, C-PTS-P-15, C-PTS-P-16, C-PTS-P-17, C-PTS-P-18, and C-PTS-P-19. The
heating rate and cooling rate was 50 K/minute and 5 K/minute, respectively. The
maximum temperature was held for 20 minutes. The pressure was held at 20 MPa during
heating until the specimen reached the maximum temperature. Once the specimen
reached 673 K, the pressure was increased to 60 MPa. To reduce possible residual
stresses, the specimen was cooled to 573 K and thermally annealed for 120 minutes. The
pressure was slowly reduced in steps during cooling.

xxii

Figure B.7 ................................................................................................................................. 272
The temperature-pressure-time profile for PECS-processed specimens, C-PTS-P-20, CPTS-P-21, C-PTS-P-22, C-PTS-P-23, and C-PTS-P-24. The heating rate and cooling rate
was 50 K/minute and 5 K/minute, respectively. The maximum temperature was held for
20 minutes. The pressure was held at 20 MPa during heating until the specimen reached
the maximum temperature. Once the specimen reached 723 K, the pressure was
increased to 60 MPa. The pressure decreased during cooling at a ramp rate of 0.64
MPa/minute.
Figure B.8 ................................................................................................................................. 273
The temperature-pressure-time profile for PECS-processed specimens C-PTS-P-25 and
C-PTS-P-29. The maximum temperature of 723 K was held for 16 minutes. The heating
rate and cooling rate was 100 K/minute and 10 K/minute, respectively The pressure was
held at 60 MPa until the specimen reached room temperature.
Figure B.9 ................................................................................................................................. 273
The temperature-pressure-time profile for PECS-processed specimens C-PTS-P-26 and
C-PTS-P-30. The maximum temperature of 723 K was held for 16 minutes. The heating
rate and cooling rate was 100 K/minute and 5 K/minute, respectively The pressure was
held at 60 MPa until the specimen reached room temperature.
Figure B.10 ............................................................................................................................... 274
The temperature-pressure-time profile for PECS-processed specimens C-PTS-P-27 and
C-PTS-P-31. The heating rate and cooling rate was 50 K/minute and 5 K/minute,
respectively. The ramp rate for pressure during heating was 5 MPa/min and 0.5 MPa/min
during cooling. The specimens were sintered at the maximum temperature and pressure
for 20 minutes.
Figure B.11 ................................................................................................................................ 274
The temperature-pressure-time profile for PECS-processed specimen C-PTS-P-28. The
heating rate and cooling rate was 50 K/minute and 5 K/minute, respectively. The ramp
rate for pressure during heating was 5 MPa/min and 0.5 MPa/min during cooling. The
specimen was sintered at the maximum temperature and pressure for 5 minutes.
Figure B.12 ............................................................................................................................... 275
The temperature-pressure-time profile for PECS-processed specimens, C-PTS-P-32, CPTS-P-36, and C-PTS-P-37. The heating rate and cooling rate was 50 K/minute and 5
K/minute, respectively. The ramp rate for pressure during heating was 5 MPa/min and
0.5 MPa/min during cooling. The specimens were sintered at the maximum temperature
and pressure for 5 minutes.
Figure B.13 ............................................................................................................................... 275
The temperature-pressure-time profile for PECS-processed specimen C-PTS-P-33. The
heating rate and cooling rate was 50 K/minute and 5 K/minute, respectively. The ramp
rate for pressure during heating was 5 MPa/min and 0.5 MPa/min during cooling. The
specimen was sintered at the maximum temperature and pressure for 5 minutes.
xxiii

Figure B.14 ............................................................................................................................... 276
The temperature-pressure-time profile for PECS-processed specimen C-PTS-P-34. The
heating rate and cooling rate was 50 K/minute and 5 K/minute, respectively. The ramp
rate for pressure during heating was 5 MPa/min and 0.5 MPa/min during cooling. The
specimen was sintered at the maximum temperature and pressure for 5 minutes.
Figure B.15 ............................................................................................................................... 276
The temperature-pressure-time profile for PECS-processed specimen C-PTS-P-35. The
heating rate and cooling rate was 50 K/minute and 5 K/minute, respectively. The ramp
rate for pressure during heating was 5 MPa/min and 0.5 MPa/min during cooling. The
specimen was sintered at the maximum temperature and pressure for 5 minutes.

xxiv

1.0 Introduction
PbTe-based chalcogenide thermoelectrics have potential in waste-heat recovery applications
due to a relatively high figure of merit of roughly 1.5 at 650 K. During waste-recovery, the
thermoelectric, TE, materials will undergo both thermal and mechanical stresses. Therefore,
mechanical properties, such as the Young’s modulus, shear modulus, Poisson’s ratio, and
coeffeicient of thermal expansion will be needed for stress-strain analysis (Section 1.3). The
PbTe-chalcogenide work has focused on: (i) hot pressing (HP) and pulsed electric current
sintering (PECS) of dry and wet milled LAST or PbTe-PbS powders (ii) measurements of the
temperature-dependent elastic moduli and thermal expansion, (iii) measurements of the of the
room temperature elastic moduli and hardness and (iv) comparison of the bloating behavior of
hot pressed and PECS-processed specimens.

1.1.0 Thermoelectrics for use in waste heat recovery
Thermoelectric (TE) materials have a variety of potential uses as generators that convert
waste heat into electricity. For low power supply uses, TE modules power a wristwatch [Snyder
2008, Riffat 2003] or remote sensing wireless systems [Riffat 2003]. For high power generation,
for the past 30 years TE modules have provided long-term power for deep space probes [Rowe
2006, Snyder 2008, Riffat 2003]. However, there is a terrestrial interest in thermoelectrics for
use in automotive waste-heat recovery. Automotive engine automobiles use roughly 25% of fuel
energy for accessory power and propulsion [Yang 2006]. The remaining fuel energy is lost as
coolant and waste heat, as well as parasitic losses due to friction [Yang 2006]. Thermoelectric
modules, through waste heat recovery, could provide electric power to accessories which would
aid in fuel economy.

1

In a thermoelectric module electrical power is produced from the heat flow across
temperature differential (Figure 1.1) [Riffat 2003, Snyder 2008]. An applied temperature
difference causes charged carriers in the material to diffuse from the hot side to the cold side.
The heat source drives electrons in the n-type element toward the cooler region, creating a
current through the circuit. Holes in the p-type element then flow in the direction of the current.
Therefore, thermal energy is converted into electrical energy. The introduction of a current
causes an inverse of this process, with the result of cooling instead of power generation and is
known as the Peltier effect [Nolas 2001, Riffat 2003, Fushillo 1960, Tritt 1999].

1.2.0 Figure of merit as a measure of efficiency for thermoelectrics
The dimensionless figure of merit, ZT,

ZT 

S 2 T
k

(1.1)

is a function of the Seebeck coefficient, S, electrical conductivity, , the total thermal
conductivity, k, and temperature, T. The Seebeck’s coefficient, S, is the ratio of the voltage
change, dV, to the temperature difference, dT

S

dV
.
dT

(1.2)

For TE materials, it has been empirically understood that if the conductors obey Ohm’s law, the
thermoelectric voltage is therefore dependent on the temperature difference (ΔT) and the actual
properties of the conductors [Fushillo 1960]. Therefore, a TE material must be engineered with a
high Seebeck coefficient, a high electrical conductivity, and a low thermal conductivity in order
to have a high ZT value and therefore a high efficiency.
A thermoelectric thermocouple (Figure 1.1) usually consists of one semiconductor (n2

TC (cold end)

Conductors

Conducted
heat
P-type

N-type

TH(hot end)

V

Figure 1.1 Diagram of a thermoelectric module. The application of a temperature differential
causes an electric current to run through the specimen. After from Riffat et al, Thermoelectrics:
a review or present and potential applications, Applied thermal engineering 23 (2003).

3

type) paired with another semiconductor (p-type) to form a thermoelectric device or module
[Riffat 2003]. These thermocouples are electrically connected in series and thermally in parallel
when used in modules [Riffat 2003]. Ignoring contributions such as contact resistance and
radiation effects, the figure of merit is then
ZT 

S 2 T
k

(1.3)

where  is the electrical conductivity and k is the total thermal conductivity (from the lattice and
electronic contributions) where the subscript “n” and “p” denotes the contribution from the nand p-type TE leg, respectively [Tritt, 2006].
The efficiency, , of a TE generator depends on the temperature differential between the hot,
TH, and cold, TC, sides of the thermoelectric module (Figure 1.1) and the figure of merit
[Cadoff 1960, Yang 2006]

S

dV
dT

(1.4)

The transport properties of the n- and p-type legs (Figure 1.1) vary as a function of temperature,
so therefore ZT varies with temperature [Riffat 2003]. Equation (1.4) demonstrates that a high
efficiency needs both a high ZT and a large temperature differential across the thermoelectric.
However, there is no known thermoelectric material with a high average ZT over a large
temperature range. Most TE materials have a high average ZT over a limited temperature range,
such as Bi2Te3, which has a ZT of around 0.8 between 250 K and 450 K [Yang 2006]. A
thermoelectric with a figure of merit of around 3 has the potential of approaching 50% of the
Carnot efficiency [Nolas 2001, Yang 2006].

4

1.3.0 Importance of mechanical properties for thermoelectric materials
As the ZT is a measure of the efficiency of a TE (Eq. (1.4)) and is a function of the Seebeck
coefficient and the thermal and electrical conductivity (Eq. (1.1)), most literature focuses on
these three properties. However, mechanical properties, such as hardness, fracture strength,
elastic moduli, and fracture toughness are important in understanding the response of the TE
material to in-service conditions. Hardness, H, is associated with the machinability of a material
as well as its resistance to wear [Ren 2006]. Fracture toughness is a measure of the resistance to
crack propagation in a given material [Lawn 1993, Rogl 2011]. The elastic moduli are needed
for numerical or analytical stress-strain calculations due to thermal fatigue, and can also be used
to monitor the accumulation of microcrack damage [Case 2002, Ren 2009].

1.3.1 Thermal shock/thermal fatigue resistance
Thermal shock/thermal fatigue resistance is especially important for applications for TE that
involves the recovery of waste heat from engines. When electrical energy is harvested from
automobile exhaust, the TE elements are subjected to both temperature gradients and thermal
transients. The TE waste heat recovery systems must be able to withstand hundreds or thousands
thermal fatigue cycles. The thermal stress induced by thermal cycling is a function of the
dimensionless parameter, Biot modulus (Bi)
Bi 

a(T)h(T)
k(T)

(1.5)
2

where h(T) (surface heat transfer coefficient, W/m K) measures the heat energy per unit time
transferred across the specimen/quench medium interface per unit area per Kelvin, k(T) (thermal
conductivity, W/mK) measures the rate that heat energy in the specimen can be transferred to the

5

interface, and a(T) (characteristic specimen dimension, m) is the distance from the centerline of
the specimen to the interface [Case 2002]. Thus Bi characterizes the flow of thermal energy
during quenching [Case 2002].
The maximum thermal stress, max, due to thermal cycling at the surface of a plate can be
estimated as




TH max

TH max



E TH T 
1

1.5  3.25/Bi for 0  Bi  5
1- 



(1.6)



E TH T 

1
1.5  3.25 / Bi - 0.5 exp (-16/Bi)  for 0  Bi  20
1- 



(1.7)

where TH is thermal stress,  is the Poisson’s ratio, E is the Young’s modulus, TH is the
coefficient of linear thermal expansion, and T is the quench temperature difference [Case 2002,
Ren 2008]. As E, TH , Bi are all functions of temperature, knowing how these mechanical
properties change with temperature is key to understanding how the materials withstands the
thermal transients [Case 2002, Ren 2008].

1.3.2 Elastic moduli
Elastic moduli are sensitive to defects such as microcracks and pores, thus elasticity
measurements also provide a diagnostic tool that can be used to determine the onset and the
magnitude of damage, such as microcracking due to thermal shock and thermal fatigue, leg and
module fabrication, mechanical vibration and impact [Case 2002]. A variety of thermomechanical stresses are generated during the application of thermoelectric electric (TE)
6

materials.
For waste heat recovery applications, stresses arise from the thermal gradients across the
TE element, thermal transients superimposed on the gradients, mechanical vibration, and thermal
expansion mismatch stresses among the TE module components (legs, electrical interconnects,
mounting plates, etc.). These stresses can induce macrocracks, microcracks, and failure of the
TE materials. The response of the material to the applied stress is a function of the
microstructure (grain size, porosity, inclusions), and elastic moduli, including Young’s modulus
(E) and Poisson’s ratio (). Therefore, the elastic moduli are required for stress analyses,
including a finite element analysis (FEA) of stress and strain in components.
Since the elastic moduli are needed for stress-strain calculations (Eqs. (1.6) and (1.7)), it is
important to understand how the elastic moduli decrease with increasing temperature. The
elastic moduli can be considered in terms of three temperature regimes (Figure 1.2). The low
temperature regime (Region I) corresponds to temperatures T > 0.3 to 0.5 of the Debye
temperature, θD, where slope dE/dT or dG/dT decreases as the temperature approaches 0 K
(Figure 1.2). The Debye temperature is the highest temperature for the normal mode of vibration
for a given material. In the literature, θD for LAST was approximately 175 K [Ren 2009] and for
skutterudites Ce0.9Fe3.5Co0.5Sb12 and n-type Co0.95Pd0.05Te0.05Sb3 was roughly 300 K
[Schmidt 2012].

In Region II, the elastic moduli decrease linearly with increasing temperature. For elastic
polycrystalline solids, the temperature-dependent elastic moduli in Region I and II are described
well by Wachtman [Wachtman 1961, Schmidt 2012]

E(T)  E 0  bT exp T0 / T

(1.8)
7

Elastic moduli

II

I

0.3-0.5 

III

T

ONSET

D

Temperature
Figure 1.2 Schematic of elastic moduli change with temperature. The elastic moduli decrease
with temperature in each regions. Region I is from 0 K to approximately 0.3θD and 0.5θD.
Region II is a linear region. Region III is the viscoelastic or anelastic region, beginning at the
onset temperature of grain boundary sliding, TONSET.

8

and Varshni [Varshni 1970] relationships
E(T)  E 0  cT 2 / T  d  .

(1.9)

For both the Wachtman [Wachtman 1961] and the Varshni [Varshni 1970] relationships, E0 is the
Young’s moduli at 0 K, and b, c, and d are constants [Wachtman 1961, Varshni 1970]. Anderson
[Anderson 1966] approximates T0 in the Wachtman equation as 0.3θD to 0.5θD [Anderson 1966,
Schreiber 1973]. In Region III, begins at a temperature TONSET (Figure 1.2) where grain
boundary sliding, twins and microcracks cause dE/dT to increase. The increase in dE/dT is
known as “anelastic” or “viscoelastic” behavior [Schmidt 2011 in press].
In the literature, there is limited data for the room temperature or temperature dependent
PbTe-based chalcogenides. For LAST thermoelectric materials (lead-antimony-silver-tellurium)
with compositions Ag0.86Pb19Sb1.0Te20 and Ag0.43Pb18Sb1.2Te20, Ren et al. measured the
temperature dependent elastic moduli from 300 K to 773 K. The cast and hot pressed LAST
specimens were described well by the Wachtman relationship. The room temperature Young’s
modulus for LAST and pure PbTe for a theoretically dense specimen was roughly 60 GPa. As
the Young’s modulus is a function of defects such as microcracks or pores, monitoring the
Young’s modulus yields valuable information regarding microstructural variations between
specimens (such as pores) or damage during in use conditions (microcracking) [Ren 20909]

1.3.3 Coefficient of thermal expansion
In the literature, the average CTE values measured by dilatometery and high temperature x-6

-1

ray diffraction ranged between 20 and 24 x 10 K for cast and hot pressed LAST

9

thermoelectric materials (compositions Ag0.86Pb19Sb1.0Te20 and Ag0.43Pb18Sb1.2Te20 [Ren
2009]). For updoped PbTe single crystals grown by the Czochralski technique, Houston et al.
[Houston 1968] used capacitive cell measurements to measure an average room temperature
-6

-1

CTE value of about 20.4 x 10 K . In comparison, the CTE for Ba8Ga16Ge30 and
-6

Sr8Ga16Ge30, other candidate TE materials for waste heat recovery, are roughly 14.2 x 10 K

-1

over the temperature range of 300 to 973 K [Okamoto 2008].

1.3.4 Bloating at elevated temperatures
During in-use conditions at elevated temperatures, TE materials can bloat. Bloating is an
increase in porosity that appears during annealing of densified specimens in the absence of a
confining pressure. Bloating can occur to specimens densified using elevated temperature and
pressure (hot pressing and PECS processes used in this study) when a densified specimen is
thermally annealed without the confining pressure of the hot press or PECS. Bloating can result
from a decomposition reaction in which a gaseous species evolves internally during thermal
annealing in the absence of an external confining pressure. Decomposition reactions that cause
bloating were observed in a wide range of material systems such as carbonates and sulfates
[Kingery 1976].
In this study, bloating refers to an increase in porosity generated by post-densification
annealing in the absence of a confining pressure. Bloating of as-densified specimens is known to
be a problem for hot pressed Ce0.9Fe3.5Co0.5Sb12 [Schmidt 2011 submitted],
Co0.95Pd0.05Te0.05Sb3 [Schmidt 2011 submitted], and LAST-T [Ren unpublished data].
Eliminating bloating improves specimen performance by providing microstructural thermal
10

stability for the as-sintered specimens.
Since porosity affects a broad spectrum of physical properties, pores generated by bloating
have the potential to significantly affect the performance and mechanical integrity of
thermoelectrics.

1.3.5 Effect of porosity in brittle materials
Porosity can affect electrical and thermal transport properties as well as elastic moduli and
strength. Porosity affects many physical properties including mechanical properties such as
hardness [Hoepfner 2003], elastic moduli [Rice 2000], and fracture strength [Rice 2000]. For TE
materials, porosity affects both the mechanical integrity of thermoelectrics for in-service
environments and electrical and thermal transport properties [He 2008, Yang 2004, Yang 2011,
Zhang 2010].
It is empirically believed that the mechanical and thermal transport properties, A, depend on
the volume fraction porosity, P, such that

A(P)  A d exp(b PA P)

(1.10a)

where Ad is the property of a dense material, and bPA is a material-dependent constant [Rice
2000].

For sufficiently small values of bPAP [Rice 2000] the above relationship can be

approximated using a Taylor series with the linear form

A(P)  A d (1  b

PA

P)

(1.10b)

.

For polycrystalline ceramic materials



E
1
2G

(1.11)

11

where  is the Poisson’s ratio, E is the Young’s modulus and G is the shear modulus [Rice 2000].
As the Possion’s ratio is a function of both E and G, in literature the has been observed to
increase, decrease or remain constant as a function of porosity.
Phani shows for polycrystalline Al2O3, ZnO and MgO, [Phani 2008 JACS] the Poisson’s
ratio, , can increase, decrease or remain the constant as a function of temperature. The  of
Al2O3 is relatively insensitive to volume fraction porosity, P, for 0 < P < 0.30  for ZnO
decreases for 0 < P < 0.30.  for MgO, measured by different researchers show opposite trends
where in one case ,  increases with increasing P and in the other case  decreases with
increasing P [Phani 2008 JACS].

1.3.6 Effect of porosity in thermoelectrics
In the literature, there is work to reduce the thermal conductivity by phonon scattering using
nanostructures or porosity to increase the ZT [Yang 2011, Zhang 2010]. Nanostructures are
formed by either (1) during densification through precipitation or spinodal decomposition
[Johnsen 2011, Kanatzidis 2010] or (2) by adding powder nanoparticles during fabrication [Li
2006, Liu 2011, Li 2011, Xiong 2009]. Porosity occurs naturally due to incomplete densification
[Pedersen 2010, Kingery 1976], but can also be introduced using foaming agents [Pedersen
2010] or fillers that burn out during densification [Kingery 1976, Pedersen 2010]. Both the
electrical conductivity and thermal conductivity will decrease with increasing porosity (Eq.
(1.10a)), which implies that the ZT (Eq. (1.1)) can also change with porosity, depending on how
much the properties change relative to each other.
For BiTe-thermoelectrics, volume fraction porosities of 0.0181, 0.0332 and 0.0446 were

12

intentionally introduced using ferrocene [Zhang 2010] which sublimed during PECS-processing.
The authors did not indicate the volume fraction porosity of the PECS-processed specimen
fabricated without ferrocene or how the density was measured [Zhang 2010]. The porosity was
quasi-spherical, 100-500 nm in diameter and inhomogenously distributed throughout the matrix.
Both the thermal and electrical conductivity decreased with increasing porosity (Eq. (1.10a))
over the temperature range investigated, 293 K to 473 K [Zhang 2010]. However, the Seebeck
coefficient for the specimens with P = 0.0181 and 0.0332 was 10% higher than the specimen
with P = 0.0446 and the specimen fabricated without ferrocene over the entire temperature range
[Zhang 2010]. Due to efficient phonon scattering of the “nanopores” to reduce thermal
conductivity, a maximum ZT of 1.38 at 473 K for the specimen with P = 0.0332 was roughly
50% higher than the ZT for the specimens with P = 0.0181 and 0.0446 [Zhang 2010].
Pedersen et al. PECS-processed Zn4Sb3 thermoelectric specimens with P ranging from
roughly 0.0 to 0.15 by varying the sintering pressure, temperature and sintering time [Pedersen
2006]. The density of each specimen was measured using the Archimedes method [Pedersen
2006]. For the Zn4Sb3 specimens with P > 0.03, the Seebeck coefficient was roughly double at
400 K than the specimens with P < 0.09 [Pedersen 2006]. Consistent with equation (1.10a and
10b), the electrical and thermal conductivity also decreased with increasing porosity over the
entire temperature range, 0 K to 400 K [Pedersen 2006]. Similar to the BiTe-thermoelectrics
[Zhang 2010], a maximum ZT of 0.5 at 320 K was obtained for the specimen with P =
0.03[Pedersen 2006]. Furthermore, the higher porosity specimens, P = 0.09 and 0.15, had ZT
values less than 50% of the theoretically dense specimen [Pedersen 2006], indicating that there
was a saturation of beneficial effects of the pores.
In the literature, there is little work for the mechanical properties as a function of
13

porosity for thermoelectrics. Rogl et al. compiled a discussion of hardness, Young’s modulus
and shear modulus as a function of composition, porosity, and temperature for unfilled and filled
skutterudites [Rogl 2011]. For five different compositions of skutterudites [Rogl 2011], the
hardness decreased with increasing porosity monotonically (Eq. (1.10)) over a narrow porosity
range, 0.005 > P > 0.03. For a skutterudite with composition DD0.65Fe3CoSb12 [Rogl 2011],
where DD was didymium, the Young’s modulus decreased with increasing porosity consistent
with the empirical exponential (Eq (1.9)) relationship over 0.02 > P > 0.09 . A material
dependent constant bPE was 3.5 and the Young’s modulus of the theoretically dense material, ED,
was 138.8 GPa (Eq. (10a)).

1.4.0 Fabrication and mechanical testing of thermoelectric materials
Thermoelectrics fabricated using a casting method typically have grain sizes on the order of
several hundreds of microns [Ren 2006, Pilchak 2007]. The fracture strength, f, of brittle
materials is function of the inverse square root of grain size [Barsoum 2003]. Therefore, TE
legs fabricated using casting can have a low fracture strength, and therefore poor mechanical
integrity. Thermoelectric materials, including LAST, a lead telluride doped with silver and
antimony, have low mechanical strength. Ren et al. reported a biaxial fracture strength of ~ 15
MPa for a cast Ag-Sb-Sn-doped PbTe with a mean grain size of 706 

The use of

planetary milling reduces the particle size cast ingots and therefore produces grain sizes that
range from the submicron to ten’s of microns when densified via hot pressing [Ren 2009, Horio
2004, Ueno 2005, Caillat 1997] or pulse electric current sintering [Jiang 2005, Kishimoto 2002].
The elastic modulus can be measured using static or dynamic methods. Current static

14

methods used are nanoindentation and Knoop indentation. Dynamic methods include sonic
resonance, pulse echo, and resonance ultrasonic spectroscopy.

For nanoindentation, the elastic

recovery is measured during unloading at relative low loads [Oliver 1992], and for Knoop
indentation the elastic recovery of the in-plane indentation is measured [Marshall 1982, Rogerio
de Oliveira Hein 2010]. The dynamic methods, though not destructive, need a precise geometry
in order to accurately calculate the elastic moduli. For some materials, the fabrication and
machinability of parallelepipeds and cylinders is difficult and therefore the static methods are
needed.
There has been interest in adding nanoparticle additions, such as SiC or ZnO, to
thermoelectric materials to increase phonon scattering [Zhao 2008, Li 2006]. In addition to
possibly enhancing the thermal transport properties, nanoparticles can improve the mechanical
properties by inhibiting grain growth. When the grain size is greater than or equal to the critical
flaw, hardness, fracture toughness and fracture strength are all proportional to the inverse square
root of grain size [Barsoum 2003]. Therefore, if the grain growth is inhibited, the hardness,
fracture toughness and fracture strength will remain constant during thermal cycling. The
nanoparticles selected are insoluble in the thermoelectric matrix at the processing and use
temperatures, have a higher fracture toughness than the matrix, to allow for crack deflection, and
inhibit grain growth induced during long periods at high temperatures. If the fracture toughness
increases the fracture strength increases for the composite thermoelectric.
In this study, the LAST and PbTe-PbS thermoelectric specimens were fabricated using hot
pressing or pulse electric current sintering (PECS) with powders that were planetary ball milled
from ingots. Room temperature hardness and fracture toughness were measured using Vickers
indentation. The room temperature and high temperature elastic moduli were measured using

15

resonant ultrasound spectroscopy. Both dilatometery and high temperature x-ray diffraction
were used to determine the coefficient of thermal expansion for bulk and powder specimens,
respectively.

16

REFERENCES

17

1.5.0 References
[Anderson 1966] O.L. Anderson, Derivation of Wachtman's equation for temperature
dependences of elastic moduli of oxide compounds, Phys. Rev. 144 (1966) 553-557.
[Androulakis 2007] J. Androulakis, C-H Lin, H-J Kong, C. Uher, C-I Wu, T. Hogan, B.A. Cook,
T. Caillat, K.M. Paraskevopoulos, M. G. Kanatzidis, Spinodal Decomposition and Nucleation
and Growth as a Means to Bulk Nanostructured Thermoelectrics: Enhanced Performance in
Pb1-xSnxTe− PbS, J. Am. Chem. Soc. 129 (2007) 9780-9788.
[Barsoum 2003] M.W. Barsoum, Fundamentals of Ceramics, Institute of Physics Publishing Ltd,
Philadelphia, Pennsylvania, 2003.
[Cadoff 1960] I. Cadoff, E Miller, Thermoelectric materials and devices, Reinhold Publishing
Corporation, New York, 1960, p. 18-29.
[Caillat 1997] T. Caillat, J-P Fleurial, A. Borshchevsky, Preparation and thermoelectric properties
of semiconducting Zn4Sb3, J. Phys. Chem Solids 58 (1997)1119-1125.
[Case 2002] E. D. Case, The Saturation of Thermomechanical Fatigue in Brittle Materials,
Thermo-Mechanical Fatigue and Fracture, WIT Press, Southampton, UK, editor M. H.
Alibadi, 2002, pp. 137 – 208.
[Fushillo 1960] N. Fuschillo, edited by I. Cadoff, E Miller, Thermoelectric materials and devices,
Reinhold Publishing Corporation, New York, 1960, p. 1-17.
[Hoepfner 2003] T. P. Hoepfner and E. D. Case, The influence of the microstructure on the
hardness of sintered hydroxyapatite, Ceram. Int. 29 (2003) 699-706.
[Horio 2004] Y. Horio, H. Yamashita, T. Hayashi, Microstructure and thermoelectric properties
of hot-pressed p-type Bi0.5Sb1.5Te3 alloys prepared by rapid solidification technique, Mat.
Trans. 45 (2004) 3309-3313.
[Houston 1968] B. Houston, R. E. Strakna, H. S. Belson, Elastic Constants, Thermal Expansion,
and Debye temperature of Lead Telluride, J Appl Phys 39 (1968) 3913-3917.
[Hsu 2004] K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T. Hogan, E. K.
Polychroniadis, M. G. Kanatzidis, Cubic AgPbmSbTe2+m: Bulk thermoelectric materials with
high figure of merit, Science, 303 (2004) 818-821.
[Jiang 2005] J. Jiang, L. Chen, S. Bai, Q. Yao, Q. Wang, Fabrication and thermoelectric
performance of textured n-type Bi-2(Te,Se)(3) by spark plasma sintering, Mater. Sci. Eng. B
117 (2005) 334-338.
[Johnsen 2011] Johnsen S, He JQ, Androulakis J, Dravid VP, Todorov I , Chung DY, Kanatzidis
18

MG. High Performance Thermoelectrics from Earth-Abundant Materials: Enhanced Figure of
Merit in PbS by Second Phase Nanostructures, J Am Chem Soc 2011; 133: 3460-3470.
[Joshi 2008] G. Joshi, H. Lee, Y. Lan, X. Wang, G. D. Wang, R.W. Gould, D.C. Cuff, M.Y.
Tang, M.S. Dresselhaus, G. Chen, and Z. Ren, Enhanced Thermoelectric Figure-of-Merit in
Nanostructured p-type Silicon Germanium Bulk Alloys, Nano Lett., 8 (2008) 4670-4674.
[Kingery 1976] W.D. Kingery, H.K. Bowen, D.R. Uhlmann, Introduction to Ceramics, John
Wiley and Sons, New York, 1976, 505.
[Kishimoto 2002] K. Kishimoto, T. Koyanagi, Preparation of sintered degenerate n-type PbTe
with a small grain size and its thermoelectric properties, J. Appl. Phys. 92 (2002) 2544-2549.
[Lawn 1993] B Lawn, Fracture of brittle solids, 2nd Edition, Cambridge University Press, New
York,1993.
[Li 2006] J-F Li, J Liu, Effect of nano-SiC dispersion on thermoelectric properties of Bi2 Te3
polycrystals, Phys. Stat. Sol. (a) 203 (2006) 3768 – 3773
[Li 2006] Li J-F, Liu J. Effect of nano-SiC dispersion on thermoelectric properties of Bi2Te3
polycrystals, Phys Stat Sol 2006; 203: 3768–3773.
[Li 2011] Li F, Huang X, Sun Z, Ding J, Jiang J, Jiang W, Chen L. Enhanced thermoelectric
properties of n-type Bi(2)Te(3)-based nanocomposite fabricated by spark plasma sintering, J
Alloy Compd 2011;509: 4769–4773.
[Liu 2011] Liu D-W, Li J-F, Chen C, Zhang B-P. Effects of SiC Nanodispersion on the
Thermoelectric Properties of p-Type and n-Type Bi(2)Te(3)-Based Alloys, J Electron Mater
2011; 40: 992-998.
[Marshall 1982] D. B. Marshall, T. Noma, and A. G. Evans, A Simple Method for Determining
Elastic-Modulus-to-Hardness Ratios using Knoop Indentation Measurements,
Communications of the American Ceramic Society 65 (1982) C175-C176.
[Nolas 2001] G. S. Nolas, J. Sharp, H. J. Goldsmid, Thermoelectrics: Basic Principles and New
Material Developments (Springer series in material science, v 45), Springer, Germany, 2001.
[Nolas 2006] George S. Nolas, Joe Poon, Mercouri Kanatzids, Recent Developments in bulk
thermoelectric properties, MRS Bulletin, 31, March 2006, pp. 199-205.
[Okamoto 2008] NL Okamoto, T Nakano, K Tanaka, H Inui, Mechanical and thermal properties
of single crystals of the type-I clathrate compounds Ba8Ga16Ge30 and Sr8Ga16Ge30, J. Appl.
Phys. 104 (2008) 013529.

19

[Oliver 1992] W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and
elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res.
7 (1992) 1564-1583.
[Pedersen 2006] B. L. Pedersen, H. Birkedal, B. B. Iversen, M. Nygren, and P. T.
FrederiksenAppl Influence of sample compaction on the thermoelectric performance of
Zn4Sb3, Appl. Phys. Lett. 89 (2006) 242108
[Phani 2008 JACS] K. K. Phani, A novel method of predicting ultrasonic and elastic properties
of isotropic ceramic materials after sintering from the properties of partially sintered or green
compacts, J. Amer. Ceram. Soc. 91 (2008) 215 – 222.
[Pilchak 2007] A. L. Pilchak, F. Ren, E. D. Case, E.J. Timm, H.J. Schock, C-I Wu, T.P. Hogan,
Characterization of dry milled powders of LAST (lead-antimony-silver-tellurium)
thermoelectric material, Phil. Mag. 87 (2007) 4567-4591.
[Pudel 2008] B. Poudel, Q. Hao, Y. Ma, Y. Lan, A. Minnich, B. Yu, X. Yan, Dezhi Wang, A.
Muto, D. Vashaee, X. Chen, J. Liu, M.S. Dresselhaus, G. Chen, Z. Ren, High-Thermoelectric
Performance of Nanostructured Bismuth Antimony Telluride Bulk Alloys, Science 320
(2008) 634-638.
[Ren 2006] F. Ren, E. D. Case, E. J. Timm, M. D. Jacobs, H. J. Schock, Weibull analysis of the
biaxial fracture strength of a case p-type LAST-T thermoelectric material, Philosophical
Magazine Letters, 86 (2006) 673 – 682.
[Ren 2008] F. Ren, E. D. Case, J.R. Sootsman, M.G. Kanatzidis, H. Kong, C. Uher, E. LaraCurzio, R.M. Trejo, The high-temperature elastic moduli of polycrystalline PbTe measured
by resonant ultrasound spectroscopy, Acta Materiala, 56 (2008) 5954-5963.
[Ren 2009] Ren, F. , Hall, B. D. , Case, E. D. , Timm, E. J., Trejo, R. M. , Meisner, R. A. and
Lara-Curzio, E. Temperature-dependent thermal expansion of cast and hot-pressed LAST
(Pb-Sb-Ag-Te) thermoelectric materials', Philosophical Magazine, 89 (2009) 1439 — 1455.
[Ren unpublished data]
[Rice 2000] R. W. Rice, Mechanical Properties of Ceramics and Composites, Marcel Dekker
Inc., New York, 2000.
[Riffat 2003] S.B. Riffat, X. Ma, Thermoelectrics: a review of present and potential applications,
Applied thermal engineering 23 (2003) 913-935.
[Rogerio de Oliveira Hein 2010] L. Rogerio de Oliveira Hein, K. Amato de Campos, P. Carelli
Reis de Oliveira Caltabiano, A. Lúcia Horovistiz, 3-D reconstruction by extended depth-offield in failure analysis – Case study I: Qualitative fractographic investigation of fractured
bolts in a partial valve, Engineering Failure Analysis 17 (2010) 515–520.

20

[Rogl 2011] Gerda Rogl and Peter Rogl, Mechanical Properties of Skutterudites, Science of
Advanced Materials 3 (2011) 517–538.
[Rowe 2006] D.M. Rowe, Thermoelectric waste heat recovers as a renewable energy source,
International Journal of Innovations in Energy Systems and Power, 1 (2006) 13-23.
[Schmidt 2011 submitted] R.D. Schmidt, E. D. Case, J.E. Ni, J.S. Sakamoto, R.M. Trejo, E.
Lara-Curzio, E.A. Payzant, M.J. Kirkham, R.A. Peascoe-Meisner, The temperature
dependence of thermal expansion for p-type Ce0.9Fe3.5Co0.5Sb12 and n-type
Co0.95Pd0.05Te0.05Sb3 skutterudite thermoelectric materials, Philosophical Magazine,
accepted.
[Schreiber 1973] E. Schreiber, O.L. Anderson, N. Soga, Elastic constants and their measurement,
McGraw-Hill, New York, 1973.
[Snyder 2008] G. Jeffrey Snyder, Small Thermoelectric Generators, The Electrochemical Society
Interface (2008) 54-56
[Tritt 1999] T. Tritt, Holey and unholey semiconductors, Science 283 (1999) 804-805.
[Ueno 2005] K. Uneo, A Yammoto, T. Inoue, S. Sodeoka, and H. Obara, Optimization of hotpress conditions of Zn4Sb3 for high thermoelectric performance III. Effect of starting particle
size on thermoelectric and mechanical properties, J. Alloys Compds. 392 (2005) 295-299.
[Varshni 1970] Y. P. Varshni, Temperature dependence of the elastic constants, Phys. Rev. B, 2
(1970) 3952-3958.
[Wachtman 1961] J.B. Wachtman, Jr., W.E. Tefft, D.G. Lam, Jr., C.S. Apstein, Exponential
temperature dependce of Young’s modulus for several oxides ,Phys. Rev. 122 (1961) 17541758.
[Wei 2007] W. Wei, J. Li, H. Zhang, X. Cao, C. Tian, J. Zhang, Macrostructural influence on the
thermoelectric properties of SiC ceramics, Scripta Mater. 57 (2007) 1081 – 1084.
[Xiong 2009] Xiong Z, Chen X, Zhao X, Bai S, Huang X, Chen L. Effects of nano-TiO(2)
dispersion on the thermoelectric properties of filled-skutterudite Ba(0.22)Co(4)Sb(12), Solid
State Sci 2009;11: 1612-1616
[Yang 2004] L. Yang, J.S. Wu, L.T. Zhang, Synthesis of filled skutterudite compound
La0.75Fe3CoSb12 by spark plasma sintering and effect of porosity on thermoelectric
propertiesJ. Alloy. Compd. 364 (2004) 83-88.
[Yang 2006] J. Yang, T. Caillat, Thermoelectric materials for space and automotive power
generation, MRS Bulletin, 31 (2006) 224-229.

21

[Zhang 2010] Y.H. Zhang, G.Y. Xu, F. Han, Z. Wang, and C.C. Ge, Preparation and
Thermoelectric Properties of Nanoporous Bi2Te3-Based Alloys, Journal of electronic
materials, 39 (2010) 1741-1745.
[Zhao 2008] L. D. Zhao., B. Zhang, J. Li, M. Zhou. W. Liu, and J. Liu, Thermoelectric and
mechanical properties of nano-SiC-dispersed Bi2Te3 fabricated by mechanical alloying and
spark plasma sintering, J. Alloys Compds. 455 (2008) 259-264.

22

2.0 Experimental Procedure
2.1.0 Ingot Fabrication
Ingots were fabricated at both Michigan State University and Northwestern University.
High purity elemental and compound powders of the correct concentration for LAST, LAST-T,
and PbTe-PbS were placed in a sealed silica ampoule and cast using a rocking furnace. The
constituent elements were heated at a maximum temperature of 1350 K for 10 hours and then
cooled over 24 hours.

2.2.0 Powder processing
All powder processing was undertaken in an argon atmosphere glove box (Omni-Lab
double glove box with oxygen sensor and moisture sensor, Vacuum Atmospheres Company,
Hawthorne, CA) (Figure 2.1). After powder processing, the powders were stored in the glove
box under argon atmosphere until sintering or characterization.

2.2.1 CGSR (Crushed, Ground, Sieved, Reground)
After ingot fabrication, ingots were either cut into specimens or used for powder
processing. The ingot was crushed into centimeter sized pieces using a mortar and pestle or the
broad side of a wrench. For both the LAST and PbTe-PbS specimens, the larger centimeter sized
pieces were ground and re-ground using a tungsten carbide mortar and pestle (Retsch RM200,
Retsch GmbH, Haan, Germany) until they all passed through a 53 micron sieve (8" diameter x
2" height ASTM E 11 sieve, Retsch GmbH, Haan, Germany). A sieve with a larger grid (250
microns, 8" diameter x 2" height ASTM E 11, model 60.150.000, Retsch GmbH, Haan,
Germany) was placed
23

Planetary
Ball Mill

Ingot

Hot
Pressing or
PECS

Mechanical
Crushing
Mortar and Pestle

and Grinding

Sieving and
Re-sieving

Characterization

Figure 2.1: Schematic of powder processing procedure for PbTe-chalcogenides in this study.
Both the powder particles and the bulk specimens were characterized using scanning electron
microscopy.

24

on top of the 53 micron sieve to limit the larger pieces from damaging the sieve. A vibrating
stage (Retsch AS 200) was used for five minutes to vibrate and aid sieving. After five minutes,
the powder that passed through the 53 micron sieve was put aside, the powders that did not pass
through were re-ground using the mortar and pestle until all the powder passed through the sieve.
All powders that passed through the sieve were referred as CGSR (Crushed, Ground, Sieved,
Reground).
After each powder processing step, approximately three grams of powder was set aside for
characterization (via scanning electron microscopy, SEM, Section 2.4, or laser particle analysis,
Section 2.5). After all powders passed through the sieve the powders were stored in 25 ml glass
vials with plastic stoppers (RPI 121000, Research Products International Corp., Mt. Prospect, IL)
with the ingot name, date of collection, milling time, speed, and any wet milling liquid used on
the outside of the vial and on the lid with a permanent marker.

2.2.2 Milling jar and Media for milling
Alumina spherical media, with diameters of 3 mm (Retsch 05.368.0019), 10 mm (99.5%
alumina, 10mm diameter grinding ball , 0076-05, Union Process, Akron Ohio) and 20 mm
(Retsch 05.368.0054), was used in a 250 ml alumina lined jar (Retsch 01.462.0219) . Before the
media was first used and after each cleaning with aqua regia (Section 2.3.0), the media was
cleaned using 200 proof ethyl alcohol for five minutes in the ultrasonic cleaner to remove any
surface contaminants. The ethanol was drained and the media was rinsed with RO water for five
minutes. The media was then allowed to dry in air in a 250 mL Pyrex beaker

25

2.2.3 Milling
Each composition of LAST and PbTe-PbS had a unique alumina-lined milling jar and
spherical alumina media to limit cross-contamination between compositions. Powder processing
for the LAST and the PbTe-PbS compositions used the same dry milling procedure (Section
2.3.1). All powder processing was performed in an argon atmosphere glove box

2.2.3.1 Dry milling
To further reduce the particle size after CGSR the powders were dry milled with a
planetary mill (PM200, Retsch). For dry milling, approximately 25 grams of CGSR (Crushed,
Ground, Sieved, Reground) powders were poured into the 250 ml alumina milling jar with 50
(116 g) 10 mm diameter alumina spherical media. The alumina lined lid was clamped onto the
jar, securing it in place. The milling jar was placed in the planetary mill and secured using a
clamp. The milling jar was loaded into the planetary mill, and milled for three hours at 150 rpm
[Hall 2008].
After dry milling, approximately 3 grams was taken out and stored in a glass vial until
removed for characterization (SEM, laser particle analysis). Powder that was caked on the
alumina media was removed using a vibrating stage (Retsch AS 200) for five minutes. During
vibrations, the alumina media was placed in a 750 micron sieve (Retsch 05.368.0054. The
powder that was caked along the sides was scraped off using a metal spatula (VWR 57952-253,
VWR LabShop, Batavia, IL). A 2-3 gram sample was again removed for characterization and
stored in a glass vial.
The 10 mm diameter alumina spherical media was removed and placed in a labeled
plastic bag and the remaining powder was placed in a labeled glass vial and stored in the glove
26

box. The labeled bag for the media was to ensure that there was no cross contamination from
other materials that were also powdered processed in the same glove box.

2.2.3.2 LAST milling – Wet milling with 10 mm diameter media and hexane
To further reduce powder particle size after dry milling, ~25 g of powder was planetary
milled with 25 ml of hexane and alumina spherical media. The alumina media was a
combination of 10 mm diameter spherical media and 3 mm diameter media, 140 g and 60 g
respectively [Hall 2008]. Once the powder, media and milling liquid was in the milling jar the
lid was clamped on and the jar was placed in the planetary mill. The planetary mill ran for 6
hours at a rate of ~110 rpm.
After milling was completed, the mill jar was removed from the planetary mill and the
clamp and lid were removed. The contents of the jar, the media, powder and hexane was placed
on top of the 53 micron sieve and placed in the antechamber of the double glove box. Once the
pressurized antechamber reached ~0.2 MPa (30 psi), the evacuation valve was closed and argon
was slowly introduced to the chamber, over 30 minutes. The vibratory stage was turned on and
the powder passed through the 53 micron seive. The milled powder was placed in a glass vial
and stored in the glove box.

2.2.3.3 LAST and PbTe-PbS wet milling with 20 mm and 3 mm diameter alumina media with
hexane
After dry milling, additional milling can further reduce particle size. Wet milling
involved adding a liquid to use as a wetting agent to limit caking and further reduce particle size.
For wet milling, a milling liquid were added; in this case 25 mL hexane (the amount was
27

independent of the powder charge). The milling media consisted of 7 20 mm diameter alumina
media and approximately 60g of 3 mm diameter alumina media. The mill jar was again returned
to the planetary mill for additional milling for 6 hours at rpms that ranged from 100-120.
The slight difference in rpm’s from batch to batch (100 rpm – 125 rpm) was due to the
accuracy of the planetary mill. At 100 rpm the mill would sometime become unbalanced and
stop running every 10 – 15 minutes. By slightly increasing the rpm, the mill would not
unbalance and finish the milling cycle. This procedure was based on what was developed by
Bradley Hall [Hall 2008]. After milling was completed, the powder was removed using the
procedure described in Section 2.2.4.

2.2.3.4 PbTe-PbS Wet milling 20 mm and 3 mm diameter with ethanol – No Dry milling
Wet milling with hexane resulted in significant caking along the sides of the jar for the
skutterudite powders [Schmidt Master’s Thesis]. Therefore, skutterudite powders were wet
milled with ethanol, which reduced caking of the skutterudite powders along the sides of the
jar[Schmidt Master’s Thesis].
For the PbTe-PbS powders milled with ethanol, there was not a previous dry milling
step. The powders were taken after being crushed, ground and reground until all passed through
a 53 micron sieve (CGSR powders). Approximately 20 - 30 grams of CGSR powders were
poured in the 250 ml alumina milling jar along with 25 - 42 mL of hexane and approximately
135 g of 20 mm diameter spherical alumina media and 60 g of 3 mm diameter spherical alumina
media. The lid was clamped on and the mill jar was placed in the planetary mill. The mill was
run for nine hours at 150 rpm. After the milling was completed the media and powder was
removed. Removing media and powder from milling jar after wet milling.
28

2.2.3.5 Mixing nanoparticle additions with PbTe-PbS powders
For nanoparticle composites, the nanoparticles were mixed with the matrix powders
using the planetary mill to ensure a homogenous distribution. The nanosized powder amount
was based on the desired volumetric total and added to the milling jar. The milling media, 115 g
of 10 mm diameter alumina spheres, was added to the powders and the lid was then clamped on.
There was no milling liquid added.
The milling jar was then placed in the planetary mill and milled for 3 hours at 110 rpm.
After milling, the clamp and lid was removed. Powder that has clumped to the sides was moved
using a metal spatula. The powder and media was poured onto a 75 micron sieve. The sieve was
clamped into the sieve shakers on top of the collecting pan. The sieve shaker was run for 5
minutes. At this point all the powder was poured from the collecting pan into a labeled glass vial
and the media was removed from the sieve. The labeled glass vial was stored in an argon
atmosphere glove box.

2.2.4 Removing media and powder from milling jar after wet milling.
After wet milling, in the argon atmosphere glove box, the clamp was removed from the
jar and the lid was removed. The milling jar, with both the powder and alumina media, were
placed in the smaller evacuation chamber to evaporate the milling liquid. The 710 micron sieve
was placed on top of the milling jar to limit the powder and media from moving around the
chamber. The evacuation chamber door was then sealed and the chamber was slowly evacuated
(the knob was turned to halfway between evacuation and off). It was key to do this step slowly,
as the chamber is evacuated quickly (opening the evacuation valve completely) the milling liquid
29

will boil rapidly and cause the powders to fly around the chamber.
Once the pressure reached approximately 0.21 MPa (30 psi), the evacuation valve can be
opened all the way. The chamber was then kept at the evacuation valve opened all the way for
30 minutes. After 30 minutes has passed, the evacuation valve was turned off and the inlet valve
was opened partway to slowly replenish the chamber with argon.
Once atmospheric pressure was reached, the chamber was then opened again to the glove
box and the jar was removed. The jar was then scrapped along the sides to remove any powder
clumps and media and powder were overturned into the large 710 micron sieve. The 710 micron
sieve was placed over the sieve try and secured into the vibrator. After vibrating for 6 minutes
the media was contained in the 710 micron sieve and then powder has passed through the sieve
into the bottom tray. Media and powder were now separated and ready for weighing.

2.3.0 Cleaning the media, jar, and sieves
2.3.1 Cleaning the alumina milling media
After approximately 10 milling runs, the media was cleaned using an aqua regia mixture.
The aqua regia was mixed using 1 part nitric acid (HNO3) to three parts hydrochloric acid (HCl).
All mixing of aqua regia and cleaning of media was performed under a fume hood. The media
was placed in a 500 ml Pyrex beaker and enough aqua regia was made to submerge the media
(usually 400 mL of aqua regia, 300 mL of HCl and 100 mL of HNO3). Once submerged, the
media and aqua regia combination was left under the hood until all the aqua regia had
evaporated, approximately 72 hours. The spherical alumina media was then rinsed using an
ultrasonic bath of RO water for five minutes and then ethyl alcohol for five minutes, then another
30

5 minutes using RO water.

2.3.2 Cleaning the alumina lined milling jar
The alumina lined part of the jar was cleaned using aqua regia before being re-used for a
different composition. Using aqua regia needs to be approached with caution. Aqua regia
reacted with the outer stainless steel case of the milling jar causing discoloration and eventually
pitting. All cleaning of the milling jar with aqua regia was performed under a hood using proper
safety gear: a splash shield, safety glasses, lab coat, acid apron, and safety gloves.
To clean the 250 mL alumina-lined milling jars, 100 mL of aqua regia was made in a 250
mL Pyrex beaker, 25 mL nitric acid to 75 mL hydrochloric acid. The aqua regia was carefully
poured into the milling jar to limit excess splashing or dripping. The milling jar was then
slightly tipped in a circular fashion so the aqua regia would coat then entire inside, for
approximately five minutes. The top of the jar and lid was cleaned by applying a little aqua regia
to a paper towel and gently and carefully applying the aqua regia to the alumina rim along the
top of the milling jar and the alumina plate on the lid. Care was taken not to touch the stainless
steel.
After the aqua regia was evaporated over the course of 48 hours, the milling jar was
rinsed twice with RO water to remove any residual aqua regia in the jar. The milling jar was air
dried upside down on paper towels.

2.3.3 Cleaning the sieves
Before the sieves were either (1) used with a new powder composition or (2) began to
clog with residual powder, the sieves were cleaned in soapy water. The sieves were placed in an
31

ultrasonic cleaner (VWR, 98000-336) with DI water and anti-bacterial soap for 5 minutes. After
5 minutes, the sieve was rinsed using RO water and placed in a 340 K furnace for 30 minutes to
remove any residual moisture from the surface of the grid.

2.4.0 Powder particle size determination using SEM
After each step in the powder processing procedure, (1) CGSR, (2) dry milling, and (3) wet
milling, approximately 3 grams of powder samples were set aside for powder particle size and
morphology characterization. To qualitatively asses the powder particle size, the powders were
observed using scanning electron microscopy, SEM. The one side of a SEM stub (12 mm x 10
mm, 1503L-MB, SPI) was covered using adhesive carbon tabs (05077-BA, SPI) or carbon tape
(05072-AB, SPI). Approximately 0.1 grams of powders were removed from the vial using a
metal spatula and gently placed on the adhesive tape. Loose powder was removed by several
short bursts of canned air.
The powders were observed in the SEM (JEOL, 6400) at an accelerating voltage of 15
kV and a working distance of 15 mm. Images were taken at several magnifications, ranging
from 100x-10,000x. A qualitative range of the particle sizes can be determined using the SEM
micrographs.

2.5.0 Powder particle size determination using laser particle analysis
A qualitative measurement of the powder size distribution was performed by a laser particle
analysis apparatus (Saturn DigiSizer 5200 Particle Size Analyzer, Micromeritics). To ensure that
the results from the particle size analyzer were consistent, proper care and maintenance was
32

performed regularly. The three rinses are necessary to ensure accurate results by clearing out the
sample line and limit collection of particles on the sample cell. At the beginning of a series of
powder particle size distribution measurements (approximately every 24 hours or when a fresh
batch of sucrose solution was used), (1) three rinse cycles with the analysis solution and (2) a
background analysis was performed. The background analysis of the analysis solution shows the
intensity versus angle when no sample was present in the system to scatter light (Figure 2.2).
Approximately every several months or when the Saturn DigiSizer 5200 Particle Size
Analyzer sample cell was cleaned, the laser particle analysis apparatus was calibrated with a
garnet reference powder (004-16811-00, Micromeritics). If the powder size distribution of the
garnet reference powder did not agree with vendor specified powder particle size distribution,
then the system was cleaned by rinsing out the analysis liquid, cleaning the sample cell, and
cleaning the optics.

2.5.1 Analysis liquid for laser particle analysis
A 50% sucrose solution was used to ensure that the powders remain suspended in the
liquid solution during analysis particle size distribution analysis. The sucrose solution was made
with degassed RO (reverse osmosis) and sucrose crystals (4005-06, J.T. Baker). The RO water
was degassed (AquaPrep II, 056-00000-00, Micromeritics) for two hours to remove dissolved air
in the water. Dissolved air generates tiny bubbles which distorts the precision of the laser particle
analysis. The 50 wt% sucrose solution was made by mixing equal parts by weight of lab quality
sucrose crystals and degassed RO water.

33

2.5.2 Batch runs for laser particle analysis
Before a powder batch was analyzed in the laser particle size unit, approximately 0.3
grams of powder was dispersed ultrasonically (Ultramet III, Buehler, Evanston, IL) in 35 mL of
surfactant solution contained in a 50 mL Pyrex beaker for approximately 5 minutes. A surfactant
was added to the dispersion solution to aid in de-agglomeration of the powders during the laser
particle analysis. Either a 0.1 wt% sodium pyrophosphate (3850-1, J.T. Baker, Austin, TX) or a
0.1 wt% sodium lignosulfonate (Daxad 23, Micromeritics, Norcross, GA) solution was used as a
surfactant.
The laser particle analysis unit was rinsed three times with the sucrose solution, or until
<0.1% obscuration was obtained. (The obscuration was the percentage of light diffracted by the
solution. An obscuration of <0.1% indicates that the system was free of powder residue and thus
a new particle size distribution measurement can be initiated). The reservoir of the laser particle
analysis unit was cleaned with foam swabs (89022-988, VWR) and Tech Spec lens cleaner to
remove residual powders from previous test batches.
Once an <0.1% obscuration was obtained and the powders were dispersed in either the
sucrose solution or a surfactant solution (to limit agglomeration), the dispersed powder solution
was slowly added to the reservoir in the laser particle analysis unit until a obscuration of 15%
was obtained.
At least 2 separate particle size distribution runs were done for each powder batch to (1)
ensure that sampling error of the particles did not occur and (2) to obtain some consistency
between runs. Before each subsequent run in the laser particle analysis unit, the powder solution
was then re-dispersed in the ultrasonic bath before adding to the liquid reservoir.

34

2.6.0 Densification via Hot pressing (HP)
The hot pressed specimens induced in this study were densified using an inductively
heated hot press (Hot Press Model HP200, Thermal Technology LLC, Santa Rosa, CA) at
Michigan State University. This hot press (HP) simultaneously supplies heat and pressure on the
green powder compact to aid in sintering and densification. The powder was stored in the argon
atmosphere double glove box before loading in a 22 mm diameter graphite die. The powder was
loaded into the die while the powder and die were both in the glove box.
The die was lined with Grafoil (GrafTec, Parma, Ohio) which is used to aid in removing
the pressed billet from the die. The powder was cold pressed in the die before removing from the
glove box to ensure that the plungers did not displace when removed from the glove box and
transferred to the hot press. The maximum pressure was 60 MPa and the maximum
temperatures ranged from 623 K to 723 K.
The hot pressing cycle began with heating the die from room temperature to 523 K at 0 MPa
pressure over 20 minutes, then to 623 K to 723 K and 74.4 MPa of pressure over 20 minutes.
While maintaining pressure, the temperature was raised to the maximum temperature over 10
minutes and then held for 90 minutes. After holding at the maximum temperature, the
temperature was lowered to 100 K less than sintering temperature and pressure reduced to 0 MPa
over 20 minutes. Finally the temperature was reduced to a set temperature of 323 K over 120
minutes before allowing cooling to room temperature, but, in practice, cooling occurred at a
slower rate due to the natural slow cooling rate of the furnace. A typical cycle takes about 1 day
to complete due to the speed of cooling to room temperature.

35

2.7.0 Densification via Pulsed Electric Current Sintering (PECS)
The Pulsed Electric Current Sintering (PECS) system (SPS 10-4, Thermal Technology
LLC, Santa Rosa, CA) was investigated as an alternative to hot pressing due to the shorter
fabrication times (in comparison to inductive heating hot pressing). The PECS system can
rapidly heat a specimen by sending a pulsed electric current through both the die and green
compact while simultaneously also applying pressure. This therefore localizes the heating and
results in the specimen reaching temperature at a faster rate. The faster heating results in shorter
overall pressing times.
As with hot pressing, the powders were stored in an argon atmosphere glove box before
being pressed using the PECS system. The 22 mm graphite die was lined with Grafoil to aid
with specimen removal after pressing (this was done outside the glove box). The powders were
added to the die (with a disc of Grafoil along the top and bottom of the powder along the
punches) and were cold pressed using a table top Arbor press to secure the powder and punches
in the glove box. The die was then placed in a one quart resealable plastic bag (00140 737840,
Gold Seal) before it was removed from the glove box to limit oxygen from interacting with the
powders. The punches and die were inserted into the PECS chamber and set up according to
manufactures directions. An initial pressure of 5 MPa was placed on the specimen during
loading. The chamber was then pumped down for five minutes and then backfilled with
99.999% pure argon. During the pressing run, there was flowing argon. The controller was
programed with the rates and times for pressure and temperature during ramp up and down of the
pressure and temperature. The temperature-time-pressure profiles varied between specimens to
determine the optimal profile (Table 2.1, Figures 2.2-2.3, Appendix B) . The sintering time
ranged between five to 30 minutes and the maximum temperature ranged between 273 K and
36

Table 2.1 The maximum temperatures, pressures and times used for sintering via pulsed electric
current sintering (PECS) PbTe-PbS specimens in this study.

Specimen Label
C-PTS-P-01
C-PTS-P-02
C-PTS-P-03
C-PTS-P-04
C-PTS-P-05
C-PTS-P-06
C-PTS-P-07
C-PTS-P-08
C-PTS-P-09
C-PTS-P-10
C-PTS-P-11
C-PTS-P-12
C-PTS-P-13
C-PTS-P-14
C-PTS-P-15
C-PTS-P-16
C-PTS-P-17
C-PTS-P-18
C-PTS-P-19
C-PTS-P-20
C-PTS-P-21
C-PTS-P-22
C-PTS-P-23
C-PTS-P-24
C-PTS-P-25
C-PTS-P-26
C-PTS-P-27
C-PTS-P-28
C-PTS-P-29
C-PTS-P-30
C-PTS-P-31
C-PTS-P-32
C-PTS-P-33
C-PTS-P-34
C-PTS-P-35

SiCnp
volume
percent
0.0
0.0
2.5
2.5
0.0
1.0
3.5
0.0
0.0
0.0
0.0
2.5
0.0
3.0
0.0
2.5
3.0
2.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

Temperature
(K)

Pressure
(MPa)

Time
(minutes)

823
823
823
823
823
823
823
873
823
823
823
823
673
673
673
673
673
673
673
723
723
723
723
723
823
823
823
673
823
823
823
623
573
533
493

60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60

20
20
20
20
21
21
21
21
30
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
16
16
20
5
16
16
20
5
5
5
5

37

Pressure
Temperature

60
50

700
40
600

30

500

20

400

10

300
0

50
100
150
Time (minutes)

Pressure (MPa)

Temperature (K)

800

0

Figure 2.2 Temperature-Pressure versus time for pressing specimens C-PTS-P-09. The
maximum temperature and pressure was 823 K and 60 MPa, respectively. The heating rate was
50 K/minute and the cooling rate was 5 K/minute. The pressure reached a maximum of 60 MPa
60 seconds after the temperature reached a maximum of 823 K.

38

Pressure
Temperature

60
50

700
40
600

30

500

20

400

10

300
0

50 100 150 200 250 300
Time (minutes)

Pressure (MPa)

Temperature (K)

800

0

Figure 2.3 Temperature-Pressure versus time for pressing specimens C-PTS-P-11 and CPTS-P-12. The maximum temperature and pressure was 823 K and 60 MPa, respectively.
The heating rate was 50 K/minute and the cooling rate was 5 K/minute. During cooling, the
specimen was thermally annealed at 573 K for 200 minutes to reduce residual stresses.

39

873 K (Appendix B). The maximum pressure remained constant at 60 MPa for all the specimens
(Table 2.1).

2.8.0 Specimen Cutting and polishing
For ingot specimens, the cast ingot cylinder was cut into discs that were approximately 5 mm
thick. For both pressed (hot pressed and PECS) discs and ingot discs, specimens were diced
using a slow speed saw. The dimensions of the specimens varied from 7 mm x 5 mm x 4 mm to
10 mm x 7 mm x 5 mm
For ellipsometry measurements (Chapter 2, Section 10.0), grain size analysis, indentation
tests, and fracture tests, a polished mirror surface was needed. Depending on the type of test, the
specimens were mounted on aluminum stubs or in epoxy.

2.8.1 Mounting in epoxy
For a specimen mounted in epoxy, a specimen with at least one flat edge was needed.
The mass and dimensions were measured to determine density (when possible). If the specimen
is irregularly shaped, the mass was measured.
The epoxy (Epoxicure Resin, Buehler, Evanston, IL) and hardener (Epoxicure Hardener,
Buehler, Evanston, IL) were mixed using a five to one weight ratio, respectively, per the
vendor’s instructions. The epoxy was measured into a 1 oz polypropylene cup (4304002301,
Medical Action) using an electronic balance (Adventurer AR2140, Ohaus Corp, Pine Brook, NJ).
The hardener was added using a syringe to the epoxy to match the five to one ratio of epoxy to
hardener.
The epoxy and hardener were mixed using a wooden rod (740745, Royal Paper), using
40

small circular motions to limit air bubbles in the epoxy mixture. The specimens were placed flat
side down on an 8 in x 8 in aluminum plate (McMaster-Carr, 89155K32) and 1” outer diameter
Bakelite rings (811-221, LECO, St. Joseph, MI) were placed around the specimens. The mixed
epoxy and hardener was poured over the specimens, filling the Bakelite rings and covering the
specimens. The specimens were left to cure for a minimum of one day, and then engraved with
the specimen label using a rotary tool on both the side of the Bakelite ring and top of the epoxy.
Any epoxy that leaked under the phenolic ring was cut off with a steel razor.

2.8.2 Mounting on an aluminum stub.
An alternate way to prepare specimens for polishing were to mount them using
thermoplastic on an aluminum stub. The aluminum stubs were made by cutting a 6061 aluminum
rod (McMasterCarr, 8974K133) into 2.5 cm diameter stubs. Before setting in thermoplastic, the
mass of the each specimen was measured using an electronic balance (Adventurer AR2140,
Ohaus Corp, Pine Brook, NJ). The specimen dimensions were measured using micrometers
(Mitutoyo CD-6”CSX, Kanagawa, Japan). The thermoplastic (Lakeside 70, Buehler, Evanston,
IL) was placed on the aluminum stub along with the specimens during heating on the hot plate
(Stirrer/Hot Plate Model 4658, Cole-Palmer, Chicago, IL). To reduce thermal transients in the
specimen and the potential for thermal shock, specimens were heated slowly on the hot plate,
over approximately 30 minutes. The thermoplastic was arranged around the specimen when it
became malleable (at approximately 350 K). The specimen edges were oriented as nearly
parallel to the aluminum stub as possible. The hot plate was then slowly cooled to room
temperature.

41

2.8.3 Polishing specimens
Specimens in epoxy or thermoplastic were polished with a Leco automated polishing wheel
(Leco Vari/Pol VP-50, Leco Corporation, St. Joseph, MI). Three to six specimens were mounted
in a 12-specimen polishing wheel. The specimens were affixed to the polishing wheel by
tightening screws into the sides of the aluminum or Bakelite ring. Care was taken to ensure the
specimens were as level as possible. Affixed to each of the polishing laps was an adhesive
polishing pad. For grits between 6 microns to 90 microns a White Tec pad was used (White Tec
#812-454, Leco, St. Joseph, MI), for grits less than 6 microns an adhesive red felt polishing pad
(Red Tec #812-445, Leco, St. Joseph, MI) was used. When the polishing pads became
contaminated the pads were removed and the polishing laps were cleaned.
The diamond compound grit was placed on the polishing pads in a spiral pattern of dots
approximately 10 cm apart. Diamond compound extender (Microid Diamond Compound
Extender #811-004, Leco, St. Joseph, MI) was added by squeeze bottle to wet the surface of the
polishing pad. Polishing extender was applied during the polishing process approximately every
15 minutes to lubricate the polishing pads. The specimens were polished using a series of pastes
with the following diamond sizes: 90 micron, 67 micron, 35 micron, 25 micron, and 10 micron, 6
micron, and 1 until a mirror finish was achieved on the specimen surface (Table 2.2). Before
each subsequent step the specimen holder was washed thoroughly to remove the previous
diamond grit to reduce contamination.

2.8.4 Washing the polishing wheel by hand
Between each diamond compound grit, the specimens and polishing holder was washed

42

Table 2.2: Diamond Polish Table. Each diamond grit was used in succession to polish a
specimen until reaching the desired polished surface on the specimen. The last polish used was
either the 1 μm or 0.5 μm polishing grit compound.
Nominal
Diamond
Grit Size
90 m

Diamond
Grit Size
Range
80-100 m

67 m

54-80 m

35 m

Not listed

15 m

Not listed

9 m

Not listed

6 m

Not listed

1 m

Not listed

0.5 m

Not listed

Manufacturer

Part Number

Warren Superabrasives,
Anaheim, CA
Warren Superabrasives,
Anaheim, CA
Warren Diamond Powder
Company, Olyphant, PA
Warren Diamond Powder
Company, Olyphant, PA
Leco Corporation,
St. Joseph, MI
Warren Diamond Powder
Company, Olyphant, PA
Leco Corporation,
St. Joseph, MI
Leco Corporation,
St. Joseph, MI

80-100MB MUS 20gm

43

54-80MB MUS 20gm
#35 MUS MB 20G
#15 MUS MB 20G
810-913
#6 MUS MB 20G
810-870
810-868

with soap and water to limit cross contamination. A dime-sized drop of soap was placed on each
specimen and rinsed under a running faucet (with a steady flow) for five minutes. The
thermoplastic and epoxy was also visually examined to determine if there were macropores in
the epoxy that were sequestering diamond compound. The tip of a push pin was used to remove
any polishing compound that remained. The cleaning between diamond compound steps was
important to limit contamination.

2.8.5 Washing the polishing wheel using an ultrasonic cleaner
To clean the polishing holder an ultrasonic cleaner (VWR, 98000-336) that was large enough
to immerse the polishing holder was used (with interior dimensions 30 cm x 15 cm x 15 cm).
The ultrasonic cleaner was filled with RO water and Aquinox liquid soap. The amount of liquid
soap added was per the soap manufacturer’s
directions (14.5 milliliters per 4 liters of water). Before immersion in the ultrasonic cleaner the
specimen holder was rinsed with soap and water in the sink to remove residual polishing
compound. The specimen holder was immersed in the ultrasonic cleaner for 5 minutes to
thoroughly clean the specimens.

2.9.0 Index of refraction and extinction coefficient measured via ellipsometry
Optical ellipsometry [Blanchard 2010] determined the real and imaginary parts of the
optical index of refraction for the n-type skutterudite, n-type LAST, and PbTe-PbS specimen
using facilities. The indices of refraction were used for to determine the particle size distribution
with the laser particle analysis unit.
The thermoelectric specimens for which index of refraction measurement were
44

performed included: n-type skutterudite (Ce0.1Co0.95Pd0.05Te0.05Sb3), PbTe-PbS, and LAST
specimens which were parallelepipeds, with dimensions between 10 mm x 10 mm x 6.7 mm to
10 mm x 7 mm x 5 mm. The 10 mm x 10 mm and 10 mm x 7 mm surfaces were polished to a
mirror-like finish using a series of diamond paste with grit size ranging from 67 microns to 1
micron (Section 2.8).
The ellipsometer (EC110, J. A. Woollam Co.) and corresponding software (WVASE32
v3.154, J. A. Woollam Co.) were calibrated using a SiO2 wafer standard provided by the
manufacturer (J. A. Woollam Co.). The optical scans were performed over the range of 4138 Å to
7463 Å, with measurements taken approximately every 75 Å.

Each of the ellipsometer scans

were taken at a different location on the 10 mm X 10 specimen surface. (The specimen was
translated on the instrument stage using metal tweezers). For the Skutterudite, LAST, and PbTePbS specimens, 25 total ellipsometer scans were performed.

2.10.0 X-ray diffraction
Approximately 3 grams of dry milled powders (Section 2.2.3.1) was set aside for x-ray
diffraction. In this study, the high temperature x-ray diffraction was performed at Oak Ridge
National Laboratory (ORNL) [Payzant 2010]. The XRD stage (Anton Paar XRK900) at ORNL
was 14 mm in diameter and 0.5 mm in depth. For the high temperature XRD testing,
approximately 0.63 g of powder PbTe-PbS was used. The XRD at ORNL was a Panalytical
X’Pert Rom MPD (instrument type: PW3040-PRO). A mixture of 96%N2-4%H2 gas flowed in
the reaction chamber during the entire heating and cooling cycle. The temperature range was
o

o

o

o

o

30 C to 420 C using 30 C intervals. The diffraction scan was from 2 15 to 2 with a
45

o

step size of 0.02 . After the run, the lattice parameter was determined using reitveld analysis
using commercial software (X’Pert HighScore Plus , PANalytical, v2.2.4) .

2.11.0 Hardness measured via Vickers indentations
2.11.1 Calibration of indenters at each load
Prior to the hardness testing, the Vickers indenters (Buehler Semimacro Indenter and
Shimadzu HMV-2000) were calibrated using a standard calibration block with hardness of 7.75
GPa (761-048, Yamamoto Scientific Tools Lab, Co LTD, Japan). The calibration factor was
determined by doing 10 indents at each testing load for both the Buehler, at loads of 2.94 N and
4.9 N, and Shimadzu, at loads of 0.98 N, 1.9 N, 2.94 N and 4.9 N, indenter. The measured
hardness was then compared to the expected hardness to determine the calibration factor.

2.11.2 Vickers Hardness
The specimen’s hardness, H, was determined using the Buehler Semimacro Indenter and
Shimadzu HMV-2000 indenters with 10 to 20 Vickers indentations on the polished specimen
surfaces using a 2.94 N load and a loading time of 5 seconds. The indentation centers were
placed at least 500 microns apart, and at least 1000 microns from the specimen edge. After each
indentation, the indention width, 2c, was measured using the indenter’s microscope.
In addition to the indentation testing at a fixed (2.94 N) load, a possible load dependence
of hardness was explored using the Shimadzu HMV-2000 with Vickers indentations made as a
function of load, with 10 indentations per load, (0.25 N, 0.49 N, 0.98 N, 1.96 N, 2.94 N, 4.90 N,
and 9.81 N).
For all of the Vickers indentation data, the hardness, H, was calculated from equation
46

[Wachtman 2009]

H

1.854 P
a2

(2.1)

where 2a is the diagonal length of the indentation impression and P is the indentation load.
When a developed radial cracks system was present, the fracture toughness, KC, was estimated
using equation (2.2), which in the literature was the most frequently used form of the relationship
for the indentation fracture toughness of brittle materials via Vickers indentations [Barsoum
2003].

1/ 2 P
E
KC   
H
c3 / 2

(2.2)

where E is the Young’s modulus, P is the indentation load, c the radial crack length for Vickers
indentation and  is 0.016.

2.13.0 Fracturing specimens
Specimens, both LAST and PbTe-PbS were fractured in order to examine the
microstructure, such as grain size and porosity. The specimens were fractured by wrapping them
loosely in a Kimwipe. The sharp edge of a razor blade was placed against the specimen and then
the razor blade was tapped sharply with a hammer to fracture the specimen.

2.14.0 Thermal annealing to determine grain size and generate bloating
Specimens with both fractured surfaces and polished surfaces were thermally annealed
for grain size analysis. For all specimens, the mass was measured using an electronic balance
before annealing to aid in documenting volitization during the annealing process and to aid in
47

identifying specimens after anneal if they were jostled during set-up.
A mullite tube, an alumina D-tube, alumina boat, and furnace seal was dedicated to each
chemical composition in order to limit contamination. The selected mullite tube, D-tube,
alumina boat and specimen were placed in a resistance-heated furnace (Carbolite, Watertown,
Wisconsin). The specimens were placed on the alumina D-tube and the alumina boat was set
over the specimens to avoid mullite dust from the muffle tube from settling on the specimen
during annealing. The mullite tube was evacuated using a mechanical pump for 5 minutes and
then backfilled with Argon (before July 2009) or 96% Ar + 4% H2 gas (post August 2009). Then
the mullite tube was refilled with the gas until there was positive pressure in the mullite tube. At
this point the furnace seal was checked to be air tight using a soap-water solution. The mullite
tube was evacuated and backfilled three more times, for a total of 4 times.
After the final backfill of Ar or 96% Ar + 4% H2 or Ar gas, the outlet was connected to a
bubbler valve. The gas flow was maintained where there was approximately 1 bubble per every
10 seconds. The furnace controller was set to the maximum temperature and time. The cooling
and heating rates ranged between 2 K/min to 5K/min. The specimens were annealed from 1
hour to 4 hours at temperatures that ranged from 543 K to 936 K.

2.15.0 Grain size measured by linear intercept method
For grain size analysis, both as-fractured and polished surfaces were imaged using a SEM at
magnifications ranging from 300x to 10,000x. The grain size was measured using the linear
intercept method on (1) thermally etched polished surfaces and (2) freshly fractured surfaces of
as-densified and annealed specimens. For the linear intercept method, a set of approximately
48

20 to 30 straight lines were randomly drawn over a micrograph. The total length of each line was
measured and scaled using the imprinted scale bar. For each line, the number of grain boundary
a line crossed was counted. At least 200 grain boundary intercepts per micrograph were
evaluated. The sum of the scaled line length was divided by the sum of grain boundary
intercepts to calculate an average intercept length. The average intercept length was multiplied
by a stereographic projection factor, 1.5 [Fullman 1953].
To compare grain sizes among specimens and to determine grain growth due to postdensification annealing, a statistically sufficient number of micrographs per specimen, N, was
calculated to reduce the uncertainty in grain size measurements. Assuming a lognormal
distribution for the grain size, GS, for the PbTe-chalcogenide matrix, we determined N using a
lognormal 95% confidence interval such that
 * *2
 2 
 GS s , GS* s*    (LL, UL)







(2.3)

*
where GS was the log transformed grain size and s* is the empirical standard deviation

[Limpert 2001]. A conservative estimate of the GS range of the PbTe-PbS matrix was assumed to
be 1 micron to 15 microns, the lower limit, LL, and upper limit, UL, respectively. Using the
conservative estimate of the UL and LL, we solved for s *
 *2 
* 2 
s 
GS  s* 

 UL




  s*4  UL  15  15

.
LL
LL
1
* *2
*2
GS s
1 s

49

4 UL 15
s* 

 15
LL 1
4
 
1 
 
2 
  1 N   GS   2 
4 

i
s*  exp 
 log *     15
   N  1 i 1  GS   

 
 
 


 



*
Using Limpert et al. [Limpert 2001] definition of GS and s*

1
N
1 N
 N
*
GS  exp   log GSi     GSi 

N
 
 i 1
  i 1


(2.4)

and

1


2 2 
 1 N   GS 


log i   
s*  exp 

  N  1   GS*   
 
i 1 

 





(2.5)

we solved for N as follows,

 
1 
 
2  2 
4
   1 N   GSi   
s*  15  s*  151 / 4  s*  exp 
 log    151/ 4
  N  1   GS*   

 
i 1 
 
 


 



1

N   GS  2  2
N   GS  2
2
1/ 4 )   1
i     ln(151 / 4 )   1
i

 ln(15


 log * 
 N  1  log *  



N  1   GS 



 
i 1  GS  
i 1

2

 N 1 

2

N   GS 
N   GS 
1
log i   N 
log i   1
2    * 
2    * 
 ln(151 / 4 )  i 1  GS 
 ln(151 / 4 )  i 1  GS 








1

50

(2.6)

Ten ‘pilot studies’ were used to determine N, the sample size. Each ‘pilot study’ consisted of
ten randomly generated grain sizes [Matlab] that were between the lower limit of 1 micron and
an upper limit of 15 microns. Using Eq. (2.4) and the ten randomly generated grain sizes, GS,
*

GS was calculated for each pilot study. For the ten ‘pilot studies’, N ranged between 1.9 to

4.7, indicating a statistically sufficient number of micrographs per specimen, N, was five.

2.16.0 Room temperature elastic moduli measured via Resonant Ultrasound Spectroscopy (RUS)
The elastic moduli measurements at ORNL and at MSU were performed using Resonant
Ultrasound Spectroscopy (RUS) (Figure 2.4) to evaluate the elastic moduli, Young’s modulus,
shear modulus and Poisson’s ratio. All specimens in this study were either parallelepipeds or
cylindrical discs. The parallelepipeds ranged in size from 2 mm x 1.5 mm x 5 mm to 10 mm x
12 mm x 7 mm. The cylindrical discs were 20 mm in diameter and ranged in height from 2 mm
to 5 mm.
The specimens were placed on a tripod arrangement of RUS transducers, with one driver
transducer and two pickup transducers (Figure 2.4). The mechanical resonance frequencies of
each specimen were determined from a driving frequency range of 20 kHz to 700 kHz. For a
difference in driving frequencies delta f, were delta f = max f – min f, during the “sweep” of the
frequencies by the hardware, each frequency increment (step) delta f/29,999. The frequency
range was chosen to encompass at least the 75 lowest resonance frequencies for a given
specimen. At each frequency step the sinusoidal frequency was applied by the driving
transducer. A resonance frequency response was detected as a spike in the amplitude from either
of the two pickup transducers (Figure 2.5).
At least three RUS resonant spectra were taken for each specimen. For each RUS
51

Intensity (A.U.)

Figure 2.4: Schematic of the Resonant Ultrasound Spectroscopy (RUS) apparatus used for
Young’s modulus measurements. The specimen was balanced on the three transducers.

100

200

300

400

Frequency (KHz)
Figure 2.5: An example of an acoustic vibrational spectrum induced in a mechanically driven
specimen. The resonant peak positions were functions of the elastic moduli, geometry,
dimensions and mass density of the specimen. This spectrum is from C-PTS-P-07 at 363 K.

52

measurement the specimen was rotated or repositioned to limit the loss of peaks due to the
specimen being positioned on an anti-node of the standing wave [Ren 2009]. The resonance
frequency spectra that was that chosen for analysis displayed the resonant frequencies that were
sharp and distinct.
Based on the specimen dimensions, mass, and resonant frequency spectrum, the Young’s
modulus, shear modulus and Poisson’s ratio were calculated using the software available on the
RUS apparatus (Quasar Galaxy RI2000 with RPModel and CylModel software, Quasar
International). The software was chosen depending on the geometry of the specimen,
parallelepiped (RPModel) or cylindrical disc (CylModel). Between approximately12 and 40
resonance frequencies from the RUS spectra were used to calculate the elastic moduli for each
specimen. Initial estimates for Young’s modulus and Poisson’s ratio, were required to iterate the
resonance expected frequencies. Initial guesses of Young’s modulus and Poisson’s ratio were
first taken from published values for similar PbTe-chaclogenides [Ren 2009, Simmons 1971].
The commercial software was iterated with the measured frequencies from the RUS spectra until
the RMS error of the fitted model was less than 0.20% or 0.40% , for the parallelepiped and
cylindrical discs, respectively.

2.17.0 High temperature elastic moduli measured via RUS
All temperature-dependent modulus measurements were performed using the apparatus at
Oak Ridge National Laboratories, which was similar to that used at Michigan State University
for room temperature RUS measurement (Section 2.16), with the addition of a custom-built high
temperature chamber for the specimen.
The high temperature transducers (Quasar International, Albuquerque, NM) were
53

commercially fabricated with a high temperature silicon nitride probe extending from the
transducer approximately 15 cm, ending in a spherically rounded tip. The ends of each of the
three probes extended through a bottom refractory plate. The ends of the three transducers were
aligned in the middle of the chamber, positioned to support a specimen in a tripod arrangement.
Once the specimen was in the desired location on the transducers, the thermocouple was placed
approximately 1 cm from the specimen. An additional thermocouple, located at the bottom of
the high temperature chamber, was used to measure the temperature of the thermal chamber. A
ceramic refractory plate was placed on top of the high-temperature heating chamber and then the
metallic lid of the chamber was tightened in place.
The furnace chamber was pumped down using a mechanical pump for approximately 10
minutes until the pressure gauge read -600 Torr. The chamber was then backfilled with argon or
argon 96% + hydrogen 4% mixture until there was positive pressure in the chamber. The
chamber was again pumped down and refilled with gas three more times. During this gas
purging process, RUS scans were taken to ensure that the specimen had not fallen off the
transducers during either pump-down or backfilling. After the chamber was refilled the last time
the gas output was connected to a bubbler. The gas line was connected to a rotameter (FL1442S, Omega Engineering, Inc., Stamford, CT) that controlled the flow to 100 mm.
Concurrently with the set-up of the heating chamber, the furnace controller was
programed with the desired temperature-time profile. Three different temperature time profiles
were used for the LAST and PbTe-PbS system. For each of the three temperature profiles,
between succeeding RUS measurements, the temperature increased at a rate of 5 K per minute.
The LAST specimens had a RUS spectra taken every 50 degrees from room temperature to 873
K, both during heating and cooling. In contrast, the hot pressed and PECS-processed LAST
54

PbTe-PbS specimens had a RUS spectra taken every 30 degrees during heating and cooling
cycles where the maximum temperatures ranged from 543 K to 663 K. At each temperature
interval there was a 10 minute hold . At approximately 8 minutes into the dwell time, the RUS
spectra were taken.

2.18 Calculating the acoustic Debye temperature
In addition to measuring the elastic moduli, the RUS spectra is also a function of the shear
and longitudinal velocities, vs and vl. The acoustic Debye temperature, D, for the specimens in
this study were calculated from the longitudinal acoustic velocity, vl, and shear acoustic velocity,
vs, using [Anderson 1966].
h  3q N 1/ 3
D  
vm
k  4 M 


(2.7)

where h is Plank’s constant, k is Boltzmann’s constant, N is Avogadro’s number,  is the mass
density, M is the molecular weight, and vm is the averaged sound velocity The polycrystalline
hot pressed and PECS processed specimens in this study are assumed to be isotropic, therefore
the average sound velocity, vm, was determined using [Anderson 1966].

 

1 
1  2

vm  

 3  v3 v3  

l 
  s

1/ 3

(2.8)

where vl and vs were measured using RUS at 293 K.
2.19 Thermal Expansion Measurements
55

Thermal expansion was measured on bulk specimens using a Thermomechanical Analyzer
(TMA) (Q400, TA Instruments, New Castle, DE) in the High Temperature Materials Laboratory
at Oak Ridge National Laboratories. The TMA was calibrated using standard weights following
the software instructions and recalibrated after any change in the machine components. A
constant 0.1 N force was applied and maintained throughout testing with the glass expansion
probe. The chamber was flushed with 50 mL/min of 96% Argon 4% Hydrogen gas for an hour
before testing. The chamber is not sealed, so to limit the amount of oxygen during testing, 1
hour isothermal hold was conducted before thermal cycling.

2.19.1 Maximum temperature of the thermal cycle during thermal expansion measurements was
603 K in each experiment

The temperature dependent thermal expansion was measured for LAST and PbTe-PbS
specimens from room temperature to 603 K back to room temperature. This thermal cycled was
repeated two to four times, with heating and cooling rates of 1.5 K/minute.

2.19.2 Thermal expansion measured using two different maximum temperatures
To monitor bloating of PbTe-PbS specimens, the thermal expansion was measured using two
different maximum temperatures, 603 K and 663 K. The first temperature profile was a cycle
from room temperature to 603 K and back, for 3 heating and cooling cycles, for a total of 6 half
cycles. Immediately following the first temperature profile, the specimens was cycled from
room temperature to 663 K for an additional 3 heating and cooling cycles (6 half cycles) The
heating and cooling rate was 2 K/minute for both temperature profiles.
56

REFERENCES

57

2.20.0 References

[Anderson 1966] O.L. Anderson, Derivation of Wachtman's equation for temperature
dependences of elastic moduli of oxide compounds, Phys. Rev. 144 (1966) 553-557.
[Blanchard 2010] Gary J. Blanchard, Department of Chemistry, Michigan State University, East
Lansing, MI.
[Fullman 1953] R. L. Fullman, Measurement of particles in opaque bodies Trans AIME 197
(1953) 447 – 452.
[Hall 2008] Bradley D. Hall, Masters of Science Thesis, “Powder processing, powder
characterization, and mechanical properties of LAST (Lead-Antimony-Silver-Tellurium)
and LAST-T (Lead-Antimony-Silver-Tellurium-Tin) thermoelectric materials”, Materials
Science, College of Engineering, Michigan State University, 2008.
[Limpert 2001] Limpert E, Stahel WA, Abbt M. Log-normal distributions across the sciences,
BioScience 51; 2001: 341-352.
[Payzant 2010] Dr. E. Andrew Payzant, High temperature Materials Laboratory, Oak Ridge
National Laboratory, Oak Ridge, TN.
[Ren 2009] Ren, F., Case, E. D., Ni, J. E., Timm, E. J., Lara-Curzio, E., Trejo, R. M., Lin, C. -H.
and Kanatzidis, M. G. Temperature-dependent elastic moduli of lead telluride-based
thermoelectric materials, Philosophical Magazine,89 (2009) 143 — 167
[Schmidt 2010] Robert Schmidt, Masters of Science Thesis, “Mechanical properties of
thermoelectric skutterudite materials”, Materials Science, College of Engineering, Michigan
State University, 2010.
[Simmons 1971] G. Simmons and H. Wang, Single Crystal Elastic Constants and Calculated
Aggregate Properties. A Handbook, 2nd edition, The MIT Press, 1971.
[Wachtman 2009] J.B. Wachtman, Mechanical Properties of Ceramics, Wiley and Sons,
NewYork, 2009.

58

The full citation for this chapter is: Jennifer E. Ni, Fei Ren, Eldon D. Case, Edward J. Timm,
Porosity dependence of elastic moduli in LAST (Lead–antimony–silver–tellurium) thermoelectric
materials, Materials Chemistry and Physics 118 (2009) 459–466

3.0 Porosity dependence of elastic moduli in LAST (Lead-antimony-silver-tellurium)
thermoelectric materials
1
1,
1
2
Jennifer E. Ni *, Fei Ren , Eldon D. Case , Edward J. Timm
1

Chemical Engineering and Materials Science Department, Michigan State University, East
Lansing, MI 48824 USA
2
Mechanical Engineering Department, Michigan State University, East Lansing, MI 48824 USA
Abstract
Porosity in thermoelectric materials affects the thermal, electrical and mechanical properties of
the materials.

In this study, the Resonant Ultrasound Spectroscopy technique was used to

determine the Young’s modulus, E, shear modulus, G, and Poisson’s ratio, ν, of 12 hot pressed
and five cast polycrystalline specimens of the thermoelectric material LAST
(lead-antimony-silver-tellurium) as a function of volume fraction porosity, P, for P ranging from
0.01 to 0.14. A least-squares fit of the Young’s and shear moduli data to the relationships E = ED
(1-bPE P) and G = GD (1-bPG P), respectively yielded ED = 58.4 ± 0.6 GPa and GD = 23.0 ± 0.2
GPa, where ED and GD are the estimated Young’s modulus and shear modulus at room
temperature for theoretically dense specimens, respectively. The unitless, material-dependent
constants bPE and bPG were bPE = 3.5 ± 0.2 and bPG = 3.5 ± 0.2.

Keywords: semiconductors, elastic properties, ultrasonic measurements, microstructure
Please direct correspondence to: Jennifer E Ni, Chemical Engineering and Materials Science
Department, Room 2527 Engineering Building, Michigan State University, East Lansing,
Michigan, 48824-1226, USA, e-mail nijennif@egr.msu.edu, FAX (517)-432-1105.

59

3.1. Introduction
Thermoelectric materials in use today are predominantly heavily doped semiconductors [1]
although a number of ceramic oxide materials have been investigated as thermoelectrics [2 - 4].
Although the thermal and electric properties of thermoelectric materials have been studied
extensively, there is limited mechanical property information available for many thermoelectric
materials.

Furthermore, there is currently no study in the literature that includes a systematic

characterization of the elasticity-porosity relationship for any thermoelectric material.
This study of the porosity dependence of elastic moduli in LAST was motivated in part by the
lack of elasticity-porosity data in the literature, which is significant when one considers recent
observations of the enhancement of thermoelectric properties with increasing porosity for volume
porosity ranges similar [5, 6] to the 0.01 to 0.14 range of the LAST specimens included in the
present study.

Thus, given the interest in the effects of porosity on thermoelectric properties, it

is important to also consider the effects of similar porosity levels on the mechanical properties of
thermoelectric materials.
In this study, the Young’s modulus, shear modulus and Poisson’s ratio of five cast and 12
hot pressed LAST (lead-antimony-silver-tellurium) specimens were measured by Resonant
Ultrasound Spectroscopy (RUS). The observed decrease in the Young’s and shear moduli with
increasing porosity can be described relatively well by either an empirical exponential or linear
function of porosity.

For the range of volume fraction porosity (0.01 to 0.14) included in this

study, this result is consistent with the trends found in the literature for other brittle materials [7,
8]. The behavior of Poisson’s ratio as a function of porosity is more complex than that observed
for the Young’s and shear moduli, with the literature showing that the Poisson’s ratio may
increase, decrease, or remain approximately constant as a function of porosity. In this study, the

60

Poisson’s ratio decreased slowly with increasing porosity. In addition, selected specimens were
examined by SEM for microstructural study.

3.2. Background
In general, porosity can occur during specimen fabrication via either casting or sintering.
In this study, polycrystalline LAST specimens are produced by (i) casting and by (ii) hot pressing
powders obtained by milling the cast ingots [9].

Since the strength of brittle materials tends to

increase with the reciprocal square root of the grain size [10, 11], hot pressing has the advantage
of producing stronger materials with smaller grain size than cast materials [12 – 14].

In

addition to strength considerations, the elastic moduli are required for either numerical or
analytical stress-strain calculations for both the cast and hot pressed materials.

3.2.1 Effect of porosity on physical properties
This section is a brief overview of the role of porosity in the physical properties of materials
(including mechanical properties) while the following two sections address the effect of porosity
effects on the thermal and electric properties of thermoelectric materials.
While this study focuses on the porosity-induced changes in the elastic moduli of LAST, it is
important to note that in addition to the elastic moduli, porosity in brittle materials affects a wide
range of electrical, thermal and mechanical properties, such as electrical conductivity [5,15],
dielectric constant [16], thermal conductivity/diffusivity [5, 6, 15, 17, 18], hardness [19], and the
fracture strength [7].

For example, exponential decreases in hardness [19], dielectric constant

[16], fracture strength [7, 20], Young’s modulus and shear moduli [7] have been observed for a
variety of materials as porosity increases.

In particular, the dependence of Young’s modulus, E,

61

on the volume fraction porosity, P, can be written as [7]
E (P)  E D exp( b PE P)

(3.1)

where E is a function of the volume fraction porosity, P, ED is the Young’s modulus of dense
material, and bPE is a material-dependent constant. Similarly, the porosity dependence of the
shear modulus, G, can be written as [7]

G(P)  G D exp(b PG P)

(3.2)

where G is a function of the volume fraction porosity, P, GD is the shear modulus of dense
material, and bPG is a material-dependent constant.
For small P, expanding exp(- bPEP) in Taylor series gives

b PE 2 P 2
E(P)  E D (1  b PE P 
 ...)
2

(3.3)

For sufficiently small values of bPEP the above relationship can be approximated with the linear
form
(3.4)

E(P)  E D (1  b PE P)

Similarly, as with the exponential form, the linear form for the porosity dependence of the shear
modulus, G, can be written as
(3.5)

G(P)  G D (1  b PG P)
3.2.2 Effect of porosity on thermoelectric properties
The dimensionless figure of merit, ZT, for a thermoelectric material can be written as

62

ZT 

S 2 T
k

(3.6)
2

where S = the Seebeck coefficient, σ = the electrical conductivity, S σ = the power factor, k = the
thermal conductivity, and T = the temperature in Kelvin. Most thermoelectric materials
(including LAST) that are promising for applications such as converting waste heat into
electricity have a peak ZT > 1.
As discussed in the previous section, the electrical conductivity and thermal conductivity are
functions of porosity.

In addition, the Seebeck coefficient, S, has recently been observed to

increase as a function of increasing porosity [5, 6]. Thus, ZT can either increase or remain
relatively constant as a function of porosity due mainly to the porosity dependence of the
electrical conductivity and the thermal conductivity.

ZT is crucial in technical applications

since the energy conversion efficiency, η, for a thermoelectric device with a heat source
temperature TH and a heat sink temperature TC is in turn related to ZT of the thermoelectric
material such that [21]



 TH  TC 
1  ZT  1


 T

H

 1  ZT   TC

T

 H











(3.7)

Thus, if ZT increases by changing the porosity, then the energy conversion efficiency of the
thermoelectric material also increases.
Three recent studies report the effect of porosity on the transport properties of thermoelectric
materials [5, 6, 15].

For two specimens of filled skutterudite La0.75Fe3CoSb12, Yang and

coworkers studied the effect of volume fraction porosity, P (P = 0.003 and 0.148), on the
dimensionless figure of merit, ZT, over the temperature range 300 K to 475 K [5].
63

The filled

skutterudite specimen with P = 0.003 has a thermal conductivity approximately two times higher
than the skutterudite specimen with P = 0.148 over the entire temperature range [5].
Conversely, the electrical resistivity for the specimen with P = 0.148 is approximately two times
higher than the low porosity specimen (P = 0.003) over the entire temperature range [5].

Thus,

the effects of porosity leave the electrical conductivity/thermal conductivity ratio essentially
unchanged. Yang et al. [5] also found the Seebeck coefficient to be a weak function of porosity
that generally increases with increasing porosity, which implies that ZT is also a weak function
of porosity as well (Eq. 3.6).

Thus despite the difference in the porosity levels (P = 0.003 and

0.148), over the temperature range from 300 K to 475 K , the ZT values of the filled skutterudite
La0.75Fe3CoSb12 specimens are essentially the same, with a ZT of approximately 0.3 at 475 K
[5].
Wei et al. compared the thermal conductivities, electrical resistivity, and ZT between SiC
foam ceramic and bulk ceramic for temperatures between 300 K and 873 K [15]. At 873 K, the
-4

-4

estimated ZT values are 1.338 x 10 for SiC foam and 0.365 x 10 for bulk SiC [15]. Thus, at
873 K the ZT of the highly porous SiC foam was about 3.6 times higher than that of the dense
SiC bulk specimen at the same temperature.
For two different skutterudite compositions, Co0.9Ni0.1Sb3 and Co0.8Ni0.2Sb3, He et al.
studied the electrical conductivity, thermal conductivity, Seebeck coefficient, and ZT of porous
(P = 0.08) and fully dense specimens over the temperature range of 300 K to 773 K [6].

For

both skutterudite compositions (Co0.9Ni0.1Sb3 and Co0.8Ni0.2Sb3), the introduction of porosity
did not alter the electrical conductivity [6].

However, the porosity reduced the thermal

conductivity by approximately 75% for both compositions [6]. In addition the porosity increased

64

the Seebeck coefficients by at least ~50 V/K (approximately 25%) and ~100 V/K
(approximately 75%) for Co0.9Ni0.1Sb3 and Co0.8Ni0.2Sb3, respectively over the temperature
range [6]. At 773 K the ZT of the porous skutterudite specimens were approximately 0.55 (for
composition Co0.9Ni0.1Sb3) and 0.65 (for composition Co0.8Ni0.2Sb3).

In contrast, the ZT

values of the dense specimens were approximately 0.3 (Co0.9Ni0.1Sb3) and 0.15 (Co0.8Ni0.2Sb3)
[6]. Thus, for the porous specimens of Co0.9Ni0.1Sb3 and Co0.8Ni0.2Sb3 at 773 K, ZT was
approximately two to four times higher, respectively, than the dense specimens [6].
Therefore, in addition to affecting the mechanical properties of materials (as will be
discussed in the following sections) porosity can affect the transport properties of thermoelectric
materials. In terms of ZT, the filled skutterudite La0.75Fe3CoSb12 is not sensitive to porosities
between about 0.003 and 0.15 [5] while highly porous SiC foams yield ZT values of up to 3.6
times higher than the bulk, dense SiC [15]. Also, compared to dense specimens, a modest
porosity of P = 0.08 resulted in up to a four-fold increase in the ZT of cobalt-nickel-antimonide
skutterudites [6].
Porosity in thermoelectric materials can occur as an unintended consequence of the
fabrication process.

For example, hot pressing may result in a residual porosity of several

percent or more, depending on the hot pressing conditions. However, as reviewed in this section,
recently some researchers have intentionally processed thermoelectric materials to include
porosity in an attempt to tailor the ZT value [5, 6, 15,].
Thus, porosity in thermoelectric materials is of great interest both in terms of their
thermoelectric and mechanical performance. In this paper we focus on the effects of porosity on
Young’s modulus, shear modulus and Poisson’s ratio of two compositions in the LAST family of

65

thermoelectric materials.

3.3. Experimental procedure
3.3.1 Specimen preparation
A total of 17 specimens were investigated in the current work including five cast and 12 hot
pressed specimens.

High purity elemental powders for ingot specimens N138, N155, N160-4,

N160-5, and N160-9 (Table 3.1) were sealed in fused silica ampoules and placed in a three-zone
split tube rocking furnace.

Ingot N138 has composition Ag0.43Pb18Sb1.2Te20, where as ingots

N155 and N160 have composition Ag0.86Pb19Sb1.0Te20. Figure 3.1 shows the
time-temperature profiles for the cast ingots.
The hot pressed specimens HP5, HP6, and HP7 have the same composition as N138
(Ag0.43Pb18Sb1.2Te20) (Table 3.1); while specimens HP10M, HP10N, HP12, HP11, HP20,
HP30, HP38, HP40, and HP41 have the same composition as ingots N155 and N160
(Ag0.86Pb19Sb1.0Te20) (Table 3.1). All hot pressed specimens were processed using powder that
was milled from the cast ingots [9].

Table 3.2 summarizes the hot pressing conditions for the

hot pressed specimens used in this study.

Using a low speed diamond saw, the cast ingots and

hot pressed billets were cut into rectangular parallelepipeds. Table 3.1 summarizes the
dimensions, mass, composition, and processing method of each specimen included in this study.
The mass density was calculated from the mass and dimensions of each of the cast and hot
pressed specimens.

The length, height and width of each specimen were measured five times

using an electronic caliper (Mitutoyo, 500-196-20, Aurora, IL) with has a vendor specified
uncertainty of + 0.0025 cm.

The volume was computed using the mean of the measured

66

Table 3.1. Processing method, chemical composition, dimensions, and mass for the specimens
included in this study. All specimens were rectangular parallelepipeds.

Ag0.43Pb18Sb1.2Te20 6.32 x 4.81 x 3.83 0.921
Ag0.43Pb18Sb1.2Te20 10.54 x 7.58 x 2.26 1.360

7.91

Volume
Fraction
Porosity
0.02

7.54

0.06

Ag0.43Pb18Sb1.2Te20 13.98 x 9.57 x 3.29 3.239
Ag0.43Pb18Sb1.2Te20 7.12 x 4.92 x 4.92 1.378

7.23

0.10

8.00

0.01

Ag0.86Pb19Sb1.0Te20 6.96 x 4.65 x 4.54 1.180
Ag0.86Pb19Sb1.0Te20 6.99 x 4.59 x 4.54 1.176

8.05

0.03

8.08

0.03

Ag0.86Pb19Sb1.0Te20 7.15 x 5.10 x 5.10 1.324
Ag0.86Pb19Sb1.0Te20 7.07 x 4.89 x 4.88 1.378

7.13

0.14

8.15

0.02

Ag0.86Pb19Sb1.0Te20 6.88 x 4.90 x 4.94 1.345
Ag0.86Pb19Sb1.0Te20 6.61 x 4.92 x 4.91 1.291

8.08

0.03

8.09

0.03

Ag0.86Pb19Sb1.0Te20 6.94 x 5.05 x 4.92 1.515
Ag0.86Pb19Sb1.0Te20 7.07 x 4.91 x 4.93 1.377

8.07

0.03

8.05

0.03

Ag0.86Pb19Sb1.0Te20 7.18 x 4.59 x 4.54 1.155
Ag0.86Pb19Sb1.0Te20 12.6 x 9.00 x 2.50 2.363

7.71

0.07

8.14

0.02

8.15

0.02

Cast

Ag0.86Pb19Sb1.0Te20 6.72 x 4.93 x 4.93 1.327
Ag0.86Pb19Sb1.0Te20 6.85 x 4.92 x 5.00 1.354

8.04

0.03

Cast

Ag0.86Pb19Sb1.0Te20 7.00 x 4.95 x 4.95 1.383

8.07

0.03

Specimen

Processing
Technique

N138

Cast

HP6

HPed

HP7

HPed

HP3

HPed

HP10M

HPed

HP10N

HPed

HP12

HPed

HP20

HPed

HP30

HPed

HP38

HPed

HP40

HPed

HP41

HPed

HP 11

HPed

N155

Cast

N160-4

Cast

N160-5
N160-9

Composition

Dimensions (mm)

67

Mass Density
(g) (g/cm3)

Table 3.2 Processing conditions, including maximum temperature, maximum pressure and total
time at maximum temperature for the hot pressed specimens used in this study.
Maximum Temperature
(K)
673
623
573
673
673
623
673
673
673
673
673
673

Specimen
HP3
HP6
HP7
HP10M
HP10N
HP11
HP12
HP20
HP30
HP38
HP40
HP41

Time (Minutes)
235
235
235
235
235
365
365
365
235
235
235
235

Temperature-Time Profile for N138
Temperature-Time Profile for N155
Temperature-Time Profile for N160

1400

Temperature (K)

Maximum Pressure
(MPa)
75
60
60
75
75
60
75
75
75
75
75
75

1200
1000
800

N160

N138

N155

600
400
0

50

100

150

200

250

Time (hours)
Figure 3.1

Time-temperature profile for the fabrication of the five ingots specimens included in

this study. N138 (Ag0.43Pb18Sb1.2Te20), N155, and N160-4, -5 and -9 (Ag0.86Pb19Sb1.0Te20)
(Table 3.2a). Specimens N160-4, -5 and -9 were cut from a single ingot.

68

dimensions for the length, height and width.

The mass was determined using an electronic

balance (Ohaus Adventurer, AR2140, Pinebrook, NJ) with a vendor-specified precision of + 1.0
-4

x 10 g.

3.3.2 Specimen Preparation and Microstructural Examination
Specimens were polished using a series of diamond pastes with grit sizes down to 0.5
micron. After ultrasonically cleaning the specimen surfaces, the as-polished surfaces of each
specimen were examined with a scanning electron microscope (JEOL 6400, JEOL Ltd., Japan)
using a working distance of 15 mm and an accelerating voltage of 15 kV.
specimen surfaces allowed the surface pores to be viewed.

The as-polished

Also, the as-polished surfaces of

each specimen were carefully examined to determine whether or not cracks were present.
Thermal etching on selected specimens was performed in a sealed mullite tube in flowing argon
gas at temperatures of 598 K to 698 K for times between 1 hour and 4 hours.

3.3.3 Resonant Ultrasound Spectroscopy (RUS) measurements
Room temperature resonant ultrasound spectroscopy (RUS) [22] was performed in air using
a commercial RUS system (RUSpec, Quasar International Inc., Albuquerque, NM, USA) with a
tripod transducer configuration.

Details of the RUS experimental procedure and calculations

are given elsewhere [23].

3.4. Results and Discussion
3.4.1 Microstructural analysis
The as-polished surfaces of the specimens were examined via SEM.

69

No cracks were

visible in the as-polished surfaces of the hot pressed and cast specimens, although the specimens
did show varying amounts of porosity. The presence of pores and the absence of detectable
surface cracks in the as-polished specimens are significant.

While increasing porosity

decreases the elastic moduli of materials [7, 8] cracks also act to decrease the elastic moduli [24].
Also, in additional work by the present authors, the Young’s and shear modulus versus
temperature data of specimens N138 and HP6 did not show hysteresis between the heating and
cooling curves [25]. The absence of a modulus-temperature hysteresis indicates there was no
significant microcracking in those specimens [24].

In addition, no hysteresis has been

observed for modulus-temperature measurements performed by the authors on LAST specimens
not included in this study. The SEM observations included in this study and our previous study
on the modulus-temperature of LAST materials [25] indicate that pores rather than cracks or
microcracks are likely responsible for the decrease in elastic moduli observed in this study.
Also, as will be discussed in Section 3.4.2.2, the modulus decrease is a relatively smooth
function of porosity which suggests that additional modulus decrement mechanisms (such as
cracks) are either absent or at a constant level in each specimen.
SEM images of thermally etched surfaces (Figs. 3.2d - 3.2e) show that the grain size
distribution is bimodal for hot pressed specimens.

The larger grain sizes varied from about 20

(Figs. 3.2e and 3.2f) to 50 microns (Fig. 3.2d). The smaller grained matrix included grains from
roughly 1 to 10 microns in diameter (Figs. 3.2d – 3.2f). Similarly prepared cast LAST
specimens have grain sizes in the range of 500 – 700 microns [25].

3.4.2. Room temperature elastic moduli as a function of porosity
Room temperature RUS measurements were performed on a total of 17 specimens (Table
3.1) to determine the behavior of the elastic moduli as a function of porosity (Fig. 3.3). In the

70

Figure 3.2 SEM micrographs of the as polished surfaces of specimens (a) HP3 (P = 0.01) (b)
HP30 (P = 0.01) (c) HP7 (P = 0.10), as well as the thermally etched surfaces (d) HP3 (P = 0.01,
thermally etched at 598 K for 2 hrs) (e) HP30 (P = 0.01, thermally etched at 673 K for 2 hrs) (f)
HP7 (P = 0.10, thermally etched at 698 K for 2 hrs)
71

following section, we discuss the observed porosity-induced-changes in both Young’s modulus
and shear modulus, which can be described in terms of an exponential or a linear function of the
volume fraction porosity, P (Section 3.2.1, Eqs. 3.1, 3.2, 3.4, and 3.5). Changes in Poisson’s ratio
as a function of porosity will be discussed in Section 3.4.2.3.

3.4.2.1. Young’s modulus and shear modulus as a function of porosity
The decreasing Young’s modulus with increasing porosity data was fit to both the
exponential and linear functions given by Eqs. (3.1) and (3.4).

For both the hot pressed and the

combined hot pressed-cast data sets, the linear relationship was a slightly better fit to the data
(Table 3.3).
For the 12 hot pressed specimens, the linear fit of the room temperature Young’s modulus
data to Eq. (3.4) was excellent, ED = 58.3 ± 0.3 GPa, bPE = 3.6 ± 0.1 and an coefficient of
2

determination, r = 0.994 (Fig.3a, Table 3.3). When the five cast ingot specimens were
included in the combined data set with the hot pressed specimens (a total of 17 specimens), ED =
2

58.4 ± 0.6 GPa, bPE = 3.5 ± 0.2 with an r of 0.962 (Fig. 3.3b, Table 3.3).

2

The r values

obtained by fitting to the linear and exponential relationships (Eqs. 3.1 and 3.4) were essentially
2

the same for the Young’s modulus data for the hot pressed specimens , that is, r for the fit to the
2

exponential equation (Eq. 3.1) was 0.988 and r for the fit to the linear relationship (Eq. 3.4) was
0.994 (Table 3.3).

However, for the combined data set (the 5 cast and 12 hot pressed
2

specimens), the fit of the Young’s modulus-porosity data to the linear equation (Eq. 3.1) gave a r
2

value of 0.962, while r was somewhat lower (0.949) for the fit to the exponential equation

72

Hot Pressed Specimens
Composition: Ag0.43Pb18Sb1.2Te20

Young's Modulus (GPa)

60

Hot Pressed Specimens
Composition: Ag0.86Pb19Sb1.0Te20

50

40

30

0.00

0.03

0.06

0.09

0.12

0.15

Volume Fraction Porosity
Figure 3.3a For the hot pressed specimens only (compositions Ag0.43Pb18Sb1.2Te20 and
Ag0.86Pb19Sb1.0Te20), the solid line indicates the least-squares fit to linear relationship (Eq. 3.4)
for Young’s modulus (determined by room temperature RUS) as a function of porosity.

73

Hot Pressed Specimens
Composition: Ag0.43Pb18Sb1.2Te20
Hot Pressed Specimens
Composition: Ag0.86Pb19Sb1.0Te20

Young's Modulus (GPa)

60

Cast Ingots
Composition: Ag0.43Pb18Sb1.2Te20
Cast Ingots
Composition: Ag0.86Pb19Sb1.0Te20

50

40

30

0.00

0.03

0.06

0.09

0.12

0.15

Volume Fraction Porosity

Figure 3.3b For the combined data set (12 hot pressed specimens and 5 cast specimens), the solid
line indicates the least-squares fit to linear relationship (Eq. 3.4) for Young’s modulus
(determined by room temperature RUS) as a function of porosity.

74

Shear Modulus (GPa)

24

Hot Pressed Specimens
Composition: Ag0.43Pb18Sb1.2Te20

21

Hot Pressed Specimens
Composition: Ag0.86Pb19Sb1.0Te20

18

15

12

0.00

0.03

0.06

0.09

0.12

0.15

Volume Fraction Porosity
Figure 3.3c For the hot pressed specimens only, the solid line indicates the least-squares fit to
linear relationship (Eq. 3.5) for shear modulus (determined by room temperature RUS) as a
function of porosity.

75

Hot Pressed Specimens
Composition: Ag0.43Pb18Sb1.2Te20

24

Hot Pressed Specimens
Composition: Ag0.86Pb19Sb1.0Te20
Cast Ingots
Composition: Ag0.43Pb18Sb1.2Te20

Shear Modulus (GPa)

21

Cast Ingots
Composition: Ag0.86Pb19Sb1.0Te20

18

15

12

0.00

0.03

0.06

0.09

0.12

0.15

Volume Fraction Porosity
Figure 3.3d For the combined data set (12 hot pressed specimens and 5 cast specimens), the solid
line indicates the least-squares fit to linear relationship (Eq. 3.5) for shear modulus (determined
by room temperature RUS) as a function of porosity.

76

Hot Pressed Specimens
Composition: Ag0.43Pb18Sb1.2Te20

24

Hot Pressed Specimens
Composition: Ag0.86Pb19Sb1.0Te20

Shear Modulus (GPa)

21

Cast Ingots
Composition: Ag0.43Pb18Sb1.2Te20
Cast Ingots
Composition: Ag0.86Pb19Sb1.0Te20

18

15

12

0.00

0.03

0.06

0.09

0.12

0.15

Volume Fraction Porosity

Figure 3.3e For the combined data set (12 hot pressed specimens and 5 cast specimens), the solid
line indicates the least-squares fit to the exponential relationship (Eq. 3.2) for shear modulus
(determined by room temperature RUS) as a function of porosity.

77

0.28
0.27

Poisson's Ratio

0.26
0.25
0.24
0.23

Hot Pressed Specimens
Composition: Ag0.43Pb18Sb1.2Te20

0.22

Hot Pressed Specimens
Composition: Ag0.86Pb19Sb1.0Te20

0.21
0.20
0.00

0.03

0.06

0.09

0.12

0.15

Volume Fraction Porosity
Figure 3.3f For the hot pressed specimens only, the Poisson’s ratio determined by room
temperature RUS measurements versus volume fraction porosity.

78

0.28

Poisson's Ratio

0.26

Hot Pressed Specimens
Composition: Ag0.43Pb18Sb1.2Te20

0.24

Hot Pressed Specimens
Composition: Ag0.86Pb19Sb1.0Te20

0.22

0.20
0.00

Cast Ingots
Composition: Ag0.43Pb18Sb1.2Te20
Cast Ingots
Composition: Ag0.86Pb19Sb1.0Te20

0.03

0.06

0.09

0.12

0.15

Volume Fraction Porosity
Figure 3.3g For the combined data set (12 hot pressed specimens and 5 cast specimens),
Poisson’s ratio determined by room temperature RUS measurements versus volume fraction
porosity of the combined data (hot pressed and cast ingot specimens.

79

Table 3.3. Parameters bPE, ED, bPG, and GD obtained from the least-squares fit to the linear (Eqs.
3.4 and 3.5) and exponential (Eqs. 3.1 and 3.2) empirical relationships for the Young’s and shear
2
moduli. N is the number of specimens included in each analysis and r is the coefficient of
determination

Young’s Modulus
Empirical
Specimens
relationship
Exponential
Hot Pressed
Linear
Hot Pressed
Exponential
Cast and Hot Pressed
Linear
Cast and Hot Pressed
Shear Modulus
Empirical
Specimens
relationship
Exponential
Hot Pressed
Linear
Hot Pressed
Exponential
Cast and Hot Pressed
Linear
Cast and Hot Pressed

2

N

r

bPE

ED (GPa)

12
12
17
17

0.988
0.994
0.949
0.962

4.8 ± 0.2
3.6 ± 0.1
4.7 ± 0.3
3.5 ± 0.2

60.0 ± 0.5
58.3 ± 0.3
59.8 ± 0.8
58.4 ± 0.6

N

r

2

bPG

GD (GPa)

12
12
17
17

0.984
0.991
0.942
0.956

4.7 ± 0.2
3.5 ± 0.1
4.6 ± 0.3
3.5 ± 0.2

23.5 ± 0.2
22.9 ± 0.1
23.6 ± 0.3
23.0 ± 0.2

80

(Table 3.3).
As was the case for the Young’s modulus, the decrease in shear modulus with increasing
porosity was fit to both the linear and exponential forms (Eqs. 3.2 and 3.5). The fit to the linear
2

relationship (Eq. 3.5) for the hot pressed data gave GD = 22.9 ± 0.1 GPa, bPG = 3.5 ± 0.1 with r
= 0.991 (Fig. 3.3c). For the shear modulus, a fit to the linear relationship (Eq. 3.5) for the 17
2

specimen combined data set gave GD = 23.0 ± 0.2 GPa, bPG = 3.5 ± 0.2 with r = 0.956 (Fig.
2

3.3d, Table 3.3). The r values for the fit to the exponential and linear equations for the
combined data set were 0.942 and 0.956, respectively. To illustrate the apparently improved fit of
the linear equation (Eq. 3.5) compared to the exponential equation (Eq. 3.2), we include plots of
shear modulus versus porosity for the combined data sets for both the linear (Fig. 3.3d) and
exponential fit (Fig. 3.3e).
Thus, for the range of P included in this study (0.01 < P < 0.14), the Young’s and shear
modulus behavior as a function of porosity described relatively well by either the linear
relationships (Eqs. 3.4 and 3.5) or the exponential relationships (Eqs. 3.1 and 3.2), with the linear
relationships having a somewhat better fit in some cases (Table 3.3, Figs. 3.3b - 3.3e).

3.4.2.2. Simulation of errors in modulus-porosity parameters as a function of the uncertainty in
mass density measurement.
Since there are uncertainties in the measurements of the dimensions and mass of the
specimens (Section 3.3), there is a subsequent uncertainty in the mass density (and hence also in
the volume fraction porosity, P) of the specimens.

In order to estimate the effect of the

uncertainty in mass density measurements on the least-squares determination of the parameters

81

ED and bPE (Eqs. 3.1 and 3.4) as well as GD and bPG (Eqs. 3.2 and 3.5), a numerical study was
performed.
The uncertainty,  in the determination of mass density, , calculations was obtained from
the following equation

2

2

2

2

  
2   
2   
2   
2
  
 (m)    (l)    (h )  
 (w )
 m 
 l 
 h 
 w 

(3.8)

where l = average specimen length, w = average specimen width, h = average specimen height,
m = specimen mass, and  = specimen mass density.

The uncertainty in mass measurement,

-4

m, was assigned the value of 1.0 x 10 g, which is the vendor specified precision of the Ohaus
Adventurer electronic balance used in this study.

The uncertainties assigned to each of the

dimensional measurements (l, h and w) was 0.0025 cm, which the vender specified precision
of the electronic caliper (Mitutoyo, 500-196-20, Aurora, IL) used in this study.

The calculated

3

uncertainty in ,  was 0.07 g/cm .
A series of modulus-porosity data sets were generated (Table 3.4) in which the measured
mass density,  for each specimen was perturbed by adding a quantity  to the measured mass
density for each of the 17 specimens in the entire (cast plus hot pressed, Table 3. 1)
modulus-porosity data setThe calculated values were distributed randomly and uniformly
3

over the interval from to -where0.07 g/cm )using a commercial uniform
random number generator (Matlab v7.20.232).

After adding the uniformly distributed

uncertainties to the mass density values, a least-squares fit of the “perturbed” Young’s

82

Table 3.4.Using perturbed density data (Section 3.4.2.2), a least-squares analysis was used to
simulate the effect of the uncertainty in density measurement. This table lists maximum,
2
minimum and standard deviations (std) of parameters bPE, ED, bPG, and GD and r (coefficient of
determination) obtained from the least-squares fit to the linear (Eqs. 3.4 and 3.5) and exponential
(Eqs. 3.1 and 3.2) empirical relationships for the Young’s and shear moduli using the perturbed
density data.

Young’s Modulus
Empirical
Specimens
relationship
Hot Pressed
Exponential
Data
(12
Linear
specimens)
Hot Pressed
Exponential
and Cast Data
(17
Linear
specimens)

2

r range (std)
0.951 - 0.986
(0.010)
0.971 - 0.988
(0.006)
0.890 - 0.949
(0.017)
0.921 - 0.967
(0.014)

bPE range
(std)

ED (GPa ) range
(std)

4.5-5.0 (0.2)

58.9 – 60.5 (0.4)

3.4 - 3.7
(0.1)
4.1 - 4.8
(0.2)
3.2 - 3.7
(0.1)

57.5 - 58.4 (0.2)
58.6 - 60.3 (0.5)
57.7 - 58.9 (0.4)

Shear Modulus
Specimens
Hot Pressed
Data
(12
specimens)
Hot Pressed
and Cast Data
(17
specimens)

Empirical
relationship
Exponential
Linear
Exponential
Linear

2

r range (std)
0.950 - 0.980
(0.009)
0.961 - 0.987
(0.007)
0.881 - 0.941
(0.020)
0.913 - 0.964
(0.016)

83

bPG range
(std)
4.5 - 4.8
(0.1)
3.4 - 3.6
(0.1)
4.0 - 4.7
(0.2)
3.2 - 3.6
(0.1)

GD (GPa) range
(std)
23.3 - 23.8 (0.2)
22.8 - 23.1 (0.1)
23.1 - 23.7 (0.2)
22.7 - 23.2 (0.2)

modulus versus porosity (Eqs. 3.1 and 3.4) and shear modulus (Eqs. 3.2 and 3.5) versus porosity
data was performed to determine the shift in the fitting coefficients that resulted from the
perturbation in the mass density values. The minimum, maximum, and standard deviation were
calculated for the Young’s modulus and shear modulus, for both the 17 specimens (hot pressed
and cast) and the 12 specimens (hot pressed) (Table 3.4).
For the full data set, including the 5 cast specimens and 12 hot pressed specimens, the ranges
of the parameters obtained from the least-squares fit on the perturbed data is significantly wider
than that for the 12 specimen (hot pressed specimens only) data set (Table 3.4). The five cast
specimens lie in a limited porosity range 0.02 < P < 0.03, which could explain the wider ranges
of parameters obtained from the least-squares fit.

The uncertainty range, , is fixed, and

therefore, the calculated generated by a uniform random generator) added to the mass
density are more significant when applied to the lower porosity range.
The computer simulations (Table 3.4) indicate that due to the uncertainty in mass density
2

measurement, the r values for the experimental data (Table 3.3) are likely too similar to allow a
definitive choice of which empirical form (linear or exponential) best fits the modulus-porosity
data. Regardless of the details of the least squares calculations, the plots of Young’s modulus
versus porosity (Figs. 3.3a and 3.3b) and shear modulus versus porosity (Figs. 3.3c – 3.3e)
demonstrate that in this study the modulus-porosity relationships are generally quite linear

3.4.2.3. Poisson’s ratio as a function of porosity
In this study and in the literature, the Young’s modulus and shear modulus of solid materials
decrease monotonically with increasing volume fraction porosity P [7]. However, for the
Poisson’s ratio,, the situation is much more complicated. The Poisson’s ratio has been

84

observed to increase, decrease or remain constant as a function of porosity.

For example, in a

review of the literature data for polycrystalline Al2O3, ZnO and MgO, Phani [26] shows that  of
Al2O3 is relatively insensitive to porosity, P, for 0 < P < 0.30, while in contrast  for ZnO
decreases for approximately the same interval of P. Even for a single material (polycrystalline
MgO),  measured by different researchers show opposite trends where in one case  increases
with increasing P and the other case,  decreases with increasing P [26]. In another review of
the literature, Boccaccini presented  versus P data on 16 oxides as well as graphite and AlN
[27]. Although there was considerable scatter in the data for the 18 materials, Boccaccini
classified the data in terms of 0 (the Poisson’s ratio of the fully dense material). Boccaccini
found that for materials with 0 > 0.25,  tends to decrease with increasing P and for 0 < 0.25
Poisson’s ratio tends to increase with increasing P [27].

In addition to polycrystalline materials,

Poisson’s ratio of glassy materials is also a function of P. For example,  values of porous
Pd42.5Cu30Ni7.5P20 glassy alloys decreased monotonically from approximately 0.40 for dense
specimens to about 0.31 for a P = 0.60 [28].
In addition to the experimental observations, several researchers have proposed models of
 versus P behavior.

A number of the theories that treat the porosity dependence of Poisson’s

ratio [26, 29 - 31] are based on the Mori-Tanaka effective field model (MTM) [32], which
describes the elastic properties of two phase composite materials in terms of an effective or mean
strain field. In the MTM, the composite is modeled as an elastically isotropic solid with a matrix
phase with spheroidal inclusions distributed randomly and homogeneously throughout the bulk
of the solid [32]. Work by Tandon and Wang [29], Zhao et al. [30] as well as Dunn and

85

Ledbetter [31] extend the MTM to include non-spherical inclusions (the pore phase). Based on
their model, Dunn and Ledbetter note that “Unlike the other elastic constants which
monotonically decrease with pore concentration, Poisson's ratio may increase, decrease, or
remain unchanged as a function of pore concentration, depending on the pore shape and
Poisson's ratio of the bulk solid” [31].

Thus, in addition to emphasizing pore shape (pore aspect

ratio) Dunn and Ledbetter’s theoretical work supports Boccaccini’s observation that the  versus
P behavior is a function of 0.
However, there are a number of difficulties in applying the theories such those by Dunn and
Ledbetter [31], Tandon [29] and Zhao [30].

If one sinters a powder compact, the pores

morphology evolves continuously during the densification process [33, 34], so the pore aspect
ratio differs for differing values of P. For example, based on theoretical work by Zhao [30],
Martin et al. predict that during densification, the pore aspect ratio first increases, then goes
through a maximum and then decreases for sintered ZnO, Fe and MgO [34]. Thus applying these
theories to materials undergoing densification means that both the pore aspect ratio and the total
volume porosity P varies simultaneously.

In addition, direct experimental measurement of the

pore size and aspect ratio is extremely difficult [35]. Also, adding to difficulties with both
experiment and theory, rather than having a single pore size or a pore aspect ratio,
experimentally a given specimen has a distribution of pore sizes and aspect ratios and the nature
of these distributions may depend on the details of the powder processing technique for sintered
material.

Thus, while the literature shows that  may increase, decrease or remain constant

with increasing P, there are difficulties in applying the available theories to a given data set.
Furthermore, the theories of Dunn and Ledbetter [31], Tandon [29] and Zhao [30] all assume an
isotropic, homogeneous spatial distribution of pores, but depending on the details of processing it

86

may be expected that in some cases specimens may exhibit inhomogeneous pore distributions.
In this study, the Poisson’s ratio was 0.27 for the most dense specimen (P = 0.01). With
increasing volume fraction porosity, Poisson’s ratio tended to decrease slowly with increasing
volume fraction porosity (Figs. 3. 3f and 3.3g), which was in agreement with the literature
review of Poisson’s ratio-porosity data by Boccaccini [27]. Comparing the data for the hot
pressed specimens only (Fig. 3.3f) with the data for the combined data set (Fig 3.3g), the scatter
in the Poisson’s ratio values for the volume fraction porosity range 0.02 < P < 0.03 is accentuated
by the scatter in Poisson’s ratio data for the cast specimens, where P for each of the five cast
specimens lies in the porosity range 0.02 < P < 0.03.

3.5. Summary and Conclusions
For the 17 LAST specimens (12 hot pressed and five ingot specimens) included in this study
the Young’s modulus, shear modulus and Poisson’s ratio were determined using resonant
ultrasound spectroscopy as a function of the volume fraction porosity, P, for 0.01  P  0.14.
For the 12 hot pressed specimens, the least-squares fit of the E versus P data E = ED (1-bPEP)
(Eq. 3.4), yielded ED = 58.3 ± 0.3 GPa and bPE = 3.6 ± 0.1 with a coefficient of determination, r

2

= 0.994 (Fig. 3a, Table 3.3). If the five ingot specimens (which have a more limited porosity
2

range) are included in the analysis along with the 12 hot pressed specimens, r decreases to 0.962
with no significant changes in the ED and bPE values (Table 3.3). For the shear modulus, G,
versus P behavior was similar to that observed for E versus P with a linear decrease in G with
increasing P (Eq. 3.5). For the 12 hot pressed specimens, the linear fit yielded GD = 22.9 ± 0.1
2

GPa, bPG = 3.5 ± 0.1 with r = 0.991 (Fig. 3.3c, Table 3.3). When the five ingot specimens (17
87

2

specimens total) are included in the analysis, r = 0.956 (Fig. 3d, Table 3.3). As was the case
for the Young’s modulus combined data set, there are no significant changes (Table 3.3) in the
GD and bPG values compared to the fit obtained from the hot pressed specimens only.

The fit

to the linear relationships (Eqs. 3.4 and 3.5) was in each case either slightly better than the
exponential relationships (Eqs. 3.1 and 3.2) (Table 3.3). The Poisson’s ratio tended to decrease
slowly with increasing volume fraction porosity.
In Section 4.2.2, we considered the effect of the uncertainty in mass density calculation on
the least-squares fit of the modulus-porosity relationships (Eqs. 3.1, 3.2, 3.4, and 3.5). When
computer-generated perturbations in density uniformly distributed between  and -, Eq.
3.8), were added to the measured specimen densities, a subsequent least-squares analysis of the
perturbed data (Table 3.4) shows that for the data included in this study it is difficult to
definitively determine whether the linear or exponential empirical equations best fit the
experimental data (Table 3.3). This is consistent with the numerical values of volume fraction
porosity, P, and the coefficients bPE and bPG being such that the exponential function is well
approximated by a linear function (Eq. 3.3), as shown graphically in Figures 3.3a - 3.3e.
Knowledge of the porosity dependence of the elastic moduli is critical to numerical or
analytical stress-strain calculations for both the cast and hot pressed materials (where the
Young’s modulus is needed). For the specimens included in this study, no microcracking was
observed, however when microcracking is present, understanding the decrement in moduli due to
porosity can help us separate the effects of microcracking and porosity for a given porous,
microcracked specimen.
Furthermore, in the literature, researchers have recently intentionally included porosity in

88

thermoelectric materials in an effort to enhance the ZT values and hence the energy efficiency of
the thermoelectric. This interest in intentionally fabricating porous thermoelectrics also gives
impetus to the study of the elasticity of porous thermoelectric materials such as LAST.

Acknowledgements
The authors acknowledge the financial assistance of the U. S. Department of Energy Grant
DE-FC26-04NT42281 and Office of Naval Research MURI Grant number N000140310789. The
authors also acknowledge the Defense University Research Instrumentation Program (DURIP)
Grant No. N00014-09-1-0785, Office of Naval Research, which provided funding for the
purchase of the Resonant Ultrasound Spectroscopy apparatus utilized in this research.

89

REFERENCES

90

3.6 References
[1] T. P. Hogan, A. Downey, J. Short, J. D’Angelo, C.-I Wu, E. Quarez, J. Androulakis, P.F.P.
Poudeu, J.R. Sootsman, D.Y. Chung, M.G. Kanatzidis, S. D. Mahanti, E.J. Timm, H.
Schock, F. Ren, J. Johnson, E.D. Case, Nanostructured thermoelectric materials and
high-efficiency power-generation modules, J. Elect. Mater. 36 (2007) 704.
[2] S. Urata, R. Funahashi, T.Mihara, A. Kosuga, S. Sodeoka, T. Tanaka, Power generation of a
p-type Ca3Co4O9/n-type CaMnO3 module, Int. J. Appl. Ceram. Technol. 4 (2007) 535.
[3] R. Funahashi, S. Urata, Fabrication and application of an oxide thermoelectric system, Int. J.
Appl. Ceram. Technol. 4 (2007) 297.
[4] D. Flahaut, T. Mihara, R. Funahashi, N. Nabeshima, K. Lee, H. Ohta, K. Koumoto,
Thermoelectrical properties of A-site substituted Ca1-xRexMnO3 system, J. Appl. Phys.
100 (2006) 084911.
[5] L. Yang, J.S. Wu, L.T. Zhang, Synthesis of filled skutterudite compound La0.75Fe3CoSb12
by spark plasma sintering and effect of porosity on thermoelectric properties, J. Alloy.
Compd. 364 (2004) 83.
[6] Q. He, S. Hu, X. Tang, Y. Lan, J. Yang, X. Wang, Z. Ren, Q. Hao, G. Chen, The great
improvement effect of pores on ZT in Co1−xNixSb3 system Appl. Phys. Lett. 93 (2006)
042108.
[7] R. W. Rice, Porosity of Ceramics, Marcel Dekker, Inc., New York, 1998, pp. 100-131.
[8] E. A. Dean, J. A. Lopez, Empirical dependence of elastic moduli on porosity for ceramic
materials, J. Am. Ceram. Soc. 66 (1983) 366.
[9] A. L. Pilchak, F. Ren, E. D. Case, E.J. Timm, H.J. Schock, C.-I Wu, T. P. Hogan, Phil. Mag.
87 (2007) 4567.
[10] M. W. Barsoum, Fundamentals of Ceramics McGraw Hill, New York, 1997, pp. 377 – 378.
[11] R. W. Rice, Mechanical Properties of Ceramics and Composites: Grain and Particle Effects,
Marcel Dekker, Inc., New York, 2000, p. 9.
[12] F. Ren, B. D. Hall, J. E. Ni, E. D. Case, J. Sootsman, M. G. Kanatzidis, E. Lara-Curzio, R. M.
Trejo, E. J. Timm, in: T.P. Hogan(Ed.), J. Yang(Ed.), R. Funahashi(Ed.), T. Tritt(Ed.),
Thermoelectric Power Generation, Mater. Res. Soc. Symp. Proc. Vol. 1044, Warrendale,
PA, 2008, p. 121-126.
[13] S. S. Kim, S. Yamamoto, T. Aizawa, Thermoelectric properties of anisotropy-controlled
p-type Bi-Te-Sb system via bulk mechanical alloying and shear extrusion, J. Alloys and

91

Compd. 375 (2004) 107.
[14] K. Ueno, A. Yamamoto, T. Noguchi, T. Inoue, S. Sodeoka H. Obara, Optimization of
hot-press conditions of Zn4Sb3 for high thermoelectric performance. II. Mechanical
properties, J. Alloy. Compd. 388 (2005) 118.
[15] W. Wei, J. Li, H. Zhang, X. Cao, C. Tian, J. Zhang, Macrostructural influence on the
thermoelectric properties of SiC ceramics, Scripta Mater. 57 (2007) 1081.
[16] T. P. Hoepfner, E. D. Case, The porosity dependence of the dielectric constant for sintered
hydroxyapatite, J. Biomed. Mater. Res. 60 (2002) 643.
[17] R. Barea, M. A. Osendi, J. M. F. Ferreira, P. Miranzo, Thermal conductivity of highly
porous mullite material, Acta Mat. 53 (2005) 3313.
[18] B. Nait-Ali, K. Haberko, H. Vesteghem, J. Absi, D.S. Smith, Thermal conductivity of highly
porous zirconia, J. Eur. Ceram. Soc. 26 (2006) 3567.
[19] T. P. Hoepfner, E. D. Case, The influence of the microstructure on the hardness of sintered
hydroxyapatite, Ceram. Int. 29 (2003) 699.
[20] SY Shan, JF Yang, JQ Gao, WH Zhang, ZH Jin, R Janssen, T. Ohji, Porous silicon nitride
ceramics prepared by reduction-nitridation of silica, J. Am. Ceram. Soc. 88 (2005) 2594.
[21] T. M. Tritt, M. A. Subramanian, Thermoelectric materials, phenomena, and applications: A
bird's eye view, MRS Bulletin 31, 2006, pp 188-194.
[22] A. Migliori, J. L. Sarrao, Resonant Ultrasound Spectroscopy: Applications to Physics,
Materials Measurements, and Nondestructive Evaluation, Academic Press, New York,
1997, p. 28.
[23] F. Ren, E. D. Case, J. R. Sootsman and M. G. Kanatzidis, H. Kong, C. Uher E. Lara-Curzio
and R. M. Trejo, C. Uher, The high-temperature elastic moduli of polycrystalline PbTe
measured by resonant ultrasound spectroscopy, Acta Mat, 56 (2008) 5954.
[24] E. D. Case, in: M. H. Alibadi (Ed.), Thermo-Mechanical Fatigue and Fracture, WIT Press,
UK, 2002, pp. 137 – 208.
[25] F. Ren, E.D. Case, J. E. Ni, E.J. Timm, E. Lara-Curzio, R.M. Trejo, C.-H. Lin, M.G.
Kanatzidis, Temperature-dependent elastic moduli of lead telluride-based thermoelectric
materials, Phil. Mag. 89 (2009) 143.
[26] K. K. Phani, A novel method of predicting ultrasonic and elastic properties of isotropic
ceramic materials after sintering from the properties of partially sintered or green
compacts, J. Amer. Ceram. Soc. 91 (2008) 215.

92

[27] A. R. Boccaccini, Effective elastic moduli of porous ceramic materials, J. Amer. Ceram.
Soc. 77 (1994) 2779.
[28] M. Fukuhara, T. Wada, A. Inoue, Ultrasonic characteristics of porous Pd42.5Cu30Ni7.5P20
glassy alloys, J. Appl. Phys. 102 (2007) 083502.
[29] G. P. Tandon, G. J. Weng, Average stress in the matrix and effective moduli of randomly
oriented composites, Comp. Sci. Tech. 27 (1986) 111.
[30] Y. H. Zhao, G. P. Tandon, G. J. Wang, Elastic moduli for a class of porous materials, Acta
Mech. 76 (1989) 105.
[31] M. L. Dunn, H. Ledbetter, Poissons ratio of porous and microcracked solids-theory and
application to oxide semiconductors, J. Mater. Res. 10 (1995) 2715.
[32] T. Mori, K. Tanaka, Average stress in matrix and average elastic energy of materials with
misfitting inclusions, Acta Met., 21 (1973) 571.
[33] J. B. Wachtman, Mechanical Properties of Ceramics, Wiley Interscience, New York, 1996,
pp. 33-35, 412.
[34] L. P. Martin, D. Dadon, M. Rosen, Evaluation of ultrasonically determined
elasticity-porosity relations in zinc oxide, J. Amer. Ceram. Soc. 79 (1996) 1281.
[35] J. Kovacik, Correlation between elastic modulus, shear modulus, Poisson's ratio and
porosity in porous materials, Advanced Engineering Materials 10 (2008) 250.

93

The full citation for this chapter is: Jennifer E. Ni, Eldon D. Case, Kristen N. Khabir, Ryan C.
Stewart, Chun-I Wu, Timothy P. Hogan, Edward J. Timm, Steven N. Girard, Mercouri G.
Kanatzidis, Room temperature Young's modulus, shear modulus, Poisson's ratio and hardness of
PbTe-PbS thermoelectric materials, Mat. Sci. Eng. B, 170, 58–66 (2010)
4.0 Room temperature Young’s modulus, shear modulus, Poisson’s ratio and hardness of PbTePbS thermoelectric materials
1

1*

1

1

2

Jennifer E. Ni , Eldon D. Case , Kristen N. Khabir , Ryan C. Stewart , Chun-I Wu , Timothy
2

3

4

P. Hogan , Edward J. Timm , Steven N. Girard , Mercouri G. Kanatzidis

4

1

Chemical Engineering and Materials Science Department, Michigan State University, East
Lansing, MI 48824 USA,
2
Electrical and Computer Engineering Department, Michigan State University, East Lansing, MI
48824 USA
3
Mechanical Engineering Department, Michigan State University, East Lansing, MI 48824 USA
4

Department of Chemistry, Northwestern University, Evanston, IL, USA

Abstract
Two-phase PbTe-PbS materials, in which PbS is a nanostructured phase, are promising
thermoelectric materials for the direct conversion of heat energy into electricity. In this study, a
Vickers indentation mean hardness of 1.18 + 0.09 GPa was measured for hot pressed specimens
Pb0.95Sn0.05Te – PbS 8% while the mean hardness of cast specimens was 0.68 + 0.07 GPa. The
1/2

mean fracture toughness of the not pressed specimens was estimated as 0.35 ± 0.04 MPa·m

via Vickers indentation. Resonant Ultrasound Spectroscopy (RUS) measurements on hot pressed
specimens gave mean values of Young’s modulus, shear modulus and Poisson’s ratio of 53.1
GPa, 21.4 GPa and 0.245, respectively while for the cast specimens the Young’s and shear
moduli were about 10 percent lower than for the hot pressed, with a mean value of Poisson’s
ratio of 0.245. The differences between the hardness and elastic moduli values for the cast and
hot pressed specimens are discussed.
Keywords: thermoelectric; lead telluride; powder processing; elasticity; hardness

94

4.1.0 Introduction
PbTe-PbS is an emerging thermoelectric material that has potential for waste-heat recovery
applications. For the PbTe-PbS system [1] and other thermoelectric materials such as LAST
(Lead-Antimony-Silver-Tellurium) [2, 3] and LASTT (Lead-Antimony-Silver-Tellurium-Tin) [3,
4], phonon scattering from nanometer scale heterogeneities reduces the lattice thermal
conductivity and hence enhances ZT, the non-dimensional figure of merit for thermoelectric
materials [5]. For the PbTe-PbS system in particular, both PbTe-rich and PbS-rich nanoregions
have been observed [1].
The characterization of hardness and elastic moduli is important in order to better understand
the thermoelectric material’s response to thermal and mechanical stresses generated by in-service
conditions. For example, hardness is associated with a material’s machinability as well as its
resistance to wear [6]. The elastic moduli are required for stress-strain calculations [7 - 9] and,
in addition, the elastic moduli can be used to monitor the level of microcrack damage that may
accumulate during processing, fabrication or use of thermoelectric materials [10 - 12].
The mechanical property data in the open literature is very limited for most thermoelectric
materials, although recently the authors and co-workers have studied the mechanical properties
of PbTe-based thermoelectric materials, including PbTe, LAST, and LASTT [6, 13 - 18]. These
studies include the fracture strength and Weibull modulus of LASTT [13], the fracture strength
of LAST [19], the Young’s modulus as a function of composition for LAST [14], the high
temperature elastic moduli of polycrystalline PbTe [15], LAST [16, 17] and LASTT [19], the
porosity dependence of the elastic moduli of LAST [18], and the composition dependence of the
hardness of LAST [6].
However, for the PbTe-PbS material system, no data on the elastic moduli exists in the

95

literature. Hardness data for the PbTe-PbS 5% and PbTe-PbS 10% is present in the literature, but
no hardness data is available for the particular thermoelectric composition Pb0.95Sn0.05Te – PbS
8%. In this study, we used resonant ultrasound spectroscopy (RUS) to determine the Young’s
modulus, shear modulus, and Poisson’s ratio of cast and hot pressed Pb0.95Sn0.05Te – PbS 8%
specimens. The hardness of the cast and hot pressed specimens were measured by Vickers
indentation. In addition, the fracture toughness of the hot pressed specimens was estimated from
Vickers indentation. Both cast and hot pressed specimens were included since for the PbTe-PbS
materials included in this study, the initial step of specimen fabrication casting, but the
specimens are then powder processed and hot pressed in order to reduce the mean grain size and
thereby enhance the mechanical integrity of the specimens.

4.2.0 Experimental Procedure
The Pb0.95Sn0.05Te – PbS 8% ingots included in this study were fabricated either at
Michigan State University (MSU) or at Northwestern University (NW) using the same
procedures. The raw materials for all ingots (used either for mechanical properties or for
powder processing) consisted of Pb, Te, SnTe, and PbS powders of at least 99.99% purity. The
constituent powders were loaded into a 22 mm diameter fused silica ampoule, sealed under a
-4

pressure of ~10 Torr and then heated to 1323 K for 12 hours in a rocking furnace. The sealed
ampoule was held at the melting temperature for 6 hours with 2 hours of rocking. The specimen
was then cooled with an isothermal hold at 773 K for at least 10 hours. The ingots were then
cooled from 773 K to room temperature during a 5 hour period.
All powder processing steps for the Pb0.95Sn0.05Te–PbS 8% ingots were performed in an

96

argon atmosphere inside a double glove box (Omni-Lab, Vacuum Atmospheres Company, CA).
The as-cast ingots were powder crushed and ground using a mechanical mortar and pestle
(Retsch RM200, Retsch GmbH, Germany). The powders were sieved and re-ground until all
powder passed through a 53 micron sieve. The powders were then loaded into a planetary ball
mill (Glenn Mills, Retsch, PM100, NJ), also located within the argon atmosphere of the double
glove box. The powders were then dry milled for 3 hours at 150 rpm using a 250 ml alumina
mill jar with approximately 113 g of 10 mm diameter spherical alumina milling media.
Following the dry milling, the powders were then wet milled for 6 hours at 150 rpm using 25 cc
of hexane with 200 g of alumina media (140 g of 20 mm diameter spheres and 60 g of 3 mm
diameter spheres). Dry milling, followed by wet milling was employed in this study since while
dry milling decreases the particle size more quickly than wet milling, wet milling can give a
smaller final particle size and less tendency for powder agglomeration during milling [20 - 22].
The particle size distributions of the dry/wet milled PbTe-PbS powders were analyzed using
a laser light scattering apparatus (Micromeritics Saturn DigiSizer 5200 Low Volume Liquid
Sample Handling Unit) with a 50 wt% sucrose solution as the analysis liquid. (The sucrose
adjusts the settling rate of the powders in the liquid so that powders remain suspended during the
analysis). Each measurement of particle size distribution consisted of eight consecutive trials
where the particle size distribution was calculated from the mean of the eight trials (Figure 4.1).
Prior to adding the powders to the sucrose solution, they were dispersed ultrasonically in RO
water with a 0.1 wt% sodium lignosulfonate dispersant added to reduce powder agglomeration
during the particle size analysis.
The PbTe-PbS powders were hot pressed using a maximum pressure of ~75 MPa, a
maximum temperature of 723 K, and the total time was 5 hours to press a 32 mm diameter billet.

97

F
igure 4.1. Particle size distribution obtained from laser light scattering apparatus.

98

The hot pressed billets were cut into parallelepiped specimens using a low speed diamond saw.
The mass density of the rectangular parallelepiped specimens was calculated from the average
dimensions measured by electronic calipers (Mitutoyo, 500-196-20, Aurora, IL, with a vendorspecified uncertainty of + 0.0025 cm) and the specimen mass determined by an electronic
balance (Ohaus Adventurer, AR2140, Pinebrook, NJ, with a vendor-specified precision of + 1.0 x
-4

10 g).
Prior to microstructural analysis or Vickers indentation, the specimens were polished
using successively smaller diamond grit from 90 microns to 1 micron. Both the as-polished and
fractured specimen surfaces were examined using a scanning electron microscope (JEOL 6400,
JEOL Ltd., Japan) using a working distance of 15 mm and an accelerating voltage of 15 kV. The
as-polished specimen surfaces were cleaned ultrasonically and then examined to determine the
size and shape of the surface pores and to determine whether or not surface-breaking cracks were
present.
The fractured hot pressed specimens MSUHP-53 and MSUHP-54 were annealed at 573
K for 5 hours and 693 K for 2 hours, respectively, to determine grain size. Both specimens were
annealed in a mullite muffle tube with flowing 96% Ar + 4% H2 gas in a resistance-heated
furnace (Carbolite, Watertown, Wisconsin). A thermal etch on a fracture surfaces was used
rather than a chemical etch, since chemical etching of PbTe-based materials is problematic. For
example, in a biaxial fracture strength study of a cast p-type LASTT (lead-antimony-silvertellurium-tin) thermoelectric material (Ag0.9Pb9Sn9Sb0.6Te20), Ren et al. [13] used a solution of
1.0M KOH + 0.7M K3(Fe(CN))6 in deionized water at room temperature as a wet chemical
etchant [23] to reveal grain boundaries in the LASTT specimens. Although Robozerov et al. [23]

99

developed their etchant solution for use on lead chalcogenide compounds, it was still very
difficult to obtain a suitable etch on the cast LASTT materials in the biaxial strength study [13]
and essentially impossible to obtain an adequate chemical etch on specimens of hot pressed
LASTT and both cast and hot pressed LAST. Thus, in subsequent mechanical property studies
of PbTe-based compounds by the authors, microstructural analyses have been performed on
fracture sections or on thermally etched surfaces [6, 14, 16, 18].
Prior to the hardness testing, the Vickers indenters (Buehler Semimacro Indenter and
Shimadzu HMV-2000) were calibrated using a standard calibration block (761-048, Yamamoto
Scientific Tools Lab, Co LTD, Japan). Following the calibration, the specimen’s hardness, H,
was determined using the Buehler indenter with at least 20 Vickers indentations on the PbTe-PbS
specimen surfaces using a 2.94 N load and a loading time of 5 seconds. In addition to the
indentation testing at a fixed (2.94 N) load, a possible load dependence of hardness was explored
using the Shimadzu HMV-2000 with Vickers indentations made as a function of load, with 10
indentations per load. For all of the Vickers indentation data, the hardness, H, was calculated
from equation (4.1).
H

1.854 P
a2

(4.1)

where 2a = the diagonal length of the indentation impression and P = the indentation load.
Also, using the Vickers indentations, the fracture toughness, KC, was estimated using
equation (4.2), which in the literature is the most frequently used form of the relationship for the
indentation fracture toughness of brittle materials via Vickers, Berkovich or cube corner
indentation [24, 25].

100

1/ 2 P
E
K C   
H
c3 / 2

(4.2)

where E = the Young’s modulus, H = the hardness, P = the indentation load, c = the radial crack
length for Vickers indentation, in this case. While  is a function of the indenter angle [25], for
Vickers indentation, the constant  = 0.016 + 0.004 [26].
The room temperature elastic moduli (Young’s modulus, E, shear modulus, G, and Poisson’s
ratio, ν) were measured using a commercial resonant ultrasound spectroscopy (RUS) apparatus
(RUSpec, Quasar International Inc., Albuquerque, NM, USA). The spectrum of acoustic
resonances was analyzed using commercial software supplied by the RUS vendor [27]. Details
of the RUS measurement technique are given elsewhere [15, 16]

4.3.0 Results and Discussion
As measured by the laser scattering apparatus, the powder particle size for both hot pressed
MSUHP-53 and MSUHP-54 ranged in size from ~200 nm to ~15 microns (Figures 4.1a and b).
The mean and median powder particle sizes were 2.4 microns and 1.5 microns, respectively for
MSUHP-53, while the mean and median powder particle sizes were 2.1 microns and 1.4
microns, respectively for MSUHP-54. Per the operator’s manual provided by the vendor [28],
the laser light scattering apparatus has a measurement range of 100 nanometers to 750 microns
equivalent particle diameter [28]. For equivalent particle diameters between 100 nanometers and
one micron, the laser light scattering apparatus has accuracy of ± 10%, and for those particles
with equivalent diameters between one and 750 microns, the accuracy is ± 3% [28]. Thus, the
particle size determination is less accurate for the submicron particle sizes that for particles one
micron and larger in diameter and furthermore, particles smaller than the lower threshold of

101

instrumental resolution (about 100 nm) will not be represented in the mean particle size
determination.
The mass density of the cast Pb0.95Sn0.05Te – PbS 8% specimens included in this study
3

3

ranged from about 7.85 g/cm to 8.08 g/cm while the mass densities of the hot pressed
3

3

specimens were 7.71 g/cm and 7.91 g/cm , respectively (Table 4.1). For the cast specimens the
microstructural analysis of the as-polished specimens showed the majority of pores were isolated
and quasi-spherical from roughly one to five microns in diameter with a few oblong pores having
a major axis length up to ~ 20 microns (Figure 4.2a). For the hot pressed specimens (Figures
4.2b and 4.2c), most pores were quasi-spherical with diameters less than about one micron
(Figures 4.2b and 4.2c), although occasionally pores as large as five microns across were
observed (Figure 4.2c). No surface cracks were observed in the hot pressed specimens (Figures
4.2b and 4.2c) although a few large cracks were observed in the surfaces of the cast specimens
prepared for microstructural study (Figure 4.2a).
For the as-cast specimens, grains about 1 mm across and larger were observable by the
unaided eye. For each of the two hot pressed billets (MSUHP-53 and MSUHP-54), the average
grain size was determined using the linear intercept method [29] on two SEM micrographs for
each billet with at least 270 intercepts per micrograph. A stereographic projection factor of 1.5
[29] was used to convert the mean intercept length to a grain size for a planar surface, with an
additional correction factor of 1.10 applied to account for the fracture surfaces [30]. The
calculated mean grain sizes for hot pressed specimens MSUHP-53 and MSUHP-54 were 1.4
microns and 1.2 microns, respectively (Figures 4.3a and b). Thus, the mean grain sizes for the
hot-pressed specimens correspond relatively well with the median powder particle sizes (1.5

102

Figure 4.2. SEM micrographs of the as-polished surfaces of Pb0.95Sn0.05Te – PbS 8%
specimens fabricated by (a) casting from the melt and (b and c) hot pressing.

103

Table 4.1. Comparison of Vickers indentation hardness, H, for the polycrystalline (PC)
specimens included in this study (Pb0.95Sn0.05Te–8% PbS) with hardness data from the literature
for PbTe-PbS, PbTe and PbS polycrystalline (PC) and single-crystal (SC) specimens for N
indentations per specimen.
Avg.
Avg. Indentation
H
Specimen Fabrication
N
Reference
Crystallinity Density
(GPa)
Label
Technique
3 Porosity Load (N)
(g/cm )
Cast
PC
0.63 ±
This
NW-In #F
8.05
0.02
2.9
20
0.02
study
Cast
PC
0.64 ±
This
NW-In #G
8.05
0.02
2.9
20
0.05
study
Cast
PC
MSU-In
0.75 ±
This
7.85
0.04
2.9
20
#7A
0.06
study
MSU-In
Cast
PC
0.70 ±
This
7.85
0.04
2.9
20
#7B
0.06
study
a
PC
MSUHP1.10 ±
This
HP
7.71
0.06
2.9
20
53 #2
0.07
study
a
PC
1.15 ±
This
MSUHPHP
7.71
0.06
2.9
20
0.07
study
53 #3
a
PC
1.10 ±
This
MSUHPHP
7.71
0.06
2.9
20
0.08
study
53 #4
a
MSUHPPC
1.28 ±
This
HP
7.91
0.03
2.9
20
54 #A
0.05
study
a
PC
1.23 ±
This
MSUHPHP
7.91
0.03
2.9
20
0.06
study
54 # B
a
PC
1.21 ±
This
MSUHPHP
7.91
0.03
2.9
20
0.07
study
54 #C
Cast
PC
PbTe-PbS
b
b
d
0.15
10
[36]
NS
NS
0.72
5%
Cast
PC
PbTe-PbS
b
b
d
0.15
10
[36]
NS
0.81
NS
10%
Un-doped
Cast
PC
b
b
d
0.39
10
[36]
NS
NS
0.37
PbTe
Un-doped
NS
SC
b
c
d
0.49
10
[37]
NS
SC
0.29
PbTe
Cast
PC
Un-doped
b
b
d
0.39
10
[36]
NS
NS
0.73
PbS
NS
SC
Un-doped
b
c
d
0.49
10
[37]
NS
SC
0.59
PbS
a

Hot pressed

b
c
d

Not stated.
Single crystal specimen, presumably near theoretical density
The standard deviation in the H data was not given by the authors.

104

Figure 4.3. SEM micrographs of annealed fractured surfaces of hot pressed Pb0.95Sn0.05Te –
PbS 8% specimens cut from hot pressed billets (a) MSUHP-53 and (b) MSUHP-54. MSUHP-53
was annealed for 5 hours at 573 K and MSUHP-54 was annealed for 5 hours at 693 K, both in a
96% Ar + 4% H2 atmosphere.

105

Figure 4.4. SEM micrograph of wet milled powders used to fabricate billet MSUHP-54. Note
that a significant factor of the powders particles have a diameter less than about 100 nm, which is
below the effective measurement threshold of the laser scattering apparatus. A fracture surface
of a specimen hot pressed from this powder is shown in Figure 4.3b.

106

microns and 1.4 microns, respectively for MSUHP-53 and MSUHP-54) measured by the laser
scattering apparatus. SEM micrographs of the processed powders used to hot press the specimens
show a significant fraction of powder particles with sizes in the submicron range, including
powder particles with diameters on the order of 100 nm and smaller (Figure 4.4).
The Vickers indentation hardness and the elastic moduli (Young’s modulus, E, shear
modulus, G, and Poisson’s ratio, ν) were measured for both (i) cast ingots and (ii) powder
processed and hot pressed specimens (Tables 4.1 and 4.3). For the PbTe-PbS specimens, Vickers
indentation at a 2.94 N load gave a mean hardness of 0.68 + 0.07 GPa for cast specimens and
1.18 + 0.09GPa for hot pressed specimens (Table 4.1). The differences in hardness for the hot
pressed and cast specimens are consistent with the general trend that hardness increases as the
grain size decreases [31], where the mean grain size of the hot pressed specimens was
approximately one micron while the grain size of the as-cast specimens was at least several
hundred microns.
From the literature, for both metals [32] and ceramics [33, 34] with grain sizes in the micron
range, the observed hardness-grain size relationships often described by the Hall-Petch
relationship, namely

H  H0  kd0.5

(4.3)

where H0 = the hardness of a single crystal, k = the material-dependent Hall-Petch constant and d
= the grain diameter [33, 34]. Thus, the “normal” Hall-Petch relationship for hardness describes
the increase in H with decreasing grain size. However, for nanocrystalline materials with grains
in the size range less than about 50 to 100 nm, the hardness can either decrease or remain
relatively constant with decreasing grain size [32, 33, 35]. In this study, the mean grain sizes are
in the micron range, so one would expect the H versus grain size behavior to be described by

107

equation (4.3). This is consistent with the observation that the hardness of the hot pressed
specimens is higher than the hardness of the cast specimens.
In comparison, for polycrystalline specimens indented at 0.15 N load, Darrow et al. [36]
obtained H values of 0.72 GPa and 0.81GPa for PbTe-PbS 5% and PbTe-PbS 10%, respectively
(Table 4.1), which lie between the H values obtained in this study for the cast and hot pressed
Pb0.95Sn0.05Te – PbS 8% specimens. Although Darrow et al. [36] do not specify the grain size
for their PbTe-PbS 5% and PbTe-PbS 10% specimens, they do state that their specimens were
cast from a melt, which implies a large (typically several hundred microns or larger) grain size.
Thus the hardness data obtained for the PbTe-PbS specimens included in this study is consistent
with H data for similar (but not identical) compositions found in the literature [36].
No hardness data other than that given by Darrow et al. [36] currently exists in the literature
for PbTe-PbS materials, however hardness data is available for undoped PbTe and PbS in the
both the polycrystalline (cast) [36] and the single crystal [37] forms (Table 4.1). The cast
polycrystalline [36] and single crystal [37] undoped PbTe and PbS specimens have lower H
values than those measured for the PbTe-PbS system by Darrow et al. [36] and in this study
(Table 4.1), but as expected from equation (4.3), the single crystal H values for the single crystal
specimens of PbTe and PbS were lower than the polycrystalline (cast) specimens of the
corresponding compositions (Table 4.1).
As a further comparison of the results of this study to the H values measured for PbTe-based
materials, the range of H measured for the cast PbTe-PbS specimens included in this study (0.63
to 0.75 GPa) is roughly comparable to the range of H values measured for 14 different chemical
compositions of cast LAST (AgaPbbSbcTed) [6]. As is the case for the PbTe-PbS data reported
in Table 4.1 for this study, Vickers indentation at a 2.94 N load was used to determine the cast
108

LAST (AgaPbbSbcTed) hardness, which ranged from H = 0.53 GPa for a = 0.006, b = 0.480 c =
0.011 and d = 0.503 to H = 0.92 GPa for a = 0.030, b = 0.422, c = 0.042 and d = 0.506 [6].
In addition to grain size effects, for indentation hardness measurements one must also
consider the possibility of indentation size (indentation load dependent) effects. For a number of
metals and brittle materials, the measured hardness can has been observed to increase as the load
decreases, which is typically called the Indentation Size Effect or ISE [38 - 40]. More recently, a
Reverse Indentation Size Effect (RISE) also has been identified where the measured hardness
decreases as the load decreases [41, 42]. The Vickers indentation hardness data from Darrow
[36] on the cast PbTe-PbS 5% and PbTe-PbS 10% specimens was collected using a lower
Vickers indentation load (0.15 N) than the 2.94 N load for this study’s Pb0.95Sn0.05Te – PbS 8%
data given in Table 4.1. Thus the lower H values for the Darrow cast specimens than for the hot
pressed specimens included in this study could be due to either to a reverse indentation size
effect, a grain size effect, or a combination of the two effects. In order to distinguish among
these possibilities, a series of 10 indentations per load were performed at each of seven loads
(0.25 N, 0.49 N, 0.98 N, 1.96 N, 2.94 N, 4.90 N, and 9.81 N) for specimens from hot pressed
billets MSUHP-53 and MSUHP-54 (Figure 4.5). The H values for the hot pressed specimens
were relatively independent of load, where for the total of 70 indentations per billet, the mean
and standard deviation of H was 1.14 + 0.04 GPa and 1.04 + 0.08 GPa respectively for MSUHP53 and MSUHP-54 (Figure 4.5).
For the two cast Pb0.95Sn0.05Te – PbS 8% specimens, 10 indentations per load were
performed at six loads from 0.25 N and 4.90 N (Figure 4.5). The cast specimens showed
extensive chipping and multiple cracking near the Vickers indentation impressions for an

109

Figure 4.5. The mean hardness as a function of the applied Vickers indentation load for hot
pressed (open symbols) and cast (filled symbols) specimens in the PbTe-PbS system. The mean
hardness values, averaged over all loads for the Pb0.95Sn0.05Te – PbS 8% hot pressed MSUHP53 and MSUHP-54 specimens are shown by the dotted and dashed lines, respectively. The mean
hardness values averaged over all loads for the Pb0.95Sn0.05Te – PbS 8% cast NW-Ingot G and
MSU-Ingot 7A specimens are indicated by the dot-dashed and dot-dot-dashed lines, respectively.
The hardness data from Darrow et al. [36] for cast PbTe-PbS 5% and PbTe-PbS 10% specimens
is shown for comparison (half-filled symbols).

110

indentation load of 9.81 N, so no data is given here for cast specimens indented 9.81 N (Figure
4.5). (Chipping and multiple cracking is often observed for large-grained and single crystal
specimens indented at high loads). Averaging the H values obtained from both cast specimens
for the entire load range gives a mean and standard deviation of 0.77 ± 0.07 GPa and 0.64 ± 0.06
GPa for the cast Pb0.95Sn0.05Te – PbS 8% MSU-Ingot 7a and NW-Ingot G, respectively. These
values are comparable to H values of 0.72 GPa and 0.82 GPa reported by Darrow et al. [36] for
cast specimens of PbTe-PbS 5% and PbTe-PbS 10%, respectively (Figure 4.5).
From Figure 4.5, no ISE or RISE are apparent for the cast and hot pressed Pb0.95Sn0.05Te –
PbS 8% specimens included in this study, meaning that the hardness is essentially independent of
load over the a relatively broad load range (0.25 N to 9.81 N for the hot pressed specimens and
0.25 to 4.90 N for the cast specimens). In addition, the H values for Darrow’s cast PbTe-PbS 5%
and PbTe-PbS 10% specimens [36] are comparable to the H measured for the cast
Pb0.95Sn0.05Te – PbS 8% specimens included in this study (Figure 4.5). However, the H values
of the hot pressed and cast Pb0.95Sn0.05Te – PbS 8% are significantly different. In the absence
of an indentation size effect, the difference between the H values for the hot pressed and cast
materials is most likely attributable to a grain size effect (equation (4.3)).
The average fracture toughness of the PbTe-PbS 8% specimens was approximately 0.35 ±
1/2

0.04 MPa·m

(Table 4.2a). SEM micrographs of the indentations showed that no radial cracks

occurred for the ingot specimens while usable radial crack systems occurred only the 1.96 N,
2.94 N and 4.90 N loads (Figure 4.6). For the hot pressed specimens, the 0.25 N and 0.49 N
indentations did not produce radial cracks, while the 0.98 N indentations produced an incomplete
set of radial cracks. For the 1.96 N, 2.94 N and 4.90 N loads, Vickers indentation produced a

111

Table 4.2a Fracture toughness, Kc, determined using Vickers indentation for the hot pressed
polycrystalline (PC) Pb0.95Sn0.05Te–8% PbS specimens included in this study.

Specimen
Label
MSUHP-53
#2
MSUHP-53
#3
MSUHP-53
#3
MSUHP-53
#3
MSUHP-53
#4
MSUHP-54
#A
MSUHP-54
#B
MSUHP-54
#C
MSUHP-54
#C

Load
(N)

Kc
1/2
(MPa·m )

Coefficient
of Variation

Number of
indentations with
complete radial
crack systems

Total
Number of
indentations
attempted

4.90

0.35 ± 0.03

0.08

9

20

2.94

0.35 ± 0.04

0.10

19

20

1.96

0.36 ± 0.01

0.03

6

10

4.90

0.37 ± 0.03

0.08

14

20

2.94

0.34 ± 0.04

0.11

20

20

2.94

0.31 ± 0.01

0.04

20

20

2.94

0.32 ± 0.02

0.05

19

20

2.94

0.34 ± 0.03

0.08

20

20

4.90

0.44 ± 0.04

0.08

8

10

112

Table 4.2b. The fracture toughness (Kc) for polycrystalline (PC) or glasses (G) from literature for
various thermoelectrics, semiconductors, and chalcogenides using Vickers indentation (VI),
single edged notched beam (SENB), or double-torsion and double-cantilever-beam (DTDCB)
methods.
Kc

Composition

Crystallinity

Measurement
method

ε-Zn4Sb3

PC

SENB

0.6 – 1.0

[48]

Bi2Te3 + x vol% SiCnp nanoparticles
(x = 0, 0.1, 0.5, 1.0)

PC

VI

1.12 – 1.35

[49]

Binary Ge–Se & Ternary Ge–Sb–Se

G

VI

0.2 - 0.8

[50]

62.5(GeS2)– 12.5(Sb2S3)–25(CsCl)
(mol%)

G

VI

0.12 – 0.2

[51]

GexSe100-x (x = 0, 5, 10, 15, 20)

G

VI

0.09 – 0.59

[52]

ZnSe

PC

DTDCB

0.9

[53]

ZnS

PC

VI

1.0

[47]

113

MPa·m

1/2

Reference

Figure 4.6 SEM micrographs of Vickers indentations at a) 0.25 N, b) 2.0 N, and c) 4.9 N for
MSU-In #7A, and d) 0.25 N for MSUHP-54 #C, e) 2 N for MSUHP-53 #3, and f) 4.9 N for
MSUHP-54 #C.

114

complete radial crack pattern in most cases, while at the 9.81 N load, considerable spalling
occurred along the indent impression edges. Thus, only the 1.96 N, 2.94 N and 4.90 N load
levels produced usable KC data (Table 4.2a). The observed crack threshold behavior is consistent
with the literature since for sharp indenters, including Vickers, Berkovich and cube-corner
indenters, brittle materials typically display a crack initiation threshold [43, 44, 45, 46] such that
below the threshold load, radial cracks do not occur.
The fact that Vickers indentation cracks were observed for the hot pressed specimens and not
observed for the cast specimens may be related to the very large (roughly 1 mm) grain size of the
cast specimens compared to the 1.2 to 1.4 mean grains sizes of the hot pressed specimens. In a
paper that focused on crack initiation beneath sharp indenters, Lawn and Evans [47] state that “It
is nevertheless apparent that the appropriate refinement of microstructure (e.g. refinement of
grain size in polycrystals, reduction of pile-up length in monocrystals, elimination of
microinhomogeneities in glasses) could be an important factor in the design and manufacture of
ultra-high strength ceramics for contact situations. In the context of the indentation fracture, the
micro-mechanics of nucleation processes is a relatively unexplored area of study”.
1/2

While the mean value a mean KC value of 0.35 ± 0.04 MPa·m

is relatively low, Table

4.2b shows that roughly similar KC values have been reported in the literature for other
thermoelectric materials and other chalcogenides (PbTe-PbS 8% is a chalcogenide based
compound). For example, for the three chalcogenide glass systems listed in Table 4.2b, the
1/2

measured KC values range from 0.09 to 0.8 MPa·m

.

Zhao et al. [49] found that for the

thermoelectric Bi2Te3 , addition of SiC nanoparticles (SiCnp) in x vol%, where x = 0, 0.1, 0.5, or
1.0, resulted in an increase in KC with the nanoparticle addition. The authors are now in the
115

initial stages of work involving additions of SiCnp to PbTe-PbS, in anticipation that the SiCnp or
other nanoparticle additions may also increase the KC of PbTe-PbS.
It must be noted that Quinn and Bradt [54] have recently criticized the reliability of the via
Vickers indentation for determining KC via in part due to (i) the complicated crack system that
arises from Vickers indentation (namely the four orthogonal radial cracks associated with Vickers
indentation rather than the single crack that is preferred for fracture toughness measurements)
and (ii) the lack of a sufficiently rigorous analytical treatment of the radial crack system.
However, the Vickers indentation technique continues to be used in KC determinations of brittle
materials [24, 25] and Leonardi and Furgiuele recently provided an analytical approach to the
evaluation KC via indentation which agrees with the functional form of the fracture toughness
relationship used in this study (equation (4.2)) [24].
No data is available in the literature for the elastic moduli (Young’s modulus, shear modulus
or Poisson’s ratio) for materials in the PbTe-PbS system. However, the elastic moduli for the two
Pb0.95Sn0.05Te – PbS 8% hot pressed specimens gave room temperature moduli values (E, G
and ν) that were only a few percent lower than the values obtained by Ren et al. [15] for undoped
PbTe and PbI2-doped PbTe (Table 4.3). In addition, the moduli for this study’s hot pressed
Pb0.95Sn0.05Te – PbS 8% specimens were also comparable to the aggregate elastic modulus
values calculated from single crystal PbTe measurements by Houston et al. [55] and by
Einspruch and Manning [56]. The aggregate or polycrystalline moduli (Table 4.3) for the data
from both Houston et al. [55] and Einspruch and Manning [56] were calculated from the mean of
the Hashin and Strikman bounds [57] determined from the measurements on single crystal PbTe

116

Table 4.3 Room temperature Young’s modulus, E, shear modulus, G, and Poisson’s ratio,
measured by Resonant Ultrasound Spectroscopy (RUS) for the PbTe-PbS (Pb0.95Sn0.05Te–8%
PbS) polycrystalline (PC) specimens included in this study compared to doped and un-doped
polycrystalline (PC) and single-crystal (SC) room-temperature modulus data from the literature.
Density
Specimen Fabrication
E
Crystallinity
3 Porosity
Label Technique
(GPa)
(g/cm )

G
(GPa)



Reference

NW-In -A

Cast

PC

8.08

0.01

47.9 ±
0.1

19.15 ±
0.01

0.250
±
This study
0.001

NW-In -C

Cast

PC

8.00

0.02

47.6 ±
0.2

19.15±
0.01

0.244
±
This study
0.003

MSU-In
#7

Cast

PC

7.85

0.04

47.6 ± 19.17 ±
0.2
0.03

0.242
±
This study
0.003

MSUHP53 #A

Hot
pressed

PC

7.75

0.05

52.1 ±
0.1

20.94 ±
0.004

0.243
±
This study
0.002

MSUHP54 #1

Hot
pressed

PC

7.91

0.03

54.0 ±
0.1

21.83 ±
0.01

0.236
±
This study
0.002

Un-doped
PbTe

Cast

PC

7.96

NS

57.5 ±
0.3

22.32 ±
0.04

0.293
±
0.003

[6]

PbI2doped
PbTe

Cast

PC

7.88

NS

57.5 ±
0.2

22.81 ±
0.02

0.260
±
0.003

[6]

Un-doped Czochralski
PbTe
Technique

SC

8.24

*

58.05

22.95

0.264

[48]

Un-doped Teal-Little
PbTe
Process

SC

8.16

*

56.95

22.48

0.268

[49]

NS Not stated.
* Single crystal specimen, presumably near theoretical density

117

specimens. However, comparing the cast and the hot pressed specimens, the average Young’s
moduli and shear moduli for the as-cast Pb0.95Sn0.05Te – PbS 8% specimens were about 10
percent lower than the averages calculated for the powder processed/hot pressed specimens
(Table 4.3).
In contrast to the grain size dependence of hardness given by equation (4.3), in the absence
of microcracking the elastic moduli (Young’s modulus, shear modulus and Poisson’s ratio) are
independent of grain size for polycrystalline specimens with grain sizes larger than about 100
nm. However, the Young’s modulus of nanograined metals [58, 59] is a function of grain size.
For metals such as iron, copper, titanium and palladium, the elastic moduli for specimens with a
mean grain size of about 100 nm is essentially unchanged from that for specimens with micronsized grains, but a rapid decrease in Young’s modulus is observed smaller than approximately 20
to 30 nm, with a modulus drop of 10 to 15 percent in grain sizes about 10 nm compared to the
modulus values for polycrystalline specimens with grain sizes larger than 100 nm [58, 59].
For nanocrystalline ceramics MgO [60] and ZrO2- 3 wt% Y2O3 [35], the elastic moduli are
also a function of grain size. Yeheske et al. [60] found that for fully dense, transparent MgO with
an average grain size of 41 nm that the Young’s and shear moduli were approximately 13% lower
the moduli for polycrystalline MgO with grain sizes at the submicrometer size range and larger.
In a study of dense nanocrystalline ZrO2- 3 wt% Y2O3 with mean grains sizes ranging from 23
nm to 130 nm, Chaim et al. found the measured Young’s modulus decreased monotonically with
decreasing grain size. Thus while the elastic moduli of both metals and ceramics can be grain
size dependent for grain sizes smaller than about 100 nm, the elastic moduli (Young’s and shear
moduli) are expected to be independent of grain size for the hot pressed and cast PbTe-PbS

118

specimens included in this study, since the mean grain sizes are roughly one micron and 1 mm
for the hot pressed and cast specimens, respectively. However, if future studies generate
polycrystalline PbTe-PbS specimens with mean grain sizes smaller than roughly 50 nm to 100
nm, then a grain-size dependent decrease in elastic moduli may be observed.
Even for grain sizes in the micron range and larger, the elastic moduli may display a grain
size dependence if thermal expansion anisotropy (TEA) is present in the material. Since PbTePbS has cubic symmetry, the material is isotropic with respect to thermal expansion [61] and thus
no thermal-expansion-anisotropy-induced microcracking will be present [62] to explain the
observed differences in the elastic moduli between the as cast and the hot pressed specimens.
Nevertheless, if microcracks are present through some mechanism other than TEA (such as
polishing, grinding, thermal shock, or crystallographic phase change), then the Young’s and shear
modulus of materials do decrease as the volumetric number density and size of microcracks
increase [10]. Since the fracture strength of the brittle, large grained materials decreases with
increasing grain size [63], the as-cast specimens are likely more susceptible to microcrack
damage during the cutting and polishing processes involved in specimen preparation, which may
in turn lead to the lower moduli for the cast compared to the hot pressed specimens (Table 4.3).
This study focuses on the room temperature mechanical properties of thermoelectric
materials with the composition PbTe-PbS 8%. For thermoelectric materials, the dimensionless
figure of merit, ZT, given by
ZT 

S2T


(4.4)

is very important, since ZT is used to measure the efficiency of the thermoelectric,
where S is the Seebeck coefficient, s is the electrical conductivity, k is the total (lattice plus
electronic) thermal conductivity and T is temperature in Kelvin. In the past decade,
119

improvements in ZT have been accomplished largely by decreasing the lattice thermal
conductivity of thermoelectric materials [64, 65]. For the same PbTe-PbS 8% composition as is
included in this study, Girard et al. calculated the thermal conductivity from thermal diffusivity
and specific heat measurements performed on a laser flash system [66]. The room temperature
value of thermal conductivity, k, determined by Girard et al. was about 1.6 W/mK at room
temperature, but k decreased to about ~1 W/mK to ~0.4 W/mK for temperature between 400 –
500 K [66].

4.4. Summary and Conclusions
Powder processing of Pb0.95Sn0.05Te – PbS 8% ingots gave dense (relative densities of 0.94
and 0.97) hot pressed billets with grain sizes in the micron range. The mean hardness of the hot
pressed specimens was 1.18 + 0.09 GPa, which is comparable to that of hot pressed LAST
(AgaPbbSbcTed). However the hot pressed PbTe-PbS specimens have a hardness, H, that is
about 70 percent higher than the as-cast specimens included in this study (Figure 4.5), although
there are no compositional differences between the cast and hot pressed Pb0.95Sn0.05Te – PbS
8% specimens included in this study. The higher hardness observed in this study for the powder
processed and hot pressed specimens (compared to the as-cast specimens) is likely a grain size
effect, where the hardness increases with decreasing grain size (equation (4.3)) for materials with
grain sizes in the micron range and larger. No indentation size effect (ISE) or reverse indentation
size effect (RISE) is observed for the range of indentations loads included in this study (Figure
4.5).
This study is the first to report Young’s modulus, shear modulus and Poisson’s ratio values

120

for any composition in the PbTe-PbS system. For the hot pressed Pb0.95Sn0.05Te – PbS 8%
specimens, the measured elastic moduli were comparable to those measured in earlier studies for
LAST, PbTe and PbI2-doped PbTe [15, 55, 56] (Table 4.3). However, the Young’s and shear
modulus of the hot pressed PbTe-PbS specimens were about 10 percent higher than the moduli
measured for the cast specimens, although for the elastic moduli the difference in grain sizes
between the cast and hot pressed specimens likely does not account for the observed differences
in the elastic moduli (Table 4.3). Nevertheless, the differences in moduli may stem of low
strength values (and hence greater susceptibility to microcracking) in the cast specimens due to
their large grain sizes. Future studies are needed to address this point.

Acknowledgements
The authors acknowledge the financial assistance of the Office of Naval Research Grant
N00014-08-1-0613. The authors also acknowledge the Defense University Research
Instrumentation Program (DURIP) Grant No. N00014-09-1-0785, Office of Naval Research,
which provided funding for the purchase of the Resonant Ultrasound Spectroscopy apparatus and
the laser scattering apparatus utilized in this research. In addition, funding for the hot press
facility through U. S. Department of Energy Grant DE-FC26-04NT42281 is acknowledged.

121

REFERENCES

122

4.5 References
[1] J. Androulakis, C-H Lin, H-J Kong, C. Uher, C-I Wu, T. Hogan, B. A. Cook, T. Caillat, K.M.
Paraskevopoulos, and M.G. Kanatzidis, Spinodal decomposition and nucleation and
growth as a means to bulk nanostructured thermoelectrics: Enhanced performance in
Pb1-xSnxTe-PbS, J. Am. Chem. Soc. 129 (2007) 9780-9788.
[2] E. Quarez, K. F. Hsu, R. Pcionek, N Frangis, E. K. Polychroniadis, M. G. Kanatzidis,
Nanostructuring, compositional fluctuations, and atomic ordering in the thermoelectric
materials AgPbmSbTe2+m. The myth of solid solutions, J. Am. Chem. Soc. 127 (2005)
9177 - 9190.
[3] T. P. Hogan, A. Downey, J. Short, J. D’Angelo, C-I Wu, E. Quarez, J. Androulakis, F. P.
Poudeu, J. Sootsman, D-Y Chung, M. G. Kanatzidis, S. D. Mahanti, E. Timm, H Schock,
F. Ren, J. Johnson, E. D. Case, Nanostructured thermoelectric materials and highefficiency power-generation modules, J. Elect. Mater. 36 (2007) 704-710.
[4] J. Androulakis, K. F. Hsu, R. Pcionek, H. Kong, C. Uher, J. D’Angelo, A. Downey, T.
Hogan M. G. Kanatzidis, Nanostructuring and high thermoelectric efficiency in p-type
Ag(Pb1-ySny)(m)SbTe2+m , Adv. Mater. 18 (2006) 1170 – 1173.
[5] D.M. Rowe (Ed.), CRC Handbook of Thermoelectrics, CRC Press, Boca Raton, Florida
1995.
[6] F. Ren, E. D. Case, E. J. Timm, H. J. Schock, Hardness as a function of composition for ntype LAST thermoelectric material, J. Alloys Compd. 455 (2008) 340-345.
[7] N. E. Dowling, Mechanical Behavior of Materials, Second Ed., Prentice Hall, Upper Saddle
River, New Jersey, 1999.
[8] S. S. Manson, Thermal Stress and Low Cycle Fatigue, McGraw-Hill, New York, 1966.
[9] J. N. Reddy, An Introduction to the Finite Element Method , Third Ed., McGraw-Hill Higher
Education, New York, 2006.
[10] E. D. Case, in: M. H. Alibadi (Ed), Thermo-Mechanical Fatigue and Fracture, WIT Press,
Southampton, UK, 2002, pp. 137 – 208.
[11] E.D. Case, Y. Kim, The effect of surface-limited microcracks on the effective Young’s
modulis of ceramics 2. Application of analysis to particular microcrack geometries, J.
Mater. Sci., 28 (1993) 1885-1900.
[12] E. D. Case, C. Glinka, Characterization of microcracks in YCrO3 using small-angle neutronscattering and elasticity measurements, J. Mater. Sci. 19 (1984) 2962-2968.
[13] F. Ren, E. D. Case, E. J. Timm, M. D. Jacobs, H. J. Schock, Weibull analysis of the biaxial

123

fracture strength of a cast p-type LAST-T thermoelectric material, Philos. Mag. Lett. 86
(2006) 673 – 682.
[14] F. Ren, E. D. Case, E. J. Timm, H. J. Schock, Young's modulus as a function of composition
for an n-type lead-antimony-silver-telluride (LAST) thermoelectric material, Philos. Mag.
87 (2007) 4907 - 4934.
[15] F. Ren, E. D. Case, J. R. Sootsman, M. G. Kanatzidis, H. Kong, C. Uher E. Lara-Curzio, R.
M. Trejo, C. Uher, The high-temperature elastic moduli of polycrystalline PbTe measured
by resonant ultrasound spectroscopy, Acta Mater. 56 (2008) 5954 – 5963.
[16] F. Ren, E. D. Case, J. E. Ni, E. J. Timm, E. Lara-Curzio, R. M. Trejo, C.-H. Lin, M. G.
Kanatzidis, Temperature-dependent elastic moduli of lead telluride-based thermoelectric
materials, Philos. Mag. 89 (2009) 143- 167.
[17] F. Ren, E. D. Case, E. J. Timm, E. Lara-Curzio, R. M. Trejo, Anomalous temperaturedependent Young's modulus of a cast LAST (Pb-Sb-Ag-Te) thermoelectric material, Acta
Mater. 58 (2010) 31-38.
[18] J. E. Ni, F. Ren, E. D. Case, E. J. Timm, Porosity dependence of elastic moduli in LAST
(Lead-antimony-silver-tellurium) thermoelectric materials, Mater. Chem. Phys. 118
(2009) 459-466.
[19] F. Ren, B. D. Hall, J. E. Ni, E. D. Case, E.J. Timm, H. J. Schock, C-I. Wu, J. J. D’Angelo, T.
P. Hogan, R. M. Trejo, E. Lara-Curzio, in: T.P. Hogan, J. Yang, R. Funahashi (Eds)
Thermoelectric Power Generation, Materials Research Society Proceedings, Vol. 1044.
Materials Research Society, Warrendale, PA, 2008, pp 121 – 126.
[20] C. Suryanarayana, Mechanical alloying and milling, Prog. Mater. Sci 46 (2001) 13.
[21] M. N. Rahaman, Ceramic Processing and Sintering, Second Ed., Marcel Dekker, New York,
2003, p. 57.
[22] B. D. Hall, E. D. Case. F. Ren, J. Johnson and E. J. Timm, Agglomeration during wet
milling of LAST (lead-antimony-silver-tellurium) powders, Mater. Chem. Phys. 113
(2009) 497 – 502.
[23] V.V. Robozerov, V.A. Zykov and T.A. Gavrikova, Chemical etching of lead chalcogenides,
Inorg. Mater. 36 (2000) 127 – 131.
[24] A. Leonardi and F. Furgiuele, Analytical Approaches to Stress Intensity Factor Evaluation
for Indentation Cracks, J. Amer. Ceram. Soc. 92 (2009) 1093 - 1097.
[25] J. Jang and G. M. Pharr, Influence of indenter angle on cracking in Si and Ge during
nanoindentation, Acta Mater. 56 (2008) 4458 – 4469.

124

[26] G. R. Anstis, P. Chantikul, B. R. Lawn, D. B. Marshall, A critical-evaluation of indentation
techniques for measuring fracture-toughness. 1. Direct crack measurements, J. Amer.
Ceram. Soc. 64 (1981) 533 -538.
[27] A. Migliori, J. L. Sarrao, Resonant Ultrasound Spectroscopy: Applications to Physics,
Materials Measurements, and Nondestructive Evaluation, Academic Press, New York,
1997.
[28] Saturn Digisizer 5200 Operators Manual v1.12, Micromertics Instrument Corporation,
Norcross, GA, 2007, pp. 1-9.
[29] R. L. Fullman, Measurement of particle sizes in opaque bodies, Trans AIME 197 (1953)
447 – 452.
[30] E. D. Case, J. R. Smyth, V. Monthei, Grain size determinations, J. Am. Ceram. Soc. 64
(1981) C24-C25.
[31] R. W. Rice, Mechanical Properties of Ceramics and Composites, Marcel Dekker Inc., New
York, 2000.
[32] H. Conrad, J. Narayan, On the grain size softening in nanocrystalline materials, Scr. Mater.
42 (2000) 1025-1030.
[33] D. Ehre, R.Chaim, Abnormal hall-petch behavior in nanocrystalline MgO ceramic, J. Mater.
Sci. 43 (2008) 6139-6143.
[34] F.L. Kennard, R.C. Bradt, V.S. Stubican, Mechanical-proprties of directionally solidified
MgO-MgAl2O4 eutectic, J. Am. Ceram. Soc. 59 (1976) 160-163.
[35] R. Chaim, M. Hefetz, Effect of grain size on elastic modulus and hardness of
nanocrystalline ZrO(2)-3 wt% Y(2)O(3) ceramic, J. Mater. Sci. 39 (2004) 3057 – 3061.
[36] M. S. Darrow, W. B. White, R. Roy, Micro-indentation hardness variation as a function of
composition for polycrystalline solutions in systems PbS/PbTe, PbS/PbTe and PbS/PbSe,
J. Mater. Sci., 4 (1969) 313-319.
[37] M.S. Ablova, Sov. Effect of donor and acceptor additions on mechanical properties of PbTe,
PbSe, and PbS, Phys. Solid State, 12 (1971) 2910.
[38] M. L. Weaver, M. E. Stevenson , R. C. Bradt, Knoop microhardness anisotropy and the
indentation size effect on the (100) of single crystal NiAl, Mater. Sci. Eng. A345 (2003)
113 -117.
[39] A. Ghosh, H. Li, Y.H. Han, R.C. Bradt, The frictional component of the indentation size
effect in low load microhardness testing, J. Mater. Res. 8 (1993) 1028 -1032.

125

[40] W.D. Nix, H.. Gao, Indentation size effects in crystalline materials: A law for strain gradient
plasticity, J. Mech. Phys. Solids 46 (1998) 411-425.
[41] K Sangwal, A. Klos, Study of microindentation hardness of different planes of gadolinium
calcium oxyborate single crystals, Cryst. Res. Technol. 40 (2005) 429 – 438.
[42] K . Sangwal, On the reverse indentation size effect and microhardness measurement of
solids, Mater. Chem. Phys. 63 (2000) 145 – 152.
[43] D. S. Harding, W. C. Oliver, and G. M. Pharr, Materials Research Society Symposium
Proceedings, Thin Films: Stresses and Mechanical Properties. S. P. Baker, P. Borgesen, P.
H. Townsend, C. A. Ross, and C. A. Volkert (Eds.) Vol. 356, Materials Research Society,
Warrendale, PA, 1995, pp. 663–69.
[44] G. M. Pharr, Measurement of mechanical properties by ultra-low load indentation, Mater.
Sci. Eng., A253 (1998) 151–159.
[45] K. Kese and D. J. Rowcliffe, Nanoindentation method for measuring residual stress in brittle
materials, J. Am. Ceram. Soc.86 (2003) 811– 816
[46] D. J. Morris, S. B. Myers, R. F. Cook, Indentation crack initiation in ion-exchanged
aluminosilicate glass, J. Mater. Sci. 39 (2004) 2399 – 2410.
[47] B. R. Lawn and A. G. Evans, Model for crack initiation in elastic-plastic indentation fields,
J. Mater. Sci. 12 (1977) 2195-2199.
[48] K. Ueno, A Yammoto, T. Inoue, S. Sodeoka, and H. Obara, Optimization of hot-press
conditions of Zn4Sb3 for high thermoelectric performance: III. Effect of starting particle
size on thermoelectric and mechanical properties, J. Alloys Compds. 392 (2005) 295-299.
[49] L. D. Zhao, B. Zhang, J. Li, M. Zhou. W. Liu, and J. Liu, Thermoelectric and mechanical
properties of nano-SiC-dispersed Bi2Te3 fabricated by mechanical alloying and spark
plasma sintering, J. Alloys Compds. 455 (2008) 259-264.
[50] A. K. Varshneya and D. J. Mauro, Microhardness, indentation toughness, elasticity,
plasticity, and brittleness of Ge-Sb-Se chalcogenide glasses, J Non-Cryst Solids 353
(2007) 1291–1297.
[51] S. Zhu, H. Ma, L. Calvez, X. Zhang, J. Lucas, J. Adam, H. Shang, and T. Rouxel, Optical
and mechanical properties of far infrared transmitting glass-ceramics, J Non-Cryst Solids
353 (2007) 1298–1301.
[52] J.Guin, T. Rouxel, and J. Sangleboeuf, Hardness, toughness, and scratchability of
germanium-selenium chalcogenide glasses, J. Am. Ceram. Soc. 85 (2002) 1545–1552.
[53] A. G. Evans and H. Johnson, Fracture mechanical study of ZnSe for laser window

126

applications, J. Am. Ceram. Soc. 58 (1975) 244–249.
[54] G. D. Quinn and R. C. Bradt, On the Vickers indentation fracture toughness test, J. Amer.
Ceram. Soc. 90 (2007) 673-680.
[55] B. Houston, R. E. Strakna, H. S. Belson, Elastic constant thermal expansion and Debye
temperature of lead telluride, J. Appl. Phys. 39 (1968) 3913.
[56] NG Einspruch, RJ Manning, Elastic constants of compound semiconductors ZnS, PbTe,
GaSb, J. Acoust. Soc. Am. 35 (1963) 215.
[57] G. Simmons, H. Wang, Single Crystal Elastic Constants and Calculated Aggregate
Properties, MIT Press, Cambridge, MA, 1971.
[58] J. Zhou, Z. Li, R. Zhu, Y. Li, Z. Zhang, A mixtures-based model for the grain size
dependent mechanical behavior of nanocrystalline materials, J. Mater. Process. Technol.,
197 (2008) 325-336.
[59] H. S. Cao, J. J. Hunsinger, O. Elkdim, Determination of elastic modulus of nanocrystalline
iron and titanium by means of acoustic microscopy, Scr. Mater. 46 (2002) 55 – 60.
[60] O. Yeheskel, R. Chaim, Z. Shen, M. Nygren, Elastic moduli of grain boundaries in
nanocrystalline MgO ceramics, J. Mater. Res. 20 (2005) 719 – 725.
[61] J. F. Nye, Physical Properties of Crystals: Their Representation By Tensors And Matrices,
Clarendon Press, Oxford, 1957.
[62] E. D. Case, J. R. Smyth, O. Hunter, Grain size dependence of microcrack intiation in brittle
materials, J. Mater. Sci. 15 (1980) 149-153.
[63] M. W. Barsoum, Fundamentals of Ceramics, McGraw Hill, New York, 1997.
[64] K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T Hogan, E. K. Polychroniadis, M.
G. Kanatzidis, Cubic AgPbmSbTe2+m: Bulk thermoelectric materials with high figure of
merit, Science 303 (2004) 818-821.
[65] B Poudel, Q Hao,Y. Ma, Y. C. Lan, A. Minnich, B Yu, X Yan, D. Z. Wang, A. Muto, D
Vashaee, X. Y. Chen, J. M. Liu, M. S. Dresselhaus, G Chen, Z. Ren, Highthermoelectric performance of nanostructured bismuth antimony telluride bulk alloys,
Science 320 (2008) 634-638.
[66] S. N. Girard, J. He, C. Li, S. Moses, G. Wang, C. Uher, V. P. Dravid, and M. G. Kanatzidis,
In Situ Nanostructure Generation and Evolution within a Bulk Thermoelectric Material to
Reduce Lattice Thermal Conductivity, Nano Letters 10 (2010) 2825-2831

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The citation for this paper is: Jennifer E. Ni, Eldon D. Case, Ryan Stewart, Chun-I Wu, Timothy
P. Hogan, Mercouri G. Kanatzidis, Bloating in (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055%PbI2
Thermoelectric Specimens as a Result of Processing Conditions, J Electron Mater, in press,
DOI: 10.1007/s11664-011-1853-0.

5.0 Bloating in (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 thermoelectric specimens as a result
of processing conditions
1

1

1

1

1

Jennifer E. Ni , Eldon D. Case , Ryan Stewart , Chun-I Wu , Timothy P. Hogan , Mercouri G.
Kanatzidis

2

1

Michigan State University, East Lansing, MI USA

2

Northwestern University, Evanston, IL USA

Lead chalcogenides such as (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 have received
attention due to their encouraging thermoelectric properties. For the hot pressing (HP) and
pulsed electric current sintering (PECS) techniques used in this study, decomposition reactions
can generate porosity (bloating). Porosity in turn can degrade electrical, thermal, and mechanical
properties. In this study, microstructural observations (scanning electron microscopy) and room
temperature elasticity measurements (resonant ultrasound spectroscopy) were used to
characterize bloating generated during post-densification anneals. Although every HP specimen
bloated during post-densification annealing, no bloating was observed for the PECS specimens
processed from dry milled only powders. The lack of bloating for the annealed PECS specimens
may be related to the electrical discharge intrinsic in the PECS process which reportedly cleans
the powder particle surfaces during densification.
KEYWORDS: thermoelectrics, porosity, Young’s modulus, resonant ultrasound spectroscopy
Please direct correspondence to: Eldon D. Case, Chemical Engineering and Materials Science
Department, Room 2527 Engineering Building, Michigan State University, East Lansing,
Michigan, 48824-1226, USA, e-mail casee@egr.msu.edu, FAX (517)-432-1105.
128

5.1 Introduction
Powder processing of thermoelectric materials can yield specimens with much smaller
grain sizes than cast specimens [1]. A reduction in grain size can in turn greatly enhance fracture
strength of brittle materials [1, 2]. During powder processing, porosity, P, can result from (1)
incomplete sintering [2] or (2) from gas evolution within the specimens during processing. The
internal gas evolution in specimens during processing can occur via either liquid phase [3, 4] or
solid phase decomposition reactions [5-9].
Solid phase decomposition reactions [5-9] may occur when the specimen is densified
using high externally applied pressures. High temperature anneals in the absence of an
externally applied pressure can result in increases in P with increasing temperature due to local
deformation caused by pressure generated by gases evolved by decomposition reactions. Thus
in this study, the volume fraction porosity P is given by P = PR + PB, where PR is the porosity
contribution due to residual pores and PB is the porosity generated by bloating.
The porosity dependence of thermal, electrical and mechanical properties on porosity, P,
can be written as
A(P)  A D exp( b PA P)

(5.1)

where A can be thermal conductivity [10], electrical conductivity [10], dielectric constant [11],
or elastic modulus [10, 12]. AD is the value of the material property, A, for at P = 0. Also, bPA
is a material dependent constant [10, 12] and P = PR + PB. This study focuses on microstructural
observations of bloating generated porosity and P versus Young’s modulus, E, measurements,
especially where P is generated by bloating for Ag0.86Pb19Sb1.0Te20 (LAST) and
(Pb0.95Sn0.05Te)0.92(PbS)0.08- 0.055% PbI2 (PbTe-PbS) [13] specimens.
129

For both hot pressing (HP) and pulsed electric current sintering (PECS), the powder
charge is placed between two movable plungers within a cylindrical die. Also, for both HP and
PECS, the powder charge is heated while pressure is simultaneously applied via the plungers.
However, HP and PECS are distinct powder processing techniques in that for HP the powders
and die are heated by an external furnace while for PECS the powders are heated by high-current
electrical pulses that pass through both the die assembly (plungers plus die) and the enclosed
powder charge. Regardless of the powder processing technique, our HP specimens bloated after
annealing while the specimens that are PECS processed from dry milled only powders did not
bloat upon annealing (Results and Discussion). During densification, gas phase generation from
decomposition reactions can be inhibited by the elevated pressures due to hot pressing (HP) and
pulsed electric current sintering (PECS). However, during post-densification thermal annealing
(in the absence of an externally applied confining pressure) decomposition reactions can generate
porosity (bloating) which in turn can degrade electrical, thermal, and mechanical properties [10 –
12, 14]. Changes in thermal and electrical conductivity are extremely important since the
efficiency of a thermoelectric device is a function of the dimensionless figure of merit, ZT,
which is written as

ZT 

S2


(5.2)

where  is the electrical conductivity, S is the Seebeck coefficient,  is the thermal conductivity,
and T is the temperature.
Since decreases with increasing porosity  14], low thermal conductivity is required
for a high ZT for thermoelectric materials (equation (2)). However, the electrical conductivity,
also decreases with increasing porosity [10]. Thus, one must consider the overall effect of

130

porosity on ZT to determine whether increasing porosity enhances or degrades the thermoelectric
properties of a material.
Calculations of the effect of nanopores on the thermal conductivity of Ge [15] and Si [16]
indicate dramatic decreases in  with nanoporosity. For nanoporous Ge with pore diameters =
1.0 nm and pore spacings = 0.7 nm, the calculated  was 180 times smaller than the bulk value
[15]. Similar decreases in  were calculated for Si [16] but as was the case for Ge [15] the
decreases in  become large only for extremely high values of volume fraction porosity, P (P ~
0.64 to 0.89) [16]. However, ZT may decrease with increasing nanoporosity, as noted by Lee,
Dresselhaus and co-workers [14] who state that “Porous nanograined materials have enhanced
Seebeck coefficient due to energy filtering effect and low thermal conductivity, which are
favorable for thermoelectric applications. However, the benefit is not large enough to overcome
the deficit in the electrical conductivity, so that a high sample density is necessary for
nanograined SiGe” [14]. Thus bloating generated porosity may degrade both ZT and mechanical
properties.

5.2 Experimental Procedure
The specimens were densified with HP or PECS with Ag0.86Pb19Sb1.0Te20 and
(Pb0.95Sn0.05Te)0.92(PbS)0.08- 0.055% PbI2 powders that were (i) crushed, ground, sieved, and
re-ground (CGSR), (ii) dry milled (DM), (iii) wet milled (WM) with hexane, or (iv) dry and then
wet milled with hexane (D/WM) (Table 5.1). A 53 micron sieve (Retsch, Newtown, PA) was
used for each powder processing technique in this study (Table 5.1). The hot pressed and PECS
specimens were pressed using the temperature-pressure-time profiles in Table 5.1 with a 22 mm
diameter graphite die. In this study, two separate sets of specimens were used to (i) directly
131

Table 5.1 The powder processing conditions and sintering parameters for the hot pressed (HP) and
pulsed electric current sintering (PECS) densified specimens processed using powders that were
crushed, ground, sieved, and re-ground (CGSR) powder was either (1) set aside for densification,
(2) dry milled (DM), (3) dry milled and then wet milled (D/WM), or (4) wet milled (WM). For
the post-densification anneals, the heating and cooling rates were 5 K/min and 2 K/min for
specimens prepared for SEM observation and RUS elasticity measurements, respectively.
Specimen
(composition)

Powder
Processing

Sintering Max
Temperature/ Pressure/
Time

Post-densification annealing
parameters
Temperature
Time

Bloating observed via SEM
a

HP-DM-01
HP-CGSRa
01

HP-D/WM-01
PECS-WM01
PECS-DM-01

673 K/74.4 MPa/90 min

723 K

4 hours

CGSR

673 K/74.4 MPa/90 min

973 K

6 hours

673 K/74.4 MPa/90 min

693 K

2 hours

823 K/60 MPa/20 min

823 K

2 hours

823 K /60 MPa/20 min

663 K, 823 K, 936 K

2 hours

D/WM
WM

d

DM

c

Bloating measured via RUS elasticity measurements
HP-D/WM723 K/74.4 MPa/120
c
D/WM
02a
min
HP-D/WM723 K/74.4 MPa/120
c
D/WM
02b
min
HP-D/WM723 K/74.4 MPa/120
c
D/WM
02c
min
HP-D/WM723 K/74.4 MPa/120
c
D/WM
01a
min
HP-D/WM723 K/74.4 MPa/120
c
D/WM
01b
min
723 K/74.4 MPa/120
d
HP-WM-01a
WM
min
723 K/74.4 MPa/120
d
HP- WM-01b
WM
min
PECS-D/WMc
823 K /60 MPa/20 min
D/WM
01
PECS-DM-02
623 K /60 MPa/20 min
DM
a

c
d
e

603 K, 633 K, 663 K,
693 K
543 K, 573 K, 603 K,
633 K, 663 K, 693 K
603 K, 633 K, 663 K,
693 K
603 K, 633 K, 663 K,
693 K

Annealed in flowing Ar atmosphere
Wet milled with hexane as the milling fluid
Wet milled with ethanol as the milling fluid
Annealed in flowing Ar (96%) – H2(4%) atmosphere
132

1 min
1 min
1 min
1 min

663 K, 693 K

1 min

663 K, 693 K

1 min

603 K, 633 K, 663 K,
693 K
603 K, 633 K, 663 K,
693 K
773 K

Specimen composition is Ag0.86Pb19Sb1.0Te20, all other specimens in the table are

(Pb0.95Sn0.05Te)0.92(PbS)0.08- 0.055% PbI2
b

b

DM

1 min
1 min
1 min

b
b
e
e

e
e
e
e
e
e
e
e
e

examine the microstructure of fracture surfaces using scanning electron microscopy (SEM) and
(ii) non-destructively measure the porosity dependent Young’s modulus using resonant
ultrasound spectroscopy (RUS) analysis (Table 5.1). Four SEM specimens were annealed at
temperatures ranging from 693 K to 973 K (Table 5.1) and one SEM specimen was successively
annealed at 663 K, 823 K, and 936 K (Table 5.1). The nine RUS specimens were successively
annealed for temperatures ranging from 543 K to 773 K (Table 5.1). Details of the RUS
experimental procedure are given elsewhere [12].

5.3 Results and Discussion
Using planetary milled powders, the mean grain sizes of the as-densified
(Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 specimens were 1 micron to 10 microns for both HP
and PECS processing [12, 17]. The mean grain size for the HP as-densified specimen was 20
microns starting from CGSR powders. Both the HP and PECS produced specimens that ranged
in density from about 0.92 to 0.97 with spherical or quasi-spherical pores at grain boundaries and
triple points, with submicron to 3 microns diameter pore sizes (Figures 5.1-5.3).
However, upon annealing bloating occurred (Figures 5.1 and 5.2) for the as-densified HP
specimens processed from powders that were (i) CGSR (Figure 5.1), (ii) DM (Figure 5.1), and
(iii) D/WM (Figure 5.2). The as-densified PECS specimens processed from WM powders
bloated (Figure 5.2). Bloating in both the HP and PECS specimens generated spherical or quasispherical pores along grain boundaries with pore diameters ranging from 1 micron to 20 microns
(Figures 5.1 and 5.2). Also, the PECS PbTe-PbS WM and HP LAST CGSR specimens had
lenticular pores from 10 microns in length and 1 micron wide to about 30 microns in length and
5 microns wide (Figures 5.1 and 5.2).
133

Fig. 5.1 The as-densified fracture surfaces of (a) HP-DM-01 and (c) HP-CGSR-01 do not show
bloating. Annealing (b) HP-DM-01 at 723 K for 4 hours and (d) HP-CGSR-01 at 973 K for 6
hours resulted in bloating as evidenced by the increased porosity of the internal fracture surfaces.
All annealing was performed in flowing Ar.

134

Fig. 5.2 The as-densified fracture surfaces of (a) HP-D/WM-01 and (c) PECS-WM-01 do not
show bloating. Annealing (b) HP-D/WM-01 at 693 K for 2 hours and (d) PECS-WM-01 at 823
K for 2 hours resulted in bloating as evidenced by the increased porosity of the internal fracture
surfaces. All annealing was performed in flowing Ar or Ar (96%)-H2 (4%).

135

Fig. 5.3 In contrast to the annealing behavior depicted in Figures 5.1 and 5.2, the (a) as-densified
PECS-DM-02 did not bloat after annealing at (b) 663 K for 2 hours, (c) 823 K for 2 hours, and
(d) 936 K for 2 hours. All annealing was performed in flowing Ar (96%)-H2 (4%).

136

After annealing from two to six hours at temperatures from 693 K to 973 K (Table 5.1),
the areal number density of pores increased by 10 to 30 fold compared to the pore areal density
on the fracture surfaces of the as-densified specimens of HP specimens from powder processed
by CGSR (Figure 5.1), DM (Figure 5.1), and D/WM (Figure 5.2) and PECS from powder
processed by WM (Figure 5.2). The series of anneals from 543 K to 693 K on hot pressed
specimen HP-D/WM-02b (Table 5.1) induced surface blistering that ranged from 0.5 mm to 1
2

mm in diameter and internal porosity that consisted of six lenticular pores per 12,000 m that
were about 20 microns long and 5 microns wide. In contrast, the PECS densified specimens
fabricated using DM powders did not bloat (Figure 5.3) or blister when annealed for 2 hours at
663 K, 823 K, and 936 K (Table 5.1).
For the nine as-densified RUS specimens, the mass and volume were measured before
and after each post-densification anneal to monitor the change in density. Before postdensification annealing, P = PR where PR ranged from 0.03 to 0.08. Following postdensification anneals PB increased as temperature increased. For example, after the 603 K postdensification anneal, P ranged from 0.04 to 0.11 and after the 693 K anneal, P ranged from 0.05
to 0.22 (Figure 5.4). For the RUS analysis, the exception was the PECS-DM-02 specimen which
did not bloat after a series anneals, including a 773 K post-densification anneal (Figure 5.4,
Table 5.1). The decrease in the Young’s modulus, E, with increasing porosity is consistent with
2

equation (1) (Figure 5.4), where the least-squares fit of E versus P (equation (1)) yielded an r =
0.990, bPE = 1.33 ± 0.02 and ED = 56.17 ± 0.13 GPa for the 9 as-densified and 32 postdensification annealed elastic moduli measurements.

137

Fig. 5.4 The bloating (Figures 5.1 and 5.2) or lack of bloating (Figure 5.3) observed in the SEM
study is also evident in the RUS measurements of Young’s modulus, E, versus volume fraction
porosity, P. For the nine as-densified HP and PECS specimens along with the 32 annealing
measurements on the same nine specimens (Table 5.1), as P increased, E decreased. The filled
symbols and open symbols represent the E values for the as-densified and annealed specimens,
respectively. Equation (5.1), widely used to describe the E versus P behavior for brittle
2
materials [10, 11], also fits the E versus P behavior well (r = 0.990) for the 41 RUS
measurements included in this study. The dashed line represents the least-squares fit to equation
(5.1).

138

In order to compare the value of the Young’s modulus, ED, found from equation (1) to
the literature, we can use values of the aggregate Young’s modulus calculated from single crystal
PbTe data where E was 58.08 GPa [18] or 56.95 GPa [19]. Thus the ED value of 56.17 ± 0.13
GPa that was calculated from the least-squares fit of equation (1) to this study’s modulusporosity data for (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 specimens is within approximately
two percent of the mean of the two literature values for PbTe [18,19] listed above.
Groza et al. found that the electrical discharge that is intrinsic to the PECS process
cleaned the oxide surface layers from the AlN particles during sintering [20]. In this study, the
PECS densification process may have removed contaminating surface layers from the powder
processed (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 particles. This surface cleaning may have
in turn removed the source of a solid phase decomposition reaction, thus allowing the densified
PECS specimens to be annealed up to 936 K without bloating (Table 5.1, Figure 5.3). Although
the dry milled PECS specimens did not bloat (Figure 5.3), in contrast the wet milled PECS
specimens did bloat during post-densification anneals (Figure 5.2d). Perhaps the hexane or
ethanol used during the wet milling (Table 5.1 footnotes) left a carbonaceous residue which was
not entirely removed by the PECS process. Such a residue could decompose during postdensification annealing, causing bloating (Figure 5.2d).

5.4 Summary and Conclusions
As-densified specimens fabricated by both PECS and HP for each of the four powder
processing modes (CGSR, DM, WM, and D/WM) gave dense specimens with spherical porosity
confined to grain boundaries. Post-densification anneals resulted in bloating (P increased) for all
139

HP specimens. For the PECS fabrication, bloating occurred for the specimens processed with
WM and D/WM powders. Only the PECS DM specimens did not bloat upon annealing, perhaps
due to the intrinsic cleaning of the powder particle surfaces during sintering [20].
Acknowledgements
This research was supported by the Office of Naval Research, Grant N00014-08-1-0613 and the
Department of Energy, “Revolutionary Materials for Solid State Energy Conversion Center,” an
Energy Frontiers Research Center funded by the U.S. Department of Energy, Office of Basic
Energy Sciences under award number DE-SC0001054. Ed Timm of the Mechanical Engineering
Department, Michigan State University assisted the authors with hot pressing and cutting the
specimens.

140

REFERENCES

141

5.5 References

[1] F. Ren and E. D. Case, E. J. Timm, M. D. Jacobs and H. J. Schock, Weibull analysis of the
biaxial fracture strength of a cast p-type LAST-T thermoelectric material, Philos. Mag.
Lett., 86 673 – 682 (2006)
[2] M.W. Barsoum, Fundamentals of Ceramics, ed. by B. Cantor and M.J. Goringe (IOP
Publishing, London, 2003)
[3] N.M.P. Low, Formation of cellular-structure glass with carbonate compounds and natural
mica powders, J. Mater. Sci. 16 800-808 (1981)
[4] P. Colombo, Conventional and novel processing methods for cellular ceramics, Phil. Trans.
R. Soc. A, 364 109-124 (2006)
[5] D. Holz, S. Wu, S. Scheppokat, N. Claussen, Effect of processing parameters on phase and
microstructure evolution in RBAO ceramics, J. Am. Ceram. Soc., 77, 2509-17 (1994)
[6] M. H. O'Brien, O. Hunter, Jr., E. D. Case, Mechanical effects of thermal cycling on United
State and Australian Synroc-B, J. Mater. Sci. Lett., 4, 367-369 (1985)
[7] H. Wen, Y. Zhao, Z. Zhang, O. Ertorer, S. Dong, E. J. Lavernia, The influence of oxygen
and nitrogen contamination on the densification behavior of cryomilled copper powders
during spark plasma sintering, J. Mater. Sci., 46, 3006–3012 (2011)
[8] V.N. Antsiferov, V.B. Kul’met’eva, S.E. Porozova, B.L. Krasnyi, V. P. Tarasovskii, A.B.
Krasnyi, Russ. Application of mechanochemical activation in production of zircon
ceramics, J. Non-Ferrous Metals 51, 82–187 (2010)
[9] L. Stoch, Explosive thermal dehydration of solids, J. Thermal Analy., 37, 1415-1429 (1991)
[10] R.W. Rice, Porosity of Ceramics (Marcel Dekker, New York, 1998)
[11] T.P. Hoepfner, E.D. Case, The influence of the microstructure on the hardness of sintered
hydroxyapatite, Ceram. Int., 29 (2003) 699–706
[12] J.E. Ni, F. Ren, E.D. Case, E.J. Timm, Porosity dependence of elastic moduli in LAST
(Lead-antimony-silver-tellurium) thermoelectric materials, Mater. Chem. Phys, 118, 459–
466 (2009)
[13] J. Androulakis, C-H Lin, H-J Kong, C. Uher, C-I Wu, T. Hogan, B.A. Cook, T. Caillat,
K.M. Paraskevopoulos, M.G. Kanatzidis, Spinodal decomposition and nucleation and
growth as a means to bulk nanostructured thermoelectrics: Enhanced performance in Pb1xSnxTe-PbS, J. Am. Chem. Soc. 129, 9780-9788 (2007)

142

[14] H. Lee, D. Vashaee, Z. Wang, M.S. Dresselhaus, Z.F. Ren, G. Chen Effects of nanoscale
porosity on thermoelectric properties of SiGe, J. Appl. Phys. 107, 094308, (2010)
[15] Lee J.H., Grossman, J.C, Thermoelectric properties of nanoporous Ge, Appl. Phys. Lett. 95,
013106 (2009)
[16] Lee J.H., Grossman, J.C, J. Reed, G. Galli, Lattice thermal conductivity of nanoporous Si:
Molecular dynamics study, Appl. Phys. Lett. 91, 223110 (2007)
[17] J.E. Ni, E.D. Case, K.N. Khabir, R.C. Stewart, C.I. Wu, T.P. Hogan, E.J. Timm, S.N.
Girard, M.G. Kanatzidis, Room temperature Young's modulus, shear modulus, Poisson's
ratio and hardness of PbTe-PbS thermoelectric materials, Mat. Sci. Eng. B, 170, 58–66
(2010)
[18] B. Houston, R.E. Strakna, H.S. Belson, Elastic constants thermal expansion and Debye
temperature of lead telluride, J. Appl. Phys., 39, 3913 - 3917 (1968)
[19] N.G. Einspruch, R.J. Manning, Elastic constants of compound semiconductors ZnS, PbTe,
GaSb, J. Acoust. Soc. Am., 35, 215 - 216 (1963)
[20] J.R. Groza, S.H. Risbud, K. Yamazaki, Plasma activated sintering of additive-free AlN
powders to near-theoretical density in 5 minutes, J. Mater. Res., 7, 2643 - 2645 (1992)

143

6.0 Fracture mode, microstructure, and temperature-dependent elastic moduli for
thermoelectric composites of PbTe-PbS with SiC nanoparticle additions
1

1

1

2

2

Jennifer E. Ni , Eldon D. Case , Robert D. Schmidt , Chun-I Wu , Timothy Hogan , Rosa
3

3

4

Trejo , Edgar Lara-Curzio , Steven N. Girard , Mercouri G. Kanatzidis
1

4

2

Chemical Engineering and Materials Science and Electrical and Computer Engineering,
Michigan State University, East Lansing, MI, 48824
3
High Temperature Materials Laboratory, Oak Ridge National Laboratory, Oak Ridge TN 37380
4

Department of Chemistry, Northwestern University, Evanston, IL, 60208

Abstract
Twenty-six (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 –SiC nanoparticle (SiCnp)
composite thermoelectric specimens were hot pressed or pulsed electric current sintered (PECS)
from powders that were dry milled, wet milled, or a combination of dry and wet milled. The
Young’s modulus, E, and Poisson’s ratio, ν, were measured by resonant ultrasound spectroscopy
(RUS) as a function of temperature, T, from room temperature to 663 K. Also, porosity-induced
bloating was monitored (1) indirectly through E versus T measurements (2) directly via
observation of fracture surfaces (scanning electron microscopy) or (3) by measurements of
volume change. For hot pressed specimens, an observed hysteresis in E versus T for T > 603 K
was attributed to bloating. For two hour post-densification anneals up to 936 K, seven out of
seven specimens densified by PECS from dry milled powders showed no observable bloating,
but post densification annealing increased the porosity of three hot pressed and three PECS
specimens, likely via bloating. SiCnp additions (1 to 3.5 vol %) changed the fracture mode from
intergranular to transgranular, and inhibited grain growth. SiCnp additions limited bloating in
the wet milled PECS specimens yet led to limited bloating in the dry milled specimens at high
temperatures.
Keywords: Elastic properties; Porosity; Thermoelectric; Nanocomposites
144

6.1.0 Introduction
Thermoelectric (TE) materials undergo numerous thermal cycles during waste heat recovery
applications. However, it has been reported recently that thermoelectric materials, including
CoSb3-based n-type skutterudite, FeSb3-based p-type skutterudite [Schmidt 2012, Schmidt DOI
2012] and PbTe-PbS [Ni DOI 2012 ] can undergo bloating at elevated temperatures, where
bloating refers to a process observed in a variety of solids in which there is a temperaturedependent generation of pores within a dense specimen that is caused by internal gas evolution
[Oppenheimer 2010] and/or solid or liquid decomposition reactions [Low 1981, Colombo 2006,
O'Brien 1985, Wen 2011] during heating. Such an instability of microstructure in a
thermoelectric could lead to porosity-dependent decreases in thermal and electrical conductivity
[Jung 2011, Lee 2010, Alvarez 2010] which in turn could affect the figure of merit, ZT, where
ZT 

S2eT
k

(6.1)

where S is the Seebeck coefficient, e is the electrical conductivity, T is the temperature and k is
the thermal conductivity. In addition to e and k, other porosity-dependent thermal and
electrical properties include thermal diffusivity [Park 2009], the dielectric constant [Geis 2002,
Hoepfner 2002, Yang 2010] and dielectric breakdown voltage [Geis 2002, Kishimoto 1991]. In
addition, porosity-dependent mechanical properties include fracture strength [Park 2009, Hu
2010], internal friction [Wang 2000], fracture surface energy [Vandeperre 2004, Case 1981],
hardness [Hoepfner 2003], Young’s modulus [Ni 2009, Ren 2009 HA] and shear modulus [Ni
2009, Ren 2009 HA]. Since porosity affects a broad spectrum of physical properties, pores

145

generated by bloating have the potential to significantly affect the performance and mechanical
integrity of thermoelectrics.
(Pb0.95Sn0.05Te) 0.92(PbS)0.08-0.055% PbI2 has a maximum ZT of 1.5 at 642 K
[Androulakis 2007] making it a candidate for waste-heat recovery applications. For TE materials
used in harvesting waste energy, the temperature-dependent Young’s modulus, E(T), Poisson’s
ratio, (T), and thermal expansion, (T), are required for both analytic and finite element
analysis of stress, , induced by thermal gradients or thermal transients, such that
(T) 

E(T)(T)T
1  (T)

(6.2)

where T is the temperature gradient or the temperature change experienced during a thermal
transient.
In this study, the temperature-dependent Young’s modulus, E(T), shear modulus, G(T), and
Poisson’s ratio, (T), of the (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 –SiC nanoparticle
(SiCnp) composites were measured using resonant ultrasound spectroscopy (RUS), from room
temperature to a maximum of 663 K. In addition to the E(T) and (T) measurements, bloating
was monitored for twenty-six PbTe-PbS-SiC nanocomposite specimens (1) indirectly by
analyzing the hysteresis in E(T) when it is present (Section 6.4.3.2), (2) directly by measuring
the volume change after post-densification annealing using micrometers (Section 6.4.2.3), or (3)
directly by observing the fracture surfaces (scanning electron microscopy, SEM) (Section
6.4.2.4).
Also in this study, a combination of dry milling and pulsed electric current sintering (PECS)
successfully limited bloating in PbTe-PbS after post-densification annealing for two hours at

146

temperatures up to 936 K. A maximum annealing temperature, Tann max, of 936 K was selected
since Tann max exceeds the likely maximum use temperature for PbTe-PbS (8%) [Androulakis
2007] by roughly 200 K to 300 K. Also, the addition of SiC nanoparticles changed the fracture
mode and inhibited grain growth.

6.2.0 Background: Nanostructures in thermoelectric materials
Thermoelectric nanocomposites are typically formed (i) by precipitation or spinodal
decomposition from the bulk [Johnsen 2011, Kanatzidis 2010] or (ii) by the addition of a powder
nanoparticle phase during powder processing [Li 2006, Liu 2011, Li 2011, Xiong 2009]. The
nanostructures reduce the lattice thermal conductivity by phonon scattering, which in turn
increases the figure of merit, ZT (Eq. (6.1)) [Johnsen 2011, Kanatzidis 2010]. For example, ZT
improved by 10 % to 36 % for thermoelectrics with nanoparticle additions of 0.1 vol % [Liu
2011] and 0.24% SiC [Li 2006], 0.1 vol % Al2O3 [Li 2011], and 0.4 vol% TiO2 [Xiong 2009].
In general, nanoparticles also affect mechanical properties such as fracture toughness in
nanocomposite WC–ZrO2–Co [Mukhopadhyay 2010], carbides [Karakasidis 2011, Voevodin
2000], borides [Karakasidis 2011, Voevodin 2000] and oxides [Karakasidis 2011, Voevodin
2000]. Nanoparticle inclusions from 1.0 vol% [Karakasidis 2011] to 10.0 vol% [Mukhopadhyay
2010] either increase or decrease the fracture toughness, KC, of brittle materials has been
attributed to a transition of the fracture mode from intergranular to transgranular [Yamada 2010].
For thermoelectric materials in particular, SiCnp nanoparticle additions of 0.24 vol% to
Bi2Te3 increased ZT (Eq. (6.1)) by 18% [Li 2006]. Also, additions of 0.1 vol% SiCnp to

147

Bi0.5Sb1.5Te3 increased the ZT, fracture toughness and hardness, each by roughly 10% [Liu
2011]. Zhao et al. [Zhao 2008] added from 0.1 vol% to 1.2 vol% SiCnp to PECS-processed
Bi2Te3, resulting in maximum increases of 30% in E, a 28% in hardness, and an 18 % in fracture
toughness, although ZT decreased for the SiCnp loadings that gave the optimal mechanical
properties. However, despite the numerous studies focused on the effect of nanostructures on the
transport properties of thermoelectrics, the work by Liu [Liu 2011] and Zhao [Zhao 2008] are the
only studies currently in the literature that deal with the effects of nanoparticle additions on
mechanical properties of thermoelectrics.

6.3.0 Experimental Procedure
Cast (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 (PbTe-PbS) ingots were fabricated from
PbI2, Pb, Te, SnTe and PbS powders, each of which were at least 99.99% pure [Ni 2010]. The
cast ingots were crushed and ground using a mechanical mortar and pestle until all the powders
passed through a 53-micron sieve [Ni 2010, Pilchak 2007]. The powder size was then further
reduced using a planetary mill (PM100, Retsch, Newtown, PA) by (i) dry milling, (ii) wet
milling with ethanol or (iii) dry and wet milling with hexane (Table 6.1). All powder processing
took place inside a glove box under an argon atmosphere.
Composite thermoelectric specimens were fabricated using 1.0 to 3.5 volume percent
nanoparticles of 95% pure beta SiC (Nanostructured & Amorphous Materials, Inc., Houston,
TX), with a vendor-specified average particle size of 50 nm to 60 nm. The milled PbTe-PbS
powders and SiCnp powders were first homogenously mixed by planetary milling for three hours

148

Table 6.1 The processing conditions for twenty-six (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2
specimen included in this study. Using resonant ultrasound spectroscopy, the temperaturedependent elastic moduli (E(T)) were measured for twelve specimens and the room-temperature
elastic moduli as a function of porosity (E(P)) were measured for four specimens. The
microstructure (M) was examined using scanning electron microscopy for 15 specimens.
Powder
Processing
Technique
D/WM (H)
DM
DM
DM

Sintering Max
Temperature/ Pressure/
Time
823 K /60 MPa/20 min
623 K /60 MPa/5 min
573 K /60 MPa/5 min
493 K /60 MPa/5 min

D/WM (H)

723 K/74.4 MPa/120 min

E(T) , M

0.0

D/WM (H)

723 K/74.4 MPa/120 min

E(T)

HP-53 #C

0.0

D/WM (H)

723 K/74.4 MPa/120 min

E(T)

HP-54 #1

0.0

D/WM (H)

723 K/74.4 MPa/120 min

E(T) , M

HP-54 #2

0.0

D/WM (H)

723 K/74.4 MPa/120 min

E(T) ,

HP-55 #1

0.0

WM (E)

723 K/74.4 MPa/120 min

E(T) , M

HP-55 #2

0.0

WM (E)

723 K/74.4 MPa/120 min

E(T)

PECS-01

0.0
0.0

D/WM (H)

823 K /60 MPa/20 min

E(T)

0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.0

DM
WM (E)
D/WM (H)
DM
DM
DM
DM
DM
DM
D/WM (H)

823 K /60 MPa/22 min
823 K /60 MPa/20 min
673 K /60 MPa/20 min
823 K /60 MPa/20 min
673 K /60 MPa/20 min
723 K /60 MPa/20 min
723 K /60 MPa/20 min
823 K /60 MPa/20 min
823 K /60 MPa/20 min
823 K /60 MPa/20 min

E(T)
M
M
M
M
M
M
M
M

2.0
2.5
3.0
3.5

DM
DM
DM
D/WM (H)

673 K /60 MPa/20 min

Specimen
Label

SiCnp
Vol%

PECS-05
PECS-32
PECS-33
PECS-35
HP-53 #A

0.0
0.0
0.0
0.0
0.0

HP-53 #B

PECS-06S
PECS-02
PECS-10
PECS-11
PECS-15
PECS-20
PECS-23
PECS-25
PECS-27
PECS -06

a

PECS-18
PECS-16
PECS-17
a
PECS-07
a

Measurement
technique

673 K /60 MPa/20 min
673 K /60 MPa/20 min
823 K /60 MPa/20 min

E(P)
E(P)
E(P)
E(P)
b

b
b

b

b

b

b
b
b

b

E(T) , M
b

E(T) , M
M
M
b
E(T)

Disc shaped specimen. All other specimens in the study were parallelepipeds.

b

Room-temperature elastic moduli for these specimens was reported in a previous paper, this
study reports on the temperature-dependent elastic moduli

149

at 150 rpm then densified (Table 6.1) using either hot pressing, HP, (HP200, Thermal
Technology LLC, Santa Rosa, CA) or pulsed electric current sintering, PECS, (SPS 10-4,
Thermal Technology LLC, Santa Rosa, CA). Further details of the specimen fabrication
processes are available elsewhere [Ni 2010, Ren 2009 LAST, Ni DOI 2012].
The specimen mass and dimensions were measured using a micrometer and an electronic
balance to calculate the mass density. The micrometer and electronic balance were calibrated
using blocks and test gauges, respectively [Ni DOI 2012].
Using a non-destructive method, resonant ultrasound spectroscopy (RUS) [Ren 2009 LAST,
Ren 2008, Migilori 1997], the Young's modulus, E, shear modulus, G, and Poisson's ratio,
were determined at room temperature and high temperature. The elastic moduli were
calculated using commercially available software packages (RUSpec and CylModel, Quasar
International, Inc., Albuquerque, NM) from the dimensions, mass density and resonant
frequencies of the specimen. Further details of the RUS procedure are available elsewhere [Ren
2009 LAST, Ren 2008].
The RUS mechanical resonance spectra were taken at 30 K temperature intervals from room
temperature to maximum temperatures of 543 K, 603 K, or 663 K. The heating and cooling rates
were 5 K/minute for each thermal cycle.

Both the as-densified specimens and the post-

densified specimens were annealed in flowing argon for two hours at temperatures from 693 K to
936 K. The temperature-dependent changes in specimen dimension were accounted for using the
-6

-1

coefficient of thermal expansion of 21.5 x 10 K obtained from dilatometric and x-ray
diffraction measurements for PbTe-PbS specimens with chemical compositions that were
nominally identical to the specimens in this study [Ni to be submitted].
SEM micrographs of the internal fractured surfaces were used to (1) monitor the changes
150

in porosity due to bloating and (2) measure average grain size (Table 6.1). The surface areal
fraction of pores was approximated from the number of pores and the mean pore area determined
from SEM micrographs. The average grain size was determined using the linear intercept
method [Fullman 1953, Ni 2010].
In order to determine the effect of SiCnp on the grain growth of the PbTe-PbS matrix due to
post-densification annealing (Section 6.4.2.3), we first determined a statistically sufficient
number of micrographs per specimen, N, to reduce the uncertainty in grain size measurement to
the point that grain growth trends (if any) were apparent. In order to calculate the sample size,
N, a grain size, GS, distribution must be determined. For both metallic and ceramic
polycrystalline materials a lognormal grain size distribution is often reported [Zhu 2005,
Berbenni 2007, Betz 2000]. Assuming a lognormal distribution for the PbTe-PbS matrix in our
PbTe-PbS-SiCnp composites we determined N using a lognormal 95% confidence interval for
the mean GS [Limpert 2001]
 * *2
 2 
 GS s , GS*  s*    (LL, UL)







(6.3a)

where
1
N
1 N
  N
*
GS  exp   log GS i     GS i 

N
 
 i 1
  i 1


(6.3b)

and
1


2 2
  1 N   GS  
i
s *  exp 
 log *  
  N 1
  GS  

i 1 








.





(6.3c)

151

Table 6.2a A comparison of the as-densified specimens mean grain sizes, GSDNS, for different
powder processing (dry milling (DM), wet milling (WM), and dry and wet milling (D/WM)) and
sintering techniques (hot pressed (HP) and PECS-processed). The difference in powder
processing is the likely cause of the factor of two difference between the four wet milled hot
pressed and PECS processed specimens and six dry milled PECS-processed specimens. The
PECS specimens were sintered at the stated temperature for 20 minutes. For the as-densified
dry milled PECS-processed specimens, the mode-mixity was calculated as the areal fraction of
the transgranular grains appearing on a specimen’s fracture surface. In general, as the mode
mixity increased to 1.0, transgranular fracture dominates and the fracture toughness increases.
Specimen
Label

SiCnp
additions

HP-53
HP-54
HP-55
PECS-01
PECS-15
PECS-20
PECS-27
PECS-18
PECS-16
PECS-17

0.0 vol%
0.0 vol%
0.0 vol%
0.0 vol%
0.0 vol%
0.0 vol%
0.0 vol%
2.0 vol%
2.5 vol%
3.0 vol%

Powder
Processing
Technique
D/WM (H)
D/WM (H)
WM (E)
D/WM (H)
DM
DM
DM
DM
DM
DM

Sintering
temperature

GSDNS
(microns)

Modemixity

Reference

723 K
723 K
723 K
823 K
673 K
723 K
823 K
673 K
673 K
673 K

1.6 ± 0.1
1.6 ± 0.1
1.7 ± 0.2
2.1 ± 0.2
4.9 ± 0.4
4.8 ± 0.2
4.9 ± 0.3
4.7 ± 0.2
4.7 ± 0.3
4.5 ± 0.2

0.11
0.10
0.12
0.15
0.18
0.14
0.13
0.91
0.95
0.96

This study
This study
This study
This study
This study
This study
This study
This study
This study
This study

152

Table 6.2b Mean grain sizes of the as-densified and the annealed specimens are designated by
GSDNS and GSANN, respectively. For dry milled PECS-processed specimens with 0.0 vol%
SiCnp, the GSANN increased in three specimens after post-densification anneals up to 936 K.
However, the inclusion of SiCnp limited grain growth in three specimens during postdensification anneals up to 873 K.
Sintering
Specimen
Annealing
SiCnp
GSDNS
GSANN GSANN/
a
Label
additions temperature temperature (microns) (microns) GSDNS
PECS-15 0.0 vol%
673
723 K
4.9 ± 0.4 5.9 ± 0.2
1.2
PECS-20 0.0 vol%
723
723 K
4.8 ± 0.2 5.9 ± 0.4
1.2
PECS-27 0.0 vol%
823
723 K
4.9 ± 0.3 5.9 ± 0.2
1.2
PECS-15 0.0 vol%
673
873 K
4.9 ± 0.4 6.4 ± 0.1
1.3
PECS-20 0.0 vol%
723
873 K
4.8 ± 0.2 6.4 ± 0.1
1.3
PECS-27 0.0 vol%
823
873 K
4.9 ± 0.3 6.6 ± 0.1
1.3
PECS-15 0.0 vol%
673
936 K
4.9 ± 0.4 6.9 ± 0.1
1.4
PECS-20 0.0 vol%
723
936 K
4.8 ± 0.2 7.0 ± 0.2
1.5
PECS-27 0.0 vol%
823
936 K
4.9 ± 0.3 6.9 ± 0.1
1.4
PECS-18 2.0 vol%
673
723 K
4.7 ± 0.2 4.7 ± 0.2
1.0
PECS-16 2.5 vol%
673
723 K
4.7 ± 0.3 4.6 ± 0.2
1.0
PECS-17 3.0 vol%
673
723 K
4.5 ± 0.2 4.7 ± 0.2
1.0
PECS-18 2.0 vol%
673
873 K
4.7 ± 0.2 5.4 ± 0.2
1.1
PECS-16 2.5 vol%
673
873 K
4.7 ± 0.3 5.2 ± 0.1
1.1
PECS-17 3.0 vol%
673
873 K
4.5 ± 0.2 5.3 ± 0.1
1.2
a

All specimens in this table were sintered at a maximum pressure of 60 MPa for 20 minutes

153

We proposed that a conservative estimate of the GS range of the PbTe-PbS matrix was 1 micron
to 15 microns, the lower limit, LL, and upper limit, UL, respectively (Eq. (6.3a)). Ten ‘pilot
studies’ conducted using randomly generated grain sizes (MatLab) between the LL and UL (Eqs.
6.3a – 6.3c) [CSTAT] determined that the statistically sufficient number of micrographs per
specimen, N, was five. Thus, for every GS measurement reported in this study (Table 6.2a and
6.2b), five micrographs per specimen were analyzed at the same magnification (3000x).

6.4.0 Results and Discussion
The key results presented in this study are: (1) the feasibility of tailoring the processing
procedure to inhibit post-densification bloating and (2) characterizing mechanical properties,
including elasticity measurements. Elasticity data is needed for designers to calculate stresses
and strains in thermoelectric elements (Eq. (6.2)), which arise, for example, due to thermal
transients incurred in waste heat recovery applications. Also, observed changes in the fracture
mode and grain growth behavior are linked to both processing and mechanical behavior.

6.4. Results and discussion
6.4.1.1 Room temperature elasticity measurements of as-densified specimens
Room temperature RUS measurements of Young’s modulus, E, shear modulus, G, and
Poisson’s ratio, ν, were performed for three hot-pressed and six PECS-processed specimens
(Figs. 6.1a and 6.1b). Fig. 6.1 includes data from two types of porosity (i) residual porosity PR,
from incomplete sintering of the as-densified specimens and (ii) porosity PB, generated by
bloating during post-densification annealing, where the total porosity P = PR + PB. The

154

Table 6.3 The least-squares fitting parameters EP=0 and bPE (Eq. (6.4a)) and GP=0 and bPG (Eq.
(6.4b)) to the Young’s modulus and shear modulus to the four as-densified and four postdensified specimens in Figure 6.1.
Fit to Eq. (6.3a)

Fit to Eq. (6.3b)
2

2

EP=0

bPE

r

GP=0

bPG

r

56.0 ± 0.4

1.31 ± 0.06

0.990

22.6 ± 0.2

1.31 ± 0.07

0.984

155

E and G (GPa)

(a)

60

After 693 K post-densification anneal
As-densified
HP-53 #B [Ni 2011]
PECS-32 [This study]
HP-54 #1 [Ni 2011]
PECS-33 [This study]
HP-55 #2 [Ni 2011]
PECS-35 [This study]
PECS-01 [Ni 2011]
PECS-05 [This study]

50

E
20

G

15
0.05

0.10

0.15

0.20

Volume fraction porosity
Fig 6.1

156

0.25

(b)

0.30

Poisson's Ratio

Fig. 6.1 (cont’d)

0.25

As-densified
After 693 K post-densification anneal
PECS-32 [This study]
HP-53 #B
PECS-33 [This study]
HP-54 #1
PECS-35 [This study]
HP-55 #2
PECS-05 [This study]
PECS-01

0.20
0.05

0.10

0.15

0.20

0.25

Volume fraction porosity
Fig. 6.1 (cont’d) The porosity dependence of the (a) Young’s modulus, E, shear modulus, G, and
(b) Poisson’s ratio for four as-densified PECS-processed specimens (filled symbols) and four
thermally annealed hot pressed and PECS-processed specimens with 0.0 vol% SiCnp. Each
individual specimen is represented by the same symbol in figure (a) and (b). The least-squares
fit to Eq. (6.4a) to these 8 specimens is represented by the dashed line. The solid line and dotted
lines represent the average and standard deviation in Poisson’s ratio, respectively.

157

porosity-dependent E and G behaviors for P = PR + PB are consistent with the empirical E and G
versus porosity relationships (Table 6.3) [Rice 1998],

E(P)  E P  0 exp(b PE P)

(6.4a)

G(P)  G P  0 exp(b PG P)

(6.4b)

where PB = 0 for specimens that have not bloated. Four as-densified specimens, sintered via
PECS from 493 K to 823 K had residual porosities, PR, of 0.03 < PR < 0.21 (Fig. 6.1). An
additional four specimens were annealed to 693 K [Ni DOI 2012].
In contrast to E and G, Poisson’s ratio, ν, was relatively insensitive to porosity (Fig. 6.1b),
with a mean and standard deviation value 0.236 ± 0.006 over the entire range of P included in
this study (Fig. 6.1b). These results are consistent with a review by Boccaccini in which
Poisson’s ratio is independent of P for a number of brittle materials with ν near 0.25 [Boccaccini
1994].

6.4.1.2 Microstructure of as-densified fracture surfaces
The as-densified HP and PECS-processed PbTe-PbS specimens fracture surfaces included
residual spherical or quasi-spherical pores from submicron to 3 microns in diameter located at
grain boundaries and triple points (Figs. 6.2 and 6.3).
The mean grain size of the hot pressed and the PECS processed specimens fabricated from
milled and dry/wet milled powders was 1.6 ± 0.2 microns (Table 6.2a), which is about 2.5 times
smaller than the mean grain size of 4.5 ± 0.2 to 4.9 ± 0.4 microns for the specimens densified via
PECS from powders that were dry milled only (Table 6.2a). This difference between the mean
grain sizes of the DM and WM specimens is likely due the smaller grindability limit for wet

158

Fig. 6.2 The as-densified and post-densification fracture surfaces of (a, b) D/WM PECS-10, (c,
d) DM PECS-20 and (e, f) DM PECS -18 (with 2.0 vol% SiCnp). Few pores are evident in the
SEM micrographs of the as-densified fracture surfaces. Annealing at 936 K for 2 hours resulted
in bloating for (b) D/WM PECS-10 and (f) DM PECS -18 (with 2.0 vol% SiCnp) specimens as
evidenced by the increased porosity of the internal fracture surface while, in contrast, the (d) DM
PECS-20 specimen did not bloat after annealing under identical conditions.

159

Fig. 6.3 The (a) as-densified and (b) post-densification fracture surfaces of PECS-10. After postdensification annealing to 936 K for 2 hours, long lenticular pores were observable on the fresh
fracture surface of D/WM PECS-10.

160

Fig. 6.4 The (a) fracture surfaces of the specimen without added SiCnp, PECS-15, exhibits a
much higher fraction of intergranular fracture than (b) the specimen with 2.5 vol% SiCnp, PECS16 (Table 6.2a). Both specimens were PECS-processed at 673 K for 20 minutes using a pressure
of 60 MPa.

161

milled powders compared to dry milled powders [Hall 2l09].
The literature shows that fine-grained brittle materials can be densified using short PECS
processing times, however during PECS processing grain growth may not be a strong function of
the sintering temperature [Xu 2012, Yoshida 2011, Teber 2012, Kim 2007]. For example,
Terber sintered TiC specimens via PECS for five minutes at T between 1623 K and 1923 K with
a resulting mean grain size range from only 0.43 microns to 0.76 microns [Teber 2012].
Consistent with the Teber et al. results, in this study the mean grain sizes for the six as-densified
DM PECS composite specimens (with 0.0, 2.0, 2.5, and 3.0 vol% SiCnp) were essentially
independent of the sintering temperature (Table 6.2a) when sintered at T from 673 K to 823 K.
Also, the mean grain size was independent of the volume fraction of SiCnp.
The fracture mode observed for the PbTe-PbS-SiCnp was a function of the SiCnp loading. For
specimens with 0 vol% SiCnp the fracture mode was predominantly intergranular (Fig. 6.4a)
while for specimens that included SiCnp additions, the fracture mode was mostly transgranular
(Table 6.2b and Fig. 6.2b). The effect of SiCnp additions on the fracture mode will be discussed
in the following section.

6.4.1.3 Mechanical property implications of SiCnp additions
In this study, the fracture mode shifted from intergranular to transgranular as a function of the
volume fraction loading of SiCnp (Table 6.2a and Fig. 6.4). Adding nanoparticles to brittle
materials has been observed to result in similar dramatic shifts in the fracture mode that are
associated with changes in fracture toughness, KC, where KC may either increase [Kawabata
162

1977, Mukhopadhyay 2010, Karakasidis 2011] or decrease [Karakasidis 2011, Jang 2010,
Yamada 2010].
Vickers indentation was used to attempt to directly determine whether or not the observed
change in fracture mode was accompanied by a change in KC for the PbTe-PbS-SiCnp specimens
included in this study. However, Vickers indentation loads of 2.94 N and 4.90 N failed to
produce radial cracks, a 9.81 N load generated radial cracks 150 microns long that radiated from
the sides rather than the corners of the indentation impression and a 19.6 N load fractured the
specimen. Thus, although the SiCnp addition to PbTe-PbS did result in a shift in fracture mode
(Table 6.2a and Fig. 6.4), the lack of a well-developed radial crack system made it impossible to
use the Vickers indentation technique to determine KC.

6.4.2 Room temperature microstructure and elastic moduli analysis following post-densification
annealing
In this study, three independent methods were used to study bloating in the PbTe-PbS
specimens: (1) direct measurements via micrometer of specimen volume before and after postdensification annealing (Section 6.4.2.1), (2) direct measurements of porosity on fracture
surfaces as observed on SEM micrographs of internal fracture surfaces of annealed specimens
(4.2.4), and (3) indirect measurements via elasticity measurements at room temperature as a
function of annealing temperature (Section 6.4.2.3.) and temperature-dependent elasticity
measurements taken during thermal cycling (Section 6.4.3).

6.4.2.1 Volume change after post-densification annealing
Although the mass of each of the densified specimens in this study did not change following
163

RUS measurements to temperatures up to 663 K, a volume change greater than 0.7% did occur
for the four hot pressed PbTe-PbS specimens annealed at temperatures higher then 603 K (Table
6.4). None of the PECS-processed specimens had a volume change greater than 0.4% (Table
6.4). The volume of specimen PECS-06S decreased by 1.8% which was likely due to further
densification since the post-densification annealing temperature of 663 K was higher than the
densification temperature of 623 K.
Although while specimen volume changes during annealing could be in principle produced
by either microcracking or bloating, a volume change measurable with a micrometer is likely
caused by bloating during post-densification annealing rather than microcracking, since the
strains induced by microcrack crack opening displacements (CODs) are quite small. As
discussed by Wilson [Wilson 1993] and Liu [Liu 1991, Liu 1992], microcrack-induced strains in
-6

-6

Mg-PSZ and 3Y-TZP ranged from 10 x 10 to 80 x 10 [Wilson 1993, Liu 1991, Liu 1992].
For a comparable range of strain, the PbTe-PbS specimens included in this study would
experience dimension changes of roughly 0.02 microns to 1.6 microns. In addition, for
polycrystalline YCrO3 with a mean microcrack COD of 25 nm (determined by small angle
neutron scattering [Case 1984]) and given the volumetric crack number density in YCrO3 the
corresponding dimensional change would be roughly 0.2 microns. Thus in these examples, the
dimensional changes induced by microcracking damage are too small to be resolved using a
micrometer. However, the volume changes observed by the external micrometer measurements
are consistent with the internal porosity changes observed via SEM for the specimens in this
study.

164

Table 6.4 The relative volume change twelve specimens for each HT-RUS heating/cooling
cycle.
Specimen
Label

a

HT-RUS
Relative
SiCnp
Powder
Sintering Max
Temperature Volume Bloated?
Additions Processing Temp/Pressure
Range (K)
change

HP-53 #A

0.0 vol%

HP -55 #1

0.0 vol%

HP-53 #CTC2

293 - 603

0.018

Yes

723 K /74.4 MPa

293 - 663

0.016

Yes

0.0 vol%

D/WM (H) 723 K /74.4 MPa

293 - 603

0.007

Yes

HP -54 #2

0.0 vol%

D/WM (H) 723 K /74.4 MPa

293 - 663

0.007

Yes

HP -55 #2

0.0 vol%

WM (E)

723 K /74.4 MPa

293 - 603

0.005

No

PECS-06STC1

0.0 vol%

DM

823 K /60 MPa

293 - 603

0.004

No

HP-53 #B

0.0 vol%

D/WM (H) 723 K /74.4 MPa

293 - 543

0.003

No

HP -54 #1

0.0 vol%

D/WM (H) 723 K /74.4 MPa

293 - 603

0.001

No

D/WM (H)

823 K /60 MPa

293 - 663

0.001

No

1.0 vol%

D/WM (H)

823 K /60 MPa

293 - 603

0.000

No

PECS-07-TC1 3.5 vol%

D/WM (H)

823 K /60 MPa

293 - 603

0.000

No

293 - 543

-0.003

No

PECS-07-TC2 3.5 vol%
PECS-06

HP-53 #CTC1
PECS-18
PECS-06STC2
PECS-01

0.0 vol%

D/WM (H) 723 K / 74.4 MPa
WM (E)

D/WM (H) 723 K /74.4 MPa

2.0 vol%

DM

673 K /60 MPa

293 - 663

-0.004

No

0.0 vol%

DM

823 K /60 MPa

293 - 663

-0.018

No

0.0 vol%

D/WM (H)

823 K /60 MPa

293 - 603

NA

a

b

No

For specimens with more than one thermal cycle TC- 1 denotes the first thermal cycle and TC2 denotes the second thermal cycle.
b
Volume not measured after HT-RUS

165

6.4.2.2 Bloating-induced porosity generated by post-densification annealing
Following the two hour post-densification anneals in flowing argon for temperatures up to
936 K, fresh internal fracture surfaces of fifteen hot pressed and PECS processed PbTe-PbSSiCnp nanocomposite specimens were examined by SEM (Table 6.1, Fig. 6.2). The seven asdensified PECS processed dry milled (DM) only PbTe-PbS specimens did not bloat after a two
hour anneal up to 936 K (Table 6.1, Figs. 6.2c and 6.2d).
However, one wet milled (WM) PECS-processed and three dry/wet milled (D/WM) PECSprocessed specimens did bloat, generating (i) spherical and quasi-spherical pores 1 to 5 microns
in diameter (Fig. 6.2b) and (ii) lenticular pores from 10 microns in length and 1 micron wide
(Fig. 6.2b) to about 400 microns in length and 50 microns wide (Fig. 6.3). Bloating in the WM
and D/WM PECS-processed specimens (Figs. 6.2b and 6.3b) and a lack of bloating in DM
PECS-processed specimens (Fig. 6.2d) indicates that the wet milling process may leave a residue
on the powder particle surface which decomposes during annealing, causing bloating.

6.4.2.3 Effect of SiCnp additions on bloating and grain growth
In this study, specimens that were annealed following densification were examined to
determine the effect of nanoparticle additions on both (i) bloating (porosity) and (ii) grain
growth. The relative change in volume fraction porosity, P, the associated change in Young’s
modulus, E, were calculated using
E
 E Ann
P
 PAnn
P  As  D
and E  As  D
E As  D
PAs  D

(6.5)

where PAs-D and EAs-D are the P and E for the as-densified specimens, respectively, and PAnn

166

and EAnn are the P and E for the specimens after a post-densification annealed, respectively,
where E was obtained by room temperature RUS measurements. Three dry/wet milled PECS
specimens (PECS-01, -06, and -07), each of which were densified at 823 K with 60 MPa for 20
minutes (Table 6.1), were subsequently annealed at 693 K (1 minute hold time) with heating and
cooling rates of 2 K/min (Table 6.5). PECS-01 had 0.0 vol% SiCnp, PECS-06 had 1.0 vol%
SiCnp, and PECS-07 had 3.5 vol% SiCnp (Table 6.5). SiCnp additions to the dry/wet milled
PECS specimens reduced but did not eliminate bloating, since after annealing, PECS-01(Table
6.5), P was 1.25 (Eq. (6.5)) and E was 0.12 (Eq. (6.5)), where E was measured by RUS and P
was measured using micrometers.
However for both PECS-06 and -07 (Table 6.5) P was roughly 0.25 (Eq. (6.5)) and E was
about 0.02 (Eq. (6.5)). Thus, both P and E were considerably lower for the wet milled/PECS
processed nanocomposite specimens than the specimen without SiCnp additions, so the SiCnp
limit the bloating observed in wet milled/PECS processed specimens. Nevertheless, the P and
E values were very similar for each of the SiCnp loadings, which indicate that the extent of
bloating may be relatively insensitive to the volume fraction of SiCnp added over the SiCnp
range of 1.0 to 3.5 vol% used in this study. The decrease in bloating that resulted from SiCnp
addition may be related to localized creep processes, since during bloating the local deformation
that occurs at elevated temperature due to the high local gas pressure is likely a creep
mechanism. However, it has been shown recently that Ce-based inclusions in CoSb3-based
skutterudites [Schmidt 2012] can limit grain boundary sliding and the associated anelastic drop-

167

Table 6.5 In this study, the inclusion of SiCnp inhibited porosity (bloating) for PECS-processed
PbTe-PbS specimens. After a post-densification anneal at 693 K for two hours, for the PbTePbS specimen without SiCnp, PECS-01, the volume fraction porosity, P, however, for two
specimens with SiCnp, P increased only by 20%. E is the Young’s modulus measured at room
temperature using resonant ultrasound spectroscopy.
Specimen
Label

a

PECS-01

b
b

PECS -06
PECS-07TC2
a
b
c

c

SiCnp
vol%

As-densified
specimen
P
E (GPa)

After 693 K postdensification anneal
P
E (GPa)

Reference

0.0

0.08

50.3 ± 0.1

0.18

43.9 ± 0.1

[Ni 2011]

1.0

0.04

53.3 ± 0.1

0.05

52.3 ± 0.1

This study

3.5

0.05

56.2 ± 0.1

0.06

54.3 ± 0.1

This study

PECS denotes pulsed electric current sintering
Parallelepiped-shaped specimen
Disc-shaped specimen

168

off in Young’s modulus at elevated temperatures, thus the SiCnp in the PbTe-PbS specimens in
this study may act similarly to inhibit creep locally and thus limit bloating.
Three PbTe-PbS specimens were each PECS processed for 20 minutes at 673 K with a
pressure of 60 MPa (Table 6.1) from dry milled only powders with SiCnp loadings of 2.0, 2.5,
and 3.0 volume percent and were subsequently annealed in flowing argon gas at 936 K for two
hours. SEM observations of the annealed specimens showed that in contrast to the DM PECS
specimens without SiCnp (Section 6.4.2.2) the addition of SiCnp apparently caused limited
bloating for the three PbTe-PbS specimens with SiCnp additions (Fig. 6.2f). The bloating induced
quasi-spherical pores 1 to 3 microns in diameter, located along the grain boundaries (Fig. 6.2f).
As gauged by the surface area porosity fraction measured from SEM micrographs, the bloating
in the dry milled only PbTe-PbS specimens with SiCnp additions was a factor of 10 less (Fig.
6.2f) than the bloating in the WM and D/WM PbTe-PbS specimens without SiCnp additions (Fig.
6.2e, Section 6.4.2.2). The limited bloating in the DM PECS-processed specimens with SiCnp
additions is likely related to SiCnp purity, as will be discussed in Section 6.4.2.4.
In summary, the action of the SiCnp additions to PbTe-PbS is somewhat complex. When
added to wet milled/PECS processed specimens, the SiCnp greatly suppresses, but does not
eliminate bloating. This suppression in bloating may be related to the inhibition of localized
creep (bloating) processes by SiCnp, in an analogous manner to the effect of Ce-based inclusions
in skutterudites [Schmidt 2012]. For SiCnp additions to dry milled PECS-processed specimens,
169

a minor increase in bloating was observed which is likely related to the SiCnp purity (Section
6.4.2.4).
In addition to inhibiting bloating, SiCnp also inhibited grain growth in this study (Table
6.2b), which agrees with studies of grain growth inhibition by nanoparticle addition to nonthermoelectric materials [Brochin 2000, Zhang 2011]. However, for the DM PECS-processed
specimens without SiCnp addition, post-densification anneals in flowing argon from 723 K to
936 K for 2 hours produced grain growth of up to 40 percent (Table 6.2b). In contrast, postdensification anneals up to 873 K, SiCnp additions of 2.0, 2.5, and 3.0 vol% inhibited grain
growth (Table 6.2b).
In this study, a thermal annealing/grain growth study was not performed for the hot pressed
specimens and WM PECS-processed specimens since the bloating that occurs during annealing
precludes performing a grain growth study (Section 6.4.2.2). Also, although grain growth
studies were done in DM only PECS specimens with 2.0%, 2.5% and 3.0% volume fraction
SiCnp loadings (Table 6.2b), the grain growth was not accessed after a 973 K anneal, again due
to bloating in the specimens.

6.4.2.4 Cleaning of powder surfaces by PECS
The lack of bloating in the PECS specimens processed using dry milled powders may be
related to the reported cleaning of surface contamination cleaning during PECS processing
[Groza 1992, Rishbud 1994, Anderson 1999]. For example, transmission electron microscopy of
grain boundaries in PECS densified aluminum nitride [Groza 1992, Rishbud 1994], W and NiAl
[Anderson 1999] demonstrated that the grain boundary oxide layers present in conventionally
170

densified specimens were absent in the PECS processed materials, indicating surface impurities
had been removed from the powder surfaces during PECS processing. For the PbTe-PbS
specimens included in this study, surface contaminate cleaning may explain the difference
between the hot pressing results (in which the specimens did bloat) and the PECS-processed dry
milled only powders, where the specimens did not bloat.
However, for the PECS processed PbTe-PbS specimens from DM powders, the addition of
SiCnp did lead to limited bloating, thus the PECS process likely did not entirely clean
contaminates from the SiCnp that apparently lead to bloating. Thus, for SiCnp (i) contaminants
may well be much more tenacious on the SiCnp surfaces than on the PbTe-PbS particle surfaces,
making surface cleaning much more difficult and/or (ii) the SiCnp contaminants may be
volumetrically distributed rather than being limited to surfaces, making the removal of surface
contaminant layers ineffective for SiCnp.
In addition, there was limited bloating for the PbTe-PbS wet milled powders that were
PECS processed. Thus, once again the PECS process may not have entirely cleaned
contaminants from the powder surfaces of the wet milled powders, including perhaps carboneous
residues of the hexane milling fluid.

6.4.3 High Temperature elasticity measurements
In general for temperatures above the Debye temperature and in the absence of phase
transformations [Schmidt 2012], bloating or microcracking, the Young’s and shear moduli
decrease linearly with increasing temperature for most brittle materials (shown schematically in
Fig. 6.5a) are described well by Eqs. (6.6a) and (6.6b), respectively, such that
171

E

(b)

E

(a)

Temperature
(c)

Temperature

E

E (GPa)

(d)

/

55

HP-54 #2 Heating/Cooling

50

45

Temperature

300

400

500

600

Temperature (K)

700

Fig. 6.5 Schematics of hysteresis between heating and cooling in Young’s modulus due to (a – c)
microcracking and (d) due to bloating. In this study, the specimen HP-54#2 bloated when
thermally cycled to 663 K (d). The dashed and dashed-dot lines represent the least-squares fit to
Eq. (6.6a) to heating and cooling, respectively.

172

E = ERT – bTE(T – TRT)

(6.6a)

G = GRT – bTG(T – TRT)

(6.6b)

where in Eqs. (6.6a) and (6.6b) ERT and GRT is the Young’s and shear modulus at room
temperature, bTE and bTG describes the Young’s and shear modulus-temperature behavior, T is
temperature, and TRT is the room temperature [Wachtman 2009]. However, either
microcracking (Figs. 5b and 5c) or bloating (Fig. 6.5d) can lead to a hysteresis between the
heating and cooling of the elastic moduli measured during a temperature cycle.
For the seven hot pressed and five PECS processed PbTe-PbS specimens with SiCnp
loadings of 0, 1.0, 2.0 and 3.5 vol% (Table 6.6), the slopes of the Young’s modulus as a function
of temperature, bTE (Eq. (6.6a)), were independent of temperature and ranged from 200 ± 5.2 x
-4

-4

10 GPa/K to 265 ± 7.4 x 10 GPa/K (Table 6.6). Each specimen was thermally cycled at least
once, with three specimens (Table 6.6) thermally cycled twice, for a total of 15 thermal cycles on
the 12 elasticity specimens.
The slopes of the shear modulus as a function of temperature, bTG (Eq. (6.6b)), were
-4

-4

independent of temperature and ranged from 80 ± 1.6 x 10 GPa/K to 110 ± 2.2 x 10 GPa/K
(slope values not included in Table 6.6). Also, the values of bTE (Eq. (6.6a)) and bTG (Eq.
(6.6b)) did not change systematically as the SiCnp loading increased from 0.0 vol% to 3.5 vol%
(Table 6.6). The values of bTE obtained in this study are comparable to the values reported in

173

Table 6.6 The least-squares fitting parameters, ERT and bTE, equation (6.6a) for the seven hot
pressed and five PECS-processed PbTe-PbS thermoelectrics included in this study. P is the
volume fraction porosity before thermal cycling, N is the number of E versus temperature data
2
points in the least-squares fit and r is the coefficient of determination for the least-squares fit to
equation (6.6a). For specimens where there was no observable hysteresis, a single entry is given.
Specimens HP-53 #A, HP -53 #C-TC2, HP -54 #2, and HP -55 #1 have an observable hysteresis
in E versus T, thus there are two entries, one for heating and one for cooling.

Specimen Label

4

P

0.0

0.05

b

HP-53 #A Heating

b

HP-53 #A Cooling

HP -53 #C-TC2 Heating
HP -53 #C -TC2
b
Cooling

bTE x 10

b

2

N

Temperature
range (K)

52.8 ± 0.1

(GPa K )
260 ± 3.5

r

0.999

9

333-573

51.9 ± 0.1

260 ± 4.9

0.998

9

333-573

51.9 ± 0.1

SiCnp
vol%

a

220 ± 4.1

0.998

9

333-573

50.6 ± 0.1

200 ± 5.2

0.996

8

363-573

54.5 ± 0.7

262 ± 3.0

0.998

13

293-663

53.4 ± 0.06

259 ± 3.0

0.999

13

293-663

55.4 ± 0.12

240 ± 5.6

0.994

13

293-663

ERT (GPa)

-1

0.0

0.06

0.0

0.03

0.0

0.03

54.0 ± 0.07

220 ± 3.3

0.998

13

293-663

HP -53 #C-TC1

0.0

0.07 51.0 ± 0.05

230 ± 3.6

0.996

17

293-543

HP -53 #B

0.0

0.06 53.0 ± 0.03

260 ± 2.2

0.999

17

293-543

HP -54 #1

0.0

0.03 54.5 ± 0.06

230 ± 3.3

0.997

20

293-603

HP -55 #2

0.0

0.03 54.0 ± 0.14

265 ± 7.4

0.993

41

293-603

PECS-01

0.0

0.08 50.4 ± 0.03

204 ± 1.7

0.999

21

293-603

PECS-06S-TC1

0.0

0.08 50.2 ± 0.05

230 ± 2.6

0.998

21

293-603

PECS-06S-TC2

0.0

0.08 50.3 ± 0.07

238 ± 3.2

0.996

25

293-663

PECS -06

1.0

0.05 53.5 ± 0.06

225 ± 3.3

0.996

21

293-603

PECS-18

2.0

0.06 56.4 ± 0.05 244 ± 2.5

0.998

25

293-663

PECS -07-TC1

3.5

0.07 56.1 ± 0.05 270 ± 2.2

0.998

25

293-663

c

HP -54 #2 Heating

c

HP -54 #2 Cooling

c

HP -55 #1 Heating

c

HP -55 #1 Cooling

PECS -07-TC2
3.5
0.07 56.2 ± 0.02 273 ± 1.3
0.999 21
293-603
In the specimen labels, HP denotes hot pressing and PECS denotes pulsed electric current
sintering
b
Hysteresis upon thermal cycling up to 603 K,
a

c

Hysteresis upon thermal cycling up to 663 K

174

Table 6.7 In the open literature for doped PbTe-based thermoelectrics, ERT and bTE, the leastsquares fitting parameters from equation (6.6a), are similar to the least-squares fitting parameters
in this study (Table 6.2). P is volume fraction porosity, N is the number of data points in the
2
least-squares fit and r is the coefficient of determination.
Specimen Fabrication
Composition Technique

4

P
a

PbTe

Cast

0.05

PbI2-doped
PbTe

Cast

NA

PbTe

CT

SC

Cast

Pb0.95Sn0.05

20

298 – 773

[Ren
2008]

360 ± 6.2 0.996

16

298 - 673

[Ren
2008]

c

58.5 ±
0.06

330 ± 4.4 0.999

6

50 - 303

[Houston
1968]

0.01

51.7 ±
0.04

170 ± 1.7 0.998

21

273 - 773

[Ren
2009]

Cast

0.02

51.0 ±
0.01

200 ± 3.8 0.993

20

273 - 773

[Ren
2009]

HP

0.02

53.3 ±
0.18

250 ± 1.2 0.981

10

273 - 523

[Ren
2009]

HP

0.06

46.4 ±
0.10

250 ± 5.7 0.990

21

273 - 603

[Ren
2009]

d

Sb1.2Te20
Ag0.43Pb18

Temperature
Reference
range (K)

57.9 ±
0.13

Sb1.2Te20
Ag0.43Pb18

N

b

Te0.92S0.08
Ag0.43Pb18

E RT bTE × 10
2
r
-1
(GPa) (GPa K )
57.6 ±
260 ± 2.7 0.998
0.07

Sb1.2Te20
a

The volume fraction porosity was calculated assuming the single crystal density was at
theoretical density
b
P values not specified by the authors [Ren 2008]
c

Single crystal assumed to be theoretical density

d

CT is the Czochralski Technique

175

(a)

/
/
/
/

E (GPa)

52

HP-53 #A (603 K)
HP-53 #B (543 K)
HP-53 #C-TC1 (543 K)
HP-53 #C-TC2 (603 K)

48

44
300

400

500

600

Temperature (K)

(b)

E (GPa)

56

/
/
/

HP-55 #1 (663 K)
HP-55 #2-TC1 (603 K)
HP-55 #2-TC2 (603 K)

52

48

44
300

400

500

600

Temperature (K)
Fig. 6.6

176

Fig. 6.6 (cont’d )

(c)

/
/
/
/
/
/
/

60

E (GPa)

56
52

P-01 (603 K)
P-06 (603 K)
P-07-TC1 (603 K)
P-07-TC2 (663 K)
P-18 (663 K)
P-06S-TC1 (603 K)
P-06S-TC2 (663 K)

48
44
40
300

400

500

600

T (K)

(d)

/
/

E and G (GPa)

56

HP-54 #1 (603 K)
HP-54 #2 (663 K)

52
48

E

44
24

20

G

16
300

400

500

600

Temperature (K)

177

Fig. 6.6 (cont’d )

(e)

Poisson's Ratio

0.30
0.28
0.26
0.24
0.22

/

0.20

HP-55 #2-TC1 603 K

300

400

500

600

Temperature (K)

(f)

Poisson's Ratio

0.30
0.28
0.26
0.24
0.22

/

0.20

300

PECS-07-TC2 663 K

400

500

600

Temperature (K)

Poisson's Ratio

0.30

(g)

0.28
0.26
0.24

PbTe [Houston 1968]
PbTe [Einspruch 1963]
/
HP-53 #C 603 K - TC2 [This study]
/
PbTe-0.031% PbI2 [Ren 2008]

0.22
0.20

0

150 300 450 600
Temperature (K)

178

Fig. 6.6 (cont’d ) Temperature dependence of the (a - d) Young’s modulus, E, (d) shear modulus,
G, and (e-f) Poisson’s ratio, , for hot pressed (HP) and PECS-processed PbTe-PbS specimens
upon heating (filled symbols) and cooling (open symbols). For E and G, the symbol size is
greater than the error bars. In parentheses, next to the specimen label, is the maximum
temperature for each thermal cycle. The least-squares fit to Eq. (6.6a) to the Young’s modulus
during heating, cooling, and heating/cooling is represented by the dashed, dotted, and solid lines,
respectively. A least-squares fit to Eq. (6.7) to the temperature-dependent Poisson’s ratio is
represented by the dashed-dot line. The hysteresis in E versus T for specimens HP-53 #A, HP53 #C-TC2, HP -54 #2, and HP -55 #1 is not apparent in the figures because of the number of
temperature-dependent Young’s moduli data points.

179

the literature for other PbTe-based thermoelectrics [Ren 2008, Ren 2009 LAST, Houston 1968]
(Table 6.7).

6.4.3.1 Temperature behavior of Poisson’s ratio as a function of SiCnp addition
For the twelve PbTe-PbS specimens with and without SiCnp additions the Poisson’s ratio
ranged between 0.23 and 0.28 and either stayed constant (Figs. 6.6e and 6.6f) or increased (Fig.
6.6g) between room temperature and maximum temperatures of 543 K, 603 K and 663 K.
Similar behavior was observed by Ren et al. for cast and hot pressed Ag0.43Pb18Sb1.2Te20 and
Pb0.95Sn0.05Te0.92S0.08 specimens, where the Poisson’s ratio either remained constant or
increased with increasing temperatures for maximum temperatures of 573 K, 623 K and 773 K
[Ren 2009 LAST].
In an elasticity study of PbTe, Ren et al. presented an empirical relationship the temperature
dependent Poisson’s ratio, (T), (Eq. (6.7)) for a combined data set that included (i) 0 to 300 K
data from Houston [Houston 1968], 300 K data Einspruch [Einspruch 1963] and 300 K to 670 K
for PbTe-0.031% PbI2 from [Ren 2008] such that

(T)   RT  a1 (T  TRT )  a 2 (T  TRT ) 2

(6.7)

where RT is the room temperature Poisson’s ratio, T is temperature, TRT is room temperature
2

and a1 and a2 are material-dependent constants [Ren 2008] with an r of 0.959 (Fig. 6.6g) for
temperatures from 0 K to 670 K. Similarly, in this study, the temperature dependence of
Poisson’s ratio (Fig. 6.6g) was described well by Eq. (6.7).

180

6.4.3.2 Hysteresis in elastic moduli measurements for hot pressed specimens
In general, microcracking leads to a drop in the elastic modulus [Case 1981Al2O3, Case
1983, Case 1981Gd2O3] but upon heating, microcracks may heal via mass transport mechanisms
such as (1) mass diffusion, (2) growth of reaction products or (3) flow of viscous fluid. For
example, microcrack healing by mass diffusion has been reported in alumina [Case 1981Al2O3,
Wilson 1997, Bykov 2010, Rödel 1990], Ti-, Ca-, and Mg-doped alumina [Powers 1993, Powers
1992], SiC [Narushima 2001], MgTi2O5 [Case 1983], Gd2O3 [Case 1981Gd2O3], where such
healing can occur under vacuum conditions for temperatures greater than 0.6 of the melting point
[Case 1983] . Also microcrack healing can occur via by viscous glassy-phase filling in ZrO2
cast refractories [Sibil 2009] and synthetic clay (Laponite) [Renard 2009] and by crack surface
oxidation in Ti3AlC2 [Song 2008] and zirconia-based thermal barrier coatings [Rico 2009].
For E versus T and G versus T plots, hysteresis between heating and cooling (Figure 6.5b
and 6.5c) has been observed for microcracked and thermally cycled Al2O3, [Case 1981 Al2O3,
Case 1983, Yousef 2005], Gd2O3 [Case 1983], Eu2O3 [Dole 1977] and HfO2 [Dole 1977],
MgTi2O5 [Bush 1959, Bush 1958] and cast refractories [Chotard 2008, Patapy 2009] was caused
by microcrack healing during heating and then the reformation of microcracks during cooling
(Figs. 6.5b and 6.5c) [Case 1981 Al2O3, Case 1983, Bush 1959, Chotard 2008]. The area of the
hysteresis loop (Figs. 6.5b and 6.5c) increases with increasing grain size [Case 1981 Al2O3,
Case 1983].
For the four hot pressed PbTe-PbS specimens thermally cycled at T > 603 K, a hysteresis in
the temperature dependent elastic moduli was observed between the heating and cooling

181

measurements. In contrast to the hot pressed specimens, none of the five PECS PbTe-PbS
specimens had a hysteresis in the E versus T when thermally cycled up to 663 K.

6.4.3.3 Observations in the literature of elasticity changes due to bloating during postdensification annealing of other materials
In the literature, bloating during post-densification annealing was observed in Synroc B
(with major phases of BaAl2TiO16, CaTiO3, and CaZrTiO7) [O’Brien 1985] and Ti-6V-4Al
alloys [Oppenheimer 2010]. For Synroc B, thermal annealing up to a maximum temperature of
1473 K induced bloating was observed indirectly through a decrease in E of up to roughly 25%
and directly by optical microscopy [O’Brien 1985].
Also, in order to tailor the porosity and enhance bone in-growth in the biomedical alloy Ti6V-4Al, Oppenheimer et al. intentionally induced bloating in densified specimens [Oppenheimer
2010, Oppenheimer 2009]. Ti-6V-4Al powders in sealed metal canisters backfilled with argon
[Oppenheimer 2010, Oppenheimer 2009] were hot pressed yielding specimens with P values <<
1 percent. Then, post-densification anneals to 1303 K of 18 Ti-6V-4Al specimens yielded P
values from 0.09 to 0.52 [Oppenheimer 2010] via bloating of previously dense specimens. In
this study we found that a least-squares fit Oppenheimer’s E versus P data [Oppenheimer 2010]
for bloated Ti-6V-4Al specimens to the empirical exponential relationship Eq. (6.4a) described
2

the Ti-6V-4Al bloating results well, with an r of 0.934 (Fig. 6.7). This indicates that the
decrease in E with P in Oppenheimer’s intentionally bloated Ti-6V-4Al specimens followed a
similar functional form (Eq. (6.4a)) as was observed for the bloated PbTe-PbS specimens in this
study. Thus, the present authors believe that the controlled bloating Ti-6V-4Al specimens
[Oppenheimer 2010] is directly analogous to the bloating observed in this study for PbTe-PbS.
182

120
100

Ti-6Al-4V
Isothermal anneals at 1303 K up to 250 hours
[Oppenheimer 2010]
Cyclical anneals for temperatures
(i) 1113 K and 1263 K for 2, 4 and 8 min cycles or
(ii) 1113 K and 1303 K for 8 min cycles
[Oppenheimer 2010]

E (GPa)

80
60
40
20
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

Volume fraction porosity (P)
Fig. 6.7 The Young’s modulus as a function of volume fraction porosity, P, for Ti-6Al-4V
specimens after post-densification anneals up to 1303 K [Oppenheimer 2010]. This behavior is
consistent with the empirical exponential decrease common to brittle materials (Eq. (6.4a)). The
solid line represents a least-squares fit to Eq. (6.4a) of the Oppenheimer et al. Young’s modulus
versus P data [Oppenheimer 2010].

183

6.5.0 Summary and Conclusions
In this study, a total of 26 PbTe-PbS specimens were fabricated by either hot pressing or
PECS-processing powders that were dry milled only, wet milled only, or dry/wet milled (Table
6.1). This study includes results on both processing and mechanical properties.
In terms of processing, this study expands on the previous preliminary results that for
polycrystalline PbTe-PbS, a combination of PECS-processing and dry milling inhibits bloating
during post-densification anneals up to 936 K. We propose that the absence of bloating for the
DM PECS processed specimens may be related to the reported “cleaning” of powder surfaces by
the PECS process itself [Groza 1992, Rishbud 1994, Anderson 1999]. Using dry milling
together with PECS processing to eliminate bloating will have the extremely beneficial effect of
stabilizing the high temperature microstructure of these materials.
Also, RUS measurements of the Young’s and shear moduli and Poisson’s ratio were
performed for 12 specimens over temperatures ranging from RT up to as high as 663 K (Table
6.6). For each of 15 heating and cooling cycles, E and G decreased linearly with increasing
temperature (Eqs. (6.6a) and (6.6b)) where bTE (Eq. (6.6a)) ranged from 0.020 GPa/K to 0.027
GPa/K (Table 6.6), bTG (Eq. (6.6b)) ranged from 0.008 GPa/K and 0.011 GPa/K. The elasticity
measurements provide information needed by designers to predict the stress and strain of
thermoelectric components that are incorporated in thermoelectric generators.
Annealing of as-densified specimens can generate porosity and porosity in turn affects the
thermal, electrical and mechanical properties of materials, thus the processing aspects of this
study are intertwined with the mechanical property aspects.
SEM examination of the 15 PbTe-PbS specimens that underwent post-densification thermal
anneals up to 936 K in a flowing Ar-H2 atmosphere revealed a temperature-dependent bloating
184

that was present in hot pressed specimen and each PECS specimen processed with wet milled
powders. However, for seven out of seven of dry milled, PECS-processed specimens, no
bloating was observed by SEM even for two-hour anneals at 936 K, which is roughly 200 K
higher than the proposed use temperature for these materials. Thus PECS processing in
conjunction with dry milled only PbTe-PbS powders stabilizes the high temperature
microstructure of these materials.
SiCnp addition did limit bloating in wet milled/PECS processed materials, likely due to an
enhanced resistance to grain boundary sliding/creep processes brought about by the SiCnp
inclusions, in an analogous manner to the grain boundary sliding resistance afforded by Ce-based
inclusions in a n-type skutterudite [Schmidt 2012].
Also, SiCnp additions of 2.0, 2.5 and 3.0 vol% did (i) modestly inhibit grain growth during
high temperature anneals (Table 6.2b) as well as (ii) alter the fracture mode of the specimens
(Fig. 6.4, Table 6.2a). Grain growth inhibition is favorable for enhancing fracture strength. In
addition, the dramatic change in fracture mode from intergranular to transgranular (Table 6.2a,
Fig. 6.4) likely signals an increase in fracture toughness with SiCnp additions (Section 6.3.1.2).
Future work will include examining the effect of SiCnp purity on bloating to determine if
SiCnp purities higher than 95% may reduce the bloating in specimens densified by PECS from
dry milled only powders.

Acknowledgments
The authors acknowledge the financial support of Office of Naval Research Grant N00014-08-1-

185

0613. In addition some supplemental support (assistance of Robert Schmidt) was received from
the Department of Energy, “Revolutionary Materials for Solid State Energy Conversion Center,”
an Energy Frontiers Research Center funded by the U.S. Department of Energy, Office of Basic
Energy Sciences under award number DE-SC0001054. Research through the Oak Ridge
National Laboratory's High Temperature Materials Laboratory User Program was sponsored by
the U. S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Vehicle
Technologies Program. Edward Timm and Karl Dersch, Michigan State University, assisted the
authors with hot pressing, PECS and specimen cutting. The Center for Statistical Training and
Consulting at Michigan State University provided advice on the error analysis in this study.

186

REFERENCES

187

6.6.0 References
[Aitchinson 1957] Aitchinson J, Brown JAC. The Lognormal Distribution Massachusetts:
Cambridge University Press; 1957.
[Alvarez 2010]Alvarez FX, Jou D, Sellitto A. Pore-size dependence of the thermal conductivity
of porous silicon: A phonon hydrodynamic approach, Appl Phys Lett 2010; 97: 033103.
[Anderson 1999] Anderson KR, Groza JR, Fendorf, Echer CJ, Surface oxide debonding in field
assisted powder sintering, Mater. Sci. Eng. 1999 A270: 278–282.
[Androulakis 2007] Androulakis J, Lin C, Kong H, Uher C, Wu C, Hogan T, Cook BA, Caillat
T, Paraskevopoulos KM, Kanatzidis MG. Spinodal decomposition and nucleation and
growth as a means to bulk nanostructured thermoelectrics: Enhanced performance in
Pb1-xSnxTe-PbS, J Am Chem Soc 2007; 129: 9780–9788.
[Berbenni 2007] Berbenni S, Favier V, Berveiller M. Micro-macro modelling of the effects of
the grain size distribution on the plastic flow stress of heterogeneous materials, Comput
Mater Sci 2007; 39: 96–105.
[Betz 2000] Betz U, Sturm A, Löffler JF, Wagner W, Wiedenmann A, Hahn H. Microstructural
development during final-stage sintering of nanostructured zirconia based ceramics,
Mater Sci Eng 2000; A281: 68–74.
[Boccaccini 1994] Boccaccini AR. Effective elastic moduli of porous ceramic materials, J Am
Ceram Soc 1994; 77: 2779.
[Brochin 2000] Brochin F, Lenoir B, Devaux X, Martin-Lopez R, Scherrer H. Preparation and
transport properties of polycrystalline Bi and Bi-SiO2 nanocomposites, J Appl Phys
2000; 88: 3269-3275.
[Bush 1958] Bush EA, Hummel FA. High-temperature mechanical properties of ceramic
materials-magnesium dititanate, J Am Ceram Soc 1958; 41: 189–195.
[Bush 1959] Bush EA, Hummel FA. High-temperature mechanical properties of ceramic
materials – beta-eucryptite, J Am Ceram Soc 1959; 42:388–391.
[Bykov 2010] Bykov YV, Egorov SV, Eremeev AG, Kholoptsev VV, Plotnikov IV, Rybakov
KI, Semenov VE, Sorokin AA. Effects of microwave heating in nanostructured ceramic
materials, Powder Metall Met Ceram 2010; 49; 31-41
[Case 1981 Gd2O3] ED Case, JR Smyth, Hunter O. Microcracking behavior of monoclinic
Gd2O3, J Nucl Mater 1981; 102:135-142.

188

[Case 1981] Case ED, Smyth JR. Room-temperature fracture energy of monoclinic Gd2O3, J
Mater Sci 1981; 16: 3215-3217.
[Case 1981Al2O3] Case ED, Smyth JR, Hunter Jr. O. Microcracking in large-grain Al2O3,
Mater Sci Eng 1981; 51:175–179.
[Case 1983] Case ED, Smyth JR, Hunter Jr. O. Microcrack healing during the temperature
cycling of single phase ceramics, in: Bradt RC, Evans AG, Hasselman DPH, Lange FF.
(Eds.). Fracture Mechanics of Ceramics, Vol 5. New York: Plenum; 1983, pp 507 – 530.
[Case 1984] Case ED, Glinka CJ. Characterization of microcracks in YCrO3 using small-angle
neutron-scattering and elasticity measurements, J Mater Sci 1984; 19: 2962-2968.
[Chotard 2008] Chotard T, Soro J, Lemercier H, Huger M, Gault C. High temperature
characterisation of cordierite-mullite refractory by ultrasonic means, J Eur Ceram Soc
2008;28: 2129–2135.
[Colombo 2006] Colombo P. Conventional and novel processing methods for cellular ceramics,
Phil Trans R Soc A 2006; 364:109-124.
[CSTAT] Personal communication with Center for Statistical Training and Consulting, Michigan
State University, October 2011 February 2012.
[Dole 1977] Dole SL, Hunter O, Calderwood FW, Bray DJ. Elastic properties of monoclinic
hafnium oxide at room temperature, J Am Ceram Soc 1978; 61: 486-490.
[Fullman 1953] Fullman RL. Measurement of particle sizes in opaque bodies, Trans. AIME
1953; 197: 447–452.
[Groza 1992] Groza JR, Risbud SH, Yamazaki K. Plasma activated sintering of additive-free
AlN powders to near theoretical density in 5 minutes, J Mater Res 1992; 7: 2643-2645.
[Hall 2009] Hall BD, Case ED, Ren F, Johnson J, Timm EJ. Agglomeration during wet milling
of LAST (lead-antimony-silver-tellurium) powders, Mater Chem Phys 2009; 113: 497502.
[Hoepfner 2002] Hoepfner TP, Case ED. The porosity dependence of the dielectric constant for
sintered hydroxyapatite, J Biomed Mater Res 2002; 60: 643 - 650.
[Hoepfner 2003] Hoepfner TP, Case ED. The porosity dependence of the dielectric constant for
sintered hydroxyapatite, Ceram Int 2003; 29: 699 - 706.
[Houston 1968] Houston B, Strakna RE, Belson HS. Elastic constants, thermal expansion,and
Debye temperature of lead telluride, J Appl Phys 1968; 39: 3913.
189

[Hu 2010] Hu LF, Wang CA. Effect of sintering temperature on compressive strength of porous
yttria-stabilized zirconia ceramics, Ceram Int 2010; 36: 1697 - 1710.
[Jang 2010] Jang B-K, Kim S-Y, Han I-S, Seo D-W, Hong K-S, Woo S-K, Sakka Y. Influence of
uni and bi-modal SiC composition on mechanical properties and microstructure of
reaction-bonded SiC ceramics, J Ceram Soc Jpn 2010;118: 1028-1031.
[Johnsen 2011] Johnsen S, He JQ, Androulakis J, Dravid VP, Todorov I , Chung DY, Kanatzidis
MG. High Performance Thermoelectrics from Earth-Abundant Materials: Enhanced
Figure of Merit in PbS by Second Phase Nanostructures, J Am Chem Soc 2011; 133:
3460-3470.
[Jung 2011] Jung SY, Seo WS, Lim YS, Shin S, Cho HH, Park HH. Thermoelectric Properties of
Nb-Doped Ordered Mesoporous TiO(2), J Electron Mater 2011; 40: 652-656.
[Kanatzidis 2010] Kanatzidis MG. Nanostructured Thermoelectrics: The New Paradigm?, Chem
Mat 2010; 22: 648-659.
[Karakasidis 2011] Karakasidis TE, Charitidis CA. Influence of nano-inclusions' grain
boundaries on crack propagation modes in materials, Mater Sci Eng B 2011; 176:490–
493.
[Kawabata 1977] Kawabata T, Izumi, O. Relationship between fracture toughness and
transgranular fracture in an Al-6.0% 2n-2.5% Mg alloy, Acta Matall Mater 1977; 25:
505-512.
[Kim 2007] Kim B-N, Hiraga K, Morita K, Yoshida H. Spark plasma sintering of transparent
alumina, Scripta Materialia 2007; 57: 607–610.
[Kishimoto 1991] Kishimoto A, Koumoto K, Yanagida H, Nameki M. Microstructure
dependence of mechanical and dielectric strengths, Eng Fract Mech 1991; 40: 927 - 930.
[Lee 2010] Lee H, Vashaee D, Wang Z, Dresselhaus MS, Ren ZF, Chen G. Effects of nanoscale
porosity on thermoelectric properties of SiGe, J Appl Phys 2010; 107: 094308.
[Li 2006] Li J-F, Liu J. Effect of nano-SiC dispersion on thermoelectric properties of Bi2Te3
polycrystals, Phys Stat Sol 2006; 203: 3768–3773.
[Li 2011] Li F, Huang X, Sun Z, Ding J, Jiang J, Jiang W, Chen L. Enhanced thermoelectric
properties of n-type Bi(2)Te(3)-based nanocomposite fabricated by spark plasma
sintering, J Alloy Compd 2011;509: 4769–4773.
[Liu 1991] Liu S-Y, Chen I-W. Fatigue of yttria-stabilized zirconia, J Am Ceram Soc 1991; 74:
1197-1205
[Liu 1992] Liu S-Y, Chen I-W. Fatigue deformation mechanism of zirconia ceramics, J Am
190

Ceram Soc 1992; 75: 1191-1204.
[Liu 2011] Liu D-W, Li J-F, Chen C, Zhang B-P. Effects of SiC Nanodispersion on the
Thermoelectric Properties of p-Type and n-Type Bi(2)Te(3)-Based Alloys, J Electron
Mater 2011; 40: 992-998.
[Low 1981] Low NMP. Formation of cellular-structure glass with carbonate compounds and
natural mica powders, J Mater Sci 1981; 16: 800-808.
[Migliori 1997] Migliori A, Sarrao JL. Resonant Ultrasound Spectroscopy: Applications to
Physics, Materials Measurements, and Nondestructive Evaluation, New York: Academic
Press; 1997.
[Mukhopadhyay 2010] Mukhopadhyay A, Chakravarty D, Basu B. Spark Plasma-Sintered WCZrO(2)-Co Nanocomposites with High Fracture Toughness and Strength, J Am Ceram
Soc 2010; 93: 1754–1763.
[Narushima 2001] Narushima T, Glaeser AM. High-temperature morphological evolution of
lithographically introduced cavities in silicon carbide, J Am Ceram Soc 2001; 84: 921–
28.
[Ni 2009] Ni, JE, Ren F, Case ED, Timm EJ. Porosity dependence of elastic moduli in LAST
(Lead-antimony-silver-tellurium) thermoelectric materials, Mater Chem Phy 2009; 118:
459 - 466.
[Ni 2010] Ni JE, Case ED, Khabir KN, Stewart RC, Wu C, Hogan TP, Timm EJ, Girard SN.
Kanatzidis MG. Room temperature Young's modulus, shear modulus, Poisson's ratio and
hardness of PbTe-PbS thermoelectric materials, Mater Sci Eng B 2010; 170: 58–66.
[Ni DOI 2012] Ni JE, Case ED, Stewart RC, Wu C, Hogan TP, Kanatzidis MG. Bloating in
(Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055%PbI2 Thermoelectric Specimens as a Result of
Processing Conditions, J Electron Mater, in press, DOI: 10.1007/s11664-011-1853-0.
[Ni to be submitted] Ni JE, Case ED, Schmidt RD, Wu C-I, Hogan TP, Trejo RM, Kirkham MJ,
Lara-Curzio E, Kanatzidis MG, The effect of processing on microstrain during thermal
expansion measurements for (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 thermoelectric
material, Philos. Mag. in press.
[O’Brien 1985] O’Brien MH, Hunter Jr. O, Case ED, Mechanical effects of thermal cycling on
United States and Australian Synroc-B, J Mater Sci Lett 1985; 4: 367-369.
[Oppenheimer 2009] Oppenheimer S, Dunand DC. Porous NiTi by creep expansion of argonfilled pores, Mater Sci Eng A 2009; 523: 70–76
[Oppenheimer 2010] Oppenheimer S, Dunand DC. Solid-state foaming of Ti-6Al-4V by creep or
superplastic expansion of argon-filled pores, Acta Mater 2010; 58: 4387–4397.
191

[Park 2009] Park YH, Hinoki T, Kohyama A. Development of multi-functional NITE-porous
SiC for ceramic insulators, J Nuclear Mater 2009; 386–388: 1014 - 1017.
[Patapy 2009] Patapy C, Gault C, Huger M, Chotard T. Acoustic characterization and
microstructure of high zirconia electrofused refractories, J Eur Ceram Soc 2009; 29:
3355–3362.
[Pilchak 2007] Pilchak AL, Ren F, Case ED, Timm EJ, Wu C-I, Hogan TP, Schock HJ.
Characterization of dry milled powders of LAST (lead-antimony-silver-tellurium)
thermoelectric material, Philos Mag 2007; 87: 4567 – 4591.
[Powers 1992] Powers JD, Glaeser AM. High-temperature healing of crack-like flaws in Mg-ionimplanted and Ca-ion-implanted sapphire, J Am Ceram Soc 1992; 75: 2547–2558.
[Powers 1993] Powers JD, Glaeser AM. High-temperature healing of crack-like flaws in titanium
ion-implanted sapphire, J Am Ceram Soc 1993; 76: 2225–2234.
[Ren 2008] Ren F, Case ED, Sootsman JR, Kanatzidis MG, Kong H, Uher C, Lara-Curzio E,
Trejo RM. The high-temperature elastic moduli of polycrystalline PbTe measured by
resonant ultrasound spectroscopy, Acta Mater 2008; 56: 5954–5963.
[Ren 2009 HA] Ren F, Case ED, Morrison A, Tafesse M, Baumann MJ. Resonant ultrasound
spectroscopy measurement of Young's modulus, shear modulus and Poisson's ratio as a
function of porosity for alumina and hydroxyapatite, Philos Mag 2009; 89: 1163 - 1182.
[Ren 2009 LAST]Ren F, Case ED, Ni JE, Timm EJ, Lara-Curzio E, Trejo RM, Lin C-H,
Kanatzidis MG. Temperature-dependent elastic moduli of lead telluride-based
thermoelectric materials, Philos Mag 2009; 89: 143 -167.
[Renard 2009] Renard F, Dysthe DK, Feder JG, Meakin P, Morris SJS, Jamtveit B. Pattern
formation during healing of fluid-filled cracks: an analog experiment, Geofluids 2009; 9:
365–372.
[Rice 1998] Rice RW. Porosity of Ceramics, New York: Marcel Dekker; 1998.
[Rico 2009] Rico A, Gómez-García J, Múnez CJ, Poza P, Utrilla V. Mechanical properties of
thermal barrier coatings after isothermal oxidation. Depth sensing indentation analysis,
Surf Coat Technol 2009; 203: 2307–2314.
[Rishbud 1994] Risbud SH, Groza JR, Kim MJ, Philos. Clean grain-boundries in alumnim nirtird
ceramics densified without additives by a plasma-acivated sintering process, Mag. B,
1994 69: 525–533.
[Rödel 1990] Rödel J, Glaeser AM. High-temperature healing of lithographically introduced
cracks in sapphire, J Am Ceram Soc 1990; 73: 592–601.

192

[Schmidt 2012] Schmidt RD, Case ED, Ni JE, Sakamoto JS, Trejo RM, Lara-Curzio E,
Temperature-dependent Young’s modulus, shear modulus and Poisson’s ratio of p-type
Ce0.9Fe3.5Co0.5Sb12 and n-type Co0.95Pd0.05Te0.05Sb3 skutterudite thermoelectric
materials,” Philosophical Magazine, Philos. Mag., 2012; 92: 727-759
[Schmidt DOI 2012] Schmidt RD, Case ED, Ni JE, Sakamoto JS, Trejo RM, Lara-Curzio E,
Payzant EA, Kirkham MJ, Peascoe-Meisner RA, The temperature dependence of thermal
expansion for p-type Ce0.9Fe3.5Co0.5Sb12 and n-type Co0.95Pd0.05Te0.05Sb3
skutterudite thermoelectric materials, Philos. Mag. DOI: 10.1080/14786435.2011.644815
[Sibil 2009] Sibil A, Erauw JP, Cambier F, R’Mili M, Godin N, Fantozzi G. Study of damage of
high zirconia fused-cast refractories by measurement of Young's modulus, Mater Sci Eng
A-Struct Mater Prop Microstruct. Process 2009; 521–22: 221–223.
[Simmons 1971] Simmons G and Wang H, Single Crystal Elastic Constants and Calculated
Aggregate Properties: A Handbook, second ed. Cambridge: The MIT Press; 1971.
[Song 2008] Song GM, Pei YT, Sloof WG, Li SB, De Hosson JThM, van der Zwaag S.
Oxidation-induced crack healing in Ti3AlC2 ceramics, Scr Mater 2008; 58: 13–16.
[Teber 2012] Teber A, Schoenstein F, Têtard F, Abdellaoui M, Jouini N. Effect of SPS process
sintering on the microstructure and mechanical properties of nanocrystalline TiC for tools
application, Int. Journal of Refractory Metals and Hard Materials 2012;30: 64–70.
[Vandeperre 2004] Vandeperre LJ, Wang J, Clegg WJ. Effects of porosity on the measured
fracture energy of brittle materials, Philos Mag 2004; 84: 3689-3704.
[Voevodin 2000] Voevodin AA, Zabinski JS. Supertough wear-resistant coatings with
'chameleon' surface adaptation, Thin Solid Films 2000; 370: 223-231.
[Wachtman 2009] Wachtman JB, Cannon WR, Matthewson MJ. Mechanical Properties of
Ceramics, second ed. New York: Wiley Interscience; 2009.
[Wang 2000] Wang C, Zhu ZG, Hou XH, Li HJ. Damping characteristics of CVI-densified
carbon-carbon composites, Carbon 2000; 38: 1821 – 1824.
[Wen 2011] Wen H, Zhao Y, Zhang Z, Ertorer O, Dong S, Lavernia EJ. The influence of oxygen
and nitrogen contamination on the densification behavior of cryomilled copper powders
during spark plasma sintering, J Mater Sci 2011; 46: 3006–3012.
[Wilson 1993] Wilson, BA, Case, ED. Comparison of mechanical fatigue wth thermal fatigue in
ceramics, Scr Metall Materialia 1993; 28: 1571-1576.
[Wilson 1997] Wilson BA, Lee K-Y, Case ED. Diffusive crack-healing behavior in
polycrystalline alumina: A comparison between microwave annealing and conventional
193

annealing, Mater Res Bull 1997; 32: 1607-1616.
[Wu 2006] Wu J, Norvell WA, Welch RM. Kriging on highly skewed data for DTPA-extractable
soil Zn with auxiliary information for pH and organic carbon, Geoderma 2006; 134: 187–
199.
[Xiong 2009] Xiong Z, Chen X, Zhao X, Bai S, Huang X, Chen L. Effects of nano-TiO(2)
dispersion on the thermoelectric properties of filled-skutterudite Ba(0.22)Co(4)Sb(12),
Solid State Sci 2009;11: 1612-1616
[Xu 2012] Xu C, Cai Y, Flodström K, Li Z, Esmaeilzadeh S, Zhang G-J. Int. Spark plasma
sintering of B(4)C ceramics: The effects of milling medium and TiB(2) addition, J
Refract Met H 2012; 30: 139–144
[Yamada 2010] Yamada M, Sekine K, Kumazawa T, Tanabe Y. Relationship between the cone
crack and fracture mode in ceramics under high-velocity-projectile impact, J Ceram Soc
Jpn 2010;118: 903-908.
[Yang 2010] Yang A, Wang CA, Guo R, Huang Y, Nan CW. Effects of sintering behavior on
microstructure and piezoelectric properties of porous PZT ceramics, Ceram Int 2010; 36:
549 - 554.
[Yoshida 2011] Yoshida H, Morita K, Kim B-N, Hiraga K, Yamanaka K, Soga K, Yamamoto T.,
Low-Temperature Spark Plasma Sintering of Yttria Ceramics with Ultrafine Grain Size, J
Am Ceram Soc 2011; 94: 3301–3307.
[Yousef 2005] Galal Yousef S, Rödel J, Fuller Jr. ER, Zimmermann A, El-Dasher BS.
Microcrack evolution in alumina ceramics: Experiment and simulation, J Am Ceram Soc
2005; 88: 2809–2816.
[Zhang 2011] Zhang ZH, Topping T, Li Y, Vogt R, Zhou YZ, Haines C, Paras J, Kapoor D,
Schoenung JM, Lavernia EJ. Mechanical behavior of ultrafine-grained Al composites
reinforced with B(4)C nanoparticles, Scr Mater 2011; 65: 652-655.
[Zhao 2008] Zhao L-D, Zhang B-P, Li J-F, Zhou M, Liu W-S, Liu, Thermoelectric and
mechanical properties of nano-SiC-dispersed Bi2Te3 fabricated by mechanical alloying
and spark plasma sintering, J. Journal of Alloys and Compounds 455 (2008) 259–264
[Zhu 2005] Zhu B, Asaro RJ, Krysl P, Bailey R. Transition of deformation mechanisms and its
connection to grain size distribution in nanocrystalline metals, Acta Mater 2005; 53:
4825–4838

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7.0 The effect of processing on strain during thermal expansion measurements for
(Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 thermoelectric material
1

1

1

2

2

Jennifer E. Ni , Eldon D. Case , Robert D. Schmidt , Chun-I Wu , Timothy Hogan , Rosa
3

3

3

Trejo , Melanie Kirkham , Edgar Lara-Curzio , Mercouri G. Kanatzidis

4

2
Chemical Engineering and Materials Science and Electrical and Computer Engineering,
Michigan State University, East Lansing, MI, 48824
1

3

High Temperature Materials Laboratory, Oak Ridge National Laboratory, Oak Ridge TN 37380

4

Department of Chemistry, Northwestern University, Evanston, IL, 60208

Abstract
The coefficient of thermal expansion (CTE) is a key design parameter for thermoelectric (TE)
materials, especially in energy harvesting applications since stresses generated by such factors as
CTE mismatch, thermal gradients and thermal transients scale with the CTE of the TE material.
For the thermoelectric material PbTe-PbS (8%), over the temperature ranges of 293 K to 543 K
-6

-1

and 293 K to 773 K an average coefficient of thermal expansion, αavg of 21.5 x 10 K was
measured using (1) dilatometry and (2) high-temperature x-ray diffraction (HT-XRD) for
powder, bulk specimens cut from cast ingot, hot pressed billets or pulsed electric current
sintering (PECS) processed billets. The CTE values measured via dilatometry and HT-XRD are
similar to other Pb-based chalcogenides found in the literature.
Keywords: Thermoelectrics; Coefficient of thermal expansion; Bloating

195

7.1.0 Introduction
For the thermoelectric (TE) material (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 included
in this study the ZT has been reported to be about 1.5 at 642 K [Androulakis 2007], where the
dimensionless figure of merit, ZT, is a measure of the performance of thermoelectric materials

S 2 T
ZT 


(7.1)

where Sis the Seebeck coefficient,  is the electrical conductivity,  is the thermal conductivity,
and T is temperature.
Given the dependence of ZT on thermal and electrical conductivity these transport
properties are routinely included in studies of TE materials. However the practical application of
thermoelectric materials requires that the thermoelectric materials have sufficient mechanical
integrity for in-use conditions. Waste heat recovery will subject TE materials to rapid heating
and cooling so thermomechanical properties, so designers require detailed information on the
temperature-dependent coefficient of thermal expansion (CTE) and elasticity, since for a given
temperature change, T, the induced temperature-dependent mechanical stresses, (T), is
approximated by

(T) 

E(T)(T)T
1  (T)

(7.2)

where the temperature-dependent coefficient of thermal expansion, the Young’s modulus, and
Poisson’s ratio, (T), E(T),and(T), respectively.
In general there is limited thermomechanical data for thermoelectric materials although
for PbTe-PbS the current authors have reported on the room temperature hardness and elastic
moduli [Ni 2010] and the temperature-dependent elastic moduli [Ni in preparation]. This study
196

determines (T) for (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 completes the data set needed
to evaluate Eq. (7.2). Along with the room temperature [Ni 2010] and high temperature elastic
moduli [Ni in preparation] this study comprise a portion of the authors’ and co-workers’ efforts
to characterize the temperature-dependent elasticity of LAST [Ren 2009 E LAST], PbTe [Ren
2008 E PbTe], and the skutterudites Co0.95Pd0.05Te0.05Sb3 and Ce0.9Fe3.5Co0.5Sb12
skutterudites [Schmidt 2012]. In addition to reporting E, (T) was determined for LAST (leadantimony-silver-tellurium) [Ren 2009 CTE] and Co0.95Pd0.05Te0.05Sb3 and
Ce0.9Fe3.5Co0.5Sb12 skutterudites [Schmidt 2012]. For LAST compositions, this group has also
evaluated the composition dependence of hardness [Ren 2008 Hcomp] and elastic modulus [Ren
2007 Ecomp] as well as the porosity-dependence of room temperature moduli for LAST [Ni
2009] and PbTe-PbS [Ni in press].
In both metals [Oppenheimer 2010] and ceramics [O’Brien 1985, Kingery 1976], bloating,
which is swelling, blistering or an increase porosity in the bulk material, sometimes occurs in
specimens densified using elevated temperature and pressure, such as the hot pressing and PECS
processes used in this study, when a densified specimen is thermally annealed without a
confining pressure [Ni in press, Schmidt 2011]. Bloating can result from a decomposition
reaction in which a gaseous species evolves internally during thermal annealing in the absence of
an external confining pressure [Kingery 1976]. In this study, bloating refers to an increase in
porosity due a post-densification annealing.
Specifically for thermoelectrics, both the thermal conductivity and electrical conductivity
will decrease with increasing porosity [Rice 1998]. A decrease in thermal conductivity and
electrical conductivity can affect ZT (Eq. (7.1)). In addition to thermal conductivity and

197

electrical conductivity mechanical properties, such as Young’s modulus [Ni 2009], hardness and
fracture strength, decrease with increasing porosity [Rice 1998].
In this study, the coefficient of thermal expansion,(T), was measured for powder
specimens and bulk cast, hot pressed, and pulsed electric current sintered (PECS) specimens. The
(T) was measured using (1) dilatometery and (2) high temperature x-ray diffraction from room
temperature up to a maximum temperature of 663 K. Dilatometery measurements also indirectly
monitored possible bloating in bulk specimens. Possible bloating due to post-densification
annealing was also monitored using scanning electron microscopy (SEM).

7.2.0

Experimental procedure

7.2.1

Specimen preparation

The PbTe-PbS ingots were cast in a rocking furnace using constituent powders that were at
least 99.99% pure. The cast ingots were either (i) cut into parallelepipeds or (ii) milled into
powders for subsequent densification via hot pressing (HP200, Thermal Technology LLC, Santa
Rosa, CA) or pulsed electric current sintering (SPS 10-4, Thermal Technology LLC, Santa Rosa,
CA). The powder was dry milled (DM) [Pilchak 2007], wet milled (WM) or dry/wet milled
(WM) [Hall 2009] in a planetary mill (PM100, Retsch, Newtown, PA) (Table 7.1). Powder
characterization was performed using a laser scattering apparatus (Saturn Digisizer,
Micromeritics, Norcross, GA a scanning electron microscope (SEM). After densification, the
grain sizes were measured on micrographs of fracture surfaces using a linear intercept method
and a stereo projection factor of 1.5 [Fullman 1953].

198

Table 7.1a The processing conditions for specimens included in this study that were measured
using dilatometery (TMA), high-temperature x-ray diffraction (HT-XRD) and scanning electron
microscopy (SEM) All PbTe-PbS powder and bulk specimens have the same composition,
(Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2
SiC
Powder
Specimen
Densification
nanoparticle Processing
Label
method
additions Technique
CIW040S
0.0 vol%
None
Cast
b

HP-53

0.0 vol%

WM (H)

HP -54

0.0 vol%

WM (H)

HP -55

0.0 vol%

WM (E)

PECS-02

WM (E)

PECS-10S

0.0 vol%
0.0 vol%

PECS-11

0.0 vol%

DM

PECS-15

0.0 vol%

DM

PECS-20

0.0 vol%

DM

PECS-23

0.0 vol%

DM

PECS-25

0.0 vol%

DM

PECS-27

0.0 vol%

DM

PbTe-PbS-9

0.0 vol%

WM (H)

CIW036S

0.0 vol%

c

DM

c

d

PECS

d

PECS

d

PECS

d

PECS

d

WM (H)

0.0 vol%

WM (H)

CIW063S

0.0 vol%

WM (H)

CIW064S

0.0 vol%

DM

CIW041S

0.0 vol%

WM (H)

a

PECS

Cast

e

823 K /60 MPa/20 min

e

673 K /60 MPa/20 min

SEM
SEM

e

823 K /60 MPa/20 min

SEM

e

673 K /60 MPa/20 min

SEM, TMA

e

723 K /60 MPa/20 min

SEM

e

723 K /60 MPa/20 min

SEM

e

823 K /60 MPa/20 min

SEM

e

823 K /60 MPa/20 min

SEM

PECS
PECS

d

MT

TMA
Hot pressed 723 K /74.4 MPa/120 min SEM, TMA
Hot pressed 723 K /74.4 MPa/120 min SEM, TMA
Hot pressed 723 K /74.4 MPa/120 min SEM, TMA
PECS

d

CIW040S

a

b

Sintering Max
Temp/Pressure/Time

b

Powder specimen

b

Powder specimen

HT-XRD
HT-XRD

b

Powder specimen

HT-XRD

b

Powder specimen

HT-XRD

Powder specimen

HT-XRD

Powder specimen

HT-XRD

d
b

Measurement technique

b

Dry and wet milled with hexane

c

Wet milled only with ethanol

d

Dry milled only

e

Pulsed electric current sintering

199

Table 7.1b The powder processing, measurement technique, ramp rate and temperature ranges
for the CTE measurements included in this study. For each dilatometer test, the atmosphere was
flowing 96 % Ar-4% H2, whereas for the HT-XRD measurements the atmosphere was 96 % N24% H2.
Specimen
Label

Powder
Processing
Technique

CIW040S

None

dilatometer

10.3 ║ x 7.6 x 5.1

1.5 K/min

293 K - 663 K

CIW040S

None

dilatometer

10.3 ║ x 7.6 x 5.1

1.5 K/min

293 K - 773 K

HP-53 #C

Wet milled
(hexane)

293 K - 543 K
293 K - 603 K
b
293 K - 603 K
293 K – 663 K

HP-54 #2
HP-54 #3
HP-55 #2
HP-55 #3

Wet milled
(hexane)
Wet milled
(hexane)
Wet milled
(ethanol)
Wet milled
(ethanol)
Wet milled
(ethanol)

Measurement
d
Ramp rate
Technique Dimensions (mm)

Temperature
range

a

dilatometer

6.3 ║x 5.0 x 5.0

2 K/min

dilatometer

10.0 ║ x 5.0 x 7.0

2 K/min

dilatometer

10.0║x 6.9 x 4.9

1.5 K/min

293 K - 603 K
b

dilatometer

9.9 ║ x 6.8 x 6.0

2 K/min

293 K - 603 K
293 K – 663 K

dilatometer

9.9 ║ x 6.9 x 6.0

1.5 K/min

293 K - 663 K

2 K/min

b

PECS -17

Dry milled only

dilatometer

4.1 ║ x 5.4 x 4.6

1.5 K/min

293 K - 603 K
293 K – 663 K
293 K - 663 K

PECS-15

Dry milled only

dilatometer

8.9║ x 5.0 x 3.9

1.5 K/min

293 K - 663 K

PECS -15

Dry milled only

dilatometer

8.9║ x 5.0 x 3.9

2 K/min

293 K - 603 K
293 K – 663 K

3 K/min

293 K - 603 K

3 K/min

293 K – 663 K

3 K/min

293 K – 663 K

3 K/min

293 K – 663 K

3 K/min

293 K – 693 K

3 K/min

293 K – 693 K

HP-55 #9

6.05 ║

dilatometer

c

b

Wet milled
HT-XRD
Powder specimen
(hexane)
Wet milled
CIW036S
HT-XRD
Powder specimen
(hexane)
Wet milled
CIW040S
HT-XRD
Powder specimen
(hexane)
Wet milled
CIW063S
HT-XRD
Powder specimen
(hexane)
CIW064
Dry milled only
HT-XRD
Powder specimen
Wet milled
CIW041S
HT-XRD
Powder specimen
(hexane)
a
half cycles 1-6: 293 K - 543 K, half cycles 9-12: 293 K - 603 K
b
half cycles 1-6: 293 K - 603 K, half cycles 9-12: 293 K - 663 K
c
Only one set of parallel surfaces
d
The dimension that was parallel to the probe is identified by ║
PbTe-PbS 9

200

7.2.2

Microstructural analysis via scanning electron microscopy

The size, shape and volume density of the pores were examined using micrographs from
scanning electron microscopy. Bloating was monitored on fresh fracture surfaces of asdensified and post-densification PbTe-PbS specimens using scanning electron microscopy. The
as-densified specimens were annealed at maximum temperatures between 693 K to 936 K for 2
hours in a flowing Ar (96%) – H2 (4%) atmosphere..
7.2.3

Thermal expansion experimental procedure

Two independent experimental techniques were used for thermal expansion measurements
on the PbTe-PbS specimens included in this study: (i) a dilatometer (Thermomechanical
Analyzer, TMA, Q400, TA Instruments, New Castle, DE) for the bulk specimens and (ii) x-ray
diffraction for powder specimens.
7.2.3.1 Dilatometery measurements
For the temperature-dependent thermal expansion measurements of the bulk parallelepipedshaped specimens via dilatometery, a 0.25 N force was applied to the silica dilatometer rod prior
to commencing the thermal expansion measurements. The force was held constant throughout
testing. To reduce oxidation during testing in the unsealed TMA chamber, the chamber was
flushed with a flowing atmosphere of 50 mL/min of 96% - argon/4% hydrogen gas for one hour
prior to heating the chamber. The gas flow was continued during the entire time that the
chamber was heated or cooled. For the dilatometery measurements, for each specimen, the
thermal expansion measurements were performed on six to twelve half thermal cycles, where a
heating and a cooling half cycle comprises a full thermal cycle. The specimens were either (i)
continuously cycled for three or four full thermal cycles from room temperature to 603 K, 663 K,

201

693 K, or 773 K (Table 7.1b) or (ii) continuously cycled for three full thermal cycles from room
temperature up to 543 K or 603 K and then subsequently cycled an additional three full thermal
cycles from room temperature to either 603 K or 663 K (Table 7.1b).

7.2.3.2 High-temperature x-ray diffraction measurements
The lattice parameter for the both powder specimens was determined using high-temperature
x-ray diffraction (XRD, X’Pert Pro MPD X-Ray Diffraction System, PANalytical, Natick, MA)
and the CTE was computed from the temperature-dependent changes in lattice parameter. The
XRD measurements were calibrated by running NIST standard reference material LaB6 powder,
SRM 660a, from 19° to 140°2θ, with a step size of 0.01700°2θ and a scan rate of 45.72 seconds
per step. For each of the five dry milled only and one dry/wet milled powder specimens in this
study, an XRD run was performed from 150 to 1400 2, with step size of 0.0010, using a Cu K-α
source and a fixed divergence slit size of 0.25. Using heating and cooling rates of 5 K/minute and
a nitrogen atmosphere the maximum temperatures ranged from 543 K to 663 K (Table 7.1b). A
XRD scan was collected at 30 K intervals with a 5 minute dwell time for each of the scans.

At

each 30 K interval, the lattice parameters were computed using a Reitveld analysis program
(X’Pert analysis, PANalytical, Natick, MA).

7.3.0

Results and discussion

7.3.1 Possible bloating monitored via SEM
For the as-densified fracture surfaces, each of the hot pressed and PECS-processed
specimens had spherical and quasi-spherical pores that ranged from submicron to three microns
in diameter (Figure 7.1). The mean grain size for the specimens densified from wet milled

202

Figure 7.1: The micrographs for the as-densified fractured surfaces for PbTe-PbS (a) hot pressed,
HP-53 and PECS-process specimens (c) PECS-02, and (e) PECS-10S do not show bloating. The
annealed internal fractured surfaces for (b) HP-53 and (d) PECS-02 surfaces did show evidence
of bloating, whereas PECS-10S, processed from dry milled powders, did not show evidence of
bloating. Table 7.1a gives the processing conditions for micrographs (a) – (f). All postdensification annealing was performed in flowing 96% Ar + 4% H2 gas.

203

powders (Table 7.1) was roughly 1.6 microns. The specimens densified from dry milled only
powders mean grain size was approximately 5 microns.
After annealing up to 936 K, each of the six thermally annealed PbTe-PbS specimens
processed from dry milled only powders showed no observable bloating (Table 7.1, Figure 7.1).
In contrast, the hot pressed (Figure 7.1b) and PECS-processed (Figure 7.1d) specimens annealed
over 693 K showed observable bloating. After the post-densification annealing the quasispherical pores ranged in size between three and ten microns (Figure 7.1b and 7.1d). In addition,
there were long lenticular pores that were 15 microns wide and over 100 microns long (Figure
7.1d). Thus, in this study, bloating is suppressed for PECS processed powders that were dry
milled only (no wet milling) at least under the conditions of a 2 hour anneal at 823 K in an
flowing 96% argon/4% hydrogen environment (Table 7.1).
However, bloating may occur in the dry milled only PECS specimens at higher annealing
temperature and/or annealing longer times. Further post-densification annealing studies will be
conducted to investigate the possible bloating in the (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2)
specimens for annealing times up to 24 hours and annealing temperatures up to 900 K.
For both the PbTe-PbS included in this study and included in previous studies, the bloating
is likely linked with a volatile phase that generates a gaseous phase (and hence bloating) upon
annealing the specimens outside the confining pressure of PECS or a hot press.

7.3.2

Thermal Expansion Results

7.3.2.1 CTE measurements via dilatometer (TMA)
The average linear CTE, CTE, was calculated between 325 K and 595 K for each half cycle
for the 11 specimens using

204

Table 7.2. The mean CTE, calculated from the TMA thermal expansion data for four hot pressed
(HP- specimens), one PECS pressed (PECS- specimens) and two cast ingot (CIW)
(Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 specimens. The specimens were thermally cycled
three or four times from room temperature to a maximum temperature, which is indicated in the
table. The temperature range over which the data was analyzed was 325 K – 595 K.

CIW040S
CIW040S
HP-53 #C
HP-54 #2

Fabrication
technique
Cast
Cast
Hot pressed
Hot pressed

HP-54 #3
HP-55 #1
HP-55 #2
HP-55 #3
PECS -15
PECS -15

Hot pressed
Hot pressed
Hot pressed
Hot pressed
PECS
PECS

Specimen Label

Maximum
temperature
603 K
773 K
a

543K, 603 K
a
603K, 663 K
603 K
a

603K, 663 K
a
603K, 663 K
693 K
663 K
a

6

21.5 ± 0.1
21.5 ± 0.1
21.7 ± 0.3
21.9 ± 0.1
21.3 ± 0.3
21.1 ± 0.1
21.6 ± 0.1
21.4 ± 0.1
21.4 ± 0.1
21.7 ± 0.1

603K, 663 K
a
This specimen was thermally cycled for six half cycles to the first temperature, and then
subsequently cycled an additional six half cycles to the second temperature

205

-1)

Mean CTE (x 10 K

avg 

LTmax  LTmin
LTmin
T2  T1
1

(7.3a)

where LT
and LT
are the length of the of the specimen at 325 K and 595 K,
max
min
respectively and Tmin and T max are temperatures 325 K and 595 K, respectively (Table 7.2).
For each half thermal cycle of the (i) six hot pressed specimens, (ii) one PECS processed
specimen and (iii) two cast PbTe-PbS specimens, the average CTE values were between 21.3 X
-6

-1

-6

-1

10 K to 21.5 X 10 K (Table 7.2).
Thus, despite the fact that the specimens were processed via three different techniques,
namely cast, hot pressed and PECS processed, the average CTE values were very similar (Table
7.2). The consistency among the average CTE values for each half cycle might be expected
since the CTE is relatively insensitive to microstructural parameters such as porosity and grain
size [Rice 2000, Charvat 1957, Panigrahi 2005, Turi 1995].
-6

-1

For the 10 specimens, the mean  avg was approximately 21.5 x 10 K (Table 7.2). The
meanavg was calculated without the first heating cycle, HT1, as settling of the dilatometer
probe on the specimen during the first heating cycle can result in a hysteresis between the first
heating cycle and the cooling cycle [Ren 2009 CTE] (Figure 7.2).
An unrecovered dimensional change was observed between the half cycles for the hot
pressed specimens thermally cycled at T > 603 K (Figure 7.2). This will discussed further in
Section 7.3.3.

206

Dimension Change (m)

(a)
80
60

HT1 / CL1
HT2 / CL2
HT3 / CL3
HT4 / CL4

40

TMAX = 693 K
No hysteresis

20
0

300

(b)
Dimension Change (m)

/
/
/
/

80
60

/
/
/
/
/
/

400
500
600
Temperature (K)

700

1HT / 1CL
2HT / 2CL
3HT / 3CL
4HT / 4CL
5HT / 5CL
6HT / 6CL

40

TMAX = 693 K

20

No hysteresis

0

300

400
500
600
Temperature (K)
Figure 7.2

207

700

Figure 7.2 (cont’d)

/
/
/

Dimension Change (m)

(c)

HT1 / CL1
HT3 / CL3
HT5 / CL5

/
/
/

HT2 / CL2
HT4 / CL4
HT6 / CL6

80
60
40

Cycles 1 - 6
TMAX = 603 K

0
300

400

500

No hysteresis

Cycles 7 - 12
TMAX = 663 K

20

Hysteresis

600

Temperature (K)

Figure 7.2 (cont’d) The dimensional change as a function of temperature for (a) a cast ingot
(CIW040S) from room temperature to 693 K, (b) a PECS-processed specimen (PECS-15) from
room temperature to 663 and (c) a hot pressed specimen (HP-55) from room temperature to 603
K and 663 K. For MSUHP-55 #1, hot pressed from wet milled powders, the hysteresis between
heating and cooling increased when the maximum temperature increased from 603 K to 663 K.
Although a hysteresis between the heating and cooling curves was observed for the hot pressed
specimen, no hysteresis between the heating and cooling curves was observed for the cast ingot
and the PECS-processed specimen.

208

Table 7.3 For six powder PbTe-PbS specimens thermally cycled over the given temperature
range, the average coefficient of thermal expansion,  measured using HT-XRD. Equation
(7.3b) described well the temperature dependence of the lattice parameter. The least-squares fit
2
of the data to equation (7.3b) yielded a coefficient of determination, r , greater than 0.992 in
each case.

Powder Name
CIW041S
CIW064S
PbTe-PbS-9
CIW036S
CIW040S
CIW063S

Powder
Processing
Method
Wet milled
(hexane)
Dry milled
only
Wet milled
(hexane)
Wet milled
(hexane)
Wet milled
(hexane)
Wet milled
(hexane)

Fabrication Temperature
Technique
range (K)

Average

-6 -1
 (10 K )

r

2

Powder

300 – 693 K

20.9 ± 0.1

0.999

Powder

300 – 693 K

20.9 ± 0.1

0.999

Powder

300 – 603 K

21.7 ± 0.2

0.998

Powder

300 – 663 K

21.7 ± 0.3

0.992

Powder

300 – 663 K

21.1 ± 0.3

0.994

Powder

300 – 663 K

21.4 ± 0.3

0.993

209

7.3.2.2. CTE measurements via x-ray diffraction
For six different powder specimens annealed up to 693 K using high temperature x-ray
diffraction (HT-XRD), the mean coefficient of thermal expansion, mean, was 21.4 ± 0.3 x 10

-6

-1

K (Table 7.3). The temperature-dependent coefficient of thermal expansion,  was
calculated using
a0(T)= T-TRT) a0-RT

b 

where a0(T) was the temperature-dependent lattice parameter, T was temperature in Kelvin, TRT
was the room temperature, and a0-RT is the lattice parameter at room temperature. During
heating of HT-XRD measurements, for each of the five powder specimens, a peak appeared at
approximately 440 K, identified as PbSnS, that was present during cooling. The PbSnS peak dspacing was 2.97852 Å and hkl was [002]. Upon the emergence of the PbS peak, the lattice
parameter increased (Figure 7.3). The average CTE,  was therefore calculated from the
temperature dependent lattice parameter during cooling for each of the six powder specimens
(Figure 7.3).

7.3.2.3 Comparison of the CTE results to the literature
For the specimens PbTe-PbS included in this study, the mean CTE over the temperature
-6

-1

range from room temperature to 603 K was about 21.5 x 10 K for the cast, hot pressed and
PECS processed specimens (Table 7.2 and Figure 7.1), which is comparable to the CTE values
determined for other PbTe-based thermoelectric materials [Ren 2009, Houston 1968]. For
-6

example, the average CTE values ranged from 20 to 24 X 10 K

210

-1

(Table 7.4) measured by

Lattice Parameter (nm)

(a)

Least-squares fit to Eq (7.3b)
Extrapolation of heating to 693 K
From 303 K - 453 K
From 693 K - 303 K

0.648

0.645
CIW064SHeating
CIW064SCooling

0.642
300

400

500

600

700

Temperature (K)

Lattice Parameter (nm)

(b)

Least -squares fit to Eq (7.3b)
Extrapolation of heating to 693 K
From 303 K - 453 K
From 693 K - 303 K

0.648

0.645
CIW041S Heating
CIW041S Cooling

0.642
300

400

500

600

Temperature (K)
Figure 7.3

211

700

Figure 7.3 (cont’d)

Lattice Parameter (nm)

(c) 0.651

Least -squares fit to Eq (7.3b)
Extrapolation of heating to 693 K
From 303 K - 453 K
From 693 K - 303 K

0.648

0.645

PbTe-PbS 9 HT1
PbTe-PbS 9 CL1
PbTe-PbS 9 HT2
PbTe-PbS 9 CL2

0.642
300

400

500

600

700

Temperature (K)

Lattice Parameter (nm)

(d)0.651

Least -squares fit to Eq (7.3b)
Extrapolation of heating to 693 K
From 303 K - 453 K
From 693 K - 303 K

0.648

0.645

CIW036S HT1
CIW036S CL1
CIW036S HT2
CIW036S CL2

0.642
300

400

500

600

Temperature (K)

212

700

Figure 7.3 (cont’d)

Lattice Parameter (nm)

(e) 0.651

Least -squares fit to Eq (7.3b)
Extrapolation of heating to 693 K
From 303 K - 453 K
From 693 K - 303 K

0.648

0.645

CIW063S HT1
CIW063S CL1
CIW063S HT2
CIW063S CL2

0.642
300

400

500

600

700

Temperature (K)

Lattice Parameter (nm)

(f) 0.651

Least-squares fit to Eq (7.3b)
Extrapolation of heating to 693 K
From 303 K - 453 K
From 693 K - 303 K

0.648

0.645

CIW040S HT1
CIW040S CL1
CIW040S HT2
CIW040S CL2

0.642
300

400

500

600

Temperature (K)

213

700

Figure 7.3 (cont’d) The apparent shift in lattice parameter at about 450 K to 500 K is likely
correlated with the appearance of a PbSnS peak in HT-XRD that begins to appear at roughly 440
K. For powder specimens that were (a) dry milled only and (b) – (f) wet and dry milled (Table
7.1a) the shift in lattice parameter occurred only during the first thermal cycle. The solid lines
represent the least-squares fit of equation (7.3b) between 303 K and 453 K for the first thermal
cycle. The dashed-dot line is an extrapolation of the temperature-dependent lattice parameter
during heating to 693 K. The dashed lines represent the least-square fit of the temperaturedependent lattice parameter heating and cooling data to equation (7.3b). The arrows indicate the
cycling direction.

214

Table 7.4 The average CTE for thermoelectrics in the literature. The fabrication technique,
density, temperature range, and measurement method for each composition.
Specimen
Composition
Ag0.86Pb19Sb

Fabrication Density Temperature Measurement
Technique (g/cm3)
range (K)
Method
Cast
8.16

1.0Te20

RT - 673

Dilatometer

22.2 ± 0.4

[Ren 2009
CTE]

RT - 673

Dilatometer

20.6 ± 0.5

[Ren 2009
CTE]

7.81

RT - 673

Dilatometer

21.0 ± 0.2

[Ren 2009
CTE]

7.58

RT - 623

HT-XRD

20.8 ± 0.5

[Ren 2009
CTE]

Powder

RT - 623

HT-XRD

24.2 ± 0.3

[Ren 2009
CTE]

8.24

RT

8.24

RT

Cast
Hot pressed

1.2Te20 (HP6)

Ag0.86Pb19Sb

[Ren 2009
CTE]

7.58

1.2Te20 (N43)

Ag0.43Pb18Sb

22.1 ± 0.3

Hot pressed

1.2Te20 (HP6)

Ag0.43Pb18Sb

Dilatometer

Hot pressed

1.0Te20 (HP20)

Ag0.43Pb18Sb

RT -673

8.06

1.0Te20

(N155)
Ag0.86Pb19Sb

Average
CTE
Reference
-6 -1
(10 K )

Planetary
Milled

(N155)
PbTe
PbTe
Ba8Ga16Ge30
Sr8Ga16Ge30
Co0.95Pd0.05T
e0.05Sb3+ 0.1
atomic% Ce
Co0.95Pd0.05T
e0.05Sb3
Ce0.9Fe3.5Co0.
5Sb12

CoSb3

Czochralski
Technique
Czochralski
Technique
Czochralski
Technique
Czochralski
Technique
Hot pressed
Planetary
Milled
Hot pressed
Planetary
Milled
Hot pressed
Planetary
Milled
Hot pressed

Capacitive
cell
Capacitive
cell

20.4 ± 0.4
19.7

a

300 - 973

Dilatometer

14.2

a

300 - 973

Dilatometer

14.1

7.58

323 - 698

Dilatometer

11.6 ± 0.3

Powder

303 – 773

HT-XRD

7.27

323 - 723

Dilatometer

Powder

303 – 773

HT-XRD

7.56

323 - 573

Dilatometer

Powder

303 - 773

HT-XRD

120 - 220

Dilatometer

[Houston
1968]
[Houston
1968]
[Okamoto
2008]
[Okamoto
2008]

NS
NS

NS

a

a

Not given by the author

215

[Schmidt
2012 DOI]
10.7 ± 0.2
10.1 ± 0.2

[Schmidt
10.3 ± 0.1 2012 DOI]
13.0 ± 0.1

[Schmidt
13.3 ± 0.3 2012 DOI]
9.1

[Rogl
2010]

TMA and HT-XRD for cast and hot pressed LAST thermoelectric materials (lead-antimonysilver-tellurium, with compositions Ag0.86Pb19Sb1.0Te20 and Ag0.43Pb18Sb1.2Te20 [Ren 2009]).
For updoped PbTe single crystals grown by the Czochralski technique, Houston et al. [Houston
1968] used capacitive cell measurements to measure an average room temperature CTE value of
-6

-1

about 20.4 X 10 K (Table 7.4). The CTE of PbTe-based materials is greater than many
thermoelectric materials. For example the CTE for clathrates, Ba8Ga16Ge30 and Sr8Ga16Ge30,
-6

-1

is 14.2 X 10 K [Okamoto 2008] (Table 7.4) and for skutterudites, the CTE is roughly 10 x
-6

-1

10 K [Rogl 2010, Schmidt 2012 DOI] (Table 7.4).

7.3.3 Hysteresis in thermal expansion measured by dilatometery
7.3.3.1 Hysteresis in thermal expansion caused by bloating
In the literature, a hysteresis has been observed in dilatometric L/L0 measurements
between heating and cooling for alumina-magnesia refractory castables [Auvray 2007, Auvray
2008], SiC refractory castables [Bahloul 2010], Al1.8Mg0.1Ti1.1O5 [Giordano 2002], aluminaaluminum titanate composite [Hasselman 1993], alumina-based cement castables [Kakroudi
2009, Nonnet 1999], magnesium dititanate [Bush 1958], beta-eucryptite (Li2O-Al2O3-2SiO2)
[Bush 1959], corderite-mullite refractory [Chotard 2008], itacolumite (natural occurring quartz)
[Doncieux 2008], MgTi2O5 [Kyszyk 1973], Y4Al2O9 [Yamane 1995] and thermoelectric
skutterudites [Schmidt in press]. The hysteresis in thermal expansion between heating and
cooling has been attributed to microcracking due to thermal expansion anisotropy and thermal
216

expansion mismatch [Auvray 2007, Auvray 2008, Giordano 2002 Bahloul 2010, Kakroudi 2009,
Nonnet 1999, Bush 1958, Bush 1959]. Other secondary mechanisms cited were dehydration
[Auvray 2007, Auvray 2008] and sintering [Bahloul 2010].
For the hysteresis caused by microcracking, the temperature dependent thermal
expansion curve during heating is greater than then thermal expansion curve during cooling
[Auvray 2007, Auvray 2008, Bahloul 2010, Bahloul 2010, Hasselman 1993, Kakroudi 2009,
Nonnet 1999, Bush 1958, Bush 1959, Bejjauoui 2010, Chotard 2008, Doncieux 2008, Kyszyk
1973, Yamane 1995]. During heating, microcracks in the specimen heal due to diffusion [Case
1983, Hasselman 1993], then during cooling microcracks are reinitiated and reformed, causing
the hysteresis between heating and cooling [Case 1983, Hasselman 1993] . However, for the
PbTe-PbS specimens in this study and skutterudites in the literature [Schmidt in press], the
thermal expansion curve during cooling was greater than the thermal expansion curve during
heating, indicating a different hysteresis mechanism, such as bloating. In addition to the
hysteresis in thermal expansion, there was also an observable increase in volume fraction
porosity (bloating) after post-densification annealing observed in SEM (Section 7.3.1, Figure
7.1).
In this study, possible bloating was measured indirectly using dilatometery by thermal
cycling up to 543 K, 603 K, 693 K or 773 K. To quantify the hysteresis, the strain, , was
calculated using

  (LT  LiRT ) / LiRT

(7.4)

where LT  LiRT is the change in specimen length as a function of temperature and L iRT is the
specimen’s length at the beginning of the test. The  was calculated at 10 degree intervals from

217

room temperature to 543 K, 603 K, 693 K or 773 K for each cycle, ci, where “i” represents the
ith half cycle.
The thermal expansion of a polycrystalline alumina specimen, measured between room
temperature and 1273 K, with a maximum strain of 0.008, was used as a standard. The cast and
PECS-processed PbTe-PbS specimens, which did not have an observable hysteresis in
temperature when thermally cycled between room temperature to 773 K and 663 K (Figure 7.2a
and 7.2b), respectively, had a maximum strain of 0.008, similar to the strain of the
polycrystalline alumina standard.
The five hot pressed PbTe-PbS specimens, thermally cycled between room temperature and
T < 603 K (Figure 7.2c and Table 7.2b), had an average maximum strain between 0.006 and
0.008 and no observable hysteresis. In contrast, the four hot pressed specimens thermally cycled
between room temperature and 663 K < T < 693 K average maximum strain was roughly 0.014
and had an observable hysteresis in thermal expansion between heating and cooling when
(Figure 7.2).
At room temperature, the average strain (Equation (7.3b)) for cycles < c2 was 0.0005 ±
0.0001 for the specimens without an observable hysteresis, the alumina standard and the cast
(Figure 7.2a) and PECS-processed PbTe-PbS specimens (Figure 7.2b). For the four hot pressed
specimens with an observable hysteresis, the average strain (Equation (7.3b)) at room
temperature for cycles < c2 was 0.004 ± 0.0001, a factor of 40 higher than the microstrain for the
specimens with no observable hysteresis. The increase in microstrain for specimens thermally
cycled between room temperature and T > 603 K indicates that the bloating-causing
decomposition reaction likely occurs at temperatures greater than 603 K.

218

7.3.3.2 Comparison to bloating monitored by elastic moduli measurements
In a previous study of hot pressed PbTe-PbS specimens of the same composition and
processing conditions, Ni et al. observed a hysteresis in Young’s and shear modulus during
thermal cycling up to 663 K [Ni in preparation]. However, the dilatometery in this study is more
sensitive to changes in porosity then the temperature-dependent elastic moduli measurements.
The change in porosity, P, due to the change in Young’s modulus, E, can be extrapolated using
the empirical porosity-modulus relationship
E(P) = E0exp(-bPEP)  P = bPE [E(P)]E

(7.5)

where the E0, the Young’s modulus of a theoretically dense specimen and bPE, the change in
modulus with porosity, P, were 1.5 and 56 GPa, respectively. The elastic moduli measurements
were sensitive to changes in volume fraction porosity greater than 0.01.
For thermal expansion measurements, dilatometery measures the change in dimension as a
function of temperature. There was not a change in mass during thermally cycling, so the
fractional change in volume measured using dilatometery resulted in a change in porosity. The
change in porosity, P, is a function of the change in volume, V, due to annealing
P 

m
 th V 2

V

(7.6)

where m is the mass,th is the theoretical density of the material, and V is volume. For the
specimens in this study, P was calculated using equation (7.6) and the measured mass and
dimensions before thermal expansion measurements. The change in volume was calculated
using the strain at room temperature and the dimensions of the specimens measured using
219

micrometers before thermal cycling. The dilatometeric measurements were more sensitive then
elastic moduli measurements and distinguished changes in volume fraction porosity greater than
0.005.
7.4.0 Summary and Conclusions
For PbTe-PbS specimens, the CTE, measured for five powder specimens using HT-HRD and
ten bulk specimens using dilatometery, were in agreement, with a mean CTE of 21.4 ± 0.3 x 10

-6

-1

K . An unrecoverable strain for the hot pressed and wet milled bulk specimens was observed at
temperatures greater than 603 K. This hysteresis between thermal cycles is likely a result of
bloating. However, there was no hysteresis in the PECS dry milled PECS specimen when
annealed up to 663 K or any observable bloating for the micrographs of the fracture surfaces.
The bloating in the four hot pressed specimens measured indirectly using dilatometry was
confirmed by comparing the porosity of fracture surfaces of as-densified and post-densified
surfaces. There was no bloating observed for DM PECS-processed specimens, where as there
was bloating at temperatures as low as 693 K for hot pressed specimens.

Acknowledgements
The authors acknowledge the financial support of Office of Naval Research Grant N00014-08-10613. Equipment purchases were funded by the Defense University Research Instrumentation
Program (DURIP) Grant No. N00014-07-1-0735 (Resonant Ultrasound Spectroscopy apparatus
and the laser scattering apparatus) and N00014-09-1-0785 (pulsed electric current sintering
apparatus) Office of Naval Research. Research through the Oak Ridge National Laboratory’s
High Temperature Materials Laboratory User Program was sponsored by the U. S. Department of
Energy, Office of Energy Efficiency and Renewable Energy, Vehicle Technologies Program. The
220

authors also acknowledge Ed Timm, Mechanical Engineering Department, Michigan State
University and Karl Dersch, Computer and Electrical Engineering Department, for their
assistance with hot pressing and cutting selected hot pressed specimens and Pulsed Electric
Current Sintering apparatus. All microscopy was performed at the Center for Advanced
Microscopy at Michigan State University.

221

REFERENCES

222

7.5.0 References
[Androulakis 2007] Androulakis, J., Lin, C. H., Kong, H. J., Uher, C., Wu, C. I., T, H. Cook, B.
A., T, C., Paraskevopoulos, M., Kanatzidis, M. G. J. Am. Chem. Soc. 2007, 129, 9780.
[Auvray 2007] Jean-Michel Auvray, Christian Gault, Marc Huger, Evolution of elastic
properties and microstructural changes versus temperature in bonding phases of alumina and
alumina–magnesia refractory castables, Journal of the European Ceramic Society 27 (2007)
3489–3496
[Auvray 2008] Jean-Michel Auvray, Christian Gault, Marc Huger, Microstructural changes and
evolutions of elastic properties versus temperature of alumina and alumina–magnesia
refractory castables Journal of the European Ceramic Society 28 (2008) 1953–1960.
[Bahloul 2010] O. Bahloul, T. Chotard, M. Huger, C. Gault Young’s modulus evolution at high
temperature of SiC refractory Castables, J Mater Sci (2010) 45:3652–3660
[Bejjaoui 2010] R. Bejjaoui, A. Benhammou, L. Nibou, B. Tanouti, J.P. Bonnet, A. Yaacoubi, A.
Ammar, Synthesis and characterization of cordierite ceramic from Moroccan stevensite and
andalusite, Applied Clay Science 49 (2010) 336–340
[Bush 1958] E. A. Bush and F. A. Hummel, “High-Temperature Mechanical Properties of
Ceramic Materials: I, Magnesium Dititanate,” Journal of the American Ceramic Society,
Volume 41, Issue 6, pages 189–195, June 1958
[Bush 1959] E. A. Bush and F. A. Hummel, “High-Temperature Mechanical Properties of
Ceramic Materials: II, Beta-Eucryptite,” Journal of the American Ceramic Society, Volume
42, Issue 8, pages 388–391, August 1959.
[Charvat 1957] F.R. Charvat, W. D. Kingery, Thermal Conductivity: XIII, Effect of
Microstructure on Conductivity of Single-Phase Ceramics, Journal of the American Ceramic
Society, 40 (1957) 306–315.
[Chotard 2008] T. Chotard, J. Soro, H. Lemercier, M. Huger, C. Gault, High temperature
characterisation of cordierite–mulliterefractory by ultrasonic means, Journal of the European
Ceramic Society 28 2129–2135 (2008)
[Doncieux 2008] A. Doncieux , D. Stagnol, M. Huger, T. Chotard, C. Gault, T. Ota, S.
Hashimoto, Thermo-elastic behaviour of a natural quartzite: itacolumite, J Mater Sci (2008)
43:4167–4174
[Francome 1958] M. H. Francome, British Journal of Applied Physics, 9 (1958) 415.
[Fullman 1953] R. L. Fullman, Measurement of particle sizes in opaque bodies, Trans AIME 197
(1953) 447 – 452.

223

[Giordano 2002] L. Giordano, M. Viviania, C. Bottinoa, M.T. Buscagliaa, V. Buscagliaa, P.
Nannib, Microstructure and thermal expansion of Al2TiO5–MgTi2O5 solid solutions
obtained by reaction sintering, Journal of the European Ceramic Society 22 (2002) 1811–
1822
[Hall 2009] Hall BD, Case ED, Ren F, Johnson J, Timm EJ. Agglomeration during wet milling
of LAST (lead-antimony-silver-tellurium) powders, Mater Chem Phys 2009; 113: 497- 502.
[Hasselman 1993] D. P. H. Hasselman, K.Y. Donaldson, E.M. Anderson, T.A. Johnson, Effect of
Thermal History on the Thermal Diffusivity and Thermal Expansion of an Alumina–
Aluminum Titanate Composite, J. Am. Ceram. Soc. 76 (1993) 2180-2184.
[Houston 1968] B. Houston, R. E. Strakna, H. S. Belson, J. Appl. Phys. 39 (1968) 3913.
[Hsu 2004] KF Hsu, S Loo, F Guo, W Chen, JS Dyck, C Uher, T Hogan, EK Polychroniadis,
MG Kanatzidis, Science, 303 (2004) 818.
[Joshi 2008] Giri Joshi, Hohyun Lee, Yucheng Lan, Xiaowei Wang, Gaohua Zhu, Dezhi Wang,
Ryan W. Gould, Diana C. Cuff, Ming Y. Tang, Mildred S. Dresselhaus, Gang Chen, and
Zhifeng Ren, Enhanced thermoelectric figure-of-merit in nanostructured p-type silicon
germanium bulk alloys, Nano Lett. 8, 4670-4674, (2008).
[Kakroudi 2009] M. Ghassemi Kakroudi, E. Yeugo-Fogaing, M. Huger, C. Gault, T. Chotard,
Influence of the thermal history on the mechanical properties of two alumina based
castables, Journal of the European Ceramic Society 29 (2009) 3197–3204.
[Kanatzidis 2010] M. G. Kanatzidis, Nanostructured Thermoelectrics: The New Paradigm?,
Chem. Mater. 2010, 22, 648–659.
[Kuszyk 1973] J. A. Kuszyk and R. C. Bradt, “Influence of Grain Size on Effects of Thermal
Expansion Anisotropy in MgTi2O5,” Journal of the American Ceramic Society, Volume 56,
Issue 8, pages 420–423, August 1973
[Lin 2009] Lin, H., Bozin, E. S., Billinge, S. J. L., Androulakis, J., Malliakas, C. D., Lin, C. H.,
Kanatzidis, M. G. Phys. Rev. B 2009, 80, (4).
[Ni 2009] J.E. Ni, F. Ren, E.D. Case, E.J. Timm, Porosity dependence of elastic moduli in LAST
(Lead–antimony–silver–tellurium) thermoelectric materials, Materials Chemistry and
Physics 118 (2009) 459–466.
[Ni 2010] J.E. Ni, E.D. Case, K.N. Khabira, R.C. Stewart, C-I Wu, Timothy P. Hogan, E.J.
Timm, S.N. Girard, M.G. Kanatzidis, Room temperature Young’s modulus, shear modulus,
Poisson’s ratio hardness of PbTe–PbS thermoelectric materials Materials Science and
Engineering B 170 (2010) 58–66.
[Ni in preparation] J.E. Ni, E.D. Case, R.D. Schmidt, C-I Wu, T. Hogan, R.M. Trejo, E. Lara-

224

Curzio, S N. Girard, M.G. Kanatzidis, Fracture mode, microstructure, and temperaturedependent elastic moduli for thermoelectric composites of PbTe-PbS with SiC nanoparticle
additions, to be submitted
[Ni in press] J.E. Ni, E.D. Case, R. Stewart, C-I Wu,T.P. Hogan, M.G. Kanatzidis, Bloating in
(Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055%PbI2 Thermoelectric Specimens as a Result of
Processing Conditions Journal of Electronic Materials, DOI: 10.1007/s11664-011-1853-0, in
press
[Nonnet 1999] Emmanuel Nonnet, Nicolas Lequeux and Philippe Boch, Elastic Properties of
o
High Alumina Cement Castables from Room Temperature to 1600 C, Journal of the
European Ceramic Society 19 (1999) 1575-1583.
[O’Brien 1985] O’Brien MH, Hunter Jr. O, Case ED, Mechanical effects of thermal cycling on
United States and Australian Synroc-B, J Mater Sci Lett 1985; 4: 367-369.
[Okamoto 2008] Okamoto, N. L., Nakano, T., Tanaka, K., Inui, H., Mechanical and thermal
properties of single crystals of the type-I clathrate compounds Ba8Ga16Ge30 and
Sr8Ga16Ge30, J. Appl. Phys. (2008) 104: AR 013529.
[Oppenheimer 2009] Oppenheimer S, Dunand DC. Porous NiTi by creep expansion of argonfilled pores, Mater Sci Eng A 2009; 523: 70–76
[Oppenheimer 2010] Oppenheimer S, Dunand DC. Solid-state foaming of Ti-6Al-4V by creep or
superplastic expansion of argon-filled pores, Acta Mater 2010; 58: 4387–4397
[Panigrahi 2005] B.B. Panigrahi, V.V. Dabhade, M.M. Godkhindi, Thermal expansion behaviour
of nanocrystalline titanium powder compacts, Materials Letters 59 (2005) 2539–254.
[Pilchak 2007] A. L. Pilchak, F. Ren, E. D. Case, E.J. Timm, H.J. Schock, C-I Wu, T.P. Hogan,
Characterization of dry milled powders of LAST (lead-antimony-silver-tellurium)
thermoelectric material, Phil. Mag. 87 (2007) 4567-4591.
[Poudel 2008] B. Poudel, Q. Hao, Y. Ma, Y. Lan, A. Minnich, B. Yu, X. Yan, D. Wang, A. Muto,
D. Vashaee, X. Chen, J.Liu, M.S. Dresselhaus, G. Chen, Z. Ren, Antimony telluride bulk
alloys high-thermoelectric performance of nanostructured bismuth, Science 320, 634-638
(2008).
[Ren 2007 Ecomp] F.Ren, E.D.Case, E.J.Timm, H.J. Schock, Young's modulus as a function of
composition for an n-type lead-antimony-silver-telluride (LAST) thermoelectric material,
Philosophical Magazine, 87 (2007)4907-4934.
[Ren 2008 E PbTe] F. Ren, E.D. Case, J.R. Sootsman, M.G. Kanatzidis, H. Kong, C. Uher, E.
Lara-Curzio, R.M. Trejo, The high-temperature elastic moduli of polycrystalline PbTe
measured by resonant ultrasound spectroscopy Acta Materialia 56 (2008) 5954–5963.

225

[Ren 2008 Hcomp] F. Ren, E.D. Case, E.J. Timm, H.J. Schock, Hardness as a function of
composition for n-type LAST thermoelectric material, Journal of Alloys and Compounds
455 (2008) 340–345
[Ren 2009 CTE] F. Ren, B.D. Hall, E.D. Case, E.J. Timm, R.M. Trejo, R.A. Meisner, E. LaraCurzio, Temperature-dependent thermal expansion of cast and hot-pressed LAST (Pb-SbAg-Te) thermoelectric materials, Philosophical Magazine, 89: (2009) 1439 -1455.
[Ren 2009 E LAST] F. Ren, E.D.Case, J.E.Ni, E.J.Timm, E. Lara-Curzio, R.M. Trejo, C.-H Lin,
M.G. Kanatzidis, (Temperature-dependent elastic moduli of lead telluride-based
thermoelectric materials, Philosophical Magazine,89 (2009) 143-167.
[Rice 1998] Rice RW. Porosity of Ceramics, New York: Marcel Dekker; 1998.
[Rice 2000] R. W. Rice, Mechanical Properties of Ceramics and Composites, Marcel Dekker
Inc., New York, 2000.
[Rogl 2010] G. Rogl, L. Zhang, P. Rogl, A. Grytsiv, M. Falmbigl, D. Rajs, M. Kreigisch, H.
Müller, E. Bauer, J. Koppensteiner, W. Schranz, M. Zehetbauer, Z. Henkie and M.B. Maple,
J. Appl. Phys. 107 (2010) 043507.
[Schmidt 2012] R.D. Schmidt, E.D. Case, J.E. Ni, J.S. Sakamoto, R.M. Trejo, E. Lara-Curzio
Temperature-dependent Young’s modulus, shear modulus and Poisson’s ratio of p-type
Ce0.9Fe3.5Co0.5Sb12 and n-type Co0.95Pd0.05Te0.05Sb3 skutterudite thermoelectric
materials, Philosophical Magazine, 92 (2012) 727-759.
[Schmidt in press CTE] R.D. Schmidt, E.D. Case, J.E. Ni, J.S. Sakamoto, R.M. Trejo, E. LaraCurzio, E. A. Payzant, M.J. Kirkham, R.A. Peascoe-Meisner, The temperature dependence
of thermal expansion for p-type Ce0.9Fe3.5Co0.5Sb12 and n-type Co0.95Pd0.05Te0.05Sb3
skutterudite thermoelectric materials, Philosophical Magazine,
DOI:10.1080/14786435.2011.644815 in press
[Turi 1995] T. Turi, U. Erb, Mater. Sci. Eng. A, Thermal expansion and heat capacity of
porosity-free nanocrystalline materials, 204 (1995) 34-38.
[Yamane 1995] Hisanori Yamane, Kazuhiro Ogawara, Mamoru Omori, Toshio Hirai, Thermal
expansion and a thermal phase transition of Y4Al2O3 ceramics, Journal of the American
Ceramic Society, 78 : 5, 1230-1232, 1995

226

8.0 Summary and Conclusions
8.1.0 Porosity dependence of the elastic moduli for LAST
Similar to other brittle materials [Rice 2000], the hot pressed LAST specimens in this
study Young’s and shear moduli decrease with porosity can be best described by the linear
empirical equations

E(P)  E d (1  b PEP) and G(P)  G d (1  b PGP) .

(8.1)

over the range of porosity, 0.01 < P < 0.14 (Figure 3.3). For specimens with porosity higher than
in this study the exponential form might be a better fit [Rice 1998]. There was scatter in the
Poisson’s ratio, especially between about 0.03 < P < 0.04, however, with increasing P, Poisson’s
ratio value tended to decrease.
Knowledge of the porosity dependence of the elastic moduli is critical to numerical or
analytical stress-strain calculations for both the cast and hot pressed materials. When
microcracking is present, understanding the decrement in moduli due to porosity can help us
separate the effects of microcracking and porosity for a given porous, microcracked specimen.

8.2.0 Room temperature mechanical properties for PbTe-PbS
This is the first study to measure the hardness, fracture toughness and elastic moduli for
(Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 specimens. As mentioned in the previous section
(Section 8.1.0), the elastic moduli are needed for stress-strain analysis. The hardness and
fracture toughness are associated with a material’s machinability as well as its resistance to wear.

227

8.2.1 Hardness measured via Vickers indentation
The mean hardness of the six dense (P = 0.03) hot pressed PbTe-PbS 8% specimens was
1.18 + 0.09 GPa which is comparable to that of hot pressed LAST (AgaPbbSbcTed) (Table 6.1).
The mean hardness was 0.70 + 0.06 for four as-cast specimens, which is 70 % lower than the
mean hardness of the hot pressed specimens of same composition (Table 6.1). The higher
hardness observed in this study for hot pressed specimens (compared to the as-cast specimens) is
likely a grain size effect. Therefore, specimens that are fabricated using powder processing
techniques and densified using hot pressing or PECS will likely have better machinability and
resistance to wear then those specimens that are cut from cast ingots.

8.2.2 Fracture toughness measured via Vickers indentation
Measured using Vickers indentation, the average fracture toughness of the six hot pressed
PbTe-PbS specimens with no SiCnp was approximately 0.35 ± 0.04 MPa·m

1/2

(Table 6.2). The

mean fracture toughness is comparable to other thermoelectric materials [Lawn 1977, Uneo
2005, Zhao 2008, Evans 1975] and other chalcogenides [Varshneya 2007, Zhu 2007, Guin
2002].

8.2.3 Elastic moduli measured via resonant ultrasound spectroscopy
For PbTe-PbS specimens, the 13 as-densified and 32 post-densification annealed elastic
moduli measurements with volume fraction porosities ranging from 0.03 to 0.32 the decrease in
E with increasing P was consistent with

E(P)  E D exp(  b PE P)

(8.2)

228

where ED is the E when P = 0 and bPE is a material dependent constant over the porosity range,
0.03< P < 0.21 . For PbTe-PbS the least-squares fit to the exponential relationship (Eq. 8.2) had
2

an r = 0.990, bPE = 1.33 and ED = 56.17 GPa. The ED is consistent with the literature where
for single crystal PbTe, the aggregate Young’s modulus, 58.08 GPa [Houston 1968] and 56.95
GPa [Einspruch 1963]. As was discussed in Section 8.1.0, knowledge of the E versus P
relationship are used for stress-strain calculations and decoupling E decreases due to porosity or
microcracking damage.
For the nine as-densified HP and PECS specimens, along with the 32 annealing
measurements on the same nine specimens, each of the hot pressed specimens modulus
decreased with a corresponding increase in P after post-densification anneals between 603 K and
693 K (Figures 5.4 and 6.1). The decrease in E due to post-densification annealing is consistent
with an increase in porosity (likely due to bloating). The PECS specimens processed from wet
milled powders (Table 5.1) also bloated during post-densification annealing up to 693 K (Figure
5.1) The further implications of bloating during post-densification annealing will be discussed in
the following section (Section 8.3.0).

8.3.0 Bloating monitored via SEM for PbTe-PbS specimens
Seven PECS-processed dry milled only specimens had no observable bloating for postdensification annealing < 936 K (Figure 5.3). After post-densification annealing T < 723 K hot
pressed LAST specimens had observable bloating for post-densification annealing for dry milled
only and CGSR specimens (Figure 5.1). In addition, hot pressed and PECS-processed PbTe-PbS
specimens had observable bloating for post-densification annealing T < 693 K for dry/wet milled
specimens and wet milled only specimens (Figure 5.2).
229

No observable bloating for the combination of dry milling only and densification via
PECS for Pb0.95Sn0.05Te – PbS 8% + 0.055 mol% PbI2 in observation via SEM up to 936 K
and when monitored via elasticity measurements up to 773 K. The lack of bloating is perhaps
due to the inherent cleaning of surface contamination of the powder particle surfaces during
sintering [Groza 1992]. The D/WM process may have produced organic-based residues on the
powder particle surface that were not present in the DM powders.
Microstructural instability, such as bloating, during in-use temperatures will cause a
decrease in both electrical and thermal conductivity, which in turn can affect ZT (Eq. (1.1)). In
addition, the increase in bloating-dependent porosity will decrease both elastic moduli and
fracture strength. As the PbTe-PbS TE in-use high temperature will range between 723 K and
823 K, this fabrication technique inhibits (for specimens without SiCnp) or limits (for specimens
with SiCnp) bloating during in use conditions, providing a more stable microstructure.

8.4.0 Temperature-dependent elastic moduli and CTE for PbTe-PbS
8.4.1 Temperature dependent elastic moduli measured via RUS
For the 15 (Pb0.95Sn0.05Te)0.92(PbS)0.08-0.055% PbI2 heating cooling cycles (11
specimens) included in this study the elastic moduli decreased with increasing temperature, T,
according to
E = ERT – bTE(T – TRT) and G = GRT – bTG(T – TRT)

(8.3)

were bTE and bTG describes the Young’s and shear modulus-temperature behavior, and the
room-temperature, TRT, Young’s modulus, ERT, and shear modulus, GRT, values were 53.0 ±

230

2.2 GPa (Table 6.6) and 21.2 ± 0.8 GPa, respectively. For the PbTe-PbS-SiCnp composite
specimens bTE and bTG ranged from 0.020 GPa/K to 0.027 GPa/K and 0.008 GPa/K to 0.011
GPa/K (Table 6.6), respectively. The values for bTE and bTG are similar to the slopes for PbTe
and PbTe-doped specimens in the literature where bTE (Eq. 8.3) ranged from 0.017 GPa/K to
0.036 GPa/K [Ren 2009] and bTG (Eq. 8.3) ranged from 0.008 GPa/K to 0.016 GPa/K [Ren
2009]. The temperature-dependent elastic moduli

8.4.2 Temperature dependent coefficient of thermal expansion measured via dilatometry and
high-temperature x-ray diffraction
For temperature ranges of 293 K to 543 K and 293 K to 693 K, the average coefficient of
-6

-1

thermal expansion was (i) 21.5 ± 0.2 x 10 K measured using dilatometry and (ii) 21.3 ± 0.4 x
-6

-1

10 K measured using high-temperature x-ray diffraction (HT-XRD). These values of CTE
agree with similar PbTe-based chalcogenides in the literature with an average CTE of roughly
-6

-1

20.5 x 10 K [Houston 1968, Ren 2009]. The coefficient of thermal expansion was used to
calculate the change in dimensions during high-temperature RUS measurements.

8.4.3 Bloating monitored using HT-RUS and dilatometry
Hot pressed specimens showed a hysteresis in elastic moduli (Figure 6.5) and thermal
expansion (Figure 7.1) between heating and cooling when thermally cycled over 603 K. In
contrast, the PECS-processed specimens showed no hysteresis in both the elastic moduli (Figure

231

6.1) and thermal expansion (Figure 7.1) measurements between heating and cooling up to 693
K.
However, the bloating monitored using temperature-dependent elastic moduli measurements
could only distinguish changes in volume fraction porosity that were greater than 0.01. In
comparison, the dilatometry measurements of the thermal expansion were sensitive to changes
in P as low as 0.006. Therefore, though RUS is a non-destructive method to monitor changes in
elastic moduli with temperature, unsurprisingly, dilatometry has a higher sensitivity to changes
in porosity.

8.5.0 Room temperature elastic moduli for LLZO
This work (Appendix A) presents the first room temperature Young’s modulus, shear
modulus, bulk modulus, Poisson’s ratio, and hardness values for Li7La3Zr2O12 garnet fabricated
using hot pressing. The mean Vickers hardness was 6.3 ± 0.3 GPa and 5.2 ± 0.4 for the P = 0.03
and 0.06 hot pressed LLZO specimens, respectively. The Young’s modulus was 149.8 ± 0.4
GPa for P = 0.03 and 132.6 ± 0.2 GPa for P = 0.06.
As this is the first work in the literature for the mechanical properties of the Li7La3Zr2O12
composition, the values of hardness and elastic moduli were compared to the H, E, and G of
other garnet materials in the literature. The mechanical properties were consistent with the trend
(equation (A.2)) of a power law decrease in E(Fig. A.2a), G (Fig. A.2b), and H (Fig. A.2c). The
elastic moduli measured in this study are used to help model stress-strain calculations that a
solid-state battery undergoes during in use conditions.

232

8.6.0 Future Work
8.6.1 Higher purity SiCnp
Currently limited bloating is observed in dry milled PECS-processed specimens with SiCnp. The
vendor specified purity of the SiCnp is 95% metals basis. The limited bloating could be a result
of contaminants on the SiCnp powder particle surfaces that are resistant to the PECS “cleaning”
process.

A bloating study of higher purity SiCnp powders (for example vendor specified 99%

purity, Alpha Asear) in PbTe-PbS is needed to investigate this further.

8.6.2 SiCnp fracture toughness
The fracture mode changed from transgranular to intergranular for PbTe-PbS specimens with and
without SiCnp, respectively. The change of fracture mode may indicate a possible change in
fracture toughness [ Kawabata 1977, Mukhopadhyay 2010, Karakasidis 2011]. Unfortunately,
Vickers indentations failed to produce a complete radial crack system to measure fracture
toughness. Future work would involve using a cube corner Berkovich indentation tip to indent
the specimens to calculate fracture toughness. The lower crack pop-in thresholds of a cube
corner Berkovich indentation tip could potentially cause a complete radial crack system to
measure fracture toughness.

233

8.6.3 Fracture strength and Weibull analysis of PbTe-PbS specimens with and without SiCnp
During in use conditions, the TE materials are subjected to mechanical loads and vibrations,
as well as thermal stresses. Therefore, an understanding of the fracture strength for the
specimens both with and without SiCnp are needed for modeling. In addition, as the TE legs are
electrically in series, the entire module will fail if one leg fractures. Therefore, a Weibull
analysis, which is a based on extremal value statistics, is needed to evaluate the fracture strength
of brittle materials. Weibull analysis is a “weakest link" model in which failure in brittle
materials occurs at the largest flaw.
The fracture strength is measured using either a four point bending or biaxial fracture, with
parallelepipeds or cylindrical disks, respectively. To date, we have been unable to fabricate the
20 specimens needed for a complete Weibull analysis.

234

REFERENCES

235

8.7.0 References
[Bateman 1966] T.B. Bateman, Elastic moduli of single crystal europium iron garnet and yttrium
iron garnet, J. Appl. Phys. 37 (1966) 2194-219
[Clark 1961] A.E. Clark and R.E. Stranka, Elastic constants of single-crystal YIG, J. Appl. Phys.
32 (1961) 1172-1173.
[Evans 1975] A. G. Evans and H. Johnson, J. Am. Ceram. Soc. 58 (1975) 244–249.
[Graham 1970] L.J. Graham and R. Change, Elastic moduli of single-crystal gadolinium gallium
garnet, J. Appl. Phys. 41 (1970) 2247-2248.
[Guin 2002] J.Guin, T. Rouxel, and J. Sangleboeuf, J. Am. Ceram. Soc. 85 (2002) 1545–1552.
[Karakasidis 2011] Karakasidis TE, Charitidis CA. Influence of nano-inclusions' grain
boundaries on crack propagation modes in materials, Mater Sci Eng B 2011; 176:490–493.
[Kawabata 1977] Kawabata T, Izumi, O. Relationship between fracture toughness and
transgranular fracture in an Al-6.0% 2n-2.5% Mg alloy, Acta Matall Mater 1977; 25: 505512.
[Lawn 1977] B. R. Lawn and A. G. Evans, J. Mater. Sci. 12 (1977) 2195-2199.
[Mezeix 2006] L. Mezeix and D.J. Green, Comparison of the Mechanical Properties of Single
Crystal and Polycrystalline Yttrium Aluminum Garnet, Int. J. Appl. Ceram. Technol. 3
(2006) 166–176
[Mukhopadhyay 2010] Mukhopadhyay A, Chakravarty D, Basu B. Spark Plasma-Sintered WCZrO(2)-Co Nanocomposites with High Fracture Toughness and Strength, J Am Ceram Soc
2010; 93: 1754–1763.
[Ren 2009] Ren, F., Case, E. D., Ni, J. E., Timm, E. J., Lara-Curzio, E., Trejo, R. M., Lin, C. -H.
and Kanatzidis, M.G. Temperature-dependent elastic moduli of lead telluride-based
thermoelectric materials,Philosophical Magazine, 89 (2009) 143 —167.
[Rice 2000] R. W. Rice, Mechanical Properties of Ceramics and Composites, Marcel Dekker
Inc., New York, 2000.
[Saunders 1992] G. A. Saunders, S. C. Parker, and N. Benbattouche, H. I. Alberts, Elastic and
nonlinear acoustic properties of the terbium iron garnet Tb3Fe5O12, in relation to those of
other garnets, Phys. Rev. B 46 (1992) 8756 – 8767
[Schmidt 2012] Schmidt RD, Case ED, Ni JE, Sakamoto JS, Trejo RM, Lara-Curzio E,
Temperature-dependent Young’s modulus, shear modulus and Poisson’s ratio of p-type

236

Ce0.9Fe3.5Co0.5Sb12 and n-type Co0.95Pd0.05Te0.05Sb3 skutterudite thermoelectric
materials,” Philosophical Magazine, Philos. Mag., 2012; 92: 727-759
[Simmons 1971] G. Simmons, H. Wang, Single crystal elastic constants and calculated aggregate
properties: A handbook, Cambridge, MA, The MIT Press, 1971.
[Uneo 2005] K. Uneo, A Yammoto, T. Inoue, S. Sodeoka, and H. Obara, J. Alloys Compds. 392
(2005) 295-299.
[Varshneya 2007] A. K. Varshneya and D. J. Mauro, J Non-Cryst Solids 353 (2007) 1291–1297.
[Winkler 1955]H.G.F. Winkler, Struktur und Eigenshaften der Kristalle, Springer Vaerlag,
Berlin, Germany, 1955.
[Zhao 2008] L. D. Zhao., B. Zhang, J. Li, M. Zhou. W. Liu, and J. Liu, J. Alloys Compds. 455
(2008) 259-264.
[Zhu 2007] S. Zhu, H. Ma, L. Calvez, X. Zhang, J. Lucas, J. Adam, H. Shang, and T. Rouxel, J
Non-Cryst Solids 353 (2007) 1298–1301.

237

APPENDICES

238

APPENDIX A

239

This chapter was submitted to Journal of Alloys and Compounds
Appendix A: Room temperature elastic moduli and Vickers hardness of hot pressed LLZO
cubic garnet
1

1

1

1

Jennifer E. Ni , Eldon D. Case , Jeffrey S Sakamoto , Ezhiyl Rangasamy ,
2

Jeffrey B Wolfenstine
1

Chemical Engineering and Materials Science Department, Michigan State University,
East Lansing, MI 48824 USA
2
Army Research Laboratory, RDRL-SED-C, 2800 Powder Mill Road, Adelphi, MD 20783, USA
ABSTRACT
Cubic garnet Li6.24La3Zr2Al0.24O11.98 (LLZO) is a candidate material for use as an electrolyte
in Li-Air and Li-S batteries. The use of LLZO in practical devices will require LLZO to have
good mechanical integrity in terms of scratch resistance (hardness) and an adequate stiffness
(elastic modulus). In this paper the powders were fabricated using powder processing. All
specimens were then densified via hot pressing. The room temperature elastic moduli (Young’s
modulus, shear modulus, bulk modulus, and Poisson’s ratio) and hardness were measured using
resonant ultrasound spectroscopy (RUS), and Vickers indentation, respectively. For volume
fraction porosity, P, the Young’s modulus was 149.8 ± 0.4 GPa (P = 0.03) and 132.6 ± 0.2 GPa
(P = 0.06). The mean Vickers hardness was 6.3 ± 0.3 GPa for P = 0.03 and 5.2 ± 0.4 for P =
0.06.
Keywords: energy storage materials, elasticity, ultrasonics, mechanical properties.

240

A.1.0 Introduction
Recently, there has been interest in the development of Li-Air and Li-S batteries for high
energy applications [1]. One Li-Air configuration involves the use of a lithium anode in a nonaqueous electrolyte which is separated from an aqueous electrolyte containing the air cathode by
a solid state Li-ion conducting membrane [2-4]. For the case of Li-S a possible configuration
involves a solid Li-ion conducting membrane separating molten lithium from molten sulfur.
To be used as a membrane in these situations the material must have high relative density,
high total Li-ion conductivity and good chemical stability. In addition, the material should also
exhibit good mechanical properties. The elastic moduli are needed for stress-strain calculations
and hardness is a measure of the resistance to scratching and point contact damage. For
example, both Young’s modulus and Poisson’s ratio are often used to construct stiffness matrices
for stress-strain calculations via finite element analyses [5]. One material that has recently
become of interest as a possible membrane material for Li-Air and Li-S batteries based on the
garnet structure is a cubic Li7La3Zr2O12 (LLZO). There have been studies on the ionic
conductivity and chemical stability of cubic Li7La3Zr2O12 prepared by powder processed and
chemical methods (i.e., Pechini) [6-10].
No mechanical properties are available in the literature for cubic LLZO garnet materials.
This study is the first to report the Young’s modulus, shear modulus, bulk modulus and hardness
of dense, hot pressed cubic Li6.24La3Zr2Al0.24O11.98.

A.2.0 Experimental Procedure
A.2.1 Specimen Preparation
241

Lithium carbonate (Puratronic 99.998%, Alfa Aesar), lanthanum (III) hydroxide
(99.95%, Alfa Aesar), zirconium oxide (99.9%, Inframat Advanced Materials LLC) and gamma
aluminum oxide (99.9 %, 50 nm, Mager Scientific Inc) precursors were used to synthesize
single-phase cubic Li6.24La3Zr2Al0.24O11.98 (LLZO) [11]. The precursors were mixed in an
agate milling vial using a Retsch PM-100 planetary mill. After mixing, the powders were loaded
into a stainless steel die and cold pressed into pellets at 100 MPa. The pellets were placed in
boron nitride coated Al2O3 combustion boats (Coors Combustion boat from Sigma Aldrich)
o

fired in air at 1000 C for 4 hours and reground in an agate milling vial using a Retsch PM-100
planetary mill. The boron nitride (BN) coating prevented the reaction between the Al2O3
o

crucible and the LLZO pellets. The reground LLZO powders were hot-pressed at 1000 C under
40 MPa pressure for 1 hour under flowing argon. The resulting pellet was removed from the hot
o

press and heated in air at 1000 C for 4 hours to burn off residual graphite from the hot pressing
die. The LLZO specimens were mounted in Crystalbond wax (Buehler, Lake Bluff, Il) and cut
into rectangular parallelepipeds using a diamond saw.
The bulk densities of the rectangular parallelepiped hot-pressed specimens were
determined from the mass and dimensions (Table A.1) measured using a micrometer (Mitutoyo,
293-832, Aurora, IL) and an electronic balance (Ohaus Adventurer, AR2140, Pinebrook, NJ).
The electronic balance and the micrometer were calibrated using commercial test weights (1 g, 2
g, 5 g and 10 g, Tromner ASTM class 7) and gauge blocks (ranging in dimension from 1 mm to
20 mm, Mitutoyo Grade 0), respectively.

242

Table A.1. The specimen geometry, dimensions, density, volume fraction porosity, P and
measurement techniques for the LLZO rectangular parallelepiped, RP, and crescent-shaped, CR,
specimens included in this study. The specimens were powder processed from ingot and
densified by hot pressing. The elastic moduli were measured using resonant ultrasound
spectroscopy (RUS) and the hardness was measured via Vickers indentations.
Specimen Label

Specimen
geometry

Dimensions

Density
3
(g/cm )

P

Measurement
technique

LLZO-01a

RP

7.9 mm x 6.3 mm x
2.8 mm

4.97

0.03

RUS

LLZO-01b

CR

9.0 mm x 4.5 mm

LLZO-02a

RP

LLZO-02b

CR

7.3 mm x 2.7 mm

LLZO-02c

CR

8.2 mm x 3.0 mm

a
b

a

8.0 mm x 7.1 mm
x 2.5 mm
a
a

NA

b

4.78
NA
NA

b
b

NA

b

Vickers
indentations

0.06
NA
NA

b
b

RUS
Vickers
indentations
Vickers
indentations

Dimensions refer to length and maximum width of the crescent shaped specimens
Not available

243

The relative density values and hence, the porosity was determined by dividing the bulk
3

density by the theo of cubic Al-containing LLZO (5.107 g/cm [9]). Four crescent-shaped
specimens were cut from the edges of the disc-shaped hot pressed billets. The resulting
parallelepiped specimens were used for elasticity measurements and the crescent-shaped
specimens were used for hardness testing (Table A.1). Each of the hardness and elasticity
specimens were polished using successively smaller diamond paste with grit sizes down to one
micron (Diamond polishing compounds, Leco, St. Joseph, MI).

A.2.2 X-ray diffraction and scanning electron microscopy
The microstructure of the hot-pressed specimens was examined on uncoated fracture
surfaces using scanning electron microscopy (SEM) with an accelerating voltage of 1 and 3 kV.
Phase purity was evaluated from x-ray diffraction data obtained with a Rigaku Ultima III
diffractometer using Cu K radiation. The lattice constant was determined by obtaining the
diffraction data in parallel beam geometry and fitting the data using Rietveld refinement [12]
with RIQAS software (Materials Data Inc.).

A.2.3 Vickers indentation measurements
The Vickers hardness, H, was measured using a Shimadzu hardness tester (Shimadzu HMV2000, Kyoto, Japan). Before indentation, the indenter was calibrated using a commercially
available standard hardness block (761-048, Yamamoto Scientific Tools Lab, Co., Ltd., Japan).
The average hardness of the LLZO specimens was determined using ten indentations per load on
the polished surface at loads of 2.9 N and 4.9 N with a 5 second loading time. To avoid the
interference between stress fields of closely spaced indentations or perturbations caused by
244

specimen edge effects, separation distances of at least 500 m were maintained between adjacent
indentation sites. No indentations were placed closer than roughly 1000 m from the nearest free
edge of the specimen.
H

The H values were calculated using

1.8544F
( 2a ) 2

(A.1)

where F is the applied force and 2a is the diagonal of the diamond indentation impression [13].

A.2.4 Resonant ultrasound spectroscopy (RUS) measurements
The elastic moduli were determined using resonant ultrasound spectroscopy (RUS), which is
a non-destructive dynamic method. Two piezoelectric transducers induce mechanical vibrations
in the specimen and an additional piezoelectric transducer detects the vibrations. Using
commercially available software (Quasar, Magnuflux, Albuquerque, NM), the elastic moduli
were calculated from the resonant vibrational frequencies, the dimensions and mass of the
specimen. Additional details on the RUS experimental procedure are found elsewhere [14].

A.3.0 Results and Discussion
A.3.1 Microstructure and lattice parameter of LLZO specimens
In this study, the LLZO microstructure was observed on a (i) fracture surface of LLZO-01
(Fig. A.1a) and (ii) at five sites approximately three mm apart along a diametral fracture for
LLZO-02 (Figs. A.1b- A.1e). Measured using the linear intercept method with a stereographic
projection factor of 1.5 [15], the fracture surfaces of hot pressed LLZO-01 and 02 had equiaxed
grains with average grain sizes of 4.5 and 5.0 microns, respectively (Fig. A.1a, A.1c- A.1e).
The pores were spherical or quasi-spherical with diameters ranging from submicron to roughly

245

Figure A.1
246

Figure A.1 (cont’d). The fracture surfaces for the hot pressed specimens (a) LLZO-01 and (c – d)
LLZO-02. The fracture surface of LLZO-02 was examined at (e) five different sites along the
diametral fracture. Each site was roughly 3 mm apart and sites 1 and 5 were approximately 0.5
mm from the specimen edge. For each micrograph the grain size was measured using the linear
intercept method and a stereographic projection factor of 1.5 [15].

247

three microns. Thus the microstructure appeared to be homogenous for the two hot pressed
LLZO specimens included in this study (Fig. A.1).
X-ray diffraction confirmed that after hot-pressing the pellet was single-phase cubic LLZO.
After burning off the graphite residue, the pellet appeared bright white. Applying Rietveld
analysis to the x-ray-diffraction data yielded a lattice parameter value, a0, of 12.9773 Å for the
single-phase cubic Li6.24La3Zr2Al0.24O11.98 included in this study.

A.3.2 Elastic moduli measured via RUS
With RUS, the mechanical vibrational spectra of two hot pressed LLZO specimens were
measured (Tables A.1 and A.2) over the frequency interval from 150 kHz to 1000 kHz. The
elastic moduli were calculated using commercially available software. Table A.2 compares the
data for elastic moduli for LLZO from this study to polycrystalline yttrium iron garnets from the
literature [16, 17].
In this study, for the specimen with P = 0.03, the Young’s modulus, E, shear modulus, G,
bulk modulus, B and Poisson’s ratio,  were 149.8 ± 0.4 GPa, 59.6 ± 0.1 GPa, 102.8 ± 0.3 GPa
and 0.257, respectively (Table A.2). For P = 0.06, E = 132.6 ± 0.2 GPa, G = 52.1 ± 0.04 GPa, B
= 97.7 ± 0.2 GPa and = 0.274 (Table A.2). The elastic moduli decreased with increasing
porosity in agreement with the general trend for bulk polycrystalline specimens [14, 16, 18 - 20].

A.3.3 Hardness measured via Vickers indentation testing
For indentation loads of 2.9 N and 4.9 N, the average Vickers hardness (equation (A.1)) of 10
indentations per load was 6.4 ± 0.4 GPa and 6.2 ± 0.3 for P = 0.03 and 5.2 ± 0.4 GPa and 5.3 ±
0.4 GPa for P = 0.06. The hardness decreases with increasing porosity which is in agreement
248

Table A.2. The density, volume fraction porosity, P, Young’s modulus, E, bulk modulus, B,
shear modulus, G, and Poisson’s ratio, , for the hot pressed rectangular parallelepiped
specimens included in this study as well as for polycrystalline garnet specimens from the
literature.
Specimen Density
P
3
Label
(g/cm )
LLZO-01a
LLZO-02a
Y3Fe5O12
(YIG)
Y3Fe5O12
(YIG)
Y2.9Fe5.1
O12
Y2.7Fe5.3
O12
Y2.5Fe5.5
a

O12

Measurement
E (GPa) B (GPa) G (GPa)
Reference

Technique
149.8 ± 102.8 ±
0.257 ±
4.97 0.03
RUS
59.6 ± 0.1
This study
0.4
0.3
0.002
132.6 ± 97.7 ±
52.1 ±
0.274 ±
4.78 0.06
RUS
This study
0.2
0.2
0.04
0.001
sonic
a
5.01 0.004 resonance
196.3
76.5
0.277
[16]
NA
technique

4.572 0.115

Pulse-echo

157.7

117.4

61.8

0.276

[17]

4.825 0.064

Pulse-echo

144.9

96.3

58.0

0.249

[17]

4.901 0.043

Pulse-echo

98.4

71.3

38.8

0.270

[17]

4.833 0.047

Pulse-echo

78.3

64.3

30.2

0.296

[17]

Not available

249

with the general trend for bulk polycrystalline specimens that H decreases with increasing
volume fraction porosity, P [18, 20, 21].

A.3.4 Comparison of LLZO elastic moduli and hardness with literature data for other garnets
Since this is the first study of the elastic moduli and hardness for LLZO, it is important to
compare values obtained in this study with the moduli and hardness of other garnets in the
literature. For a given crystal structure the mechanical properties as a function of lattice
parameter, a0, can be represented by the empirical relationship

A  bAa omA

(A.2)

where mechanical property A is Young’s modulus, E, bulk modulus, B, shear modulus, G, or
hardness, H. Also bA is a material-dependent constant and mA is the exponent for the particular
mechanical property [22-24]. For example, we use mG to denote the exponent for the shear
modulus, G, in equation (A.2).
The exponents mB, mG, and mH (equation (A.2)) depend on the crystal structure [22, 23, 25 2

28] (Table A.3). The r values for the literature data (Table A.3) ranged from 0.983 to 0.999 for
2

the moduli and hardness except for an r of 0.886 for the FCC metals [25], thus equation (A.2)
describes relatively well the decrease in B, G, and H with increasing a0. Although a direct
relationship between Young’s modulus and lattice parameter has not been illustrated in the open
literature, a number of papers imply that in addition to the shear modulus the Young’s modulus
is proportional to the interatomic distance [29 - 32]. The E and G values for garnets [33-38],
including data for LLZO, are plotted in Fig. A.2a and Fig. A.2b, respectively, as function of a0.
250

Table A.3. The exponents mB, mG, and mH obtained by a least-squares fit to equation (A.2) for
bulk modulus, B, shear modulus, G, and hardness, H data, respectively from the literature for
2
various cubic crystalline structures. The coefficient of determination, r , along with the number
of particular compositions of a given crystal structure included in the least-squares fit, N, are
listed within the parentheses given below each of the numerical values of the fitted exponents.
Crystal Structure

mB

a

2

(r , N)

Alkaline halide
(rock salt)

NA

Alkaline earth
oxides (rock salt)

3.3 ± 0.1
(0.998, 8)

Alkaline earth
sulfides (rock salt)
Face-center-cubic
metals
Zincblende
semiconductors

e

e

NA

e

NA

e

NA

b

mG

mH

2

Reference

2

(r , N)

(r , N)

3.2 ± 0.2
(0.983, 7)

3.0

d

d

(0.996 , 11)

[22, 23, 24, 25]

d

3.0

e

NA

d

(0.998 , 4)

[22, 23]

d

3.0
(0.990, 4)

e

NA

c

6.4 ± 1.3
(0.886, 7)
4.7 ± 0.1
(0.999, 9)

[28]

e

[25]

e

[25]

NA
NA

a

2

Gilman reported mB = 4 for alkaline earth oxides [22]. Gilman did not report the r values
[22].
b
Gilman reported mG = 4 and 5 for alkaline halides and zincblende semiconductors, respectively
2

[22, 25]. Gilman did not report the r values [22, 25].
c

2

Exponent mG value excluding thorium. If thorium is included in the analysis, then r = 0.758

and mG = 5.2. Gilman reported mG = 6.35 when the plot included Th [25].
d

2

Reported by Gilman [23]. All other exponents and r values in this table were calculated by
the present authors.
e
Not available

251

Young's Modulus (GPa)

(a)

Gd3Ga5O12 [33, 34]

300

Y3Fe5O12 [33, 35]
Y3Fe5O12 [33, 36]

250

Y3Al5O12 [37]
Tb3Fe5O12 [38]
LLZO [This Study]

200

150

r2 = 0.955
mE = 8.9 0.9

P = 0.03
P = 0.06

12

13

Lattice Parameter (Å)

Shear Modulus (GPa)

(b)

Gd3Ga5O12 [33, 34]

120

Y3Fe5O12 [33, 35]
Y3Fe5O12 [33, 36]

100

Y3Al5O12 [37]
Tb3Fe5O12 [38]
LLZO [This Study]

80

60

r2 = 0.941
mG = 9.3 1.0

P = 0.03
P = 0.06

12

13

Lattice Parameter (Å)
Figure A.2

252

Figure A.2 (cont’d)

Vickers Hardness (GPa)

(c)

Gd3Ga5O12 [27]

Y3Al5O12 [27]

Gd3Sc2Ga3O12[27]

Eu3Ga5O12[27]

Y3F5O12[27]

30
25
20

Nd3Ga5O12[27]
Y3Ga5O12[27]
Tb3Ga5O12[27]

15

LLZO [This Study]

10

r2 = 0.840
mH = 11.7 2.0

P = 0.03
P = 0.06

5
12

12.5

13

Lattice Parameter (Å)
Figure A.2 (cont’d). The (a) Young’s modulus, (b) shear modulus, and (c) hardness as a function
of lattice parameter for the aggregate average values for single crystal garnet data in the literature
(open symbols) and the LLZO garnet specimens in this study (filled symbol). In (a), (b), and (c)
the dashed line represents the least-squares fit of equation (A.2) to the data in this study and
single crystal garnet in the literature [27, 33 - 38]. The scatter in hardness, H, is likely due to the
different mechanisms that can affect H (Section 3.3).

253

From both Fig. A.2a and A.2b it is observed that the LLZO data is in excellent agreement with
single crystal literature data for other garnets. The fit of equation (A.2) to the E and G data for
2

all garnets shown including LLZO, yielded r values of 0.936 and 0.914, respectively (Fig. A.2a
and A.2b).
In general H decreases with increasing a0 via a power law relationship (equation (A.2), Table
A.3). In particular for the cubic garnet structure, the H versus a0 relationship also follows
equation (A.2) (Fig. A.2c), as does the cubic garnet LLZO in this study. The hardness data for
LLZO (this study) agrees relatively well with the single crystal literature data (Fig. A.2c) [27].
2

However, the r value of 0.840 indicates greater scatter in the H versus a0 data fit to equation
(A.2) (Fig. A.2c) compared to the scatter observed in E (Fig. A.2a) and G (Fig. A.2b). For both
single crystal and polycrystalline garnets, the observed scatter in H (Fig. A.2c) may reflect the H
dependence on the load, loading rate, the dislocation density, or residual stresses [39]. In
general, for polycrystalline materials, H is also a function of grain size [40] and porosity [20].
The Poisson’s ratio,  (which unlike E, B, and G is relatively insensitive to P [41]) ranged
from 0.226 to 0.295 for 21 single crystal and polycrystalline cubic garnets in the literature [16,
17, 33 - 38, 42, 43]. For LLZO in this study, the Poisson’s ratio is bracketed by the  values for
cubic garnets in the literature (Table A.2).

A.4.0 Summary and Conclusions
This work presents the first room temperature Young’s modulus, shear modulus, bulk
modulus, Poisson’s ratio, and hardness values for Li7La3Zr2O12 garnet fabricated using hot
pressing. Dense (P = 0.03 to 0.06) billets with mean grain sizes of roughly 5 microns were
254

produced by hot pressing. For loads 2.9 and 4.9 N, the mean Vickers hardness, H, was 6.3 ± 0.3
GPa and 5.2 ± 0.4 for the P = 0.03 and 0.06 hot pressed LLZO specimens, respectively. The
Young’s modulus was 149.8 ± 0.4 GPa for P = 0.03 (Table A.2) and 132.6 ± 0.2 GPa for P =
0.06.
The values of E, B, G, and H for Li7La3Zr2O12 found in this study are consistent with the
trend (equation (A.2)) of a power law decrease in mechanical properties with increasing lattice
parameter observed for other garnet materials in the literature for E (Fig. A.2a) [33 - 38], B [33 38], G (Fig. A.2b) [33 - 38], and H (Fig. A. 2c) [27].

Acknowledgements
We would like to acknowledge the financial support of the U.S. Army Research Office (ARO)
and Army Research Laboratory (ARL) under grant W911NF-10-2-0089-P00001.

255

REFERENCES

256

A.5.0 References
[1] J. B. Goodenough, Y. Kim, Challenges for rechargeable batteries, J. Power Sources 196
(2011) 6688 - 6694.
[2] I. Kowalczk , J. Read, M. Salomon, Li-air batteries: A classic example of limitations owing
to solubilities, Pure Appl. Chem. 79:5 (2007) 851 - 860.
[3] S. J. Visco, B. D. Katz, Y. S. Nimon, L. C. De Jonghe, Protected active metal electrode and
battery cell structures with non-aqueous interlayer architecture, US Pat. 7,282,295 B2 (2007).
[4] J. Wolfenstine, J. L. Allen, J. Sumner, J. Sakamoto, Electrical and mechanical properties of
hot-pressed versus sintered LiTi2(PO4)3, Solid State Ionics 180 (2009) 961 - 967.
[5] J. N. Reddy, An Introduction to the Finite Element Method, Third Ed., McGraw-Hill Higher
Education, New York, 2006.
[6] Y. Shimonishi, A. Toda, T. Zhang, A. Hirano, N. Imanishi, O. Yamamoto, Y. Takeda,
Synthesis of garnet-type Li7-xLa3Zr2O12-1/2x and its stability in aqueous solutions, Solid
State Ion. 183 (2011) 48 -53.
[7] M. Kotobuki, H. Munakata, K. Kanamura, Y. Sato, T. Yoshida, Compatibility of
Li7La3Zr2O12 Solid Electrolyte to All-Solid-State Battery Using Li Metal Anode, J.
Electrochem. Soc. 157 (2010) A1076 – A1079.
[8] I. Kokal, M. Somer, P.H.L. Notten, H.T. Hintzen, Sol-gel synthesis and lithium ion
conductivity of Li7La3Zr2O12 with garnet-related type structure, Solid State Ion. 185 (2011)
42 - 46.
[9] C. A. Geiger, E. Alekseev, B. Lazic, M. Fisch, T. Armbruster, R. Langner, M. Fechtelkord,
N. Kim, T. Pettke, W. Weppner, Crystal Chemistry and Stability of Li7La3Zr2O12 Garnet: A
Fast Lithium-Ion Conductor, Inorganic Chem. 50 (2011) 1089 -1097.
[10] R. Murugan, V. Thangadurai, W. Weppner, Fast lithium ion conduction in garnet-type
Li7La3Zr2O12, Angew. Chem. In. Ed. 46 (2007) 7778 - 7781.
[11] E. Rangasamy, J. Wolfenstine, J.S. Sakamoto, The role of Al and Li concentration on the
formation of cubic garnet solid electrolyte of nominal composition Li7La3Zr2O12, Submitted
to Solid State Ion. 2011.
[12] H. M. Rietveld, A Profile Refinement Method for Nuclear and Magnetic Structures, J. Appl.
Crystallogr. 2 (1969) 65 - 71.

257

[13] J. B. Wachtman, W.R. Cannon, M.J. Matthewson, Mechanical properties of ceramics, 2nd
edition, New Jersey, John Wiley and Sons, Inc, 2009.
[14] F. Ren, E. D. Case, A. Morrison, M. Tafesse, M. J. Baumann, Resonant ultrasound
spectroscopy measurement of Young’s modulus, shear modulus and Poisson’s ratio as a
function of porosity for alumina and hydroxyapatite, Philos. Mag. 89 (2009) 1163 – 1182.
[15] R. L. Fullman, Measurement of particle sizes in opaque bodies, Trans AIME, 197 (1953)
447 – 452.
[16] H. M. Chou, E. D. Case, Characterization of some mechanical properties of polycrystalline
yttrium iron garnet (YIG) by non-destructive methods, J. Mater. Sci. Lett. 7 (1988) 12171220
[17] P.U. Sharma and K.B. Modi, Effect of Fe
iron garnet Phys. Scr. 81 (2010) 015601

3+

substitution on elastic properties of yttrium

[18] A. Dey, A. K. Mukhopadhyay, Fracture toughness of microplasma-sprayed hydroxyapatite
coating by nanoindentation, Int. J. Appl. Ceram. Technol. 8 (2011) 572–590.
[19] J. E. Ni, F. Ren, E. D. Case, E. J. Timm, Porosity dependence of elastic moduli in LAST
(Lead-antimony-silver-tellurium) thermoelectric materials, Mater. Chem. Phys. 118 (2009)
459-466.
[20] R. W. Rice, Porosity of Ceramics, Marcel Dekker, Inc., New York, 1998.
[21] T. P. Hoepfner, E. D. Case, The influence of the microstructure on the hardness of sintered
hydroxyapatite, Ceram. Int. 29 (2003) 699-706.
[22] J.J. Gilman, Micromechanics of flow in solids, New York, McGraw Hill, 1969.
[23] J.J. Gilman, Chemistry and physics of mechanical hardness, New Jersey, John Wiley and
Sons, Inc, 2009.
[24] W.A. Wooster, Physical Properties and atomic arrangements in crystals, Rep. Prog. Phys. 16
(1953) 62 – 82.
[25] J.J. Gilman, Strength of ceramic crystals, Mechanical behavior of crystalline solids,
Proceedings of American Ceramic Society Symposium, Nat'l. Bur. Std. Monograph 59,
(1963) 79-102
[26] A.R. Ruffa, Theory of the electronic polarizabilities or ions in crystals: Applications to the
alkali halide crystals, Phys. Rev. 130 (1963) 1412-1423.

258

[27] D. B. Sirdeshmukh, K. G. Subhadra, K. K. Rag, T. T. Rao, Hardness of crystals with NaCl
structure and the significance of the Gilman-Chin parameter, Cryst. Res. Technol. 30 (1995)
861 - 866.
[28] H.G.F. Winkler, Struktur und Eigenshaften der Kristalle, Springer Vaerlag, Berlin,
Germany, 1955.
[29] M. Liu, B. Shi, J. Guo, X. Cai, H. Song, Lattice constant dependence of elastic modulus for
ultrafine grained mild steel, Scr. Mater. 49 (2003) 167–171.
[30] A.K. Vijh, A correlation between dielectric breakdown and mechanical strengths of alkali
halides, J. Mater. Sci. 10 (1975) 1087-1088.
[31] D. Ravinder, K. Vijaya Kumar, B.S. Boyanov, Elastic behaviour of Cu–Zn ferrites, Mater.
Lett. 38 (1999) 22–27
[32] A. Makishima, J.D. Mackenzie, Direct calculation of Young’s modulus of glass, J. NonCryst. Solids 12 (1973) 35-45.
[33] G. Simmons, H. Wang, Single crystal elastic constants and calculated aggregate properties:
A handbook, Cambridge, MA, The MIT Press, 1971.
[34] L.J. Graham and R. Change, Elastic moduli of single-crystal gadolinium gallium garnet, J.
Appl. Phys. 41 (1970) 2247-2248.
[35] T.B. Bateman, Elastic moduli of single crystal europium iron garnet and yttrium iron garnet,
J. Appl. Phys. 37 (1966) 2194-219
[36] A.E. Clark and R.E. Stranka, Elastic constants of single-crystal YIG, J. Appl. Phys. 32
(1961) 1172-1173.
[37] L. Mezeix and D.J. Green, Comparison of the Mechanical Properties of Single Crystal and
Polycrystalline Yttrium Aluminum Garnet, Int. J. Appl. Ceram. Technol. 3 (2006) 166–176
[38] G. A. Saunders, S. C. Parker, and N. Benbattouche, H. I. Alberts, Elastic and nonlinear
acoustic properties of the terbium iron garnet Tb3Fe5O12, in relation to those of other
garnets, Phys. Rev. B 46 (1992) 8756 – 8767
[39] J.J. Gilman, Hardness-A strength microprobe, in: J.H. Westbrook, H. Conrad (Eds.), The
science of hardness testing and it’s research applications, American Society for Metals,
United States of America, 1973, pp. 51-74.
[40] R.W. Rice, Mechanical Properties of Ceramics and Composites, Marcel Dekker Inc., New
York, 2000.

259

[41] A.R. Boccaccini, Comment on Effective Elastic Moduli of Porous Ceramic Materials, J.
Am. Ceram. Soc. 77 (1994) 2779- 2781.
[42] R.K. Verma, Elasticity of some high-density crystals, J. Geophys. Research, 65 (1960) 757766.
[43] N. Soga, Elastic constants of garnet under pressure and temperature, J. Geophys. Res. 72
(1967) 4227-4234.

260

APPENDIX B

261

Appendix B: Milling parameters and processing conditions for PbTe-PbS PECS specimens

The following table and figures report the different powder processing and temperaturepressure-time profiles used to fabricate the PbTe-PbS pulsed electric current sintered (PECS)
specimens to date.

262

Table B.1 The powder processing for each PECS-processed PbTe-PbS specimen. All milling was performed using a planetary mill in
an argon-atmosphere glove box. The specimens were fabricated using powders that were (1) dry milled, (2) wet milled, or (3) dry and
wet milled. The media referenced in this table were alumina spheres. The mix mill refers to the planetary milling of PbTe-PbS
powders with SiC nanoparticles (SiC).
Name

Ingot

Dry Mill
Media=10mm, 114g.
3hr, 150RPM

Wet Mill
Media= 140g of D=20mm, 60g of
D=3mm. 150 RPM 6hrs 25 ml Hexane

Mix Mill

C-PTS-P-01

CIW063S

C-PTS-P-02

CIW063S

None

Media= 3mm, 200g Al2O3. 9 hours, 150
RPM, 35ml ethanol

None

C-PTS-P-03

CIW063S

Media=10mm, 114g.
3hr, 150RPM

Media= 140g of D=20mm, 60g of
D=3mm. 150 RPM 6hrs 25 ml Hexane

9.9g B1AH+0.1g SiC. Media= 114g
of D=10mm 110RPM 3hrs (2.5
vol% SiC)

C-PTS-P-04

CIW063S

None

Media= 3mm, 200g Al2O3. 9 hours, 150
RPM, 35ml ethanol

9.9g B1A E+0.1g SiC. Media= 114g
of D=10mm 110RPM 3hrs (2.5
vol% SiC)

C-PTS-P-05

CIW063S

Media=10mm, 114g.
3hr, 150RPM

Media= 140g of D=20mm, 60g of
D=3mm. 150 RPM 6hrs 25 ml Hexane

None

C-PTS-P-06

CIW063S

Media=10mm, 114g.
3hr, 150RPM

Media= 140g of D=20mm, 60g of
D=3mm. 150 RPM 6hrs 25 ml Hexane

9.96g B1BH+0.04g SiC. Media=
114g of D=10mm, 110RPM 3hrs (1
vol% SiC)

C-PTS-P-07

CIW063S

Media=10mm, 114g.
3hr, 150RPM

Media= 140g of D=20mm, 60g of
D=3mm. 150 RPM 6hrs 25 ml Hexane

9.86g B1BH+0.14g SiC Media=
114g of D=10mm, 110RPM 3hrs
(3.5 vol% SiC)

263

None

Table B.1 (cont’d)
Name
Ingot

Dry Mill

Wet Mill

Mix Mill

C-PTS-P-08

CIW064S

Media=10mm, 114g.
3hr, 150RPM

None

None

C-PTS-P-09

CIW063S

Media=10mm, 114g.
3hr, 150RPM

Media= 140g of D=20mm, 60g of
D=3mm. 150 RPM 6hrs 25 ml Hexane

None

C-PTS-P-10

CIW063S

Media=10mm, 114g.
3hr, 150RPM

Media= 140g of D=20mm, 60g of
D=3mm. 150 RPM 6hrs 25 ml Hexane

None

C-PTS-P-11

CIW064S

Media=10mm, 114g.
3hr, 150RPM

None

None

C-PTS-P-12

CIW064S

Media=10mm, 114g.
3hr, 150RPM

None

9.9g B2+0.1g SiC. Media= 114g of
D=10mm 110RPM 3hrs (2.5 vol%
SiC)

C-PTS-P-13

CIW064S

Media=10mm, 114g.
3hr, 150RPM

None

None

C-PTS-P-14

CIW064S

Media=10mm, 114g.
3hr, 150RPM

None

9.88g B3+0.12g SiC. Media= 114g
of D=10mm 110RPM 3hrs (3 vol%
SiC)

C-PTS-P-15

CIW064S

Media=10mm, 114g.
3hr, 150RPM

None

None

264

Table B.1 (cont’d)
Name
Ingot

Dry Mill

Wet Mill

Mix Mill
9.9g B3+0.1g SiC. Media= 114g of
D=10mm 110RPM 3hrs (2.5 vol%
SiC)

C-PTS-P-16

CIW066S

Media=10mm, 114g.
3hr, 150RPM

None

C-PTS-P-17

CIW064S

Media=10mm, 114g.
3hr, 150RPM

None

9.88g B3+0.12g SiC. Media= 114g
of D=10mm 110RPM 3hrs (3 vol%
SiC)

C-PTS-P-18

CIW064S

Media=10mm, 114g.
3hr, 150RPM

None

9.92g B3+0.08g SiC. Media= 114g
of D=10mm 110RPM 3hrs (2 vol%
SiC)

C-PTS-P-19

CIW064S

Media=10mm, 114g.
3hr, 150RPM

None

None

C-PTS-P-20

CIW066S

Media=10mm, 114g.
3hr, 150RPM

None

None

C-PTS-P-21

CIW066S

Media=10mm, 114g.
3hr, 150RPM

None

None

C-PTS-P-22

CIW064S

Media=10mm, 114g.
3hr, 150RPM

None

None

C-PTS-P-23

CIW064S

Media=10mm, 114g.
3hr, 150RPM

None

None

Media=10mm, 114g.
3hr, 150RPM

None

None

C-PTS-P-24

CIW66S

265

Table B.1 (cont’d)
Name
Ingot

Dry Mill
Media=10mm, 114g.
3hr, 150RPM

Wet Mill

Mix Mill

None

None

C-PTS-P-25

CIW064S

C-PTS-P-26

CIW066S

Media=10mm, 114g.
3hr, 150RPM

None

None

C-PTS-P-27

CIW066S

Media=10mm, 114g.
3hr, 150RPM

None

None

C-PTS-P-28

CIW066S

Media=10mm, 114g.
3hr, 150RPM

None

None

C-PTS-P-29

CIW036S

Media=10mm, 114g.
3hr, 150RPM

Media= 140g of D=20mm, 60g of
D=3mm. 150 RPM 6hrs 25 ml Hexane

None

C-PTS-P-30

CIW036S

Media=10mm, 114g.
3hr, 150RPM

Media= 140g of D=20mm, 60g of
D=3mm. 150 RPM 6hrs 25 ml Hexane

None

C-PTS-P-31

CIW036S

Media=10mm, 114g.
3hr, 150RPM

Media= 140g of D=20mm, 60g of
D=3mm. 150 RPM 6hrs 25 ml Hexane

None

C-PTS-P-32

CIW070S

Media=10mm, 114g.
3hr, 150RPM

None

None

C-PTS-P-33

CIW070S

Media=10mm, 114g.
3hr, 150RPM

None

None

C-PTS-P-34

CIW070S

Media=10mm, 114g.
3hr, 150RPM

None

None

266

Table B.1 (cont’d)
Name
Ingot
C-PTS-P-35

C-PTS-P-36

C-PTS-P-37

CIW070S

Dry Mill
Media=10mm, 114g.
3hr, 150RPM

CIW089S

9.92g PbTe-PbS+0.08g SiC. Media=
114g of D=10mm 110RPM 3hrs (2
vol% SiC)

None

267

None

None

Media=10mm, 114g.
3hr, 150RPM

Mix Mill

None

Media=10mm, 114g.
3hr, 150RPM

CIW089S

Wet Mill

9.88g PbTe-PbS +0.12g SiC.
Media= 114g of D=10mm 110RPM
3hrs (3 vol% SiC)

Pressure
Temperature

800

60

600

40

500

30

400

20

300

Temperature (K)

50

10
0

20

40

60

80

Pressure (MPa)

700

100 120 140

Time (minutes)
Figure B.1 The temperature-pressure-time profile for PECS-processed specimens, C-PTS-P-01,
C-PTS-P-02, C-PTS-P-03, and C-PTS-P-04. The heating rate and cooling rate was 50 K/minute
and 5 K/minute, respectively. The ramp rate for pressure during heating was 5 MPa/min and 0.5
MPa/min during cooling. The specimens were sintered at the maximum temperature and
pressure for 20 minutes
Pressure
Temperature

800

60

600

40

500

30

400

20

300

Temperature (K)

50

10
0

20

40

60

80

Pressure (MPa)

700

100 120 140

Time (minutes)
Figure B.2 The temperature-pressure-time profile for PECS-processed specimens, C-PTS-P-05,
C-PTS-P-06, and C-PTS-P-07. The heating rate and cooling rate was 50 K/minute and 5
K/minute, respectively. The maximum temperature was held for 20 minutes. The pressure was
held at 20 MPa during heating until the specimen reached the maximum temperature. Once the
specimen reached 823 K, the pressure was increased to 60 MPa.

268

Pressure
Temperature

60
50

700
40
600
30
500
20
400

Pressure (MPa)

Temperature (K)

800

10
300
0

20

40

60

80

100 120 140

Time (minutes)
Figure B.3 The temperature-pressure-time profile for PECS-processed specimen, C-PTS-P-08.
The heating rate and cooling rate was 50 K/minute and 5 K/minute, respectively. The maximum
temperature was held for 20 minutes. The pressure was held at 20 MPa during heating until the
specimen reached the maximum temperature, 873 K. Once the specimen reached 873 K, the
pressure was increased to 60 MPa.
Pressure
Temperature

60
50

700
40
600

30

500

20

400

Pressure (MPa)

Temperature (K)

800

10

300

0
0

50

100

150

Time (minutes)
Figure B.4 The temperature-pressure-time profile for PECS-processed specimen, C-PTS-P-09.
The heating rate and cooling rate was 50 K/minute and 5 K/minute, respectively. The maximum
temperature was held for 30 minutes. The pressure was held at 20 MPa during heating until the
specimen reached the maximum temperature, 873 K. Once the specimen reached 823 K, the
pressure was increased to 60 MPa. The longer sintering time was due to a miscommunication
with Karl Dresch.
269

Pressure
Temperature

60
50

700
40
600

30

500

20

400

10

300

Pressure (MPa)

Temperature (K)

800

0
0

50

100 150 200 250 300

Time (minutes)
Figure B.5 The temperature-pressure-time profile for PECS-processed specimens, C-PTS-P-10,
C-PTS-P-11, and C-PTS-P-12. The heating rate and cooling rate was 50 K/minute and 5
K/minute, respectively. The maximum temperature was held for 20 minutes. The pressure was
held at 20 MPa during heating until the specimen reached the maximum temperature. Once the
specimen reached 823 K, the pressure was increased to 60 MPa. To reduce possible residual
stresses, the specimen was cooled to 573 K and thermally annealed for 120 minutes. The
pressure was slowly reduced in steps during cooling.

270

Pressure
Temperature

600

60
50
40

500
30
400

20

Pressure (MPa)

Temperature (K)

700

10

300
0

50

100

150

200

250

300

Time (minutes)
Figure B.6 The temperature-pressure-time profile for PECS-processed specimens, C-PTS-P-13,
C-PTS-P-14, C-PTS-P-15, C-PTS-P-16, C-PTS-P-17, C-PTS-P-18, and C-PTS-P-19. The
heating rate and cooling rate was 50 K/minute and 5 K/minute, respectively. The maximum
temperature was held for 20 minutes. The pressure was held at 20 MPa during heating until the
specimen reached the maximum temperature. Once the specimen reached 673 K, the pressure
was increased to 60 MPa. To reduce possible residual stresses, the specimen was cooled to 573
K and thermally annealed for 120 minutes. The pressure was slowly reduced in steps during
cooling.

271

Pressure
Temperature

60

700

50

600

40

500

30
20

400

Pressure (MPa)

Temperature (K)

800

10
300
0

20

40

60

80

100 120 140

Time (minutes)
Figure B.7 The temperature-pressure-time profile for PECS-processed specimens, C-PTS-P-20,
C-PTS-P-21, C-PTS-P-22, C-PTS-P-23, and C-PTS-P-24. The heating rate and cooling rate was
50 K/minute and 5 K/minute, respectively. The maximum temperature was held for 20 minutes.
The pressure was held at 20 MPa during heating until the specimen reached the maximum
temperature. Once the specimen reached 723 K, the pressure was increased to 60 MPa. The
pressure decreased during cooling at a ramp rate of 0.64 MPa/minute.

272

900

Temperature

Pressure

60
50

700
40
600
30
500
20
400

Pressure (MPa)

Temperature (K)

800

10
300
0

20

40

60

Time (minutes)
Figure B.8 The temperature-pressure-time profile for PECS-processed specimens C-PTS-P-25
and C-PTS-P-29. The maximum temperature of 723 K was held for 16 minutes. The heating
rate and cooling rate was 100 K/minute and 10 K/minute, respectively The pressure was held at
60 MPa until the specimen reached room temperature.
900

Temperature

Pressure

60
50

700
40
600
30
500
20
400

Pressure (MPa)

Temperature (K)

800

10
300
0

20

40

60

Time (minutes)
Figure B.9 The temperature-pressure-time profile for PECS-processed specimens C-PTS-P-26
and C-PTS-P-30. The maximum temperature of 723 K was held for 16 minutes. The heating
rate and cooling rate was 100 K/minute and 5 K/minute, respectively The pressure was held at 60
MPa until the specimen reached room temperature.

273

Pressure
Temperature

60

700

50

600

40

500

30

400

20

Pressure (MPa)

Temperature (K)

800

10

300
0

20

40

60

80

100 120 140

Time (minutes)
Figure B.10 The temperature-pressure-time profile for PECS-processed specimens C-PTS-P-27
and C-PTS-P-31. The heating rate and cooling rate was 50 K/minute and 5 K/minute,
respectively. The ramp rate for pressure during heating was 5 MPa/min and 0.5 MPa/min during
cooling. The specimens were sintered at the maximum temperature and pressure for 20 minutes.
Pressure
Temperature

60
50

600
40
500

30

400

20
10

Pressure (MPa)

Temperature (K)

700

300
0

20

40

60

80

Time (minutes)
Figure B.11 The temperature-pressure-time profile for PECS-processed specimen C-PTS-P-28.
The heating rate and cooling rate was 50 K/minute and 5 K/minute, respectively. The ramp rate
for pressure during heating was 5 MPa/min and 0.5 MPa/min during cooling. The specimen was
sintered at the maximum temperature and pressure for 5 minutes.

274

Pressure
Temperature

600

60
50
40

500
30
400

20

Pressure (MPa)

Temperature (K)

700

10
300
0

20

40

60

Time (minutes)
Figure B.12 The temperature-pressure-time profile for PECS-processed specimens, C-PTS-P-32,
C-PTS-P-36, and C-PTS-P-37. The heating rate and cooling rate was 50 K/minute and 5
K/minute, respectively. The ramp rate for pressure during heating was 5 MPa/min and 0.5
MPa/min during cooling. The specimens were sintered at the maximum temperature and
pressure for 5 minutes.
Pressure
Temperature

600

60
50
40

500
30
400

20

Pressure (MPa)

Temperature (K)

700

10
300
0

20

40

60

Time (minutes)
Figure B.13 The temperature-pressure-time profile for PECS-processed specimen C-PTS-P-33.
The heating rate and cooling rate was 50 K/minute and 5 K/minute, respectively. The ramp rate
for pressure during heating was 5 MPa/min and 0.5 MPa/min during cooling. The specimen was
sintered at the maximum temperature and pressure for 5 minutes.

275

600
60
50

500
40
30
400
20
10

Pressure (MPa)

Temperature (K)

Pressure
Temperature

300
0

20

40

Time (minutes)
Figure B.14 The temperature-pressure-time profile for PECS-processed specimen C-PTS-P-34.
The heating rate and cooling rate was 50 K/minute and 5 K/minute, respectively. The ramp rate
for pressure during heating was 5 MPa/min and 0.5 MPa/min during cooling. The specimen was
sintered at the maximum temperature and pressure for 5 minutes.
Pressure
Temperature

50
40
30

400

20

Pressure (MPa)

Temperature (K)

500

60

10
300
0

20

40

Time (minutes)
Figure B.15 The temperature-pressure-time profile for PECS-processed specimen C-PTS-P-35.
The heating rate and cooling rate was 50 K/minute and 5 K/minute, respectively. The ramp rate
for pressure during heating was 5 MPa/min and 0.5 MPa/min during cooling. The specimen was
sintered at the maximum temperature and pressure for 5 minutes.

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