PROCESSING AND NANOSTRUCTURE INFLUENCES ON MECHANICAL
PROPERTIES OF THERMOELECTRIC MATERIALS
By
Robert David Schmidt

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Materials Science and Engineering – Doctor of Philosophy
2014

ABSTRACT
PROCESSING AND NANOSTRUCTURE INFLUENCES ON MECHANICAL
PROPERTIES OF THERMOELECTRIC MATERIALS
By
Robert David Schmidt
Thermoelectric (TE) materials are materials that can generate an electric current
from a thermal gradient, with possible service in recovery of waste heat such as engine
exhaust. Significant progress has been made in improving TE conversion efficiency,
typically reported according to the figure of merit, ZT, with several recent papers
publishing ZT values above 2. Furthermore, cost reductions may be made by the use of
lower cost elements such as Mg, Si, Sn, Pb, Se and S in TE materials, while achieving ZT
values between 1.3 and 1.8.
To be used in a device, the thermoelectric material must be able to withstand the
applied thermal and mechanical forces without failure. However, these materials are
brittle, with low fracture toughness typically less than 1.5 MPa-m1/2, and often less than
0.5 MPa-m1/2. For comparison, window glass is approximately 0.75 MPa-m1/2. They
have been optimized with nanoprecipitates, nanoparticles, doping, alterations in
stoichiometry, powder processing and other techniques, all of which may alter the
mechanical properties.
In this study, the effect of SiC nanoparticle additions in Mg2Si, SnTe and Ag
nanoparticle additions in the skutterudite Ba0.3Co4Sb12 on the elastic moduli, hardness
and fracture toughness are measured. Large changes (~20%) in the elastic moduli in
SnTe1+x as a function of x at 0 and 0.016 are shown. The effect on mechanical properties
of doping and precipitates of CdS or ZnS in a PbS or PbSe matrix have been reported.

Changes in sintering behavior of the skutterudite with the Ag nanoparticle
additions were explored. Possible liquid phase sintering, with associated benefits in
lower processing temperature, faster densification and lower cost, has been shown. A
technique has been proposed for determining additional liquid phase sintering aids in
other TE materials.
The effects of porosity, grain size, powder processing method, and sintering
method were explored with YbAl3 and Ba0.3Co4Sb12, with the porosity dependence of the
elastic moduli reported. Only one other TE material has the porosity dependence of the
elastic moduli previously reported in the literature, lead-antimony-silver-tellurium
(LAST), and the effect of different powder processing and sintering methods has never
been reported previously on TE materials.

ACKNOWLEDGEMENTS

I would like to acknowledge my advisor, Professor Eldon Case, for his patient
advising and teaching throughout the work on this dissertation. Particular thanks to
Professor Eldon D. Case for directing the projects and keeping everything moving,
advising in all the experiments, and extensive assistance in advancing my writing.
Thank you to Professor Timothy Hogan, Professor Donald Morelli and Professor
Jeffrey Sakamoto for their work on this dissertation, the use of their labs for portions of
the research, and for their work on my dissertation committee.
I would like to acknowledge all my co-authors on the papers in this study, my lab
mates, Jennifer Ni, Xiaofeng Fan, Cheng-Yun Liu, undergrad lab assistants Patricia
Bordon Sarac, Miguel Valdes Tabernero, Andreia Ditzel Facci, Alex Zettler, Miguel
Martinez Calderon, Luis Gonzalez Guerrero, Jesse Giles III, and summer high school
honors student Zayra Lobo. Thank you to Karl Dersch for all of the PECS sintering of
specimens.
Thank you to the High Temperature Materials Laboratory at Oak Ridge National
Laboratory. I would like to acknowledge the director, Edgar Lara-Curzio, for his support
on the study of the SnTe thermoelectric materials, and making the resources of the
laboratory available for use. I would like to acknowledge my primary contact for the user
proposal, Rosa Trejo.
Thank you to Professor Stanley Flegler, Carol Flegler and Abigail Vanderberg at
the Center for Advanced Microscopy for their advice, maintenance and work with the
scanning electron microscopes used in this dissertation.
iv

I would like to acknowledge the financial support of 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 Science, Office of
Basic Energy Sciences under award number DE-SC0001054, for the funding for the
research within this dissertation.

v

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................ vii
LIST OF FIGURES ........................................................................................................... xi
1 Introduction ...................................................................................................................... 1
1.1 Applications of thermoelectric materials .................................................................. 1
1.2 Thermoelectric efficiency ......................................................................................... 2
1.3 Mechanical properties of thermoelectric materials ................................................... 3
1.3.1 Elastic moduli .................................................................................................... 7
1.3.2 Fracture toughness ............................................................................................. 8
1.4 Porosity effects on mechanical properties ................................................................ 9
1.5 Temperature effects on mechanical properties ....................................................... 10
1.6 Sintering of thermoelectric materials ...................................................................... 11
REFERENCES ............................................................................................................. 12
2 Experimental Procedure ................................................................................................. 21
2.1 Material preparation ................................................................................................ 21
2.2 Crushing, grinding, sieving and regrinding (CGSR) process ................................. 22
2.3 Milling of CGSR powder ........................................................................................ 23
2.3.1 Planetary ball milling ....................................................................................... 23
2.3.2 Vibratory ball milling ...................................................................................... 24
2.4 Incorporation of nanoparticles ................................................................................ 26
2.5 Sintering of powders ............................................................................................... 26
2.5.1 Hot press sintering ........................................................................................... 26
2.5.2 Pulsed electric current sintering ....................................................................... 27
2.6 Sintered specimen preparation ................................................................................ 28
2.7 Mounting of specimens ........................................................................................... 28
2.7.1 Thermoplastic mounting of specimens ............................................................ 28
2.7.2 Thermoplastic dismounting of specimens ....................................................... 29
2.7.3 Epoxy mounting of specimens ......................................................................... 29
2.8 Specimen cutting ..................................................................................................... 30
2.9 Specimen polishing ................................................................................................. 30
2.10 Mass, dimensions and density............................................................................... 33
2.11 Resonant ultrasound spectroscopy ........................................................................ 33
2.12 Hardness and fracture toughness by Vickers indentation ..................................... 39
2.13 X-ray diffraction ................................................................................................... 42
2.14 Scanning electron microscopy imaging and energy dispersive x-ray spectroscopy
....................................................................................................................................... 42
2.14.1 Grain size measurement from fractured surface images ................................ 43
REFERENCES ............................................................................................................. 45

vi

3 Room temperature mechanical properties of polycrystalline YbAl3, a promising low
temperature thermoelectric material ................................................................................. 48
Abstract ......................................................................................................................... 48
3.1 Introduction ............................................................................................................. 49
3.2 Experimental procedure .......................................................................................... 51
3.2.1 Materials and specimen preparation ................................................................ 51
3.2.2 Microstructural characterization ...................................................................... 54
3.2.3 Hardness testing ............................................................................................... 55
3.2.4 Elastic modulus measurements ........................................................................ 55
3.2.5 Fracture toughness measurements ................................................................... 56
3.3 Results and Discussion ........................................................................................... 57
3.3.1 Microstructural characterization ...................................................................... 57
3.3.2 Hardness ........................................................................................................... 62
3.3.3 Fracture Toughness .......................................................................................... 65
3.3.4 Elastic modulus ................................................................................................ 67
3.3.5. Acoustic wave speeds and the Debye temperature ......................................... 76
3.3.6 Mechanical properties as a function of processing technique ......................... 78
3.4 Summary and Conclusions ..................................................................................... 79
ACKNOWLEDGEMENTS .......................................................................................... 80
REFERENCES ............................................................................................................. 81
4 Room-Temperature Mechanical Properties and Slow Crack Growth Behavior of Mg2Si
Thermoelectric Materials .................................................................................................. 86
Abstract ......................................................................................................................... 86
4.1 Introduction ............................................................................................................. 87
4.2 Experimental procedure .......................................................................................... 89
4.3 Results and Discussion ........................................................................................... 93
4.4 Conclusions ............................................................................................................. 99
ACKNOWLEDGEMENTS .......................................................................................... 99
REFERENCES ........................................................................................................... 101
5 Mechanical properties of Mg2Si thermoelectric materials with the addition of 0 to 4
volume percent silicon carbide nanoparticles (SiCNP) .................................................... 105
Abstract ....................................................................................................................... 105
5.1 Background ........................................................................................................... 105
5.2 Experimental Procedure ........................................................................................ 110
5.2.1 Materials and Specimen Preparation ............................................................. 110
5.2.2 Elasticity Measurements ................................................................................ 111
5.2.3 Hardness and toughness measurements ......................................................... 111
5.2.4 Microscopy .................................................................................................... 112
5.3 Results and Discussion ........................................................................................ 112
5.3.1 Microstructural analysis ................................................................................. 112
5.3.1.1 Starting material density and microstructure .......................................... 114
5.3.2 Elasticity results ............................................................................................. 117
5.3.2.1 Elasticity and SiCNP addition .................................................................. 117
vii

5.3.2.2 Elasticity and porosity............................................................................. 120
5.3.3 Hardness and Toughness Results ................................................................... 121
5.3.3.1 Crack bridging and toughness ................................................................. 126
5.4 Conclusions ........................................................................................................... 126
ACKNOWLEDGEMENTS ........................................................................................ 126
REFERENCES ........................................................................................................... 128
6 Influence of silver nanoparticle addition, porosity and processing technique on the
mechanical properties of Ba0.3Co4Sb12 skutterudites ...................................................... 133
Abstract ....................................................................................................................... 133
6.1 Introduction ........................................................................................................... 134
6.2 Experimental procedure ........................................................................................ 137
6.2.1 Materials and Specimen Preparation ............................................................. 137
6.2.2 Elasticity Measurements ................................................................................ 138
6.2.3 Hardness and toughness measurements ......................................................... 140
6.2.4 Energy-dispersive X-ray spectroscopy and microscopy ................................ 141
6.3 Results and Discussion ......................................................................................... 149
6.3.1 Microstructural and chemical analysis ........................................................... 149
6.3.1.1 Microstructure of the AgNP and Ag agglomerates .................................. 149
6.3.1.2 Porosity and grain size and relationship to the processing technique ..... 152
6.3.2 Chemical analysis .......................................................................................... 153
6.3.2.1 Chemistry of the AgNP and Ag agglomerates ......................................... 153
6.3.2.2 Sintering behavior changes and scavenging of Sb .................................. 156
6.3.2.3 Possible significance to other thermoelectric material systems .............. 157
6.3.3 Elasticity results ............................................................................................. 158
6.3.3.1 Elasticity as a function of AgNP addition ................................................ 158
6.3.3.2 Elastic moduli and porosity .................................................................... 161
6.3.3.3 Elastic moduli and grain size/processing effects .................................... 164
6.3.4 Hardness and fracture toughness results ........................................................ 166
6.3.4.1 Hardness and toughness as a function of Ag addition ............................ 166
6.3.4.2 Hardness and fracture toughness as function of porosity ....................... 168
6.3.4.2.1 Hardness as function of porosity...................................................... 168
6.3.4.2.2 Fracture toughness as function of porosity ...................................... 169
6.3.4.3 Hardness and fracture toughness as a function of load ........................... 170
6.3.4.4 Hardness and fracture toughness results as a function of grain size ....... 172
6.3.4.4.1 Hardness results as a function of grain size ..................................... 172
6.3.4.4.2 Fracture toughness results as a function of grain size...................... 173
6.4 Summary and conclusions .................................................................................... 175
ACKNOWLEDGEMENTS ........................................................................................ 176
REFERENCES ........................................................................................................... 177
7 High temperature elastic moduli of thermoelectric SnTe1+X –y SiC nanoparticulate
composites....................................................................................................................... 187
Abstract ....................................................................................................................... 187
7.1 Introduction ........................................................................................................... 188
viii

7.2 Experimental procedure ........................................................................................ 190
7.2.1 Specimen Preparation .................................................................................... 190
7.2.2 Specimen characterization ............................................................................. 192
7.2.3 High temperature Resonant Ultrasound Spectroscopy measurements .......... 193
7.3 Results and Discussion ......................................................................................... 194
7.3.1 Microstructural analysis ................................................................................. 194
7.3.2 Elastic modulus as a function of temperature, matrix composition and SiCNP
volume fraction ....................................................................................................... 201
7.3.2.1 Bilinear model of elastic modulus versus temperature ........................... 205
7.3.2.2 Effects of chemical composition and porosity on elastic moduli of the
SnTe1+X matrix .................................................................................................... 210
7.3.2.3 Comparison of the Young’s modulus versus elasticity behavior of
polycrystalline SnTe1+X to the literature ............................................................. 215
7.3.2.4 Effect of volume fraction of SiCNP on the elastic moduli of the SnTe1+X SiCNP composites ................................................................................................ 217
7.5 Summary and conclusions .................................................................................... 220
ACKNOWLEDGEMENTS ........................................................................................ 221
REFERENCES ........................................................................................................... 222
8 Mechanical properties of lower-cost, earth-abundant chalcogenide thermoelectric
materials, PbSe and PbS, with additions of 0 to 4% CdS or ZnS ................................... 228
Abstract ....................................................................................................................... 228
8.1 Introduction ........................................................................................................... 229
8.2 Experimental procedure ........................................................................................ 231
8.2.1 Materials and Specimen Preparation ............................................................. 231
8.2.2 Elasticity Measurements ................................................................................ 232
8.2.3 Hardness and toughness measurements ......................................................... 234
8.2.4 Microscopy and X-ray diffraction ................................................................. 234
8.3 Results and Discussion ......................................................................................... 235
8.3.1 Microstructural analysis ................................................................................. 235
8.3.2 Elasticity results ............................................................................................. 245
8.3.3 Hardness results ............................................................................................. 248
8.4 Discussion ............................................................................................................. 248
8.4.1 Microstructural analysis ................................................................................. 248
8.4.2 Elasticity analysis........................................................................................... 250
8.4.3 Hardness analysis ........................................................................................... 254
8.5 Conclusions ........................................................................................................... 257
ACKNOWLEDGEMENTS ........................................................................................ 258
REFERENCES ........................................................................................................... 259
9 Summary and Conclusions .......................................................................................... 267
9.1 Porosity dependence and processing method independence of elastic moduli..... 267
9.1.1 Grain size and processing method independence of elastic moduli .............. 268
9.2 Sintering aids and TE materials ............................................................................ 268
9.3 Elastic moduli of TE materials with nanoparticle or nanoprecipitate additions ... 269
ix

9.4 Fracture toughness and slow crack growth in Mg2Si and other TE materials ...... 270
REFERENCES ........................................................................................................... 272
10 Future work ................................................................................................................ 274
REFERENCES ........................................................................................................... 276
APPENDICES ................................................................................................................ 278
APPENDIX A. Effect of nanoparticle addition on the elastic modulus of a composite
material ....................................................................................................................... 279
APPENDIX B. Standard operating procedure for HT-RUS furnace .......................... 283
APPENDIX C. Machine drawings of the HT-RUS equipment .................................. 303
REFERENCES ........................................................................................................... 362

x

LIST OF TABLES

Table 2.1 ........................................................................................................................ 32
A series of diamond grit pastes were used to polish the specimens. A
grit size may be skipped, with additional polishing time on the next
smaller diamond grit size to compensate.
Table 3.1 ........................................................................................................................ 53
The HP and PECS processing parameters for the YbAl3 specimens
included in this study.
Table 3.2 ........................................................................................................................ 58
Specimen label, densification method (hot pressed, HP, or pulsed electric
current sintering, PECS), mass, dimensions and mass density of each of
the YbAl3 specimens included in this study.
Table 3.3 ........................................................................................................................ 58
The number of indentations, indentation load and mean hardness, <H>,
of the YbAl3 specimens and porosity, P. In each case, the loading time
was 10 s. The porosity reported is the average as measured from the disc
and bar specimen geometries.
Table 3.4 ........................................................................................................................ 66
For YbAl3 specimens included in this study, the fracture toughness, KC,
measured by Vickers indentation, including the applied load, specimen
grain size and volume fraction porosity, P. The KC was obtained from the
mean of 10 indentations per specimen.
Table 3.5 ........................................................................................................................ 69
The fitting parameters obtained from the least-squares fit of the
appropriate elastic modulus to Eqs. (5a) – (5c). The coefficient of
determination, R2, is given for each of the fitted equations.
Table 3.6 ........................................................................................................................ 69
A comparison of this study’s experimentally determined values of elastic
moduli (E, Young’s modulus, G, shear modulus, B, bulk modulus and ,
Poisson’s ratio) for YbAl3 with calculated and experimental values of
other trialuminide materials, R-Al3, from the literature for R = Yb, Sc,
Tm, or Zr [Sa 2011, Zhou 2010, Tao 2008, Hyland 1991, Fu 1990, Xu
1990, Jahnatek 2007].

xi

Table 3.7 ....................................................................................................................... 75
For the seven YbAl3 specimens included in this study, N, the number of
RUS resonant peaks measured, the RMS error in RUS, the Young’s
modulus, E, shear modulus, G, Poisson’s ratio, ν, longitudinal and shear
velocity, VL and VS, acoustic Debye temperature, θD, and porosity, P,
were measured. The RUS analysis on each specimen was performed on
the tripod configuration (Fig. 3.1a).
Table 3.8 ........................................................................................................................ 77
The fitting parameters obtained from the least-squares fit of the VL and
VS versus P data to Eqs. (6a) and (6b), respectively, with the coefficient
of determination, R2.
Table 4.1 ........................................................................................................................ 88
The Mg2Si specimens used in this study for Vicker’s hardness, H,
fracture toughness, KIC, Young’s modulus, E, shear modulus, G,
Poisson’s ratio, , and acoustic debye temperature, D, measurements.
The Mg2Si pieces were reduced using a (1) mechanical mortar and pestle
until all powder passed through a 53 µm sieve and then either densified
or further reduced using a (2) planetary mill at 150 rpm for 3 hours. For
indentation the specimens were polished to 1 μm diamond grit, further
details are available elsewhere [Ni 2010]. Due to reactions with water
[Aesar], the specimens were cleaned using ethanol instead of water
between polishing grit sizes.
Table 4.2 ........................................................................................................................ 92
The density, Young’s modulus, E, shear modulus, G, Poisson’s ratio, ,
and Debye temperature, D, from this study compared with the literature.
The moduli were determined using resonant ultrasound spectroscopy,
RUS, first principle calculation, FPC, resonance technique, RT, and
compression.
Table 4.3 ........................................................................................................................ 95
A comparisons of Vickers hardness, H, and fracture toughness, KIC, from
this study to the literature. For the PECS processed specimens in this
study, the H and KIC was determined using at least 10 indentations per
load with one standard deviation reported as error. For cast specimens in
literature, Milekhine et al. measured at least 10 indentations per load
[Milekhine 2002]and Li et al. measured 5 indentations [Li 1993].

xii

Table 4.4 ........................................................................................................................ 98
No significant slow crack growth occurred for the six Vickers
indentation cracks listed below for specimen Mg2Si-01, where the radial
crack lengths were monitored for up to 3 days (Fig. 4.5). For the radial
crack length measurements performed over the entire time range, the
measured crack lengths did not depart significantly from the mean length
of each crack, as indicated by the coefficient of variation (CV, standard
deviation/mean), where CV ranges from about 1.4% to 5%.
Table 5.1 ........................................................................................................................ 109
The fracture toughness, KC, has been improved in brittle materials,
including the thermoelectric Bi2Te3, by the addition of SiC nanoparticles.
Table 5.2 ........................................................................................................................ 109
Doped Mg2Si-based thermoelectric materials with ZT near 1 have been
reported. These reasonable ZT values for a thermoelectric material
support the use of Mg2Si as a model system.
Table 5.3 ........................................................................................................................ 115
Specimens in this study were either milled by planetary ball mill (PM) or
vibratory mill (VM), with up to 4 vol% SiCNP additions, then sintered by
pulsed electric current sintering to produce specimens with a density (ρ)
of 2.00 g/cm3 or greater for all specimens except VM-0SiC-2. The
average grain size (GS) by the lineal intercept method are a function of
the milling method, and not a function of SiCNP additions.
Table 5.4 ........................................................................................................................ 119
The Young’s modulus, E, shear modulus, G, and density, ρ, for the
specimens in this study, as compared to the range of E, G and ρ in a
previous study on three Mg2Si specimens produced by the same vendor.
Table 6.1 ........................................................................................................................ 139
Specimens of skutterudite Ba0.3Co4Sb12 used in this study varied based
on AgNP addition, sintering procedure and temperature, resulting
porosity, and powder processing. Specimens VM-PECS-673, VMPECS-723 and VM-PECS-773 were reprocessed from specimens PMHP-673, PM-HP-773 and PM-HP-873 by grinding and powder
processing by vibratory milling, and sintering by PECS.
Table 6.2 ........................................................................................................................ 154
Results of EDS scan using Point ID mode on two as-received AgNP
agglomerates.

xiii

Table 6.3 ........................................................................................................................ 154
Results of EDS scan using Point ID mode on specimen PM-HP-873-Ag.
Spacing between spots is approximately 5 to 10 µm (Figure 6.4e). Ag
areas examined are 1-3 µm in diameter.
Table 6.4 ........................................................................................................................ 154
Results of EDS scan using Point ID mode on specimen PM-HP-773-Ag.
Spacing between spots is approximately 4 µm (Figure 6.4c). Ag area
examined approximately 1-3 µm in diameter.
Table 6.5 ........................................................................................................................ 154
Results of EDS scan using Point ID mode on specimen PM-HP-673-Ag.
Spacing between spots is approximately 5 to 10 µm (Figure 6.4a). Ag
area examined is approximately 20 µm in diameter.
Table 6.6 ........................................................................................................................ 160
The linear decrease in elastic moduli, E, G, and B, according to equation
(5b), for this study of Ba0.3Co4Sb12 is consistent with the limited
information available in the literature for porosity dependence of elastic
moduli for thermoelectric materials [Schmidt 2013a; Ni 2009].
Table 6.7 ........................................................................................................................ 165
For CoSb3-based thermoelectric materials, a comparison of the KC results
from this study with the literature, including the porosity, P, the grain
size, GS, of the specimens and the KC measurement technique [Ravi
2009; Eilertsen 2013; Rogl 2011].
Table 7.1 ........................................................................................................................ 191
For each of the six SnTe-SiCNP specimens included in this study, the
volume fraction SiCNP addition, specimen mass, dimensions, mass
density, porosity, P, and mean grain size. Specimens were prepared from
one of two starting ingots, designated A or B in the specimen label.
Table 7.2 ........................................................................................................................ 200
For SiCNP clusters identified by electron backscatter images for specimen
SnTe(x = 0)V0.04 (Fig. 6), the SEM magnification, the area of the field
of view of the micrograph, along with the number, number density, and
size range of the SiCNP clusters
Table 7.3 ........................................................................................................................ 203
For the six SnTe-SiCNP specimens included in this study, results of a
least squares fit to equation (4a) for the Young’s modulus, E, versus
temperature, T, data and to equation (4b) for the shear modulus, G,
versus T, data. The coefficients of determination for the fit of the E
versus T and the G versus T data are given by
and , respectively
xiv

Table 7.4 ........................................................................................................................ 206
For two separate temperature ranges, RT – 543 K, and 543 K – 663 K,
the E versus T was fit to equation (4a).
Table 7.5 ........................................................................................................................ 206
Comparison of Δb, equation (6), for this study and LAST [Ren 2010].
Table 7.6 ........................................................................................................................ 211
Fractional changes in Young’s modulus, E, shear modulus, G, and
hardness H as a function of changes in composition from n1 to n2 [this
study, [Kawaharada 2004; Ravinder 2001; Schenk 1998].
Table 7.7 ........................................................................................................................ 214
In order to compare the room temperature experimental values of
Young’s modulus, Eexp, and shear modulus, Gexp, for this study’s
specimens without SiCNP additions to the single crystal values of E0 and
G0 values from SnTe from the literature [Beattie 1969; Simmons 1971],
equations (7c) and (7d) were used to calculate porosity corrected values
for the single crystal data using the modulus-porosity slope data for two
thermoelectric materials, namely YbAl3 (bPE = 2.34, bPG = 2.38) and
LAST (bPE = 3.5, bPG = 3.5) [Schmidt 2013; Ni 2009]. This study’s
experimental Eexp and Gexp values for the tellurium rich specimen,
SnTe(x=0.016)V0, are in the best agreement with the range of porosity
corrected values ECORR and GCORR.
Table 7.8 ........................................................................................................................ 216
Comparison of the Young’s modulus, E, versus temperature behavior for
a variety of brittle materials, SnTe [this study], PbTe [Houston 1968;
Simmons 1971; Ren 2010], and selected skutterudite TE materials
[Schmidt 2012; Ravi 2008]. The parameters ERT and bRT were obtained
via a least-squares fit of each of the data sets to equation (4a). The
coefficient of determination, R2, was equal to or greater than 0.98 for
each data set, indicating that equation (4a) describes the E versus
temperature behavior well.
Table 8.1 ........................................................................................................................ 236
Composition, theoretical density, theo, measured density, meas, volume
fraction porosity, P, average grain size, <GS>, typical observed
inclusion size range, Incl, and mode mixity, M (equation 3) for the PbSbased specimens included in this study.

xv

Table 8.2 ........................................................................................................................ 237
Composition, theoretical density, theo, measured density, meas, volume
fraction porosity, P, average grain size, <GS>, typical observed
inclusion size range, Incl, and mode mixity, M (equation 3) for the PbSebased specimens included in this study.
Table 8.3 ........................................................................................................................ 244
EDS results from four area scans of a polished PbS specimen, indicating
a higher concentration of Pb than S.
Table 8.4 ........................................................................................................................ 252
The Young’s modulus, E, the shear modulus, G, and the Poisson’s ratio
measured in this study for the polycrystalline undoped PbSe and
undoped PbS specimens compared with the aggregate average values of
E and G computed from the Hashin and Shtrikman bounds, <H-S>
[Simmons 1971] for single crystal elasticity from the literature [Dalven
1969, Bhagavantam 1951, Lippmann 1971, Hellwege 1979].
Table 8.5 ........................................................................................................................ 255
In general, hardness, H, is grain size dependent, and the single crystal
hardness results from loem and r ger [Bloem 1955] are expected to
have a lower hardness than the other, polycrystalline specimens in this
table. The grain size for the PbS and PbSe was not listed by Darrow
[Darrow 1969]. Average grain sizes for all specimens in this study are
between 1.8 µm and 18.7 µm, listed in Tables 8.1 and 8.2.
Table A.1........................................................................................................................ 255
For spherical metallic particle additions to brittle matrices [Fujieda 2012;
Hasselman 1965], comparison of the measured composite modulus, EC, with the
values predicted by the four models given in this appendix (rule of mixtures,
ROM, Reuss constant strain, RCS, Hashin particulate, HP, and Halpin-Tsai, HT
[Schmidt 2013b]). Em is the Young’s modulus of the matrix material [Fujieda
2012; Hasselman 1965]and Er is the Young’s modulus of the reinforcing material
[Lowrie 1967; Macfarlane 1965; Neighbours 1958; Chang 1966].

xvi

LIST OF FIGURES

Figure 1.1 ....................................................................................................................... 6
Schematic of a thermoelectric couple, indicating current flow when
placed in a temperature gradient.
Figure 2.1 ....................................................................................................................... 36
Typical setup of tripod arrangement of RUS transducers, with specimen
on top and the transducer tips near the edge of the specimen.
Figure 2.2 ....................................................................................................................... 36
RUS spectrum from PbSe specimen. Each sharp peak in intensity
represents a mechanical resonance at the driven frequency.
Figure 2.3 ....................................................................................................................... 37
RUS analysis software, showing setup of initial conditions for a PbSe
specimen.
Figure 2.4 ....................................................................................................................... 38
Sample output file from a CylModel RUS analysis, truncated to show
only the first 12 resonance peaks. Note that resonance frequency 10,
191.681 kHz, was not included in the analysis to improve the error. The
“chisquare increased 2% by…” section includes the highlighted values
of A, 0.47, and of D, 0.11, used in the determination of the uncertainties,
dc11 and dc44.
Figure 2.5 ....................................................................................................................... 41
Schematic representation of Vickers indentation, illustrating the
indentation impression dimensions, 2a, and the radial crack length
dimensions, 2c.
Figure 3.1 ....................................................................................................................... 58
Photographs of tripod and bipod transducer stages for the RUS
measurements of elastic modulus performed in this study.
Figure 3.2 ....................................................................................................................... 59
SEM micrographs of fracture surfaces and polished surfaces of YbAl3
specimens included in this study. The ovals indicate more porous regions
neighboring more dense areas that occur in the two HP specimens (Fig.
3.2a and b) as well as the PECS specimen intentionally processed to give
high porosity (Fig. 3.2e).

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Figure 3.3 ....................................................................................................................... 60
The fractured surfaces of specimens YbAl3-B and YbAl3-E exhibited
lower porosity regions surrounded by channels of higher porosity in (a)
and (b), both with similar porosity but each sintered by a different
method. In contrast, specimen YbAl3-D, shown in (c), exhibited a
uniform density throughout.
Figure 3.4 ....................................................................................................................... 64
The hardness, H, versus volume fraction porosity, P, for the YbAl3
specimens included in this study. The solid line represents a leastsquares fit to Eq. (4b).
Figure 3.5 ....................................................................................................................... 70
For the YbAl3 specimens included in this study, the RUS measurement
results for (a) the Young’s modulus, E, shear modulus, G, bulk modulus,
B as a function of P and (b) Poisson’s ratio as a function of P. The solid
lines in Fig. 3.5a represent least-squares fits to Eqs. (5a), (5b) and (5c)
for the Young’s modulus, shear modulus and bulk modulus, respectively.
Figure 3.6 ....................................................................................................................... 71
The RUS mechanical vibration spectra for the two-transducer stage and
tripod specimen stage.
Figure 3.7 ....................................................................................................................... 77
From the RUS measurements of the YbAl3 specimens included in this
study, (a) shear and longitudinal wave speeds as a function of P, where
the solid lines in represent least-squares fits to Eq. (6a) and (6b) for the
longitudinal and shear velocities, respectively. (b) the effective Debye
temperature as a function of P, where the solid line represents a leastsquares fit to Eq. (9).
Figure 4.1 ....................................................................................................................... 88
The time–temperature and time–pressure profiles used in the PECS
processing of each of the Mg2Si specimens included in this study.
Figure 4.2 ....................................................................................................................... 91
X-ray diffraction of planetary-milled Mg2Si powder with peaks
compared with the literature for MgO [Hazen 1976] and Mg2Si [Owen
1923].

xviii

Figure 4.3 ....................................................................................................................... 91
Fractured surface of specimens (a) Mg2Si-01 and (b) Mg2Si-05, PECS
processed from planetary mill and mechanical mortar and pestle Mg2Si
powder, respectively. Cleavage steps show mixed- mode fracture, with
both intergranular and transgranular fracture present. Entrapped pores
visible at grain boundaries were approximately 1 µm to 3 µm diameter
with polygonal shape. The dark areas between grains are porosity within
the specimens, typically around 1 µm or less in diameter.
Figure 4.4 ....................................................................................................................... 92
Typical Vickers indentation crack systems for specimens Mg2Si-01 and
Mg2Si-05, which display indentation impressions, little chipping or
spalling, and a fully developed radial crack system.
Figure 4.5 ....................................................................................................................... 97
For specimen Mg2Si-01, plots of radial crack length versus time for six
Vickers indentation crack systems loaded at 2.94 N. In figures (b) and
(e), a radial crack popped in within 1 min to 5 min following the initial
indentation event. The average crack length and one standard deviation
variation is indicated by solid and dashed lines, respectively, for each
indentation crack. The crack length may vary significantly between
indentations, resulting in the uncertainties in the reported KIC values in
Table 4.3.
Figure 5.1 ....................................................................................................................... 113
Planetary milled Mg2Si powder exhibited typical particle sizes of submicron to 5 μm in SEM. The powder has a surface area of 4.4 m2/g
measured by ET, or approximately 0.7 μm average particle size.
Figure 5.2 ....................................................................................................................... 113
Vibratory milled Mg2Si powder exhibited typical particle sizes of 0.2 μm
to 2 μm in SEM.
Figure 5.3 ....................................................................................................................... 116
For Mg2Si fracture surfaces, transgranular fracture dominate in all
specimens. The PM specimens (a-c) with varying amounts of SiCNP
addition did not show any appreciable difference in grain size, although
changing to VM processing significantly reduced the grain size (d).
Note the difference in scale between the PM images (a-c) and the VM
image (d).

xix

Figure 5.4 ....................................................................................................................... 118
The Young’s modulus (a, b) and shear modulus (c, d) of Mg2Si varied
primarily due to small variations in density. The variation in vol. %
SiCNP did not significantly affect the moduli, regardless of if the
specimens were planetary milled (a, c) or vibratory milled (b, d).
Figure 5.5 ....................................................................................................................... 118
The Young’s modulus, E, decreases linearly with porosity for the set of
13 specimens in this study.
Figure 5.6 ....................................................................................................................... 122
The hardness, (a) and (b) is not a function of the milling procedure or the
vol% SiCNP, but less scatter was observed in the (b) vibratory milled
specimens than the (a) planetary ball milled specimens. The fracture
toughness exhibited a maximum at 1 vol% SiCNP for the (c) planetary
ball milled specimens, but the fracture toughness is not a function of
vol% SiCNP for the (d) vibratory milled specimens. Open symbols in (b)
and (d) indicate a specimen with lower density of 1.93 g/cm3, relative to
the 2.00 to 2.06 g/cm3 for all other specimens in this study.
Figure 5.7 ....................................................................................................................... 124
Crack bridging, in PM Mg2Si was commonly observed in radial cracks
for all the Mg2Si specimens in this study.
Figure 5.8 ....................................................................................................................... 125
Crack bridges were commonly observed in VM specimens regardless of
SiCNP addition. Crack bridging in radial cracks was not eliminated by
reducing grain size through VM processing. Spotting is from oil residue
on the surface of the specimen.
Figure 6.1 ....................................................................................................................... 139
RUS spectrum from specimen PM-HP-873-Ag, P = 0.05 with AgNP. The
elastic moduli of each of the specimens in this study are calculated from
the specimen mass, dimensions, shape, and resonant frequencies. Each
peak in the spectrum represents a mechanical resonance at that frequency
Figure 6.2 ....................................................................................................................... 142
Silver nanoparticles exhibited agglomerates of 10 µm or greater (a-c),
but consisting of individual grains or particles consistent with the
manufacturer claimed average particle size of 20-40 nm (d)

xx

Figure 6.3 ....................................................................................................................... 143
Polished surfaces of specimen PM-HP-873-Ag, both in secondary
electron images (a) and backscatter images (b). Porosity is observed
between larger grains (a and b), but also with areas of Ag visible in
backscatter as bright areas (b), due to the higher average atomic weight
of the silver rich regions. The abundance of Ag and the relative
deficiency of Co or Sb in the bright areas of the backscatter image (b) is
confirmed by energy-dispersive x-ray spectroscopy maps (c-e)
Figure 6.4 ....................................................................................................................... 144
For each of the hot pressed specimens with AgNP additions, an EDS line
scan was performed and point ID locations were chosen. For PM-HP673-Ag, a cut surface was used (a) because the specimen was not
successfully polished. For PM-HP-773-Ag and PM-HP-873-Ag,
polished surfaces were examined (c and e). The line scan for PM-HP673-Ag (b) indicated only silver present except for two regions in the
silver where antimony and cobalt were present in concentrations
consistent with skutterudite particles. In contrast, the line scan for PMHP-773-Ag (d) and PM-HP-873-Ag (f) indicated the presence of
antimony in the silver-rich locations. No silver was observed in the
matrix outside of the silver-rich locations
Figure 6.5 ....................................................................................................................... 145
The microstructure of Ba0.3Co4Sb12, without Ag addition, changed as a
function of sintering temperature. For (a) a sintering temperature of 673
K, microstructure and porosity, P, are consistent with a specimen with
little to no observed sintering or densification. After sintering at 773 K
(b), only minimal densification and neck formation are observed. Hot
pressing at 873 K (c) enhanced both grain growth and densification in
the specimen without Ag nanoparticles, however, the microstructure still
is observed to be very porous, consistent with measurement of P = 0.16
Figure 6.6 ....................................................................................................................... 146
The microstructure of Ba0.3Co4Sb12 with 0.5 wt% AgNP addition changed
as a function of sintering temperature. At 673 K (a), little to no sintering
is observed in the microstructure. Hot pressing at 773 K (b) resulted in
limited grain growth and densification, with necks observed between the
grains but significant porosity observed, consistent with early stage
sintering. The porosity for the specimen with Ag nanoparticles sintered
at 873 K (c) is the lowest (P = 0.03) of all the specimens in this study

xxi

Figure 6.7 ....................................................................................................................... 147
Fracture surface images of reprocessed material sintered by PECS
exhibit dense regions surrounded by regions of higher porosity. All
regions of the specimens exhibit similar grain sizes. The porous areas
decrease as the sintering temperature increased from (a) 673 K, to (b)
723 K, to 773 K
Figure 6.8 ....................................................................................................................... 148
After reprocessing by SPEX milling and sintering by PECS, the samples
exhibit a unimodal, sub-micron grain size distribution.
Figure 6.9 ....................................................................................................................... 151
Hand milling of AgNP agglomerates in ethanol were not observed to
reduce the size of the nanoparticle agglomerates. After hand milling,
silver nanoparticle agglomerates of 10 µm or greater were typically
observed, similar to the size of agglomerates for the as received AgNP.
Several faces of the agglomerates appear to be deformed after hand
milling
Figure 6.10 ..................................................................................................................... 159
The (a) Young’s modulus, E, (b) shear modulus, G, and (c) bulk
modulus, B, are each a function of porosity. In each figure, the solid
lines represent a least-squares fit to equation (5b). The Poisson’s ratio
(d) is observed to be a weak function of porosity. The elastic moduli
were not observed to be a function of the addition of 0.5 wt% AgNP or of
reprocessing
Figure 6.11 ..................................................................................................................... 163
The elastic moduli for the exact composition of skutterudite in this study
are not recorded in literature, however the moduli for specimens of
similar composition [Zhang 2010] are consistent with the porosity
dependent elastic moduli relationships observed in this study. Filled
symbols indicate specimens with 0.5 wt% AgNP, unfilled for specimens
without any AgNP, and half-filled symbols for reprocessed specimens
without any AgNP. The solid lines represent a least squares fit to
equation (5b) of the data in this study

xxii

Figure 6.12 ..................................................................................................................... 167
The (a) hardness and (b) fracture toughness for the hot pressed
specimens with AgNP, filled symbols, the hot pressed specimens without
AgNP, open symbols, and the reprocessed PECS specimens without
AgNP, half-filled symbols, from Vickers indentation at four loads, 9.8 N,
4.9 N, 2.94 N, and 1.96 N. Full radial cracks were not observed on the
specimens at 1.96 N load and therefore no fracture toughness values are
available at 1.96 N load. The hot pressed specimens sintered at 673 K
were not able to be polished and were not tested. The solid lines in the
figure (a) represent hardness for the reprocessed specimens were fit to
equation (6) separately from the hot pressed specimens because hardness
is a function of grain size. Fracture toughness, figure (b), was not
observed to be a function of either porosity or load, as plotted by the
average (solid) and standard deviation (dotted) lines, with an average KC
for all 7 specimens of 1.0 ± 0.2 MPa-m½
Figure 6.13 ..................................................................................................................... 171
For each of the specimens, a plot of c3/2 versus load, F, was used to
determine the suitability of the fracture toughness by Vickers
indentation. For 5 of 7 specimens, the coefficient of determination, R2,
for a linear regression to equation (7) through the data points is 0.99 or
greater, with an R2 of 0.98 for specimen VM-PECS-773, and 0.84 for
specimen PM-HP-773. Note specimen PM-HP-773 also has a low
fracture toughness measurement at 2.94 N load. All specimens were
measured at three loads, except VM-PECS-673 and VM-PECS-773 with
a fourth measurement at a Vickers indentation load of 1.96 N
Figure 7.1 ....................................................................................................................... 191
Processing parameters (temperature and die pressure) as a function of
time for the PECS densification of the SnTe-SiCNP specimens included
in this study.
Figure 7.2 ....................................................................................................................... 195
For SnTe specimen A-06 (0 vol% SiCNP), (a) fractured specimen surface
and (b) polished specimen surface.
Figure 7.3 ....................................................................................................................... 195
The as-received SiCNP consisted of particles roughly 50 nm across
agglomerated into clusters ranging in size from approximately 100 nm to
20 µm.

xxiii

Figure 7.4 ....................................................................................................................... 195
(a) After grinding in an alumina mortar and pestle for 5 min in ethanol,
the SiCNP exhibited agglomerations of particles ranging from sub-micron
to ~10 µm diameter. (b) The agglomerations consisted primarily of
nanoparticles with diameter less than 100 nm, but with an occasional
micron-scale particle. The size distribution of the agglomerates after
manual grinding was similar to that observed prior to manual grinding
(Figure 7.3).
Figure 7.5 ....................................................................................................................... 197
Fractured specimen surface images for (a) specimen SnTe (x = 0)V0
with no SiCNP added, and for (b) SnTe (x = 0)V0.01, (c) SnTe(x =
0)V0.02, (d) SnTe(x = 0)V0.03, and (e) SnTe(x = 0)V0.04. In (b) – (e),
the location of SiCNP clusters is indicated by arrows.
Figure 7.6 ....................................................................................................................... 199
Specimen SnTe(x = 0)V0, with no added SiCNP, shows no surface
features other than surface debris in both (a) a secondary electron image
(SEI) and in (b) a backscattered electron image. Specimen SnTe(x =
0)V0.04 with 0.04 vol fraction SiCNP addition shows a difference
between the (c) secondary electron image and (d) the backscattered
electron image, with the image in the backscattered electron mode
showing dark regions indicating likely SiCNP clusters at or near the
specimen surface.
Figure 7.7 ....................................................................................................................... 200
A backscattered electron image of a polished surface of specimen
SnTe(x = 0)V0.04 indicates darker regions with a lower average atomic
weight, likely composed primarily of the SiCNP. Using EDS, silicon was
detected at the location of spectrum one, at approximately 13 at%, but
not at spectrum two, with <1 at%, confirming that the dark regions
contain a high concentration of the SiCNP. The specimen was osmium
coated prior to imaging to reduce localized charging.
Figure 7.8 ....................................................................................................................... 202
The Young’s modulus versus temperature for the six SnTe–SiCNP
specimens included in this study. For each specimen, there is no
observable hysteresis between the heating and cooling curves indicating
the lack of significant microcracking or bloating over the test
temperature range (room temperature to 663 K). The error bars are
smaller than the plotting symbols for each modulus value in (a–f).

xxiv

Figure 7.9 ....................................................................................................................... 203
Schematic representation of the bilinear Young’s modulus, E, versus
temperature, T, behavior showing TKINK and the associated slope change
in the E versus T curve.
Figure 7.10 ..................................................................................................................... 204
The residuals (equation 5) representing the difference between the
experimental Young’s modulus data and the modulus values predicted
from the least-squares fit of the E versus T data to equation (4). The
dashed lines at 0.05 GPa are a guide, representing roughly ± 0.01 ERT,
where ERT is defined as the room temperature intercept of the modulus–
porosity relationship given by equation (4a). A change in the E versus T
slope occurs at approximately 543 K (TKINK).
Figure 7.11 ..................................................................................................................... 208
Unlike Figure 7.10, the residuals represent the difference between the
experimental data and the least-squares fit performed to equation (4) in a
piecewise manner, that is least-squares fits were performed separately for
the two temperature intervals (i) TRT to TKINK and (ii) TKINK to the
maximum test temperature. As in Figure 7.10, the dashed lines at 0.05
GPa represent roughly ± 0.01 ERT, where ERT is defined as the room
temperature intercept of the modulus-porosity relationship given by
equation (4a). In (a) – (f), the vertical line at 543 K represents TKINK, the
temperature at which the change in the E versus T slope occurs.
Figure 7.12 ..................................................................................................................... 219
Comparison of the experimental Young’s modulus, E, results for the
composites SnTe1+X –ySiC (y = 0.0 to 0.04) with the four composite
models given by equations (8) – (12). Also plotted are the values of E
corrected to zero porosity using equation (7a).
Figure 8.1 ....................................................................................................................... 233
RUS scan of PbSe specimen
Figure 8.2 ....................................................................................................................... 238
Fracture surfaces of PbS specimens indicate primarily transgranular
fracture in undoped PbS (a) changing to intergranular fracture for the
Na-doped PbS specimen (b). With 1% to 4% addition of CdS, the
fracture mode changes to primarily transgranular fracture (b, d), and with
1% to 4% addition of ZnS, the fracture mode changes to mixed, with
majority transgranular and minority intergranular (c, e). Note the bright
areas in images (c) and (e) are the ZnS precipitates.

xxv

Figure 8.3 ....................................................................................................................... 239
Fracture surfaces of PbSe specimens indicate primarily intergranular
fracture for the pure PbSe specimen, the Na-doped PbSe specimen, and
the specimens with 1% addition of CdS or ZnS (a-c). With 2% to 4%
addition of CdS or ZnS, the fracture mode changes to primarily
transgranular fracture (d-f), although significant intergranular fracture
was also observed in the specimen with 4% ZnS (f). Note the bright
areas in images (d) and (f) are the ZnS precipitates
Figure 8.4 ....................................................................................................................... 240
Secondary images of the polished specimens show isolated, micron scale
spherical porosity and minor scratches from polishing. In the specimens
with 4% CdS or ZnS, precipitates of sub-micron up to approximately 15
μm were observed, particularly in backscatter electron (BSE) mode. The
images of polished PbS in both secondary electron (SE) and BSE mode
(a and b) only exhibit spherical pores ~1 µm, with no evidence of
precipitates, consistent with the material having no additions of CdS or
ZnS.
Figure 8.5 ....................................................................................................................... 242
Observed in backscatter, precipitates of CdS were up to ~4 μm, with
some micron scale precipitates with geometry of rods or plates and sharp
facets consistent with crystallographic alignment.
Figure 8.6 ....................................................................................................................... 242
Some ZnS inclusions in PbS resembled stacked plates.
Figure 8.7 ....................................................................................................................... 244
XRD pattern of the sintered PbS specimen.
Figure 8.8 ....................................................................................................................... 246
The E and G of the undoped PbS and PbSe were higher than the Nadoped PbS and PbSe. The E and G of undoped PbS are likely higher due
to reduced porosity (pure PbS P = 0.008, all other PbS P = 0.031 to
0.050), while the E and G of undoped PbSe are likely higher due to
doping effects. Only small changes in E and G were noted in Na-doped
PbS and PbSe with addition of up to 4% CdS or ZnS, with. Only small
variability in the ν noted in PbS with addition of CdS or ZnS. The ν of
PbSe increased with the addition of CdS or ZnS. Solid line is average
and dotted line is standard deviation of the specimens with 1% to 4%
CdS or ZnS addition.

xxvi

Figure 8.9 ....................................................................................................................... 247
No measurable change in hardness was noted in PbS with addition of up
to 4% CdS or ZnS. Hardness of PbSe increased from 0.5 GPa to 0.8 GPa
with the addition of either CdS or ZnS. The scatter in the fracture
toughness data of PbS increased with increasing CdS or ZnS content.
No change in the fracture toughness of PbSe was noted.
Figure B.1. ..................................................................................................................... 284
The top of the furnace has exposed leads to power the heating elements
with up to 120 VAC electricity. Do not operate the furnace with these
leads exposed.
Figure B.2. ..................................................................................................................... 285
Note feedthroughs for the thermocouples (left arrow) and heating
element power (right arrow). These feedthroughs and the wires from
them should not touch the base or the sides of the bell jar when closed.
Figure B.3. ..................................................................................................................... 285
Braided insulation must be in place around the conductors to the heating
elements to prevent a short.
Figure B.4. ..................................................................................................................... 286
The o-ring and the base of the bell jar may have some debris, particularly from the
furnace refractories. The debris is abrasive, and may inhibit a proper seal
between the bottom and side of the bell jar. The debris should be removed and
appropriate grease reapplied to the o-ring prior to operation.
Figure B.5. ..................................................................................................................... 287
Controls and power supply for furnace. Note the high voltage power supply is
activated with the red button, and indicated with a red light. Power for the
transducers is provided by a 110 VAC circuit, turned on with a toggle switch and
indicated with a green light.
Figure B.6. ..................................................................................................................... 288
Blue hoses for gas in and gas out (front bottom) and for coolant water in and out
(behind valves) should be inspected for damage such as abrasion or holes.
Figure B.7. ..................................................................................................................... 288
The bubbler (arrow), with the hose extending out, should be filled to cover the
end of the hose with liquid to prevent air from entering the hose.
Figure B.8. ..................................................................................................................... 289
Debris can be seen on the screen in the feed-through leading to the vacuum pump.

xxvii

Figure B.9. ..................................................................................................................... 290
The three transducers are mounted to copper blocks on the chiller plates
underneath the furnace. The mount swivels to allow the angle of the transducer to
be adjusted.
Figure B.10. ................................................................................................................... 291
Molybdenum sheets to be used as baffles.
Figure B.11. ................................................................................................................... 291
Molybdenum baffle being inserted around buffer rods.
Figure B.12. ................................................................................................................... 292
Front SALI board of inner furnace.
Figure B.13. ................................................................................................................... 292
Front SALI board of inner furnace, inserted into position.
Figure B.14. ................................................................................................................... 292
Front refractory bricks of outer furnace.
Figure B.15. ................................................................................................................... 292
Front refractory bricks of outer furnace, inserted into position.
Figure B.16. ................................................................................................................... 293
Hoist and controls to operate up and down. Note the hoist is mounted to a rail for
movement left and right, and that the chain has some slack when the bell jar is in
position.
Figure B.17. ................................................................................................................... 294
Clamps for the bell jar. The same clamps are used to secure the top and base of
the bell jar.
Figure B.18. ................................................................................................................... 294
High vacuum valves below the furnace. The gas in and gas out valves should be
closed before pumping down the bell jar chamber.
Figure B.19. ................................................................................................................... 295
Flow control panel, with flow controls and bypass for the inert gas in and out of
the bell jar and the coolant water from the chiller to the base of the transducers.
Figure B.20. ................................................................................................................... 296
From left, the furnace over temperature limit controller, furnace temperature
controller, and the transducer over temperature limit controller.

xxviii

Figure B.21. ................................................................................................................... 297
Furnace temperature controller, from left, in run mode, selecting set point 1, and
setting set point 1 to 60°C.
Figure B.22. ................................................................................................................... 297
208 VAC power switch with red indicator light on, and 110 VAC power switch
with green indicator on.
Figure B.23. ................................................................................................................... 298
Ammeter and voltmeter for heaters. Resistance decreases with temperature, and
the current should be monitored to not exceed 20 A. Operate heater elements at
less than 60 V for new elements, less than 120 V for elements that have aged due
to use.
Figure B.24. ................................................................................................................... 298
Heater ammeter, heater voltmeter, and variac output knob on control box.
Figure B.25. ................................................................................................................... 299
Bell jar at rest on side table and furnace opened. There should be some slack in
the chain, allowing all the weight of the bell jar to rest on the table.
Figure B.26. ................................................................................................................... 301
RUS transducer mount components.
Figure B.27. ................................................................................................................... 302
The spiral cut hot zone of the heating elements should be completely contained
within the furnace. The power connections to the heating elements should be
outside the furnace.
Figure B.28. ................................................................................................................... 303
Terminal strip on back of furnace for R-type thermocouples, with thermocouple
wires extending into the furnace.
Figure C.1. ..................................................................................................................... 303
Gantry and full assembly.
Figure C.2. ..................................................................................................................... 304
Gantry and full assembly BOM.
Figure C.3. ..................................................................................................................... 305
Gantry.
Figure C.4. ..................................................................................................................... 306
Gantry BOM.
xxix

Figure C.5. ..................................................................................................................... 307
Full assembly.
Figure C.6. ..................................................................................................................... 308
Full assembly BOM.
Figure C.7. ..................................................................................................................... 309
Bar clamp.
Figure C.8. ..................................................................................................................... 310
Bar clamp.
Figure C.9. ..................................................................................................................... 311
Bell jar base.
Figure C.10. ................................................................................................................... 312
Bell jar base assembly.
Figure C.11. ................................................................................................................... 313
Bell jar base assembly BOM.
Figure C.12. ................................................................................................................... 314
Bell jar base weldment.
Figure C.13. ................................................................................................................... 315
Bell jar base weldment BOM.
Figure C.14. ................................................................................................................... 316
Bell jar top.
Figure C.15. ................................................................................................................... 317
Cold plate mount 1.
Figure C.16. ................................................................................................................... 318
Cold plate mount 2.
Figure C.17. ................................................................................................................... 319
Flange tube.
Figure C.18. ................................................................................................................... 320
Furnace box.
Figure C.19. ................................................................................................................... 321
Furnace box BOM.
xxx

Figure C.20. ................................................................................................................... 322
Furnace support plate.
Figure C.21. ................................................................................................................... 323
Heater support 2.
Figure C.22. ................................................................................................................... 324
Heater support.
Figure C.23. ................................................................................................................... 325
Inner furnace back SALI board.
Figure C.24. ................................................................................................................... 326
Inner furnace base SALI board.
Figure C.25. ................................................................................................................... 327
Inner furnace front SALI board.
Figure C.26. ................................................................................................................... 328
Inner furnace side SALI board.
Figure C.27. ................................................................................................................... 329
Inner furnace top SALI board.
Figure C.28. ................................................................................................................... 330
Inner furnace.
Figure C.29. ................................................................................................................... 331
Inner furnace BOM.
Figure C.30. ................................................................................................................... 332
Outer furnace base center.
Figure C.31. ................................................................................................................... 333
Outer furnace base left.
Figure C.32. ................................................................................................................... 334
Outer furnace base right.
Figure C.33. ................................................................................................................... 335
Outer furnace base.
Figure C.34. ................................................................................................................... 336
Outer furnace base BOM.
xxxi

Figure C.35. ................................................................................................................... 337
Outer furnace front 2.
Figure C.36. ................................................................................................................... 338
Outer furnace front.
Figure C.37. ................................................................................................................... 339
Outer furnace side 2.
Figure C.38. ................................................................................................................... 340
Outer furnace side.
Figure C.39. ................................................................................................................... 341
Outer furnace top center.
Figure C.40. ................................................................................................................... 342
Outer furnace top left.
Figure C.41. ................................................................................................................... 343
Outer furnace top right.
Figure C.42. ................................................................................................................... 344
Outer furnace top.
Figure C.43. ................................................................................................................... 345
Outer furnace top BOM.
Figure C.44. ................................................................................................................... 346
Bell jar top.
Figure C.45. ................................................................................................................... 347
RUS and furnace.
Figure C.46. ................................................................................................................... 348
RUS clamp.
Figure C.47. ................................................................................................................... 349
RUS mount assembly.
Figure C.48. ................................................................................................................... 350
RUS mount assembly BOM.
Figure C.49. ................................................................................................................... 351
RUS mount.
xxxii

Figure C.50. ................................................................................................................... 352
RUS support leg.
Figure C.51. ................................................................................................................... 353
RUS support plate.
Figure C.52. ................................................................................................................... 354
RUS support.
Figure C.53. ................................................................................................................... 355
Splash shield mount.
Figure C.54. ................................................................................................................... 356
Splash shield.
Figure C.55. ................................................................................................................... 357
Standoff.
Figure C.56. ................................................................................................................... 358
Table top.
Figure C.57. ................................................................................................................... 359
Transducer cold cap.
Figure C.58. ................................................................................................................... 360
Valve assembly.
Figure C.59. ................................................................................................................... 361
Valve mount.

xxxiii

1 Introduction
Bulk thermoelectric (TE) materials have been developed with increasing figure of
merit, ZT, with some near or exceeding ZT of 2 [Biswas 2012; Heremans 2008], and with
improvements in the ZT made by the incorporation of nanoparticles [Androulakis 2007;
Zhao 2012a; Zhou 2008a; Alleno 2009; Ji 2007] or nanostructured bulk materials
[Toprak 2004; Mi 2008]. While the mechanical properties of many of the undoped TE
materials without nanoparticles or nanostructures have been measured and published,
doping [Gelbstein 2008], alloying [Gelbstein 2008; Darrow 1969], and incorporation of
nanoparticles [Zhao 2008; Kvetková 2013] or nanoprecipitates [Ni 2010; Ren 2010] have
each been shown to change the mechanical properties such as hardness or elastic moduli.
In addition, the hardness and elastic moduli of TE materials are a function of porosity [Ni
2009]. Furthermore, porosity may be structured similar to particles and precipitates to
engineer the properties of the material, such as has been done to improve fatigue life in
thermal barrier coatings [Giolli 2009], to improve the operational life of a TE device.
As the TE materials are optimized to achieve a high figure of merit, the
mechanical properties of the materials also need to be tested. Furthermore, the
mechanical properties may be optimized without significant change to the ZT such as by
additions of silicon carbide nanoparticles, or in some cases, improving the ZT by the
addition of nanoparticles [Zhao 2008]. Thus, the mechanical properties of TE materials
must be tested and optimized together with the ZT.
1.1 Applications of thermoelectric materials
Thermoelectric materials are capable of being used for either power generation
from a temperature gradient or for producing a temperature gradient by applying an
1

electrical potential. TE materials such those based on Mg2Si [Gao 2014], SnTe
[Vedeneev 1998; Gelbstein 2009; Leontyev 2012; Gojaev 2010], PbS [Zhao 2012b],
PbSe [Zhao 2013], and CoSb3-based skutterudites [Chubilleau 2012; Salvador 2009;
Yang 2007; Nolas 1999] are considered candidate materials for waste heat recovery, such
as from automotive exhaust heat. Other TE materials such as YbAl3-based compounds
are being developed as possible cryogenic Peltier coolers [Lehr 2013a; Lehr 2013b].
TE materials for waste heat recovery applications are subject to stresses from
multiple sources when placed in service. For waste heat recovery, the hot side of a TE
device would be placed in thermal contact with a source of heat, from sources such as
automotive or other engine exhaust, industrial boilers, or metal refineries. The waste heat
source is typically not at constant temperature, subjecting the device to stresses caused by
thermal gradients, thermal expansion mismatch, thermal transients, in addition to
externally applied stresses. In order to understand the mechanical response to these
stresses, the mechanical properties of fracture toughness, hardness and elastic moduli
must be understood. In addition, the material must be examined for reactions such as
decomposition or bloating for the possible operating temperature range.
1.2 Thermoelectric efficiency
Thermoelectric (TE) materials are typically brittle materials, heavily doped
semiconductor devices or semimetals, which may be used in either power generation or
heating or cooling. Typically, the efficiency of a TE material is characterized by the
dimensionless figure of merit, ZT, defined as [Tritt 2011; Bux 2010]
(1.1)
2

where S is Seebeck coefficient, σ is the electrical conductivity, T is temperature, and κ is
thermal conductivity. In heat recovery, the efficiency of a TE device, η, is defined as
[Tritt 2011; Bux 2010]
(

√

√

)

(1.2)

where TH is the hot side temperature and TC is the cold side temperature. The η for the
TE material is proportional to the Carnot efficiency, ηC [Tritt 2011].
(1.3)
From equations (1.2) and (1.3), it is seen that in order to achieve the efficiency closest to
Carnot in a TE device, the ZT must be maximized.
Improvements in ZT have incorporated one of several processes, including atomic
scale doping or substitution [Gelbstein 2008; Zhu 2009; Zhao 2012b], creation of
nanostructured bulk materials [Toprak 2004; Mi 2008; Hsu 2004; Zhu 2009],
incorporation of nanoparticles [Androulakis 2007; Zhao 2012a; Zhou 2008a; Alleno
2009; Ji 2007], or a combination of atomic, nanostructural, and microstructural length
scale modifications [Biswas 2012]. Until the mid-1990’s, the practical limit for ZT was 1
[Tritt 2011], although recent advancements have demonstrated bulk TE materials with ZT
> 2, such as PbTe-based compounds [Biswas 2012] and SnSe [Zhao 2014], along with
several other TE materials with ZT > 1, such as skutterudites with ZT of 1.7 [Shi 2011],
PbSe with ZT of 1.6 [Zhao 2013], and PbS with ZT of 1.3[Zhao 2012b].
1.3 Mechanical properties of thermoelectric materials
TE materials are typically incorporated into thermoelectric modules, where a
series of TE materials in the form of legs (Figure 1.1) are electrically connected in series,
3

but each leg is thermally in parallel [Bux 2010]. Thus, each leg of a TE module is subject
to the same temperature gradient individually, but the failure of a single TE leg will result
in the failure of an entire module of 10’s or 100’s of legs. Therefore, understanding the
mechanical stresses that develop due to thermal gradients, thermal transients, and applied
external loads, and how the material will respond to the stresses are critically important to
a reliable TE device.
The ZT of a TE material is a function of temperature, and therefore different
materials achieve maximum efficiency at different temperature ranges. Maximizing
efficiency depends on the material choice as well as the operational temperature. An
improvement may also be made by segmenting a TE leg, using different TE materials
within a leg based on the expected temperature at a section of a leg [Crane 2009]. For
example, replacing a part of a Bi2Te3 leg with either TAGS [(AgSbTe2)1-x(GeTe)x] or
PbTe on the high temperature side of the leg, depending on whether the leg was p-type or
n-type doped, was used to fabricate a TE generator with η > 0.1 for a temperature
difference of 500°C [Crane 2009]. A segmented design requires additional modeling to
ensure mechanical reliability because of the added complexity of two TE materials in a
single leg [Crane 2009].
Numerical simulation of the mechanical response of TE materials requires
knowledge of the mechanical properties, such as elastic moduli, hardness or fracture
toughness of the material [Kardestuncer 1987]. These mechanical properties are typically
not measured for any case of optimized TE materials. The only published elastic moduli
for TE materials are typically for undoped or single crystal case, such as elastic moduli in
SnTe [Beattie 1969] or PbS [Dalven 1969; Bhagavantam 1951], which may not be
4

comparable to doped or otherwise optimized TE materials. Thus, to understand the
mechanical response and to run simulation results, the mechanical properties, including
elastic moduli, hardness, and fracture toughness, must be measured on the optimized TE
material.
The calculation of thermal stresses in a temperature transient may be
demonstrated with the simplified case of a flat plate. The maximum surface stress on a
flat plate, Smax, is a function of the temperature-dependent Young’s modulus, E(T),
Poisson’s ratio, (T), thermal expansion, (T), and a function of the Biot modulus, f(Bi),
where [Case 2012]

Smax 

E T 
αT   T  f(Bi)
1   T 

(1.4)

The function f(Bi) increases monotonically with increasing Biot modulus Bi, where Bi =
ah/κ, and a is the characteristic dimension of the specimen, h is the surface heat transfer
coefficient and κ is the thermal conductivity of the specimen. In this case, the elastic
moduli, E(T) and (T), and thermal expansion, (T), are required mechanical/thermal
properties to determine the stress in the material.

5

Figure 1.1. Schematic of a thermoelectric couple, indicating current flow when placed in
a temperature gradient.

6

1.3.1 Elastic moduli
The elastic moduli of a specimen are required to determine the elastic response of
a material to a given stress. The moduli may change as a material system is optimized as
a TE material, such as by the addition of particles or precipitates, or through dopants.
Additions of dopants and elements to produce solid-state precipitates have been
commonly applied to thermoelectric materials. Lead telluride-based thermoelectrics have
achieved record efficiencies in part by using this technique [Zhao 2013]. Also, if
microcrack damage is accumulated, through thermal cycling or mechanical loading, the
microcrack-induced reduction in E may be used to monitor the extent of the microcrack
damage, as has been previously shown for non-TE materials [Fan 2012; Case 1993;
Ghassemi Kakroudi 2009].
For the elastic moduli, additions of well-connected, insoluble nanoparticles may be
modeled several ways, including rule of mixtures [Hashin 1962], constant strain [Hashin
1962], Hashin particulate composite model [Bedolla 2012; Couturier 1997; Hashin 1962],
and Halpin-Tsai composite [Halpin 1992]. Each of these models ignores the possible
effects of the size of nanoparticles within a matrix, but only the rule of mixtures model
predicts a significant change in elastic modulus for small additions of nanoparticles.
Additions of silver nanoparticles (AgNP) have improved the ZT of barium-filled
skutterudite by 30% [Zhou 2012], which raised interest in examining the mechanical
properties of the material. The Young’s modulus of silver and CoSb3-based skutterudite
are not dramatically different (E = 82 GPa for Ag [Neighbours 1958; Chang 1966], E =
109 GPa to 148 GPa for SKD [Rogl 2011]). Therefore, addition of 0.5 wt% silver to
skutterudite should not change the E significantly, if the models for additions insoluble
7

nanoparticles are accurate [Hashin 1962; Bedolla 2012; Couturier 1997; Halpin 1992].
However, addition of 0.5 wt% silver to skutterudite was accompanied by a modest
increase in Seebeck along with the expected change in electrical conductivity [Zhou
2012]. The change in Seebeck could indicate the nanoparticle additions are not be
completely insoluble, and therefore there may be a change in the mechanical properties of
the TE material as well that the models would not predict.
The addition of silicon carbide nanoparticles (SiCNP) or precipitates to a TE material
may improve various material properties, such as acting as a scattering site to reduce the
thermal conductivity [Zhou 2008b; Li 2006], or to inhibit bloating and creep behavior [Ni
2013]. The ZT of Bi2Te3 was improved from 0.99 to 1.04, while the hardness, fracture
toughness and E were each increased by the addition of 0.1 vol% to 1.0 vol% SiCNP
[Zhao 2008], demonstrating the possibilities of SiCNP or other particle additions to TE
materials.
Dopants, as well as solid solution changes or modifications to stiochiometry, may
have a strong influence on the elastic moduli. In a review by Ren et al., ratios between
the maximum and minimum moduli, Emax/Emin and Bmax/Bmin, of up to 3 were observed for
changes in solid solution [Ren 2007]. If additions such as AgNP or SiCNP form a solid
solution with a TE material, or if the composition of the TE material is otherwise altered,
the mechanical properties of the TE material could have significant changes.
1.3.2 Fracture toughness
In order to create a reliable TE device, the TE material must withstand the
environmental stresses and the cycling of the intended application without failure. In
general, TE materials are brittle, including Zn4Sb3 [Ueno 2005], CoSb3 [Salvador 2009,
8

Yang 2009a], PbTe [Salvador 2009], and lead antimony silver tellurium compounds
(LAST) [Ren 2006]. This generally implies that the mechanical failure mode of TE
materials is fracture, similar to ceramics [Kingery 1976]. The conditions under which
crack propagation may occur from a flaw of size a [Rice 1998] are
(6)

√

where σfract is the fracture stress, KC is the fracture toughness of a material, and Y is a
shape factor based upon the geometry of the flaw. Therefore, KC is a necessary material
property a designer requires to minimize the risk of fracture in a device.
Unfortunately, the KC of TE materials is typically low, between 0.5 and 1.5 MPam1/2 or less [Eilertsen 2013; Fan 2012; Ni 2013]. However, fracture toughness may be
changed by the addition of particles or second phases. The fracture toughness of Bi2Te3
was increased from 1.14 MPa-m1/2 to 1.35 MPa-m1/2 by the addition of 0.1 vol% SiCNP
[Zhao 2008]. Furthermore, additions of nanoparticles may influence fracture mode or
sintering behavior [Mukhopadhyay 2010; Ni 2013], and a fracture mode change has been
accompanied by either an increase [Mukhopadhyay 2010; Kawabata 1977; Karakasidis
2011] or decrease [Yamada 2010; Jang 2010] in KC.
1.4 Porosity effects on mechanical properties
The addition of porosity to a specimen may have profound effects. The elastic
modulus of several TE materials drops off according to an empirically derived
exponential relationship,
(1.4a)

9

where E is Young’s modulus, E0 is the modulus of theoretically dense specimen, P is
volume fraction porosity, and b is a fitting parameter, commonly observed to be between
2 and 6 for a wide range of solid materials [Rice 1998]. This exponential relationship
may be extended to include the shear modulus, G, and bulk modulus, B, of TE materials
[Ni 2009], as well as hardness, H [Ni 2011; Ren 2008], as the general equation
(1.4b)
where A represents the property E, G, B, or H [Rice 1998]. If the term bP is small, the
equation may be linearized by using the first two terms of the Taylor series expansion of
the exponential to give
(1.4c)
For the materials in this study, this linear approximation is appropriate for the data.
The fracture toughness of a brittle material may increase, decrease or remain
constant with increasing porosity [Rice 1995]. In particular, an evaluation including
Al2O3, B4C and Si3N4 at P = 0.1 to P = 0.15 indicated KIC values as high or higher than at
P = 0 [Rice 1995]. The maintenance of KIC values with increasing P may be due to the
pore blunting or deflecting the crack tip [Case 2012].
1.5 Temperature effects on mechanical properties
The elastic moduli decreases with increasing temperature. For temperatures
greater than 0.3 to 0.5 of the Debye temperature, the temperature-dependent change may
be represented by [Schmidt 2012]
–

–

(1.5a)

–

–

(1.5b)

10

where ERT and GRT are the room temperature Young’s and shear moduli respectively, and
the constants bTE and bTG are experimentally measured fitting factors. A change in the
slope, bTE and bTG, indicates a change within the material, such as the onset of grain
boundary sliding or an order-disorder transition [Schmidt 2012; Ren 2009; Wachtman
2009]. These changes within a material may be significant, and in some cases may be
controlled by particle additions to the material [Schmidt 2012].
1.6 Sintering of thermoelectric materials
Typically, thermoelectric materials are fabricated by sintering of a powder
processed ingot, either by hot pressing (HP) or pulsed electric current sintering (PECS)
[Ni 2011]. These two methods of sintering both may produce dense specimens, but the
microstructure, including pore shape and distribution, grain size and grain growth, may
vary considerably [Ni 2011]. The HP method is well established, but the PECS method
may permit consolidation in considerably shorter time, reducing cost of sintering and
reducing time for grain growth [Savary 2012; Recknagel 2007; Zhao 2012b; Biswas
2012]. Additionally, the use of sintering aids to create a small, < 1%, amount of liquid
phase at sintering temperature may permit the use of lower sintering temperature and
shorter time to densify a specimen [Barsoum 2003].
For TE materials, the mechanical properties of elastic moduli, hardness and
fracture toughness for specimens sintered by each of HP and PECS have not previously
been explored. Furthermore, additions of sintering aids have not been explored for Sbbased skutterudite TE materials, nor for most TE materials. The exploring of sintering
aids and creating a process for the development of new sintering aids may improve the
sintering time and cost [Barsoum 2003].
11

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Kanatzidis, M.G. Ultralow thermal conductivity and high thermoelectric figure of
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[Zhou, Li, Kita 2008b] Zhou, M., Li, J.-F., Kita, T. Nanostructured AgPb(m)SbTe(m+2)
system bulk materials with enhanced thermoelectric performance. Journal of the
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20

2 Experimental Procedure
2.1 Material preparation
For the YbAl3 (chapter 3), Mg2Si (chapters 4 and 5), Ba0.3Co4Sb12 (chapter 6),
SnTe (chapter 7), and PbS and PbSe-based thermoelectric materials (chapter 8) in this
dissertation, ingots or lump material were prepared from high purity elemental powders
at Michigan State University, Northwestern University, University of Michigan, or by
Alfa Aesar.
YbAl3 ingots (chapter 3) were arc melted at Michigan State University in an Al
flux under argon, with each ingot melted at least 5 times to ensure homogeneity. The
excess Al was removed by crushing the ingot and etching the Al with a 5 M solution of
NaOH for 24 h. The etched powder was passed through a 100-mesh (149 µm) sieve
before powder processing or sintering.
The Mg2Si lump material (chapters 4 and 5) was commercially prepared (45518,
Alfa Aesar, Ward Hill, MA) from high purity elements (99.99% metals basis). The lump
material was crushed, ground, sieved and reground (CGSR), as described in section 2.2.
Barium-doped skutterudite ingots, Ba0.3Co4Sb12 (chapter 6), were fabricated from
elemental Ba (pieces, 99.9% pure), Co (powder 99.5% pure), and Sb (shot 99.999%
pure), by sealing the elements in evacuated carbon coated quartz ampoules, heated to
1373 K for 5 h, quenched, then annealing at 1023 K for 7 days. The skutterudite ingot
produced was processed by CGSR, as described in section 2.2.
SnTe (chapter 7) ingots were prepared by combining high purity elemental
powders of Sn (Plamaterials purity 99.999 %) and Te (5 N Plus Inc., purity 99.999 %) in
a quartz ampoule and sealed under vacuum. The sealed tubes were heated to either 1273
21

K for 10 h or 1148 K for 12 h, then quenched. The ingot material produced was
processed by CGSR, as described in section 2.2.
Na-doped PbS and PbSe ingots (chapter 8) with x% CdS/ZnS, where the at
fraction x = 1, 2, 3 and 4, were produced by sealing high purity elements in evacuated
carbon coated quartz ampoules and heating to 1473 K for 4 h, then quenched. The
resulting ingots were crushed, and the crushed powder was passed through a 53 µm sieve
before sintering.
2.2 Crushing, grinding, sieving and regrinding (CGSR) process
The Mg2Si lump, Ba0.3Co4Sb12 sintered billets for reprocessing and SnTe ingot
(chapters 4 – 7) were crushed, ground, sieved and reground (CGSR), using a process
originally developed for another TE material, LAST (lead-antimony-silver-tellurium)
[Pilchak 2007], and previously used for Pb0.95Sn0.05Te-PbS 8% [Ni 2010] and other Sbbased skutterudites [Schmidt 2011]. All CGSR processing was performed in a glove box
under argon (Omni-Lab double glove box) equipped with an oxygen sensor and a
moisture sensor (Vacuum Atmospheres Company, Hawthorne, CA).
The lump or ingot material was ground for 5 minutes in a WC-lined mechanical
mortar and pestle machine (Retsch RM200, Retsch GmbH, Haan, Germany). The
powder was transferred to a sieve, 53 μm ASTM E 11 sieve (60.150.000053, Retsch
GmbH, Haan, Germany) for the Mg2Si and SnTe, or 75 μm sieve (60.150.000075, Retsch
GmbH) for the Ba0.3Co4Sb12, with a bottom collector pan (697203050, Retsch GmbH).
The top of the sieve was covered with a sheet of aluminum foil to limit possible
contamination, and then the ground powder was passed through the sieve on a shaker
table (AS 200, Retsch GmbH) for 5 to 15 minutes. The sieved powder was collected and
22

stored in glass scintillation vials (RPI 121000, Research Products International Corp., Mt.
Prospect, IL), and the powder that did not pass was returned to the mortar for regrinding.
Up to 5 grindings were performed per batch of powder to pass the ground lump or ingot
through the sieve.
Sieves were cleaned between uses with different material systems or when the
amount of ground powder noticeably decreased to indicate clogging. The sieve was
placed in an ultrasonic cleaner (VWR, 98000-336) with RO water and detergent. A drop
of ethanol was used to break the water surface tension and remove any large bubbles
trapped under the mesh before cleaning. The ultrasonic cleaner was run for 5 minutes,
the screen was rinsed with ethanol and RO water, then dried in a 353 K oven for 20 to 30
minutes.
2.3 Milling of CGSR powder
The CGSR powder was milled by one of two methods, planetary ball milling or
vibratory milling.
2.3.1 Planetary ball milling
Planetary ball milling (PM) was performed on Mg2Si CGSR powder and SnTe
CGSR powder in the same glove box under argon (Omni-Lab double glove box) as the
CGSR processing of powder was performed, allowing the material to remain in the same
argon atmosphere for the entire powder processing process.
The CGSR powder was milled in 10–30 g batches with 100 g of 10-mm diameter
spherical alumina media at 150 rpm for 3 h (planetary mill PM100 and 250 mL alumina
jar 01.462.0221, Retsch GmbH, Haan, Germany). The powder was collected from the
mill by transferring the contents of the mill jar to a coarse sieve (60.150.000, Retsch
23

GmbH) stacked on a bottom collector pan (697203050, Retsch GmbH). The jar was
scraped down with a metal spatula (82027-532, VWR, Radnor, PA) to collect material
caked to the walls of the jar. The top of the sieve was covered with a sheet of aluminum
foil, then the loose powder on the media was removed on a shaker table for 5 to 15
minutes. The milled powder was collected and stored in glass scintillation vials.
Cleaning of the PM jar and media was performed when changing the TE material
milled, or when the jar was removed from the glove box. If the jar was used for Mg2Si,
the jar and media were first soaked overnight in reverse osmosis (RO) water, then rinsed
with diluted HCl and RO water to reduce the possibility of a significant reaction between
the TE material and the cleaning chemicals. The PM jar and media were cleaned using
aqua regia (3-4 parts HCl: 1 part HNO3) in a fume hood while wearing appropriate
personal protective equipment. The media and jar were soaked in aqua regia until no
remaining TE material was visible, and for at least 20 minutes. Stirring and applying of
aqua regia was performed with disposable plastic pipets (14670-147, VWR). The used
aqua regia was disposed of in a vented container. The media and jar were thoroughly
rinsed with RO water, filling the jar multiple times with RO water, before air drying.
2.3.2 Vibratory ball milling
Vibratory ball milling (VM) was performed on Mg2Si CGSR powder (chapter 5),
Ba0.3Co4Sb12 CGSR powder (chapter 6), and YbAl3 sieved powder (chapter 3). For the
Mg2Si CGSR powder and Ba0.3Co4Sb12 CGSR powder, each batch of powder (5 g for
Mg2Si, 7.1 g for Ba0.3Co4Sb12) was milled in a WC mill jar with two 11.2 mm WC
spheres and four 7.9 mm WC spheres, sealed with Viton gaskets (WC mill jar set 8004,
WC media 5004A, Viton gasket 39322, SPEX Sample Prep, Metuchen, NJ). The mill jar
24

was filled and sealed in an argon glove box, then the cap was wrapped with electrical
tape (Super 88, 3m, St. Paul, MN), and a layer of Parafilm “M” wrapped around the
entire jar (PM-996 Pechiney Plastic Packaging, Menasha WI) to prevent air from entering
the jar. The powder, sealed in the mill jar with the media, was removed from the glove
box, then milled for 10 minutes in a vibratory mill (8000M SPEX SamplePrep). The
sealed mill jar was returned to the glove box after milling and opened to collect the
powder. The oxygen concentration in the glove box did not change when the mill jar was
opened, with a meter sensitivity of ± 0.1 ppm, indicating the mill jar remained sealed
during milling. The milled powder was collected and stored in glass scintillation vials.
For the YbAl3 sieved powder, the powder was VM in a stainless steel jar with
stainless steel media. The powder was loaded into the jar in air, thus no electrical tape or
parafilm was necessary to seal the jar.
Cleaning of the VM jar and media was performed when changing the TE material
milled, or when the jar was opened while removed from the glove box. For cleaning, the
jar and media were filled to approximately 1 cm depth with play sand and milled for 10
minutes. The milled sand was removed, the jar disassembled and rinsed with RO water
and ethanol, and the Viton gaskets wiped down with a Kim-wipe (Kimberly Clark 34155,
Neenah, Wisconsin) and ethanol. The jar and gaskets were reassembled, the jar filled
with approximately 1 cm of play sand, then with ethanol to the top of the sand and milled
for a second 10 minutes. The jar was cleaned out, rinsed and gaskets wiped down again
before reassembly. The jar was filled with approximately 1 cm of ethanol and milled for
a third 10 minutes. The jar was cleaned out, rinsed and gaskets wiped down a third time
before final reassembly. A separate set of Viton gaskets were used for each material
25

system milled in the jar. The Viton gaskets were changed during final reassembly if
necessary.
2.4 Incorporation of nanoparticles
Silicon carbide nanoparticles (SiCNP) from one of two vendors, with vendorspecified average particle size between 45 nm and 55 nm (44646, Lot number E15T018,
Alfa Aesar) or 50 nm to 60 nm (4621HW, Lot #4621-110209, Nanostructured &
Amorphous Materials Inc., Houston, TX) were incorporated into PM powder of SnTe
(chapter 7) and Mg2Si (chapter 4) by PM at 120 RPM for 3 h, and into CGSR powder of
Mg2Si by VM for 10 min. Other than the addition of SiCNP, and the change in PM speed
and time, all PM and VM processing was identical to the processing
Silver nanoparticles (AgNP) with a vendor specified purity of 99.9% and a vendorspecified size range of from 20 nm to 40 nm (45509, Alfa Aesar, Ward Hill MA), were
dispersed into the Ba0.3Co4Sb12 powder by PM at 300 rpm for 15 min (chapter 6).
2.5 Sintering of powders
Sintering of powders to make bulk specimens was performed by either hot press
(HP) or by pulsed electric current sintering (PECS).
2.5.1 Hot press sintering
Hot press (HP) sintering was employed for the sieved YbAl3 (chapter 3) and PM
Ba0.3Co4Sb12 powder (chapter 6).
HP Sintering of the Ba0.3Co4Sb12 powder (chapter 6) was performed in an argon
glove box with a graphite die and a custom-built hot press. The graphite die was lined
with grafoil (Graftech International, Lakewood, OH) to prevent the powders from
sticking to the die. The temperature was monitored by K-type thermocouple and adjusted
26

manually by varying power supplied to a resistance coil heating element in a spiral
surrounding the die. A manual hydraulic press was maintained at the desired pressure
during the HP cycle.
HP specimens of YbAl3 (chapter 3) were pressed by Edward J. Timm in a 22 mm
diameter graphite die at 973 K for 1 hour under at 70 MPa (Hot press model HP20014020-23G by Thermal Technologies LLC, Santa Rosa, CA).
2.5.2 Pulsed electric current sintering
Pulsed electric current sintering (PECS) was employed for the VM YbAl3 powder
(chapter 3), CGSR, PM and VM Mg2Si powders (chapters 4 and 5), VM Ba0.3Co4Sb12
powder (chapter 6), PM SnTe powder (chapter 7), and the CGSR PbS and PbSe powders
(chapter 8).
Specimens were densified by pulsed electric current sintering (SPS Model 10-3,
Thermal Technology LLC, Santa Rosa, CA) in a 12.7 mm or 20 mm diameter graphite
die lined with grafoil. Powder was added to the die in an argon glove box and manually
tamped down with the punch of the die. The loaded die was transferred to the PECS
machine, and then the PECS chamber was evacuated with a roughing pump. The PECS
chamber was backfilled with argon, then the sintering cycle was run from automated
control software for the desired temperature and pressure ramp rate and hold time as
specified for the individual specimens (see chapters 3-8). After cooling, the die was
removed from the PECS chamber and the specimen removed. Overhanging grafoil may
be cut with a razor blade to aid in removal of the specimen from the die.

27

2.6 Sintered specimen preparation
After sintering, the specimens remained covered with a grafoil layer requiring
removal. The bulk of the grafoil was removed with a #10 or #11 scalpel (372610 or
372611, Aspen Surgical Products, Caledonia, MI) by hand. The remaining grafoil on a
rough sintered specimen surface was primarily removed by hand sanding until most of
the rough surface was no longer visible using 600 to 1200 grit sand paper with adhesive
back, adhered to an aluminum plate. For the Mg2Si specimens, the sand paper was
wetted with ethanol due to an incompatibility between the Mg2Si and water. For all other
specimens, the sand paper was wetted with RO water.
Final cleaning of grafoil was performed with a Pyrex 50 mL beaker filled with 20
to 30 mL of ethanol (Mg2Si specimens) or a solution of 1% liquid detergent (Liquinox
detergent, Alconox, White Plains, NY) in RO water. The beaker was placed in an
ultrasonic cleaner (Ultramet III, Buehler, Evanston, IL) until the grafoil was removed, 5
to 30 minutes.
2.7 Mounting of specimens
Specimens were mounted for cutting or polishing by thermoplastic or by epoxy.
2.7.1 Thermoplastic mounting of specimens
Specimens were mounted with thermoplastic (CrystalBond 509, EMS, Hatfield,
PA) to a glass slide for cutting or to aluminum stubs for polishing. The glass slide or
stub, pieces of thermoplastic and specimen were heated simultaneously, starting with a
room-temperature hot plate, to the softening point of the thermoplastic over 5 to 30
minutes. The slow heating rate was used to avoid introducing a thermal shock to the
specimen. The specimen was placed into the softened thermoplastic such that the desired
28

side was flat against the slide or stub with only a thin layer of thermoplastic between, and
the thermoplastic extended at least half the distance up the sides of the specimen.
Additional small pieces of thermoplastic may be added if necessary to reach the required
distance for specimen support. The heat was removed and the mounted specimen air
cooled to room temperature.
2.7.2 Thermoplastic dismounting of specimens
Dismounting of thermoplastic mounted specimens was performed by slowly
reheating the mounted specimen on a hot plate, then removing the softened thermoplastic
from the specimen with a metal spatula. The roughly cleaned specimen was slowly
cooled to room temperature.
Final cleaning of the specimen was done with acetone in a fume hood. A
KimWipe with acetone was used to remove the bulk of the thermoplastic film by hand.
The specimen was then soaked in approximately 10 to 20 mL of acetone in a 50 mL
Pyrex beaker for approximately 5 minutes. The specimen was removed from the soak,
rinsed with a spray of acetone while held in a clean KimWipe, then soaked in a second 50
mL Pyrex beaker of approximately 10 to 20 mL clean acetone for another 5 minutes. The
specimen was removed from the second soak, rinsed with a spray of acetone while held
in a clean KimWipe, then air dried on a clean and dry KimWipe. If any film of
thermoplastic was observed, the final cleaning was repeated.
2.7.3 Epoxy mounting of specimens
Small or irregular pieces of specimens for polishing and indentation were
mounted in epoxy. Ring forms (Black Bakelite Ring Forms #811-221, Leco, St Joseph,
MI) were placed on an aluminum plate that had been sprayed with mold release (3470
29

Reliable Release, Crown, Woodstock, IL). Specimens for mounting were placed in each
ring form. The manufacturer specified ratio of epoxy resin and hardener (Epoxicure
Resin and Epoxicure Hardener, Buehler, Evanston, IL) were measured by weight on an
electronic balance (Adventurer AR2140, Ohaus Corp, Pine Brook, NJ) in a disposable
medicine cup to produce 20-30 mL of epoxy. The resin and hardener were mixed by
hand with a wooden stir stick until swirls of separate resin or hardener were no longer
visible. The ring forms were filled to approximately 2/3 full with the mixed epoxy, and
any bubbles that formed around the specimen were dislodged with the stir stick to
dissipate at the surface. A steel weight was sprayed with mold release and placed on top
of the ring forms to limit epoxy seepage out from the bottom of the ring forms. The
epoxy was cured for at least 1 day. After curing, the epoxy was engraved with the
specimen name using a rotary tool. Any epoxy that leaked out was cut from the sides of
the ring forms.
2.8 Specimen cutting
Specimens mounted on a glass slide were cut on a low speed diamond saw
(Isomet Low Speed Saw, Buehler, Evanston, IL) with a cutting oil bath (VP-50 cutting
oil, part number 811-024, Leco Corporation, St. Joseph, MI) set at a cutting speed
between 3 and 4. Counterweights were adjusted to cut through a 10 mm specimen in
approximately 15 to 30 minutes.
2.9 Specimen polishing
Mounted specimens were polished on an automatic polishing machine (Leco
Vari/Pol VP-50, Leco Corporation, St. Joseph, MI). Specimens were mounted in a 12position specimen holder, with 3 or 4 specimens polished at a time. A series of diamond
30

grit pastes (Table 2.1) were used to polish the specimens prior to indentation or scanning
electron microscope (SEM) imaging of polished surfaces.
The diamond grit was applied in a spiral dot pattern to a WhiteTec polishing pad
(White Tec #812-454, Leco, St. Joseph, MI) mounted to a 12-inch polishing wheel. The
wheel was wetted with diamond compound extender (Microid Diamond Compound
Extender #811-004, Leco, St. Joseph, MI). The specimens were polished for 3 to 120
minutes at each grit size, until the specimens were flat and no scratches from the previous
grit size were present (e.g., polishing with 6 µm grit is complete when no scratches are
visible that were present after polishing with 9 µm grit).
When polishing is complete for a specific grit size, the specimens and the
mounting wheel were cleaned to remove all polishing grit prior to the next polishing step.
All specimens except Mg2Si were cleaned by rinsing with tap water, then cleaning in an
ultrasonic cleaner (B3500A-MT, VWR International, West Chester, PA) with a solution
of 1% detergent (Liquinox detergent, Alconox) in RO water for 10 minutes. The
specimens were then manually cleaned with cotton tipped applicators and ethanol before
final rinse with RO water. For the Mg2Si specimens, the cleaning was performed
exclusively by hand with cotton tipped applicators and ethanol with an ethanol rinse due
to a reaction between Mg2Si and water.

31

Table 2.1. A series of diamond grit pastes were used to polish the specimens. A grit size
may be skipped, with additional polishing time on the next smaller diamond grit size to
compensate.
Nominal
Diamond Grit Manufacturer
Part Number
Diamond Grit Size Range
Size
67 µm
Warren Superabrasives,
54-80MB MUS 20gm
54-80 m
Anaheim, CA
35 µm
Not listed
Warren Diamond Powder #35 MUS MB 20G
Company, Olyphant, PA
9 µm
Not listed
Leco Corporation,
810-913
St. Joseph, MI
6 µm
Not listed
Warren Diamond Powder #6 MUS MB 20G
Company, Olyphant, PA
1 µm
Not listed
Leco Corporation,
810-870
St. Joseph, MI
0.5 µm
Not listed
Leco Corporation,
810-868
St. Joseph, MI

32

2.10 Mass, dimensions and density
Specimens of cylinder or parallelepiped geometry were measured to determine
mass and dimensions, and calculate density. The mass and dimensions were used in later
resonant ultrasound spectroscopy measurements (see section 2.11) and density was used
in the analysis of mechanical property measurements.
Each of the dimensions of a specimen were determined by 5 measurements with
micrometers (293-832, Mitutoyo, Japan), one measurement on each corner and one in the
center or similar pattern, and the 5 measurements averaged. Specimen mass was
measured by electronic balance (Adventurer AR2140, OHAUS, Pine Brook IL).
2.11 Resonant ultrasound spectroscopy
The Young’s modulus, E, shear modulus, G, and Poisson’s ratio, ν, of the
specimens were determined by resonant ultrasound spectroscopy (RUS). In RUS, the
resonant frequencies of a specimen are measured across a range of frequencies. These
measured resonant frequencies are a function of the specimen mass, dimensions,
geometry and elastic moduli [Migliori 1997; Ren 2009a].
The resonant frequencies were measured with a commercial RUS system
(RUSpec, Quasar International, Albuquerque, NM) by placing the specimen on either a
tripod arrangement of transducers (Figure 2.1) or between two transducers across a body
diagonal. The range of frequencies was set to begin measurement before the first
resonance frequency, and record at least 40 resonance frequencies (Figure 2.2). Four
measurements of the resonance frequency spectrum were taken per specimen, two per
side for the tripod arrangement, and once for each body diagonal for the two transducer
arrangement. Some resonance frequencies may be missing or poorly measured for one
33

position, possibly due to contact issues between the specimen and the transducer or other
causes [Ren 2009b], but more visible in another scan. The scan with the clearest
representation of resonance frequencies was chosen for analysis.
Analysis was performed with commercial software (Figure 2.3) for either a
parallelepiped geometry specimen (RPModel version 2.68b, Quasar International) or a
disk shaped specimen (CylModel version 2.68b, Quasar International). The measured
mass and dimensions, and an initial guess for the stiffness, c11 and c44 for isotropic
specimens, were entered, the desired number of calculated resonance frequencies, the
convergence rate (typically set to 0.5), the polynomial order (typically set to 12), and the
fit dimensions option set (typically unused). The calculated resonance frequencies were
matched to measured resonance frequencies from the spectrum (Figure 2.2), and the
model was fit to the results through an iterative process. Typically, at least 12 peaks were
included on the first fit of the model. Additional peaks may be added or removed from
the analysis and rerun the model fit to improve the output results.
For elastically isotropic specimens, the elastic moduli are calculated from the
stiffness as [Ren 2009b]
(

)

(2.1)
(2.2)

(

(2.3)

)

The output of the RUS model includes information on the confidence of fit. From
the output information, the uncertainties dc11 and dc44 in the measurement of c11 and c44
correspond to the 95% confidence levels calculated by the RUS model software [Ren
34

2009b]. The dc11 and dc44 values are computed from the first and last values, A and D,
under the “chisquare increased 2% by…” section of the RUS output file, as indicated in
Figure 2.4. The dc11 and dc44 values are used to compute dE, dG, and dν.
(2.4)
(2.5)

√(

(

)

)
(

)

(2.6)
(2.7)

√

(

(2.8)

)

The output of equations (2.6-2.8) are reported as the error for the RUS
measurements of E, G and ν, respectively.
Additional details of the RUS theory are provided in a comprehensive book by
Migliori and Sarrao [Migliori 1997].

35

Intensity (A.U.)

Figure 2.1. Typical setup of tripod arrangement of RUS transducers, with specimen on
top and the transducer tips near the edge of the specimen.

0

100

200

300

400

500

600

Frequency (kHz)
Figure 2.2. RUS spectrum from PbSe specimen. Each sharp peak in intensity represents
a mechanical resonance at the driven frequency.

36

Figure 2.3. RUS analysis software, showing setup of initial conditions for a PbSe
specimen.

37

Cylinder Calculation Report
This Report was prepared on 12/18/12 14:35:52 Eastern Standard Time
PbSe
Elastic Moduli Analysis is completed.
free moduli are c11 and c44
Poly Order = 12, Mass = 0.639300 gm, Density = 7.647000 g/cc
Convergence Rate = 0.500000
n
fmeas(kHz) fcalc(kHz) %err
1
65.404
65.227 -0.27%
2
65.404
65.227 -0.27%
3
100.989
101.377
0.38%
4
131.858
132.144
0.22%
5
131.858
132.144
0.22%
6
159.460
160.289
0.52%
7
159.460
160.289
0.52%
8
183.645
184.620
0.53%
9
183.645
184.620
0.53%
10
186.862
191.681
2.58%
...
Bulk Modulus= 38.252000 GPa
c11
67.76

c22
67.76

c33
67.76

c23
23.50

wt
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.0

k
6
4
6
2
8
3
5
7
1
2

i
2
1
3
1
1
1
1
2
2
2

c13
23.50

c12
23.50

df/d(moduli)
0.05 0.95
0.05 0.95
0.59 0.41
0.07 0.93
0.07 0.93
0.01 0.99
0.01 0.99
0.19 0.81
0.19 0.81
0.41 0.59

c44
22.13

c55
22.13

c66
22.13

Young's Modulus= 55.657217 GPa
Shear Modulus= 22.130000 GPa
Poisson's Ratio = 0.257506
Longitudinal Velocity (c11)= 2.976742 mm/us
Shear Velocity (c44)= 1.701160 mm/us
Xdiam= 0.792070 cm, Ydiam= 0.792070 cm, Height= 0.169670 cm
loop#

6, rms error=

0.3210%, changed by

length of gradient vector=
eigenvalues
1.15562
211.91354

0.000006

blamb=

-0.0000005%
0.000000

eigenvectors
1.00 0.05
-0.05 1.00

chisquare increased 2% by the following % changes in independent
parameters
0.47 -0.07
0.00 0.11

Figure 2.4. Sample output file from a CylModel RUS analysis, truncated to show only
the first 10 resonance peaks. Note that resonance frequency 10, 191.681 kHz, was not
included in the analysis to improve the error. The “chisquare increased 2% by…” section
includes the highlighted values of A, 0.47, and of D, 0.11, used in the determination of
the uncertainties, dc11 and dc44.

38

2.12 Hardness and fracture toughness by Vickers indentation
Vickers indentations were performed with a Buehler microindenter (Buehler
Semimacro Indenter, Lake Bluff, IL) and a Shimadzu hardness tester (Shimadzu HMV2000, Kyoto, Japan). The indenter machines were calibrated by use of a steel standard
(761-048, Yamamoto Scientific Tools Lab, Co LTD, Japan), and a correction factor, ζ, of
0.95 to 1.00 for the Shimadzu hardness tester and 0.99 to 1.02 for the Buehler
microindeter was calculated. The correction factor was multiplied by the measured
hardness values for the specimens.
Vickers indentations typically produce an indentation impression as well as a set
of radial cracks. If cracks are present, the dimensions of the cracks are the largest feature
size of the indentation, and if cracks are not present, the dimensions of the indentation
impression are the largest feature. Indentations were separated from the edges of the
specimen and from other indentations by a minimum of 5x the largest feature of the
indentation. This separation distance is inclusive of a minimum thickness for the
specimen. Typically, the indentations were 1.0 mm from any edge and 0.5 mm from the
nearest indentation.
Hardness was calculated from the Vickers indentation impression (Figure 2.5),
2a,
(

)

(2.9)

where P is the applied load, ζ is the indenter correction factor, and 1.8544 is a geometric
factor for the angle of the pyramidal Vickers indenter tip [Wachtman 2009].

39

Radial cracks from Vickers indentations, 2c (Figure 2.5), may be used to estimate
the fracture toughness, KIC. As Vickers indentations is not purely mode one fracture
toughness measurement, but rather an estimate, the designation of KC shall be used when
referencing fracture toughness in general rather than mode one fracture toughness, and
for values of fracture toughness determined by Vickers indentation. The KC was
determined by [Wachtman 2009]
( ⁄ ) ⁄

(2.10)

⁄

where ξ is a calibration factor set to 0.0016 [Anstis 1981], E is the Young’s modulus for
the specimen as determined by RUS analysis (see section 2.11), and P is the applied load.
The indentation method is not without controversy, with the assumption of the
crack shape and plastically deformed zone being both revised and expanded [Anstis
1981; Dukino 2006] and questioned [Eilertsen 2013; Quinn 2007], with Quinn and Bradt
stating, “the VIF technique is not suitable for the measurement of the fracture toughness,
KIc, or any other form of the fracture resistance of ceramics or other brittle materials”
[Quinn 2007]. It should be noted that some of the indentations used to question the
indentation method in Eilertson et al. [Eilertsen 2013] have crack systems that are not
suitable for determination of KC by Vickers indentation, as illustrated by Anstis et al.
[Anstis 1981], and simply illustrate that the use of poorly developed radial cracks
produce poor results for KC. Regardless, the Vickers indentation method for
determination of KC is a common test with particular value for specimens where other
methods of measuring KC are not possible or practical [Wachtman 2009; Walker 2011; Ni
2010; Zhao 2008; Anstis 1981; Evans 1976].
40

2c
2a

Figure 2.5. Schematic representation of Vickers indentation, illustrating the indentation
impression dimensions, 2a, and the radial crack length dimensions, 2c.

41

2.13 X-ray diffraction
X-ray diffraction (XRD) analysis was performed on YbAl3 (chapter 3), Mg2Si
(chapter 4), SnTe (chapter 7), and PbS (chapter 8) to verify phase, determine lattice
parameter, and detect possible contamination. Diffraction was performed with a
benchtop XRD machine (Miniflex II, Cu Kα radiation, Rigaku, Tokyo, Japan) on powder
SnTe and powder YbAl3, or with a rotating stage free-standing XRD machine (Bruker
Davinci Diffractometer) at the Michigan State University Center for Crystallographic
Research on powder Mg2Si and sintered PbS. Both XRD machines use a Cu Kα
radiation source.
Reitveld refinement and phase determination was performed with commercial
software (HighScorePlus version 3.0c, PANalytical B.V., Almelo, The Netherlands) and
patterns from the crystallography open database [Gražulis 2012; Gražulis 2009].
2.14 Scanning electron microscopy imaging and energy dispersive x-ray
spectroscopy
Scanning electron microscopy (SEM) imaging permits the examination of
micrometer- and nanometer-scale features such as determining size or morphology of
particles, pores, and grains, determination of differences in average atomic weight by
backscatter imaging, and determining distribution of particles, pores, or grains. For these
reasons, SEM imaging was performed on each of the six studies in this dissertation.
The SEMs used in this study (6400, 6610LV, and 7500F, JEOL Ltd., Japan) at the
Center for Advanced Microscopy, Michigan State University were operated at an average
working distance of 15 mm (6400 and 6610LV) or 8 mm (7500F) and an accelerating
voltage of 15 kV, unless specified.
42

Powder specimens were mounted with carbon paint (05006-AB, SPI Supplies,
West Chester, PA), and sintered specimens were mounted with epoxy and carbon paint,
or with carbon tape. Prior to imaging, each specimen was blown off with compressed air
(22531093, OfficeMax) to remove loose powder or dust on the surface.
Energy dispersive x-ray spectroscopy (EDS) was performed primarily with the
6610LV SEM because the tungsten filament and detector are capable of recording higher
counts than the 7500F SEM. The 7500F SEM was used for EDS on only the PM-HP673-Ag specimen (chapter 6) because the higher resolution of the 7500F SEM permitted
locating the necessary areas for EDS detection more readily than was possible on the
6610LV.

2.14.1 Grain size measurement from fractured surface images
Fractured surfaces were used to determine average grain sizes by the linear
intercept method [ASTM-Standard-E112-13 2014] in specimens with unimodal grain size
distributions. Specimens with bimodal grain size distributions are not appropriate for
measurement by lineal intercept method. A fractured surface image with approximately
10-30 grains along the length and clearly visible grain boundaries was chosen for
analysis. In the linear intercept method, a line of measured length is drawn in a random
orientation across a fractured surface image, and the number of grain boundaries the line
intercepts was summed. Additional lines were drawn until the number of intercepts
counted was greater than 200, typically about 10 to 15 lines. The total length of the lines
was scaled according to the printed scale bar on the image, and divided by the total
number of intercepts to determine an average line length between intercepts. The average
43

line length was multiplied by the stereographic projection factor, 1.5, to determine the
average grain size of the specimen.

44

REFERENCES

45

REFERENCES

[Anstis, Chantikul, Lawn, Marshall 1981] Anstis, G., Chantikul, P., Lawn, B., Marshall,
D. A critical evaluation of indentation techniques for measuring fracture toughness:
I, direct crack measurements. Journal of the American Ceramic Society 64 (1981)
533–538.
[ASTM-Standard-E112-13 2014] ASTM-Standard-E112-13. Standard Test Methods for
Determining Average Grain Size. In: ASTM Volume 03.01 Metals Mechanical
Testing; Elevated and Low Temperature Tests; Metallography. ASTM International,
West Conshohocken, PA, 2014.
[Dukino, Swain 2006] Dukino, R.D., Swain, M. V. Comparative Measurement of
Indentation Fracture Toughness with Berkovich and Vickers Indenters. 2 (2006)
3299–3304.
[Eilertsen, Subramanian, Kruzic 2013] Eilertsen, J., Subramanian, M. a., Kruzic, J.J.
Fracture toughness of Co4Sb12 and In0.1Co4Sb12 thermoelectric skutterudites
evaluated by three methods. Journal of Alloys and Compounds 552 (2013) 492–498.
[Evans, Charles 1976] Evans, A., Charles, E. Fracture toughness determinations by
indentation. Journal of the American Ceramic …(1976) 371–372.
[Gražulis, Chateigner, Downs, Yokochi, Quirós, Lutterotti, Manakova, Butkus, Moeck,
Le Bail 2009] Gražulis, S., Chateigner, D., Downs, R.T., Yokochi, a F.T., Quirós,
M., Lutterotti, L., Manakova, E., Butkus, J., Moeck, P., Le Bail, A. Crystallography
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crystallography 42 (2009) 726–729.
[Gražulis, Daškevič, Merkys, Chateigner, Lutterotti, Quirós, Serebryanaya, Moeck,
Downs, Le Bail 2012] Gražulis, S., Daškevič, A., Merkys, A., Chateigner, D.,
Lutterotti, L., Quirós, M., Serebryanaya, N.R., Moeck, P., Downs, R.T., Le Bail, A.
Crystallography Open Database (COD): an open-access collection of crystal
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(2012) D420–7.
[Migliori, Sarrao 1997] Migliori, A., Sarrao, J.L. Resonant Ultrasound Spectroscopy:
Applications to Physics, Materials Measurements, and Nondestructive Evaluation.
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[Ni, Case, Khabir, Stewart, Wu, Hogan, Timm, Girard, Kanatzidis 2010] Ni, J.E., Case,
E.D., Khabir, K.N., Stewart, R.C., Wu, C.-I., Hogan, T.P., Timm, E.J., Girard, S.N.,
Kanatzidis, M.G. Room temperature Young’s modulus, shear modulus, Poisson's
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ratio and hardness of PbTe–PbS thermoelectric materials. Materials Science and
Engineering: B 170 (2010) 58–66.
[Pilchak, Ren, Case, Timm, Schock, Wu, Hogan 2007] Pilchak, A.L., Ren, F., Case, E.D.,
Timm, E.J., Schock, H.J., Wu, C.-I., Hogan, T.P. Characterization of dry milled
powders of LAST (lead–antimony–silver–tellurium) thermoelectric material.
Philosophical Magazine 87 (2007) 4567–4591.
[Quinn, Bradt 2007] Quinn, G.D., Bradt, R.C. On the Vickers Indentation Fracture
Toughness Test. Journal of the American Ceramic Society 90 (2007) 673–680.
[Ren, Case, Ni, Timm, Lara-Curzio, Trejo, Lin, Kanatzidis 2009a] Ren, F., Case, E.D.,
Ni, J.E., Timm, E.J., Lara-Curzio, E., Trejo, R.M., Lin, C.-H., Kanatzidis, M.G.
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[Ren, Case, Ni, Timm, Lara-Curzio, Trejo, Lin, Kanatzidis 2009b] Ren, F., Case, E.D.,
Ni, J.E., Timm, E.J., Lara-Curzio, E., Trejo, R.M., Lin, C.-H., Kanatzidis, M.G.
Temperature-dependent elastic moduli of lead telluride-based thermoelectric
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[Schmidt, Case, Ni, Sakamoto, Trejo, Lara-curzio, Payzant, Kirkham 2011] Schmidt, R.,
Case, E., Ni, J., Sakamoto, J., Trejo, R., Lara-curzio, E., Payzant, E., Kirkham, M.
Characterization of the mechanical properties of two n-type and one p-type Sb-based
skutterudite thermoelectric compounds. 2011.
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M.J. Mechanical Properties of Ceramics. Wiley-Vch, Hoboken, N.J., 2009.
[Walker, Marotto, Rafiee, Koratkar, Corral 2011] Walker, L.S., Marotto, V.R., Rafiee,
M. a, Koratkar, N., Corral, E.L. Toughening in graphene ceramic composites. ACS
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[Zhao, Zhang, Li, Zhou, Liu, Liu 2008] Zhao, L.-D., Zhang, B.-P., Li, J.-F., Zhou, M.,
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Alloys and Compounds 455 (2008) 259–264.

47

3 Room temperature mechanical properties of polycrystalline YbAl3, a promising
low temperature thermoelectric material
Robert D. Schmidt, Eldon D. Case, Gloria J. Lehr, Donald T. Morelli
Chemical Engineering and Materials Science Department,
Michigan State University, East Lansing, MI, 48824
Published in: Intermetallics 35 (2013) 15-24.
Abstract
Intermetallic YbAl3 in the L12 (AuCu3) phase is a promising material for low
temperature thermoelectric applications. However, there is no experimental data in the
literature on the mechanical properties of YbAl3, although the design and development of
thermoelectric modules incorporating YbAl3will require mechanical property data. Using
resonant ultrasound spectroscopy (RUS), the room temperature Young’s modulus, shear
modulus, bulk modulus and Poisson’s ratio were determined as a function of volume
fraction porosity, P, for specimens densified by both hot pressing (HP) and pulsed
electric current sintering (PECS) polycrystalline specimens, where P ranged from 0.030
to 0.233 and mean grain sizes ranged from 0.5 to 1.4 µm. In addition, the longitudinal
and acoustic wave speeds and the Debye temperature were measured. Using Vickers
indentation, the hardness and fracture toughness of the specimens were also measured.
Despite microstructural differences between the HP and PECS-processed specimens, the
porosity dependence of the mechanical properties was a function of the total volume
fraction porosity, P, independent of the details of the size and spatial distribution of pores
within individual specimens.
Keywords: A. aluminides, B. elastic properties, mechanical properties at ambient
temperature
48

3.1 Introduction
Research directed at developing more efficient thermoelectric (TE) materials has
surged in the last decade with hopes that applications in thermoelectric power generation
may be realized on a large scale. TE devices convert heat directly to electricity using the
Seebeck effect. The efficiency of conversion depends on the dimensionless
thermoelectric figure of merit:

ZT 

 2
PF
T
T



(1)

In this equation, α is the Seebeck coefficient, σ the electrical conductivity, and κ
the thermal conductivity of the material; PF is termed the power factor. Historically, the
best TE materials have exhibited ZT values not exceeding unity. Recent research has
successfully demonstrated higher values of the figure of merit, most notably in bulk
nanostructured chalcogenides [Biswas 2011] and filled skutterudite [Shi 2011]
compounds, which exhibit ZT values in the range of 1.6-1.8 above 600 K.
Another application of thermoelectricity involves solid state heating and cooling
using the Peltier effect. In contrast to the very promising developments in the high
temperature range, new materials for Peltier cooling at room temperature and below have
received relatively little attention. One interesting and promising material for Peltier
cooling is the intermetallic compound YbAl3. This compound exhibits a power factor
some five to ten times that of bismuth telluride [Van Daal 1974; Rowe 2002; Mahan
1998] (the state of the art material for TE cooling), but does not possess high ZT due to
its high thermal conductivity. Thermal conductivity reduction in YbAl3-based materials
is a current area of focus of our research.
49

While it is self-evident that the electronic and thermal transport properties of a
material are important parameters in determining its suitability in a TE application,
equally important, yet often underappreciated, is an understanding of the mechanical
properties. By the very nature of their application, TE materials can be subjected to large
thermal gradients, temperature cycling, and thermal shock.
In this study, the room temperature mechanical properties (elasticity, hardness and
fracture toughness) were measured as a function of volume fraction porosity, P, for
polycrystalline intermetallic YbAl3 specimens in the L12 phase. The specimens were
densified by either hot pressing (HP) or pulsed electric current sintering (PECS).
Resonant Ultrasound Spectroscopy (RUS) was used to measure the room temperature
elastic moduli, including Young’s modulus, shear modulus, bulk modulus and Poisson’s
ratio. The elastic moduli are required for stress and strain modeling of any solid which in
turn is critical in the design of thermoelectric modules that will be subjected to both
thermal gradients and thermal transients. Also, the longitudinal and acoustic wave speeds
of YbAl3 were measured by RUS. The wave speeds were in turn used to compute the
acoustic Debye temperature which is related to thermal conductivity. Hardness, which is
a measure of the resistance of a material to plastic deformation and scratching, was
measured by Vickers indentation. Finally, the fracture toughness, KC, was estimated
using the length of radial cracks induced by Vickers indentation, where KC measures the
resistance to slow crack growth.
The mechanical properties were characterized as a function of porosity for two
reasons. First, extrapolation of the experimental modulus versus temperature data to P =
0 allows the direct comparison to theoretical modulus calculations by techniques such as
50

density functional theory. Second, determining the modulus-porosity relationship allows
comparison of the data from this study to other experimental studies by other researchers
for specimens with differing P values.
3.2 Experimental procedure
3.2.1 Materials and specimen preparation
Only two binary phases exist in the Yb-Al phase diagram [Massalski 1987]:
YbAl2 and YbAl3. YbAl3 can be difficult to synthesize in single phase form due to the
peritectic nature of the phase transformation at the 1:3 Yb:Al ratio. Samples which are
arc-melted at this composition invariably contain mixtures of YbAl3, Al, and the highmelting point YbAl2 phase which cannot be removed even after extended annealing.
Single crystals of pure YbAl3 have been synthesized by growth in an Al flux [Canfield
1992]; the excess Al prevents the formation of the YbAl2 phase. Unfortunately, the
crystals so obtained are too small for mechanical property measurements.
We have successfully synthesized pellets of YbAl3 of up to 2.54 cm in diameter
by a combination of a novel arc-melting procedure and either HP or PECS. In order to
obtain pure YbAl3 phase material, we applied the concept of growth of YbAl3 in an Al
flux to the arc-melting process. Starting materials (Al 99.999% - ULVAC and Yb 99.9%
- Alfa Aesar) were arc melted on a water-cooled copper hearth under argon with the
nominal composition YbAl7. Each ingot was melted and flipped at least 5 times to ensure
homogeneity.
This process resulted in a polycrystalline ingot comprised of a mixture of YbAl3
and Al phases, as determined by X-ray diffraction (Rigaku MiniFlex II with Cu Kα
radiation). Just as in the growth of single crystals in an Al flux, the excess Al present in
51

the arc-melting process inhibits the formation of the undesirable YbAl2 phase. To
remove the pure Al phase, the ingots were broken into small pieces and etched in a 5M
NaOH bath for 24 hours. The pieces were then rinsed in a series of H2O baths to remove
any remnant NaOH, heated on a hotplate for 10-15 minutes to dry, and then ground into
powder using a mortar and pestle. The powder was then sieved through a 100-mesh
screen. Particles larger than this were returned to the NaOH bath and the process was
repeated. The sieved powder was ball milled in a vibratory mill using stainless steel
media.
Prior to densification, the powder so obtained was determined by x-ray diffraction
to be single phase YbAl3 (cubic AuCu3 structure with lattice constant of 0.4205 nm, in
agreement with literature values [Rowe 2002; Havinga 1973]). The powder was then
sieved again through a 100-mesh screen. Two densification techniques were used, HP
and PECS, and the processing conditions are summarized in Table 3.1. The HP
specimens were pressed in a 22 mm diameter graphite die at 973 K for 1 hour under at 70
MPa (Hot press model HP200-14020-23G by Thermal Technologies LLC, Santa Rosa,
CA). The PECS samples were pressed in a 12.7 mm diameter graphite die at 1023 K to
1073 K for 1 hour at a pressure of 60 MPa (Model 10, Series 4 by Thermal Technologies
LLC, Santa Rosa, CA). X-ray diffraction on the densified pellets again revealed
predominantly single phase material. Several low intensity peaks, however, did not index
to the AuCu3 phase, but rather matched fairly closely those of Yb3Al5O12, suggesting a
slight amount of this phase exists as an impurity in the pressed pellets.

52

Table 3.1. The HP and PECS processing parameters for the YbAl3 specimens included in
this study.
Specimen

YbAl3-A
YbAl3-B
YbAl3-C
YbAl3-D
YbAl3-E

Densification
technique
HP
HP
PECS
PECS
PECS

Sintering
time
(min)
75
60
60
10
10

Sintering
temperature
(K)
1053
1023
1073
1073
873

53

Pressure
(MPa)
60
70
60
60
60

Specimen
diameter
(mm)
22
22
12.7
12.7
12.7

Although each of the YbAl3 specimens were fabricated as discs, prior to
microstructural characterization and mechanical property measurement, selected
specimens were cut to form rectangular bars and crescent- shaped specimens from the
periphery of the bar. The crescent- shaped specimens were used in the microstructural
examination and hardness testing while the RUS measurements were made on both the
uncut disks and the as-cut bar-shaped specimens. Initially the specimens were cut using
an electrical discharge machine, but due to difficulties in cutting the specimens, all
subsequent cutting was done using a surface grinder. Prior to hardness and fracture
toughness testing, the specimens were polished using diamond paste with a series of grit
sizes ranging from 90 microns to 1 micron.
3.2.2 Microstructural characterization
A scanning electron microscope (SEM, JEOL-6400, JEOL Ltd., Japan) with an
accelerating voltage of 15 kV and a working distance of 15 mm was used to examine the
size and morphology of the grains and pores for both the fractured surfaces and polished
surfaces of the YbAl3 specimens. The electrical conductivity of the specimens was
sufficiently high that no conductive surface coatings were required prior to SEM
examination.
A mean grain size was calculated using the linear intercept technique from SEM
micrographs of the fractured surfaces of specimens. The volume fraction porosity was
calculated from the specimen mass and dimensions. The mass of each specimen was
measured by an electronic balance with a vendor-specified accuracy of ± 0.0003 g. The
specimen dimensions were measured by a digital micrometer.
54

3.2.3 Hardness testing
For the polished specimens, Vickers indentation was performed at loads from
2.94 N to 19.6 N (Shimadzu Model HMV-2000 indenter). The centers of each
indentation impression were located at least 1 mm from the specimen edge, with the
indentation impression centers spaced approximately 0.5 mm apart. The hardness, H,
was calculated from [Wachtman 2009]

H

1.8544 L
2a 2

(1)

where L is the applied load and 2a is the average diagonal length of the indentation
impression. The average hardness was calculated from the mean of at least 10
indentations on a given specimen. A steel calibration block with a hardness, H, of 7.75
GPa (761-048, Yamamoto Scientific Tools Laboratory, LTD, Japan) was used to
calibrate the Vickers indenter.
3.2.4 Elastic modulus measurements
The elastic moduli were measured using a commercial resonant ultrasound
spectroscopy apparatus (RUSpec, Magnaflux Quasar, Albuquerque, NM), where the
moduli were determined from the mechanical resonance frequencies, the mass,
dimensions and geometry of the specimens [Migliori 1997, Ren 2008, Ren 2009].
Two specimen geometries were employed in this study, a disk and a rectangular
bar. Since the governing equations for these two geometries differ, the moduli for the
disk and bar-shaped specimens were calculated with different commercial software
packages, namely CylModel (Magnaflux Quasar, Albuquerque, NM) for the disk

55

geometry and RPModel (Magnaflux Quasar, Albuquerque, NM) for the rectangular bar
geometry.
Two different transducer stages were used during the modulus measurements
(Fig. 3.1a and b). For the tripod transducer stage (Fig. 3.1a), either a disk or bar-shaped
specimen was set onto the three transducers, where one driver transducer induced the
mechanical vibrations in the specimens and the remaining two transducers detected the
specimen resonances (Fig. 3.1a). In the second type of transducer configuration, namely
the two-transducer or bipod transducer stage, a bar-shaped specimen was placed along its
face diagonal between a pair of opposing transducers, one driver transducer and one pickup transducer (Fig. 3.1b). For both the tripod and bipod transducer stages, the sinusoidal
driving frequency was swept from 100 kHz to 600 kHz. The use of the two different
specimen geometries and the two different transducer stages allowed independent
measurements on a single specimen with a fixed modulus value, as will be discussed
further in Section 3.3.3.
3.2.5 Fracture toughness measurements
The fracture toughness, KC, was determined from the length of the Vickers
indentation induced radial crack lengths using the relationship [Wachtman 2009]

KC 

 ( E / H )1/ 2 L

(3)

c3/ 2

where ξ is a dimensionless calibration constant (0.0016) [Anstis 1981], L is the applied
indentation load, and c is half of the radial crack length. In Eq. 3, H is the specimen’s
hardness determined by Vickers indentation and E is the specimen’s Young’s modulus

56

determined by RUS. The mean and standard deviation of the fracture toughness were
determined from at least 10 Vickers indentations per specimen.
3.3 Results and Discussion
3.3.1 Microstructural characterization
The five YbAl3 specimens fabricated in this study had volume fraction porosity,
P, ranging from 0.030 to 0.233 (Table 3.2). For each YbAl3 specimen in this study, the
mean grain size ranged from about 0.5 to 1.4 µm (Table 3.3), thus there were no
significant differences between the average grain sizes obtained by hot pressing and by
PECS.
However, SEM micrographs of fracture surfaces of each of the five specimens
indicate that the size and spatial distribution of the HP and the PECS specimens differed
from one another (Fig. 3.2). The microstructures of both hot pressed specimens YbAl3-A
(Fig. 3.2a) and specimen YbAl3-B (Fig. 3.2b) consisted of (1) relatively dense “islands”
with roughly micron grain sizes surrounded by (2) a more porous region with submicron
average grain size. Two of the PECS specimens were relatively dense with small,
uniformly distributed pores (Fig. 3.2c and d), while a PECS specimen intentionally
processed to have higher porosity (P ¼ 0.23) than the other two PECS specimens again
showed dense regions adjacent to more porous areas (Fig. 3.2e). The less dense regions in
specimens YbAl3-A, YbAl3-B and YbAl3-E are marked by the ovals in Fig. 3.2a, b and
e respectively.

57

Figure 3.1. Photographs of tripod and bipod transducer stages for the RUS measurements
of elastic modulus performed in this study.
Table 3.2. Specimen label, densification method (hot pressed, HP, or pulsed electric
current sintering, PECS), mass, dimensions and mass density of each of the YbAl3
specimens included in this study.
Specimen
Densification Mass
Dimensions (cm)
Mass
P
label
method
(g)
Density
(g/cm3)
YbAl3-A (bar)
HP
1.0276 0.874 × 0.808 × 0.292
4.98
0.125
YbAl3-B (disc)
HP
5.3646
Ø 2.213 × 0.320
4.36
0.233
YbAl3-B (bar)
HP
0.9581 1.091 × 0.320 × 0.617
4.45
0.217
YbAl3-C (disc)
PECS
1.8983
Ø 1.256 × 0.287
5.34
0.060
YbAl3-C (bar)
PECS
0.8125 0.869 × 0.607 × 0.286
5.38
0.054
YbAl3-D (bar)
PECS
0.8675 0.922 × 0.656 × 0.260
5.52
0.030
YbAl3-E (bar)
PECS
1.2582 0.973 × 0.719 × 0.409
4.39
0.227
Table 3.3. The number of indentations, indentation load and mean hardness, <H>, of the
YbAl3 specimens and porosity, P. In each case, the loading time was 10 s. The porosity
reported is the average as measured from the disc and bar specimen geometries.
Specimen Number of
Load
<H>
Average volume
GS
label
indentations
(N)
(GPa)
fraction porosity
10
0.98
4.81 ± 0.73
0.125
YbAl3-A
20
2.94
4.86 ± 0.74
0.125
0.7
10
19.61 4.89 ± 0.39
0.125
YbAl3-B
10
0.98
2.80 ± 0.49
0.225
0.7
YbAl3-C
10
0.98
5.81 ± 0.15
0.057
1.4
YbAl3-D
10
0.98
6.81 ± 0.30
0.030
0.5
YbAl3-E
10
0.98
2.76 ± 0.66
0.227
1.2
58

Figure 3.2. SEM micrographs of fracture surfaces and polished surfaces of YbAl3
specimens included in this study. The ovals indicate more porous regions neighboring
more dense areas that occur in the two HP specimens (Fig. 3.2a and b) as well as the
PECS specimen intentionally processed to give high porosity (Fig. 3.2e).

59

Figure 3.3. The fractured surfaces of specimens YbAl3-B and YbAl3-E exhibited lower
porosity regions surrounded by channels of higher porosity in (a) and (b), both with
similar porosity but each sintered by a different method. In contrast, specimen YbAl3-D,
shown in (c), exhibited a uniform density throughout.

60

The micrographs included in Fig. 3.3 were taken at a lower magnification than
those in Fig. 3.2 in order to better illustrate differences in the spatial distribution of pores
among the YbAl3 specimens included in this study. The fractured surfaces of hot pressed
specimen YbAl3-B (P = 0.22) and PECS-processed specimen YbAl3-E (P = 0.23)
exhibited relatively dense regions surrounded by porous regions, where the pores were
either quasi-spherical or lenticular in shape with a wide size distribution from roughly
sub-micron to 10 µm dimensions (Fig. 3.3a and b). Although the total volume fraction
porosity, P, is very similar for specimens YbAl3-B and YbAl3-E, both the spatial
distribution of pores and the densification technique were different for the two
specimens. Note that for the hot pressed specimen YbAl3-B, the porous regions appear
as bands roughly 100 µm or more across, while in the PECS processed specimen YbAl3E, the bands of porosity are roughly 20 µm across with a maximum pore size that is
somewhat smaller than in YbAl3-B.
Densifying by HP yielded specimens with volume fraction porosities of 0.125
(YbAl3-A) and 0.22 (YbAl3-B). In contrast, PECS processing yielded specimens with
volume fraction porosities of 0.057 (YbAl3-C) and 0.030 (YbAl3-D). In order to produce
an YbAl3 specimen with porosity comparable to the HP specimens, the PECS-processed
specimen E was fabricated at a sintering temperature of 873 K for only 10 minutes rather
than 1073 K for 60 minutes (Table 3.1).
The differences in the processing techniques and the resulting microstructures for
the HP and the PECS-processed specimens is quite significant in terms of the observed P
dependence of the mechanical properties. As will be discussed in Sections 3.3.2 and
3.3.4, despite these processing/microstructural differences, the porosity dependencies of
61

the hardness and the elastic moduli are functions of the total volume porosity, P, only,
rather than showing property differences based on the size or spatial distribution of
porosity in individual specimens.
3.3.2 Hardness
The decrease in H with increasing volume fraction porosity, P, is often expressed
in terms of the empirical relationship
H = H0 exp (– bHP)

(4a)

where bH is a measure of the rate of decrease in H with increasing porosity P and H0 is
the value of hardness corresponding to a fully dense specimen [Rice 1998]. As reviewed
by Rice [Rice 1998], for a number of oxides, non-oxides (including Si3N4, TiC, B4C, and
glassy carbon) and the metals Cu and Fe, the decrease in H with increasing P can be
described well by Eq. (4a) with bH values ranging from roughly 2 to 6. Furthermore, for
specimens with low to intermediate values of P (such as the YbAl3 specimens included in
this study), a Taylor series expansion of Eq. (4a) leads to the linear approximation
H = H0 (1 – bHP)

(4b)

In this study, the linear form of the P versus H relationship (Eq. (4b)) describes
the YbAl3 data well, as indicated by a least-squares fit of the hardness-porosity data to
Eq. (4b) which yields a coefficient of determination, r2, of 0.965, a bH value of 2.65 +
0.18 and H0 = 6.99 + 0.15 GPa (Fig. 3.4). Thus despite the differences in processing and
microstructure observed for the specimens in this study (Section 3.3.1, Figs. 3.2 and 3.3),
the porosity dependence of H can be described well by a function of the total volume
fracture porosity (Eq. (4b)), without regard to the details of the differing sizes or spatial
distribution of pores. In addition, although no studies of the H versus P behavior of rare62

earth or transition metal trialuminides are available in the open literature, the bH value for
YbAl3 found in this study falls within the range of the values typically reported in the
literature for a broad range of solid materials.
In addition to the lack of data on the H versus P behavior of trialuminides, no
room temperature hardness data are available in the literature for a rare-earth or transition
metal L12 trialuminide material. However, a room temperature Vickers indentation
hardness value, H, of 5.0 + 0.5 GPa was measured by Milman et al. [Milman 2001] for
cast ingots of TiAl3 (tetragonal D022 phase) using a 2.34 N load which is roughly
comparable to the H value obtained in this study for PECS processed YbAl3 (cubic L12,
Au3Cu form) of 6.81 ± 0.30 GPa at an indentation load of 0.98 N (Table 3.3).
The load dependence of H for YbAl3 was also explored since in some cases H is a
function of the applied indentation load [Nix 1998, Weaver 2003, Sangwal 2000, Milman
2011, Rice 1998], where with increasing indentation load the measured H can either
increase (indentation size effect, ISE [Nix 1998, Weaver 2003, Milman 2011]) or
decrease (reverse indentation size effect, RISE [Sangwal 2000]). The ISE can be
especially pronounced in nanoindentation studies [Milman 2011]. In this study, the H
value of YbAl3 is essentially independent of the indentation load over the range from 0.98
to 19.6 N (Table 3.3). Over load ranges similar to that used in this study, the measured
hardness also has been reported to be relatively insensitive to the applied Vickers
indentation load for other brittle thermoelectric materials including Mg2Si [Schmidt
2012], PbTe-PbS [Ni 2010] and LAST [Ren 2009].

63

Hardness (GPa)

7

Hardness, PECS
Hardness, HP

6
5

H0

4
3
2
0.0

0.1

0.2

0.3

P
Figure 3.4. The hardness, H, versus volume fraction porosity, P, for the YbAl3 specimens
included in this study. The solid line represents a least-squares fit to Eq. (4b).

64

3.3.3 Fracture Toughness
For the specimens examined in this study, the fracture toughness, KC, by Vickers
indentation of YbAl3 was between 1.13 MPa m1/2 and 1.69 MPa m1/2 (Table 3.4). No KC
values for rare earth trialuminides are available in the literature. However there are the
following fracture toughness data for the following single phase L12 transition metal
trialuminides: (1) (Al +12.5 at.% Mn)3Zr, where KC increased from 1.86 MPa m1/2 to
2.16 MPa m1/2 during annealing at 800ºC to 1000ºC [Lee 2006], (2) (Al + x at.% Mn)3Ti,
x = 3 to 12, with KC ranging from 1.1 MPa m1/2 to 1.54 MPa m1/2 as a function of x [Jang
2004], (3) (Al + 8 at.% Mn)3Ti, with a KC value of 1.54 MPa m1/2 which increased to 4.12
MPa m1/2 when annealed to 1100ºC [Jang 2004], and (4) Al3Ti(9Mn), with KC ≈ 2 MPa
m0.5 for Vickers indentation loads from 200 g to 2000 g and a range of porosity from
0.005 to 0.12 [Varin 2001]. Thus, while the heat treatment and alloying of these
transition metal trialuminides from the literature was primarily aimed at optimizing the
mechanical properties, especially KC [Lee 2006; Jang 2004; Varin 2001], it is interesting
that the KC values for the thermoelectric YbAl3 specimens in this study is roughly
comparable to the KC measured for the transition metal trialuminides.

65

Table 3.4. For YbAl3 specimens included in this study, the fracture toughness, KC,
measured by Vickers indentation, including the applied load, specimen grain size and
volume fraction porosity, P. The KC was obtained from the mean of 10 indentations per
specimen.
Specimen
YbAl3-A
YbAl3-D

KC
(MPa m1/2)
1.69 ± 0.20
1.13 ± 0.07

Indentation
load (N)
19.61
0.98

66

Grain size P
(µm)
0.65
0.125
0.54
0.030

3.3.4 Elastic modulus
As is the case for hardness, the P dependence of the elastic moduli is often
expressed empirically in terms of an exponential decrease in moduli with increasing P
which can be approximated by the linear functions
E = E0(1 - bEP)

(5a)

G = G0(1 - bGP)

(5b)

B = B0(1 - bBP)

(5c)

where E is Young’s modulus, G is the shear modulus and B is the bulk modulus and E0,
G0 and B0 are the P = 0 intercepts of the E, G, and B data, respectively (Table 3.5, Fig.
3.5a). The material dependent values of bE, bG and bB are measures of the decrease in the
respective moduli as a function of increasing P.
Rice [Rice 1998] also reviewed the P dependence of the elastic moduli E, G and
B. The values of the coefficients bE, bG and bB (Eqs. (5a) – (5c)) typically range from
about 2 to 6 for metals (Fe, Co, Ni, Cu, Be, Cu-Sn), polymer-based materials (epoxy and
polyester) in addition to a number of oxide, carbide and nitride materials. For this study
of the elasticity-P behavior of YbAl3, a least-squares fit of the modulus-porosity data to
Eqs. (5a) – (5c), respectively (Fig. 3.5a), resulted in bE, bG and bB values that ranged from
2.21 + 0.17 (bB) to 2.38 + 0.05 (bG) (Table 3.5). Note that the bE, bG and bB coefficients
obtained for YbAl3 in this study fall within the range of bE, bG and bB values reported by
Rice [Rice 1998]. Thus, as was the case for the P dependence of H, the P dependence of
the Young’s, shear and bulk moduli of YbAl3 is consistent with elasticity versus P
relationships reported for a number of ceramic, polymer and metallic materials in the
literature [Rice 1998]. Also in accord with the observed P dependence of H, the P
67

dependence of the elastic moduli are described well by functions of the total volume
fraction porosity, P (Eqs. (5a) – (5c)), without taking into account the specimen to
specimen differences in the size and spatial distribution of pores (Section 3.3.1, Figs. 3.2
and 3) that are likely related to the two difference processing techniques used in this
study (HP and PECS).
No experimental or theoretical studies in the open literature treat the porosity
dependence of the elastic moduli of YbAl3 or any other trialuminide. Also, no
experimental values of the elastic moduli for YbAl3 are available in the literature for any
value of P. However, since E0, G0 and B0 (Eqs. (5a) – (5c)) represent estimates of the
elastic moduli for P = 0, they can be compared directly to the theoretically calculated
values of the elastic moduli (Table 3.6).
The YbAl3 elastic modulus values determined experimentally in this study are
presented in Table 3.6, along with a summary of calculated elastic modulus results for
YbAl3 [Sa 2011; Zhou 2010; Tao 2008]. In addition, Table 3.6 includes calculated and
experimental elastic modulus results for the additional rare earth trialuminide ScAl3 [Tao
2008; Hyland 1991; Fu 1990; Xu 1990; Jahnatek 2007] and TmAl3 [Tao 2008; Sa 2011;
Zhou 2010]. Also, Table 3.6 includes a calculated bulk modulus value of a transition
metal trialuminide, ZrAl3 [Xu 1990]. The three rare-earth and transition metal
trialuminides have roughly similar elastic moduli, with E for the theoretical values
ranging between 124.19 GPa and 165.36 GPa and the experimental YbAl3 value from
this study 174.0 GPa.

68

Table 3.5. The fitting parameters obtained from the least-squares fit of the appropriate
elastic modulus to Eqs. (5a) – (5c). The coefficient of determination, R2, is given for each
of the fitted equations.
Property
Young's
Modulus
Shear
Modulus
Bulk
Modulus

P=0 Intercept
(GPa)
173.8 ± 2.3 (E0)

b
(unitless)
2.35 ± 0.06 (bE)

R2

73.5 ± 0.9 (G0)

2.38 ± 0.05 (bG)

0.995

91.6 ± 3.4 (B0)

2.21 ± 0.17 (bB)

0.947

0.994

Table 3.6. A comparison of this study’s experimentally determined values of elastic
moduli (E, Young’s modulus, G, shear modulus, B, bulk modulus and , Poisson’s ratio)
for YbAl3 with calculated and experimental values of other trialuminide materials, R-Al3,
from the literature for R = Yb, Sc, Tm, or Zr [Sa 2011, Zhou 2010, Tao 2008, Hyland
1991, Fu 1990, Xu 1990, Jahnatek 2007].
Material E (GPa)
YbAl3
174.0 ±
2.5
YbAl3
N.A.
YbAl3
N.A.
YbAl3
124.19

G (GPa)
73.6 ±
0.9
66.0
N.A.
54.17

B (GPa)
91.3 ±
2.9
N.A
67
58.51


0.182 ±
0.003
N.A
N.A
0.146

Method
Exp (RUS)

Reference
This study

Calculated
Calculated
Calculated

[Sa 2011]
[Zhou 2010]
[Tao 2008]

ScAl3
ScAl3

69.62
68.4 ±
0.8
69
N.A.
78

88.24
91.5 ±
1.1
92
93
87

0.188
0.201 ±
0.001
0.20
N.A.
N.A.

Calculated
Exp (Pulse
echo)
Calculated
Calculated
Calculated

[Tao 2008]
[Hyland 1991]

ScAl3
ScAl3
ScAl3

165.36
164.2 ±
1.9
166
N.A.
174

TmAl3
TmAl3
TmAl3
ZrAl3

146.19
N.A.
N.A.
N.A.

61.48
60.3
N.A.
N.A.

78.3
N.A
80
100

0.189
N.A
N.A
N.A.

Calculated
Calculated
Calculated
Calculated

N.A. = Not available

69

[Fu 1990]
[Xu 1990]
[Jahnatek
2007]
[Tao 2008]
[Sa 2011]
[Zhou 2010]
[Xu 1990]

150
100

B0

50
0
0.0

G0
0.1

0.2

0.24

Poisson's Ratio

Elastic Moduli (GPa)

200

Young's Modulus, PECS
Shear Modulus, PECS
Bulk Modulus, PECS
Young's Modulus, HP
Shear Modulus, HP
Bulk Modulus, HP

(a)
E0

0.3

(b)

Poisson's Ratio, PECS
Poisson's Ratio, HP

0.22
0.20
0.18
0.16
0.0

0.1

0.2

0.3

P

P

Figure 3.5. For the YbAl3 specimens included in this study, the RUS measurement
results for (a) the Young’s modulus, E, shear modulus, G, bulk modulus, B as a function
of P and (b) Poisson’s ratio as a function of P. The solid lines in Fig. 3.5a represent leastsquares fits to Eqs. (5a), (5b) and (5c) for the Young’s modulus, shear modulus and bulk
modulus, respectively.

70

Disc-shaped specimen YbAl3-C
Tripod transducer arrangement

(b)

Bar-shaped specimen YbAl3-C
Two transducer arrangement

Intensity (AU)

Intensity (AU)

(a)

0

200

400

600

0

Frequency (kHz)

Intensity (AU)

(c)

0

200

400

600

Frequency (kHz)

YbAl3-C (bar)
Tripod transducer arrangement

200

400

600

Frequency (kHz)
Figure 3.6. The RUS mechanical vibration spectra for the two-transducer stage and
tripod specimen stage.

71

The values of the elastic moduli for YbAl3 theoretically predicted from DFT
theory are considerably lower than the experimental modulus values obtained from this
study. For example, the E0, G0 and B0 values of moduli theoretically predicted by Tao
[Tao 2008] are approximately 29%, 21% and 36% lower, respectively, than the
experimental modulus values obtained from this study (Table 3.6). Also the G0 value for
YbAl3 calculated by Sa [Sa 2011] is about 10% lower than this study’s experimental
value of G0 (Table 3.6) and Zhou’s calculated value for B0 [Zhou 2010] was about 27%
lower than this study’s experimentally value of YbAl3 (Table 3.6).
However, it is also critical to note that there are also significant disagreements
among the theoretical elastic moduli obtained for YbAl3 (Table 3.6). In particular, the G0
values calculated by Tao [Tao 2008] and Sa [Sa 2011] differ by about 18% (Table 3.6).
Also, the B0 values calculated by Zhou [Zhou 2010] and Tao [Tao 2008] differ by
approximately 13% (Table 3.6). Thus, although each of these three theoretical studies are
relatively recent (2008, 2010 and 2011) for the Tao et al. [Tao 2008], Zhou et al. [Zhou
2010] and Sao [Sao 2011] studies, respectively, the differences among these theoretical
studies of the elastic moduli YbAl3 indicate a difficulty in obtaining consistent theoretical
predictions. In contrast to the lack of agreement among the theoretical
studies/experimental studies for the elastic moduli of YbAl3, the situation appears to be
different for another rare earth trialuminide, namely ScAl3 where theoretical values for B0
for four theoretical studies [Tao 2008; Fu 1990; Xu 1990; Jahnateck 2007] are each
within about 6 - 10% of one another (Table 3.6). (B0 is used here as a basis of comparison
for the theoretical studies, as shown in Table 3.6, since B0 is the only elastic modulus that
is common to the four theoretical studies as well as the experimental study). The
72

experimentally determined moduli E0, G0 and B0 [Hyland 1991] for ScAl3 all lie within
the range defined by the maximum and the minimum of the theoretical estimates [Tao
2008, Fu 1990, Xu 1990, Jahnateck 2007] (Table 3.6). In addition, although the
agreement may be fortuitous, it is interesting to note that each of the E0, G0 and B0 values
calculated by Jahnateck et al. [Jahnateck 2007] for ScAl3 agree relatively well with the
experimental values obtained for YbAl3 in this study (Table 3.6).
Furthermore, for yet another rare earth trialuminide, TmAl3, the B0 and G0 values
calculated among the theoretical studies differ by roughly 2% (Table 3.6) [Tao 2008, Sa
2011, Zhou 2011. However, the experimental values for the elastic moduli of TmAl3 are
not available in the literature to allow comparison among the various theoretical
predictions and experimental data.
Thus, among the three rare earth trialuminides, YbAl3, ScAl3 and TmAl3, the
elasticity results summarized in Table 3.6 indicate that the difficulty in obtaining
consistent results for the elastic moduli is much more pronounced for YbAl3 than for
ScAl3 and TmAl3. The apparent difficulty in calculating the elastic moduli for YbAl3 in
particular may be related to complexities in modeling and theoretically understanding the
intermediate valent nature of the Yb ion in these compounds [4] and its effect on the
elastic properties.
As an internal check on the RUS data included in our study, the elastic moduli for
selected YbAl3 disc-shaped specimens were measured on the tripod transducer stage for
the RUS (Fig. 3.1a).The specimen was then cut into a bar shaped specimen and measured
using the two-transducer stage (Fig. 3.1b). The significance of these measurements with
the differing specimen geometries (disk and bar) and differing modes of excitation (tripod
73

and two-transducer or bipod stages) is that mechanical resonant mode patterns are
sensitive on specimen geometry [Rossing 1982, Ogi 2002] although the mechanical
resonances excited in the two-transducer stage should be similar except for the relative
intensities.
The differences in the resulting RUS resonant spectra are directly demonstrated in
Fig. 3.6, which shows differing resonance frequencies and relative intensities for the bar
specimen YAl3-C on the tripod transducer stage (Fig. 3.6a), the disc geometry on the
transducer tripod (Fig. 3.6b) and the bar specimen on the two transducer stage. Specimen
YAl3-C specimen was first measured as a disc on the tripod transducer stage, then it was
cut into a bar and measured on the both the tripod and two transducer stages. Although
the RUS measurements for the specimen YAl3-C was thus determined in three separate
experiments, the E and G values measured for the various transducer stages/specimen
geometries (Fig. 3.5) differ by less than 1 percent (Table 3.7), indicating a great deal of
internal consistency in the measurements.
As an example of modulus-porosity study for a thermoelectric material other
than YbAl3, for 12 specimens of the thermoelectric LAST (lead-antimony-silvertellurium) with the compositions Ag0.43Pb18Sb1.2Te20 and Ag0.86Pb19Sb1.0Te20 having
volume fraction porosities, P, ranging from 0.01 to 0.14, the Young’s modulus and shear
modulus versus P behavior was described well by Eqs. (5a) and (5b) respectively [Ni
2009]. In particular, for the Young’s modulus versus P data for LAST, a least-squares fit
to Eq. (5a) yielded E0 = 58.3 ± 0.3 GPa, bE = 3.6 ± 0.1 with a correlation coefficient, r2 =
0.994 [Ni 2009]. Thus, Eq. (5a) describes the Young’s modulus versus porosity behavior
relatively well for both LAST and YbAl3.
74

Table 3.7. For the seven YbAl3 specimens included in this study, N, the number of RUS
resonant peaks measured, the RMS error in RUS, the Young’s modulus, E, shear
modulus, G, Poisson’s ratio, ν, longitudinal and shear velocity, VL and VS, acoustic Debye
temperature, θD, and porosity, P, were measured. The RUS analysis on each specimen
was performed on the tripod configuration (Fig. 3.1a).
Specimen
Label

N

RMS
Error

E
(GPa)

G (GPa)

ν

VL
(m/s)

VS
(m/s)

θD
(K)

P

YbAl3-A
(bar)

20

0.19%

126.2 ±
0.3

51.65 ±
0.05

0.222 ±
0.001

5390

3220

384

0.125

YbAl3-B
(disc)

39

0.41%

77.1 ±
0.2

32.08 ±
0.05

0.201 ±
0.001

4440

2710

308

0.233

YbAl3-B
(bar)

24

0.27%

85.8 ±
0.3

36.19 ±
0.05

0.186 ±
0.002

4590

2850

326

0.217

YbAl3-C
(disc)

28

0.21%

152.1 ±
0.2

64.42 ±
0.05

0.180 ±
0.001

5560

3470

421

0.060

YbAl3-C
(bar,
tripod)

17

0.25%

152.3 ±
0.4

64.51 ±
0.08

0.181±
0.002

5550

3460

421

0.054

YbAl3-C
(bar, two
transducer)

19

0.33%

152.9 ±
0.5

64.89 ±
0.10

0.178 ±
0.002

5550

3470

422

0.054

YbAl3-D
(bar)

25

0.28%

156.7 ±
0.5

66.37 ±
0.08

0.181 ±
0.002

5560

3470

426

0.030

YbAl3-E
(bar)

22

0.21%

79.7 ±
0.2

33.2 ±
0.04

0.202 ±
0.002

4490

2750

313

0.227

75

Over the range from P = 0.030 to 0.060, the Poisson’s ratio, ν, of YbAl3 is
relatively constant at ν = 0.18 (Fig. 3.5b). For P = 0.125 the Poisson’s ratio increases
0.21, then as P increases further ν ranges from about 0.19 to 0.20 (Fig. 3.5b). In the
literature for oxide materials, Boccaccini found empirically that, although there was
considerable scatter in the ν versus P data, the increase or decrease in ν with increasing P
seemed to be correlated with the value of ν0 (ν at P = 0), that is, where ν increased with
increasing P for ν0 > 0.25 and ν decreased with increasing P for ν0 < 0.25 [Boccaccini
1994]. In this study, the apparent scatter in ν between values of about 0.18 to 0.21 makes
it difficult to discern a trend in the P dependence of ν for YbAl3 (Fig. 3.5b).

3.3.5. Acoustic wave speeds and the Debye temperature
The longitudinal acoustic wave speed, VL and the shear acoustic wave speed, VS,
are also obtained from the RUS analysis. For specimens with low to intermediate values
of P, the acoustic velocities can be approximated as a linear function of P [Aliev 2011,
Solunke 2007] such that

VL  VL0 1  cL P 

(6a)

VS  VS 0 1  cS P 

(6b)

where VL0 and VS0 are the acoustic wave speeds corresponding to a theoretically dense
material and cL and cS are material-dependent constants. For the YbAl3 specimens
included in this study, Eqs. (6a) and (6b) describe relatively well the P dependence of the
acoustic wave speeds (Table 3.8, Fig. 3.7a).

76

Table 3.8. The fitting parameters obtained from the least-squares fit of the VL and VS
versus P data to Eqs. (6a) and (6b), respectively, with the coefficient of determination,
R2.
Equation

P=0
Intercept
(mm/µs)
5.88 ± 0.09
(vl0)
3.67 ± 0.04
(vs0)

Acoustic Velocity (m/s)

Longitudinal (6a)
Velocity
Shear
(6b)
Velocity

Longitudinal Velocity, PECS
Shear Velocity, PECS
Longitudinal Velocity, HP
Shear Velocity, HP

(a)
6
5

vL0

4

vS0

3
0.0

0.1

0.2

0.3

c
(unitless)

R2

1.00 ± 0.09

0.958

1.07 ± 0.06

0.986

Debye Temperature (K)

Property

P

(b)

Debye Temperature, PECS
Debye Temperature, HP

450
400

D0

350
300
0.0

0.1

0.2

0.3

P

Figure 3.7. From the RUS measurements of the YbAl3 specimens included in this study,
(a) shear and longitudinal wave speeds as a function of P, where the solid lines in
represent least-squares fits to Eq. (6a) and (6b) for the longitudinal and shear velocities,
respectively. (b) the effective Debye temperature as a function of P, where the solid line
represents a least-squares fit to Eq. (9).

77

The Anderson approximation [Anderson 1963] was used to calculate θD, the
acoustic Debye temperature

h
D 
kB

 3q N A  
 4 M  Vm


1/ 3

(7)

where h is Planck’s constant, kB is Boltzmann’s constant, NA is Avogadro’s number, ρ is
density, M is molecular weight, and q is the number of atoms per molecule. The average
acoustic velocity, VM, was calculated from VL and VS using the relationship [Anderson
1963]

1 2
1 
VM    3  3  
 3 VS VL  

1 / 3

(8)

The linear decrease in the effective Debye temperature with increasing porosity
(Fig. 3.7b) and can be described by

 D   D 0 1  b P 

(9)

where a least-squares fit of the θD versus P data gives fitting parameters θD0 = 453 + K, bθ
= 1.32 + 0.06 with a coefficient of determination of 0.99.
3.3.6 Mechanical properties as a function of processing technique
In this study, the YbAl3 specimens were densified either by HP or PECS
processing (Table 3.2). Although some researchers have reported that differing
processing techniques can result in differing mechanical properties [Rice 1998], the
Vickers indentation hardness measurements (Fig. 3.4) and the RUS elasticity
measurements for the Young’s, shear and bulk moduli (Fig. 3.5a) as well as the acoustic
velocity (Fig. 3.7a) and the Debye temperature (Fig. 3.7b) show no significant differences

78

in the magnitudes of H, E, G, B, VL, VS or θD as a function of two processing techniques
(HP or PECS).
Thus, although the HP and PECS processing parameters (sintering temperature
and sintering time) yield differing sizes and spatial distribution of pores (Figs. 3.2 and 3.3
and Section 3.3.1), the physical properties measured for the YbAl3 specimens included in
this study were functions of the volume fraction porosity P and not the processing details.
The practical significance of this is that for the two most common techniques of
densifying thermoelectric materials, namely HP and PECS, the property-porosity
relationships found in this study for YbAl3 do not appear to be functions of the
processing technique.

3.4 Summary and Conclusions
For the low temperature thermoelectric material YbAl3, the room temperature
hardness, Young’s modulus, shear modulus, bulk modulus and Poisson’s ratio were
measured using RUS for polycrystalline specimens with volume fraction porosities, P,
over the interval 0.030 < P < 0.233. The rates of linear decrease in hardness with
increasing P (Fig. 3.4, Eq. (4b)) and the elastic moduli (Fig. 5, Eqs. (5a) – (5c)) are
consistent with the literature.
Although no fracture toughness literature is available for rare earth trialumindes,
the YbAl3 values of approximately 1.1 to 1.6 MPa m1/2 that were found in this study are
comparable to lower ranges of KC measured for transition metal trialumindes, for which
significant efforts have been directed toward enhancing KC for structural materials
applications. Therefore, it appears that the KC of YbAl3 may be sufficiently high so as not
79

to hinder its development as a low temperature thermoelectric material. Also, the
hardness value 6.81 GPa for YbAl3 (P = 0.030) is comparable to the literature hardness
value of the transition metal trialuminide TiAl3, thus the hardness of YbAl3 is likely
sufficient to impart reasonable in-service scratch and abrasion resistance. However, once
again, the lack of hardness data in the rare earth trialuminide literature limits the hardness
comparisons that can be made.
For this study, extrapolation of the elastic moduli versus porosity results to zero
porosity gives intercepts E0, G0 and B0 for YbAl3 (Eqs. (5a) – (5c), Fig. 3.6). These zero
porosity values are roughly 10 - 36% higher than the E0, G0 and B0 values predicted from
density functional theory (Table 3.6). However, the E0, G0 and B0 values predicted
theoretically for YbAl3 are also significantly different from one another (Table 3.6). In
contrast, the theoretical and experimental moduli for ScAl3 are relatively successful. The
apparent difficulty in calculating the elastic moduli for YbAl3 may be related to
complexities in modeling and understanding the nature of the intermediate valence nature
of the Yb ion in YbAl3.
ACKNOWLEDGEMENTS
GJL and DTM. acknowledge support by the Air Force Office of Scientific
Research under the MURI program “Cryogenic Peltier Cooling,” Contract #FA9550-101-0533. In addition, R.D.S. and E.D.C. acknowledge the financial support of 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 Science, Office of Basic energy Sciences under award number DE-SC0001054.

80

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81

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85

4 Room-Temperature Mechanical Properties and Slow Crack Growth Behavior of
Mg2Si Thermoelectric Materials
Robert D. Schmidt1, Eldon D. Case1, Jesse Giles III1, Jennifer E. Ni1, Timothy P. Hogan2
1
Chemical Engineering and Materials Science Department,
Michigan State University, East Lansing, MI, 48824
2
Electrical and Computer Engineering Department,
Michigan State University, East Lansing, MI, 48824
Published in: Journal of Electronic Materials 41 (2012) 1210 – 1216.
Abstract
Mg2Si is of interest as a thermoelectric (TE) material in part due to its low materials cost,
lack of toxic components, and low mass density. However, harvesting of waste heat
subjects TE materials to a range of mechanical and thermal stresses. To understand and
model the material’s response to such stresses, the mechanical properties of the TE
material must be known. The Mg2Si specimens included in this study were powder
processed and then sintered via pulsed electrical current sintering. The elastic moduli
(Young’s modulus, shear modulus, and Poisson’s ratio) were measured using resonant
ultrasound spectroscopy, while the hardness and fracture toughness were examined using
Vickers indentation. Also, the Vickers indentation crack lengths were measured as a
function of time in room air to determine the susceptibility of Mg2Si to slow crack
growth.

Keywords: Magnesium silicide, fracture toughness, elastic modulus, hardness, slow
crack growth

86

4.1 Introduction
New thermoelectric (TE) materials based on Mg2Si are candidates for a wide
variety of waste heat recovery applications due to their low mass density [~2 g/cm3 for
Mg2Si versus densities of 6 g/cm3 to 8 g/cm3 for TE materials such as PbTe, leadantimony-silver-tellurium (LAST), CoSb3, FeSb3,and Bi2Te3]. Also, Mg2Si is composed
of abundant, inexpensive, and nontoxic elements. Previous studies have determined a ZT
as high as 1.0 at 800 K for an Mg2Si-based material [Mars 2009]. Energy harvesting
applications subject TE materials to thermal cycling during the startup and operation of
the device, as well as to the thermal gradient required to operate a TE generator. The
designer must know the mechanical properties such as the elastic moduli in order to
calculate the material’s response to imposed thermal and mechanical loads. The roomtemperature elastic moduli, hardness, and fracture toughness of Mg2Si are determined in
this study. In addition, since fine powders of Mg2Si react vigorously with water, [Aesar]
a slow crack growth study was performed in which the length of Vickers radial
indentation cracks was monitored as a function of time in room air. Slow crack growth
involves a concerted chemical reaction [Michalsky 1983] of a polar molecule such as
water with the highly strained atomic bonds at a crack tip, with the result that the reaction
breaks bonds at the crack tip and the crack slowly advances [Wiederhorn 1968; West
1998; Freiman 2009]. Slow crack growth has been observed in a variety of brittle
materials, including ceramics [Freiman 2009] as well as in single crystal silicon
[Connally 1992]. If slow crack growth occurs in Mg2Si, this would imply that the flaws
produced by cutting and grinding procedures during module preparation could extend
upon exposure to either room air or an aqueous environment.
87

Temperature

Pressure
50

1000
40
800

30

600

20

400

10

200

0

5

10

15

20

Pressure (MPa)

Temperature (K)

1200

0
25

Time (min)
Figure 4.1. The time–temperature and time–pressure profiles used in the PECS
processing of each of the Mg2Si specimens included in this study.
Table 4.1. The Mg2Si specimens used in this study for Vicker’s hardness, H, fracture
toughness, KIC, Young’s modulus, E, shear modulus, G, Poisson’s ratio, , and acoustic
debye temperature, D, measurements. The Mg2Si pieces were reduced using a (1)
mechanical mortar and pestle until all powder passed through a 53 µm sieve and then
either densified or further reduced using a (2) planetary mill at 150 rpm for 3 hours. For
indentation the specimens were polished to 1 μm diamond grit, further details are
available elsewhere [Ni 2010]. Due to reactions with water [Aesar], the specimens were
cleaned using ethanol instead of water between polishing grit sizes.
Specimen
Powder Processing Form
Name

Dimensions Mass Density
(mm)
(g)
(g/cm3)

Mechanical
properties
measured

Mg2Si-01 Planetary mill

Disc

19.55 dia
3.35 ht

2.01

2.01

H, KICa, b

Mg2Si-03 Planetary mill

Parallele- 9.89 x 13.01
0.90
piped
x 3.35

2.09

E, G, , Dc

Mg2Si-05

Mechanical mortar
and pestle

Disc

12.54 dia
3.41 ht

0.88

2.08

H, KICa

Mg2Si-11

Mechanical mortar
and pestle

Parallele- 11.45 x
1.18
piped
14.86 x 3.31

2.09

E, G, , Dc

Mechanical mortar Parallele- 11.36 x
1.07 2.07
E, G, , Dc
and pestle
piped
15.06 x 3.01
a
Measured using Vicker’s indentations, b Slow crack growth monitored using this
specimen, c Measured using RUS
88
Mg2Si-12

4.2 Experimental procedure
Mg2Si (99.99% metals basis purity), purchased from Alfa Aesar (45518, Ward
Hill, MA), was reduced in size using a mechanical mortar and pestle and planetary
milling (Table 4.1). Further details of the powder processing are presented elsewhere [Ni
2010]. The powders were densified using pulsed electronic sintering (PECS) at 1073 K
for 5 min and 50 MPa pressure (Fig. 4.1) in argon.
The grain size was measured using the linear intercept technique with a
stereographic projection factor of 1.5 [Underwood 1968; Case 1981]. All of the grain
size analysis on the Mg2Si specimens was performed on micrographs of fractured
surfaces taken in the secondary electron mode on a scanning electron microscope (SEM).
The elastic moduli (Table 4.1) were calculated using a dynamic method, resonant
ultrasound spectroscopy (RUS), and commercially available software. Additional details
of the RUS elasticity technique are provided elsewhere [Ni 2010; Ren 2009].
The Vickers hardness, H, and fracture toughness, KIC, were determined using
Vickers indentations with loads ranging from 2.94 N to 9.81 N. H was calculated by
[Wachtman 2009]
(

(1)

)

where P is the indenter load and 2a is the length of the indentation diagonal. KIC was
estimated from [Wachtman 2009]
( ⁄ ) ⁄

(2)

⁄

89

where E is the Young’s modulus calculated using RUS, c is the radial crack length
extending from the center of a Vickers indentation, and ξ is a dimensionless constant
assumed to be 0.016 [Wachtman 2009].
The Vickers indentation was performed by a Buehler indenter (Buehler
Semimacro Indenter, Lake Bluff, IL) and a Shimadzu hardness tester (Shimadzu HMV2000, Kyoto, Japan). Each indenter was calibrated using a steel calibration block with H
of 7.75 GPa (761-048; Yamamoto Scientific Tools Lab, Co LTD, Japan). For both the
hardness calibration and for each Vickers indentation performed on the Mg2Si specimens
in this study, a load time of 5 s and a loading speed of 70 µm/s were used. Also, both the
calibration block and the Mg2Si specimens were indented at loads of 2.95 N, 4.90 N, and
9.81 N, with 10 indentations performed for each load on a given specimen. The radial
crack length and the diagonal length of the indentation impression were measured
optically using the movable filars on the Buehler and Shimadzu indentation machines.
To compare the hardness results obtained from the Buehler and Shimadzu
indentation machines, a Mg2Si specimen was indented 10 times at each load of 2.95 N
and 4.90 N by each machine at a load time of 5 s and a loading speed of 70 µm/s.
Possible slow crack growth was monitored using radial cracks induced by Vickers
indentation at 2.94 N load. The radial cracks were measured at intervals between 1 min
and 3 days after indentation. During the slow crack growth study, the room temperature
and relative humidity ranged between 23.2°C and 24.3°C and 46% and 51%,
respectively.

90

Counts (Arbitrary units)

400

MgO
Mg2Si

300
200
100
0
20

30

40

50

60

70

2
Figure 4.2. X-ray diffraction of planetary-milled Mg2Si powder with peaks compared
with the literature for MgO [Hazen 1976] and Mg2Si [Owen 1923].

Figure 4.3. Fractured surface of specimens (a) Mg2Si-01 and (b) Mg2Si-05, PECS
processed from planetary mill and mechanical mortar and pestle Mg2Si powder,
respectively. Cleavage steps show mixed- mode fracture, with both intergranular and
transgranular fracture present. Entrapped pores visible at grain boundaries were
approximately 1 µm to 3 µm diameter with polygonal shape. The dark areas between
grains are porosity within the specimens, typically around 1 µm or less in diameter

91

Figure 4.4. Typical Vickers indentation crack systems for specimens Mg2Si-01 and
Mg2Si-05, which display indentation impressions, little chipping or spalling, and a fully
developed radial crack system.
Table 4.2. The density, Young’s modulus, E, shear modulus, G, Poisson’s ratio, , and
Debye temperature, D, from this study compared with the literature. The moduli were
determined using resonant ultrasound spectroscopy, RUS, first principle calculation,
FPC, resonance technique, RT, and compression.

Reference

Modulus
Density
Measurement E(GPa)
(g/cm3)
Method

This Study
(Mg2Si-03)

2.09

RUS

This Study
(Mg2Si-11)

2.09

This Study
(Mg2Si-12)

G (GPa)



D
(K)

117.2 ±
0.2

49.53 ±
0.04

0.183 ±
0.001

585a

RUS

117.7 ±
0.2

50.09 ±
0.05

0.175 ±
0.001

588a

2.07

RUS

116.9 ±
0.5

48.92 ±
0.13

0.195 ±
0.001

583a

[Zhang 2009]

1.98b

FPC

115.6

49.50

0.17

N/A

[Tani 2008]

2.04b

FPC

113.5

49.2

0.161

432

RT

110.9c

47.6c

0.165c

578

[Whitten 1965] 2.00

d

[Milekhine
1.94e
Compression 76 ± 6
N/A
N/A
N/A
2002]
N/A Not available, a Acoustic Debye temperature, b Density calculated from the given
lattice parameter, c From the average of Hashin and Shtrikman bounds at 300 K
[Simmons 1971], d Debye temperature at 0 K, e Density estimated by 3% porosity and
2.00 g/cc porosity free density
92

4.3 Results and Discussion
In this study, the Mg2Si specimens had a mean mass density of 2.07 g/cm3,
calculated from the measured mass and dimensions (Table 4.1). Single- crystal Mg2Si has
mass density of 1.98 g/cm3 and 2.00 g/cm3 [Zhang 2009; Whitten 1965]. X-ray
diffraction determined that an MgO phase [Hazen 1976] was present in the Mg2Si
powder [Owen 1923] used to fabricate the specimens (Fig. 4.2), which may account for
the increase in density for the PECS Mg2Si specimens in this study. The grain size was
2.4 µm (Fig. 4.3a) and 3.9 µm (Fig. 4.3b) for the specimens fabricated using powder
reduced by the planetary mill and mortar and pestle, respectively. Based on SEM
micrographs of the specimens (Figs. 4.3, 4.4), we estimate volume fraction porosity to be
0.05 or less, and a resulting approximate volume fraction of 0.89 ± 0.03 Mg2Si and 0.08
± 0.03 MgO to account for the measured mass density.
In this study, the mean values of the measured elastic moduli for Mg2Si were
117.3 GPa for Young’s modulus, E, 49.5 GPa for shear modulus, G, and 0.184 for
Poisson’s ratio, ν. In the literature, E ranged from 110.9 GPa to 115.6 GPa,[Zhang 2009;
Whitten 1965; Simmons 1971; Tani 2008] which was comparable to this study’s mean E
of 117.3 GPa. The exception was Milekhine et al., who reported an E of 76 GPa;
however, Milekhine et al. recognized that their Young’s modulus value was not
consistent with literature [Milekhine 2002] (Table 4.2). For comparison with other TE
materials, E values include CoSb3 at 140.6 GPa [Schmidt 2010] and PbTe-PbS 8% at
53.1 GPa [Ni 2010].
The calibration factors from 10 indentations at each load for the Shimadzu were
0.98, 0.96, and 0.98 at 2.95 N, 4.90 N, and 9.81 N loads, respectively, and for the Buehler
93

were 1.10, 1.10, and 1.03 at the same loads. The calibration factor was multiplied by the
uncorrected H value for the reported H values in this study.
For indentation loads of 2.95 N, 4.90 N, and 9.81 N, the Vickers hardness, H, in
this study ranged from 4.8 ± 0.3 GPa to 5.6 ± 0.2 GPa. Over this relatively restricted load
range, no load dependence of H was observed. Also, based on the mean and standard
deviation of the measured H using the Shimadzu and Buehler indenters, there was no
statistically significant difference in the H values measured, although the measured H
was different from literature values [Milekhine 2002; Li 1993] (Table 4.3). The average
hardness of 5.1 GPa for the PECS-processed specimens in this study was higher than the
range of 3.96 GPa to 4.38 GPa for cast specimens in the literature [Milekhine 2002; Li
1993] (Table 4.3).
In general, hardness increases with decreasing grain size [Ni 2010; Lawn 1993;
Barsoum 2003]. The grain sizes of the cast speci- mens included in their studies were not
given by Milekhine et al. [Milekhine 2002] and Li et al. [Li 1993]. However, grain sizes
for cast specimens are often greater than 500 µm [Ni 2010; Ren 2008], which is
significantly larger than the roughly 33 µm or smaller Vickers impression dimensions
reported by Milekhine et al. [Milekhine 2002]. The likely grain size for the cast
specimens is also much larger than the average grain sizes of 2.4 µm for the Mg2Si-01
and 3.9 µm for the Mg2Si-05 specimen included in this study. The narrow range of grain
sizes (2.4 µm to 3.9 µm) makes it extremely unlikely that an H dependence on grain size
would be observed for the specimens included in this study. However, the H value of 5.1
GPa for this study is expected to be higher than the H values of 3.96 GPa to 4.38 GPa
measured for cast specimens [Milekhine 2002; Li 1993], since the cast specimens likely
94

Table 4.3. A comparisons of Vickers hardness, H, and fracture toughness, KIC, from this
study to the literature. For the PECS processed specimens in this study, the H and KIC
was determined using at least 10 indentations per load with one standard deviation
reported as error. For cast specimens in literature, Milekhine et al. measured at least 10
indentations per load [Milekhine 2002]and Li et al. measured 5 indentations [Li 1993].
Reference

Grain
Size (µm)

This Study
(Mg2Si-01)

2.4

Load
0.981 N

H (GPa)

This Study
(Mg2Si-05)

3.9

[Milekhine
2002]

N/A

[Li 1993]

Mechanical
Property

N/A

KIC
(MPa·m1/2)
H (GPa)
KIC
(MPa·m1/2)
H (GPa)
KIC
(MPa·m1/2)

N/A

2.94 N
4.90 N
9.81 N
5.4 ± 0.2a 5.6 ± 0.2a
a
b
b 5.4 ± 0.2
5.0 ± 0.3 5.0 ± 0.1
1.2 ± 0.2b 1.3 ± 0.3b 1.3 ± 0.5b
4.8 ± 0.2b 4.8 ± 0.2b 5.0 ± 0.2a

N/A

N/A

H (GPa)

4.38 ±
0.07

KIC
(MPa·m1/2)

N/A

a

Using a Buehler indenter
Using a Shimadzu indenter
N/A = not available
b

95

0.7 ± 0.2b 1.1 ± 0.2b 0.9 ± 0.1b
3.96

4.05

4.20

0.88

0.81

0.74

N/A

N/A

N/A

have much larger grain sizes. For other TE materials, the Vickers hardness is 1.10 GPa to
1.28 GPa for PbTe-PbS8% when powder processed [Ni 2010], 0.51 GPa to 1.2 GPa for
lead-antimony- silver-tellurium (LAST) [Ren 2008], and 5.7 GPa for MM0.7Fe3CoSb12
(where MM denotes mischmetal) [Zhang 2010].
Fracture toughness, KIC, by Vickers indentation (Fig. 4.4) was 0.7 ± 0.2 MPa m1/2
to 1.3 ± 0.5 MPa m1/2 for indentation loads from 2.94 N to 9.81 N (Table 4.3). Milekhine
et al. reported KIC values ranging from 0.81 MPa m1/2 to 0.97 MPa m1/2 measured by
indentation fracture [Milekhine 2002]. However, Milekhine et al. used their measured E
and H values (Tables 4.2 and 4.3) to calculate KIC, and their E and H values are lower
than the E and H values found in this study and in the literature (Tables 4.2 and 4.3).
Using the crack length, c, reported by Milekhine et al. and the E and H values from this
study (117 GPa and 5.1 GPa, respectively), the recalculated values for Milekhine et al.’s
KIC values would be 0.8 MPa m1/2, 0.9 MPa m1/2, and 1.1 MPa m1/2 using Eq. 2, which
are in better agreement with the data from this study (Table 4.3). The KIC values of other
thermoelectric materials include 1.12 MPa m1/2 to 1.35 MPa m1/2 for Bi2Te3 [Zhao 2008],
0.35 MPa m1/2 for PbTe-PbS 8% [Ni 2010], and 0.34 MPa m1/2 for LAST [Ren 2008].
The radial crack length was measured on six indentations of specimen Mg2Si-01.
Slow crack growth was not observed when examining the average length of the two
radial cracks per indentation (Fig. 4.4) as a function of time for six indentations for a
period of days (Fig. 4.5). Two indentations had a crack pop-in within the first 5 min after
indentation, which was not considered slow crack growth. The mean and standard
deviation of the radial crack length measurement versus time are shown in Fig. 4.5 and
Table 4.4, indicating that there was no statistically significant slow crack growth that
96

Crack Length (µm)

Crack Length (µm)

110
100
90
80

(a)
70

1

10

100

1000

110
100
90
80
70

(b)
1

10

110

100
90
80

(c)
1

10

100

Crack Length (µm)

Crack Length (µm)

110

1000

100
90
80

(d)
70

1

Time (min)

100

1000

110

Crack Length (µm)

Crack Length (µm)

10

Time (min)

110
100
90
80
70

1000

Time (min)

Time (min)

70

100

(e)
1

10

100

1000

100
90
80

(f)
70

1

10

100

1000

Time (min)

Time (min)

Figure 4.5. For specimen Mg2Si-01, plots of radial crack length versus time for six
Vickers indentation crack systems loaded at 2.94 N. In figures (b) and (e), a radial crack
popped in within 1 min to 5 min following the initial indentation event. The average
crack length and one standard deviation variation is indicated by solid and dashed lines,
respectively, for each indentation crack. The crack length may vary significantly between
indentations, resulting in the uncertainties in the reported KIC values in Table 4.3.
97

Table 4.4. No significant slow crack growth occurred for the six Vickers indentation
cracks listed below for specimen Mg2Si-01, where the radial crack lengths were
monitored for up to 3 days (Fig. 4.5). For the radial crack length measurements
performed over the entire time range, the measured crack lengths did not depart
significantly from the mean length of each crack, as indicated by the coefficient of
variation (CV, standard deviation/mean), where CV ranges from about 1.4% to 5%.
Indent identification
Mg2Si-01 (a)
Mg2Si-01 (b)
Mg2Si-01 (c)
Mg2Si-01 (d)
Mg2Si-01 (e)
Mg2Si-01 (f)

Mean crack length
(µm)
106.5
78.2
107.3
97.5
86.5
86.2

Standard deviation
(µm)
1.5
2.9
1.6
2.0
4.5
2.3

98

Coefficient of
variation (CV)
0.014
0.037
0.014
0.020
0.051
0.027

occurred for Mg2Si for times up to 3 days (Fig. 4.5). There was no pattern of crack length
growth with time outside of one standard deviation (Fig. 4.5). Differences in crack length
between Figs. 4.5a–f are based on the individual indentations. With no pattern of crack
length change with time, any variation in length measurements (Table 4.4) for an
indentation may be attributed to the error of the optical measurement technique.
4.4 Conclusions
The elastic moduli, hardness, fracture toughness, and slow crack growth were
measured on powder- processed and PECS-sintered specimens of Mg2Si. The average E
of 117.3 GPa, H of 5.3 GPa, and KIC of 1.3 MPa m1/2 obtained in this study agree well
with the literature (Tables 4.2 and 4.3).
No examination of the susceptibility of Mg2Si to slow crack growth has appeared
in the literature prior to this study. In spite of a known reaction with water [Aesar], this
reaction did not drive slow crack growth for the radial cracks observed in this study. The
lack of significant slow crack growth is beneficial to the development and fabrication of
Mg2Si, as microcracks induced by cutting or grinding during fabrication would not be
expected to grow under normal atmospheric conditions.
Mg2Si has several advantages as a potential thermoelectric material. It has low
mass density and contains only nontoxic, inexpensive, and readily available elements.
Thus, Mg2Si is a very viable candidate for widespread application as a thermoelectric
material.
ACKNOWLEDGEMENTS
The authors acknowledge the financial support of the Department of Energy,
“Revolutionary Materials for Solid State Energy Conversion Center,” an Energy
99

Frontiers Research Center funded by the US Department of Energy, Office of Basic
Energy Sciences under Award Number DE-SC0001054. Jennifer Ni (under the Office of
Naval Research Grant N00014-08-1-0613) assisted with the scanning electron
microscopy of the specimen surfaces and assisted Jesse Giles with the hardness
measurements. Financial support for Mr. Giles was provided through the Michigan Louis
Stokes Alliance for Minority Participation (MI-LSAMP) Summer Undergraduate
Research Academy (SURA), which was hosted in collaboration with the Michigan State
University Summer Research Opportunity Program (MSU SROP).

100

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101

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104

5 Mechanical properties of Mg2Si thermoelectric materials with the addition of 0 to
4 volume percent silicon carbide nanoparticles (SiCNP)
Robert D. Schmidt, Xiaofeng Fan, Eldon D. Case,
Chemical Engineering and Materials Science Department,
Michigan State University, East Lansing, MI, 48824
To be submitted to: Journal of Materials Science
Abstract
For thermoelectric generators, the individual thermoelectric elements are
subjected to a significant stresses under in-service conditions, due to thermal cycles,
transients and gradients, as well as thermal expansion mismatch and externally applied
mechanical stresses. Most thermoelectric (TE) materials are brittle and with low fracture
toughness, typically no more than 1.5 MPa m1/2 and often less than 0.5 MPa m1/2. The
combination of the stresses encountered in the device application environment and the
materials’ low fracture toughness constitute a severe challenge to the viability of
thermoelectric generators. The addition of silicon carbide nanoparticles (SiCNP) may
provide a route to improving the fracture toughness for a wide range of thermoelectric
materials. This study examines the mechanical properties, including elastic modulus,
hardness and fracture toughness for 0 to 4 vol.% SiCNP incorporated into Mg2Si
thermoelectric matrices.
5.1 Background
Thermoelectric (TE) materials for solid state energy conversion have been
extensively investigated in recent years, with the potential to recapture energy from waste

105

heat sources. Typically, the efficiency of a material is measured by use of the
dimensionless figure of merit, ZT,
(1)
where S is the Seebeck coefficient, σ is the electrical conductivity, κ is the thermal
conductivity, and T is temperature.
Thermoelectric generators, particularly when used in waste heat applications, are
subjected to multiple sources of stress, including stresses due to thermal gradients,
thermal shock, thermal expansion mismatch between materials, and externally applied
stresses. Waste heat applications typically involve a heat source, such as exhaust from an
engine. Automotive engines are typically run with several accelerations or decelerations,
and the waste heat produced will likewise involve several thermal cycles during
operation. The waste heat source therefore is a source with thermal transients, thermal
shock, and thermal gradients, which produce stresses in the TE material. These stresses
require a detailed knowledge of the mechanical properties of the material to understand
the material response to the stress, particularly the elastic properties and the fracture
toughness. The elastic moduli are necessary to understanding the mechanical response to
stresses, including stresses that cause fracture and the calculation of fracture toughness.
In addition, stresses and flaws resulting from the manufacturing processes, such
as scratches and surface microcracks during cutting or grinding, may result in fracture. A
typical TE module has tens to hundreds of legs, all thermally in parallel, but electrically
in series, creating a condition where each leg is subjected to the full thermal cycle, but the
failure in any one leg of the TE material electrically breaks the circuit and renders an
106

entire module of a generator inoperable. Therefore, an understanding and control of the
mechanical response and failure of the TE materials is critical to the reliable operation of
a TE generator.
The fracture toughness, KC, of thermoelectric materials is typically very low, less
than 1.5 MPa m1/2, and often less than 0.5 MPa m1/2 [Schmidt 2012; Eilertsen 2013; Ren
2008; Ni 2010]. For comparison, window glass has a fracture toughness of about 0.75
MPa m1/2 [Wiederhorn 1969]. Adding particles such as silicon carbide nanoparticles
(SiCNP) may improve the fracture toughness for a wide range of TE materials.
Fracture toughness may be increased by the incorporation of second phases,
additions such as particles or whiskers, microstructural changes or other mechanisms.
For the purposes of this study, these may be grouped into intrinsic or extrinsic toughening
mechanisms [Launey 2009]. Intrinsic mechanisms (such as crack blunting or crack
deflection) change the fracture toughness by acting on the area ahead of the crack tip, by
distributing the load, changing the interface properties, or other methods to “increase the
microstructural resistance” of the material [Launey 2009]. Extrinsic mechanisms (such
as fiber or grain bridging) work on the area behind the crack tip, redistributing the force
to reduce the force acting at the crack tip [Launey 2009]. These differences have
important implications in the potential for improving the fracture toughness overall, and
specific implications for materials under fatigue conditions such as thermal cycling.
Extrinsic mechanisms may, for a few cycles, significantly improve fracture
toughness. For example, in alumina the addition of 20% SiC whiskers increased KC by a
multiple of 3 [Becher 1991], and additions of 20% and 40% tetragonal zirconia increased

107

KC by a multiple of 3 and 5, respectively [Becher 1991]. Similar increases were observed
in glass and mullite [Becher 1991].
These extrinsic toughening methods, however, are not desirable in a fatigue
condition [Ritchie 1999; Launey 2009; Case 2012a; Case 2012b] and can be destructive
to the material [Lathabai 1991; Bhowmick 2007; Bhowmick 2009]. Bridging, for
example, has been observed to be defeated by fatigue and can even be destructive in
alumina [Knehans 1982; Lathabai 1991] and silicon [Bhowmick 2009]. When a bridge is
defeated, the debris may fall into the crack and act as a wedge and extend the crack.
Intrinsic toughening mechanisms, including crack deflection, crack blunting,
crack branching or bowing, are not defeated by thermal fatigue [Launey 2009].
Therefore, intrinsic toughening mechanisms acting ahead of the crack tip are the desired
type of toughening in fatigue [Launey 2009; Case 2012a; Case 2012b] as would be the
case for a TE device in waste heat recovery that is subjected to multiple thermal cycles.
The addition of nanoparticles can lead to intrinsic toughening. However,
compared to large increases in KC that are possible with extrinsic toughening, intrinsic
toughening offers smaller but significant increases in KC (Table 5.1). In alumina,
additions of 5-20% SiC nanoparticles increases the relative KC by a factor of 1.16 [PerezRigueiro 1998; Parchovianský 2013]. In Bi2Te3, a TE material, additions of 0.1 to 0.5
vol% SiC nanoparticles increased relative KC by a factor of 1.18 [Zhao 2008].
Mg2Si may be used to examine several toughening mechanisms. Literature values
of ZT show Mg2Si to be a good TE material (Table 5.2), with ZT of 0.86 at 862 K for
(Mg2Si:Bi = 1:0.02) [Tani 2005] and 0.97 at 873 K for 0.5 at.% Sb doped Mg2Si + 5 wt.
% Ni [Hayatsu 2012]. With values of ZT from 0.23 to 0.97 when doped with 2% or less
108

Table 5.1. The fracture toughness, KC, has been improved in brittle materials, including
the thermoelectric Bi2Te3, by the addition of SiC nanoparticles.
Matrix
KC
SiC addition
KC
Relative
Reference
1/2
1/2
material
(MPa·m )
(MPa·m ) change
Bi2Te3
1.14
0.1 vol %
1.35
1.18
[Zhao 2008]
0.5 vol %
1.33
1.17
1.0 vol %
1.19
1.04
a
a
Al2O3
3.7 to 3.8
5 vol. %
3.6
0.96 a
[Pérez-Rigueiro
3.0 to 3.3 b
20 vol. % a
3.4 to 3.6
0.93 a
1988]
b
b
5 vol. %
3.6
1.14
20 vol. % b
3.5 to 3.7
1.14 b
Al2O3
5.0 ± 0.3
5 vol. %
5.4 to 5.6
1.10
[Parchovianský
10 vol. %
5.6 to 6.0
1.16
2013]
15 vol. %
5.2 to 5.3
1.05
20 vol. %
5.1 to 5.3
1.04
a
Specimen tested by single-edged notched beam
b
Specimen tested by Vickers indentation

Table 5.2. Doped Mg2Si-based thermoelectric materials with ZT near 1 have been
reported. These reasonable ZT values for a thermoelectric material support the use of
Mg2Si as a model system.
Composition
Maximum ZT
Temperature for
Reference
maximum ZT (K)
Mg2Si:Bi = 1:0.02
0.86
862
[Tani 2005]
Mg2Si:Sb = 1:0.005
0.97
873
[Hayatsu 2012]
+ 5 wt.% Ni
Mg2Si0.9Sn0.1:Al =
0.68
864
[Tani 2008]
1:0.02
Mg2Si:Y = 1:0.006
0.23
600
[Meng 2011]
(2000 ppm of Y)
Mg2Si:Mg2Pb = 1:0.02 0.56
873
[Muthiah 2013]
Mg2Si:Sb = 1:0.02
0.56
862
[Tani 2007]

109

of dopant [Tani 2005; Hayatsu 2012; Tani 2008; Meng 2011; Muthiah 2013; Tani 2007],
Mg2Si may be used as a suitable TE system to test additions of SiCNP.
As reported on the MSDS, Mg2Si reacts with water [Aesar], which requires
handling without water or water-based solutions. However, this reaction is not a problem
for crack growth and mechanical integrity when the material is handled in dry air
[Schmidt 2012]. Mg2Si is a suitable material for examination of fracture properties by
Vickers indentation [Schmidt 2012].
To understand the mechanical response to the stresses, as well as the potential for
fracture, the mechanical properties of the TE material must be not only understood, but
optimized to properly withstand the thermal fatigue environment typical of many
thermoelectric generator applications.
5.2 Experimental Procedure
In this study, silicon carbide nanoparticles, SiCNP, were added to Mg2Si powders
which were then processed to produce Mg2Si- SiCNP composites.
5.2.1 Materials and Specimen Preparation
Powder was produced from lump Mg2Si (45518, 3-12 mm pieces, Alfa Aesar,
Ward Hill MA), ground and sieved through a 53 μm sieve, then milled by either (i) a
planetary ball mill (PM) using an alumina-lined mill jar with 10 mm diameter alumina
grinding media at 150 RPM for 3 h, or (ii) a vibratory mill (VM) with a WC lined jar,
two 11.2 mm spheres and four 7.9 mm spheres, and a Viton gasket, sealed in the glove
box with an additional layer of electrical tape. The PM processed Mg2Si powders were
milled in an argon-filled glove box and the VM processed powders were milled in a
sealed, argon-filled jar.
110

Specimens were densified by pulsed electric current sintering (SPS Model 10-3,
Thermal Technology LLC, Santa Rosa, CA) in a 12.7 mm diameter graphite die.
Sintering was performed at 800°C and 50 MPa for 5 min, and with ramp rates of
100°C/min and 45 MPa/min.
5.2.2 Elasticity Measurements
Elastic moduli were measured by resonant ultrasound spectroscopy (RUS). In
RUS, the specimen is placed on a tripod of transducers. One transducer was swept
through a range of frequencies and the mechanical resonance frequencies are picked up
by the other two transducers. The resonances were fit to a model for the geometry, mass
and dimensions of the specimen to determine the elastic moduli. Additional details of the
RUS procedure are provided elsewhere [Ni 2010; Schmidt 2010; Migliori 1997].
5.2.3 Hardness and toughness measurements
Prior to indentation, each specimen was mounted with thermoplastic
(CrystalBond 509, EMS, Hatfield, PA) onto an aluminum stub, then polished with a
series of diamond compounds with grit size from 35 µm to 1 µm. Cleaning of the
specimen between polishing grit sizes was performed by hand with ethanol rather than
water to lessen any surface reaction between the Mg2Si and water [Aesar].
Hardness and fracture toughness for each of the specimens were measured by
Vickers indentation. Vickers hardness, H, is calculated by the equation,
H=

1.8544 F
( 2a ) 2

(2)

111

where F is the indentation load, 2a is the diagonal impression length, and ζ is a
correction factor, set at 0.95 to 0.97 based on indentations of a steel standard calibration
block (Yamamoto Scientific Tools Lab Co. LTD, Chiba, Japan).
The fracture toughness, KC, of a material may be estimated by measuring the
radial crack length, c, of a Vickers indentation, by the equation,
KC 

 E H 1 2 P

(3)

c3 2

where ξ is a dimensionless constant, set as 0.016, E is the Young’s modulus, H is the
hardness, and P is the applied load [Wachtman 2009].
5.2.4 Microscopy
The specimens were examined by scanning electron microscope (SEM) at a
working distance of either 8 mm or 15 mm, and at an accelerating voltage of 15 kV
(JEOL 6610LV or JSM-7500F, JEOL Ltd., Japan). The average grain size (GS) of each
of the sintered specimens was determined using the linear intercept procedure (ASTM
E112) with a minimum of 200 intercepts per image, and a stereographic projection factor
of 1.5 [ASTM-Standard-E112-13 2014]. Surface details were examined with secondary
electron imaging (SEI) and elemental contrasts were examined by backscatter electron
imaging (BEI).
5.3 Results and Discussion
5.3.1 Microstructural analysis
Prior to sintering, both the PM and the VM powders were examined for size range
and morphology. For the PM powder, there was a wide distribution from sub-micron

112

Figure 5.1. Planetary milled Mg2Si powder exhibited typical particle sizes of sub-micron
to 5 μm in SEM. The powder has a surface area of 4.4 m2/g measured by BET, or
approximately 0.7 μm average particle size.

Figure 5.2. Vibratory milled Mg2Si powder exhibited typical particle sizes of 0.2 μm to 2
μm in SEM.

113

particles to 5 μm particles or greater, average particle size by BET was 0.7 μm (Figure
5.1).
To incorporate SiCNP with a vendor specified average particle size of 45-55 nm
(44646, Lot number E15T018, Alfa Aesar) into the PM powder, the PM milled Mg2Si
and SiCNP were planetary ball milled at 120 RPM for 3 h in an argon-filled glove box
with the same mill jar and media used to mill the Mg2Si powder.
For the VM powder, there was a relatively uniform distribution of powder, 0.2 μm
to 2 μm in size (Figure 2). The SiCNP (44646, Lot number E15T018, Alfa Aesar) were
incorporated into the VM powder simultaneously with milling the sieved powder.
The original PM powder average particle size of 0.7 µm (Figure 1)was smaller
than the average GS of the sintered PM specimens of 2.0 µm to 3.9 µm (Table 5.3),
indicating some grain growth during sintering (Figure 3a – c).
No BET particle size measurement was performed on the VM powder to compare
to GS, however the average GS of the VM specimens of 0.4 μm to 0.8 μm (Table 5.3) is
consistent with only limited grain growth from the original VM powder (Figure 5.2) to
the sintered specimens (Figure 5.3d).
5.3.1.1 Starting material density and microstructure
All sintered specimens in this study except one have a density of 2.00 to 2.06
g/cm3. The one specimen with a density of 1.93 g/cm3, VM-0SiC-02, is mentioned
individually, but any averages or trends in mechanical properties excluded VM-0SiC-02
as an outlier.
Most of the sintered specimen densities are higher than theoretical density for
Mg2Si of 2.00 g/cm3 reported in the literature [Whitten 1965]. The higher density is
114

Table 5.3. Specimens in this study were either milled by planetary ball mill (PM) or
vibratory mill (VM), with up to 4 vol% SiCNP additions, then sintered by pulsed electric
current sintering to produce specimens with a density (ρ) of 2.00 g/cm3 or greater for all
specimens except VM-0SiC-2. The average grain size (GS) by the lineal intercept
method are a function of the milling method, and not a function of SiCNP additions.
SiCNP
ρ
GS
Specimen
vol% addition (g/cm3) (µm)
PM-0SiC
0.0
2.03
2.4
PM-0.5SiC
0.5
2.02
2.0
PM-1SiC
1.0
2.02
2.0
PM-1.5SiC
1.5
2.01
2.1
PM-2SiC
2.0
2.06
1.3
PM-3SiC
3.0
2.04
3.9
PM-4SiC
4.0
2.02
3.6
VM-0SiC-1
0.0
2.00
0.6
VM-0SiC-2
0.0
1.93
0.4
VM-0.5SiC
0.5
2.01
0.6
VM-1SiC
1.0
2.03
0.7
VM-1.5SiC
1.5
2.03
0.8
VM-2SiC
2.0
2.03
0.6

115

Figure 5.3. For Mg2Si fracture surfaces, transgranular fracture dominate in all specimens.
The PM specimens (a-c) with varying amounts of SiCNP addition did not show any
appreciable difference in grain size, although changing to VM processing significantly
reduced the grain size (d). Note the difference in scale between the PM images (a-c) and
the VM image (d).

116

because of the presence of MgO within the material. The starting material as received
from the vendor has been shown to contain approximately 8 vol% of MgO, and likely to
have a composite theoretical density near 2.12 g/cm3 [Schmidt 2012] (see section 5.3.2).
Previous examination of the SiCNP material has shown that the as-received
nanopowder from two vendors (Alfa Aesar and Nanostructured & Amorphous Materials
Inc.) consists primarily of particles, approximately 50 nm in diameter, agglomerated into
clusters of 100 nm to 20 µm in diameter [Schmidt 2013b]. These agglomerates do not
appreciably break apart with milling [Schmidt 2013b]. In this study, the SiCNP material
was from one of the two previously examined vendors (Alfa Aesar).
5.3.2 Elasticity results
The elasticity for specimens with SiCNP, excluding the outlier specimen VM0SiC-02 with density of 1.93 g/cm3, is not a function of SiCNP addition up to 4 vol%, nor
powder processing methodology (Figure 5.4, Table 5.4). Average Young’s modulus, E,
for the PM specimens with 0 to 4 vol% SiCNP is 113.3 ± 4.0 GPa, and 111.1 ± 2.3 GPa
for VM specimens (Figure 5.4a – b). The small variations in elastic moduli observed are
not observed to be a function of the SiCNP addition (Figure 5.4), rather a function of the
limited differences in porosity among specimens (Figure 5.5).
5.3.2.1 Elasticity and SiCNP addition
If the SiCNP addition does not react with the Mg2Si matrix, the elastic modulus of
the composite material with addition of up to 4 vol% SiCNP may be modeled as a mixture
of two independent materials.

In a study of SnTe with 0 vol% to 4 vol% SiCNP addition

[Schmidt 2013b], the Hashin model [Hashin 1962; Bedolla 2012; Couturier 1997]
117

110
3

Density (g/cm )
2.070

100

2.050
2.030
2.010

90

2.000

0

2

Young's modulus (GPa)

Young's modulus (GPa)

120 (a) Planetary milled

120 (b) Vibratory milled

110
3

Density (g/cm )
2.070

100

2.050
2.030
2.010

90

2.000

4

0

Vol. % SiCNP

55 (d) Vibratory milled

3

Density (g/cm )
2.070

40

2.040
2.020

35

2.010
2.000

30
2

Shear modulus (GPa)

Shear modulus (GPa)

50

0

4

Vol. % SiCNP

55 (c) Planetary milled

45

2

4

50
45

3

Density (g/cm )
2.070

40

2.050
2.030

35

2.010
2.000

30
0

2

4

Vol. % SiCNP
Vol. % SiCNP
Figure 5.4. The Young’s modulus (a, b) and shear modulus (c, d) of Mg2Si varied
primarily due to small variations in density. The variation in vol. % SiCNP did not
significantly affect the moduli, regardless of if the specimens were planetary milled (a, c)
or vibratory milled (b, d).

Young's Modulus (GPa)

140

PM specimens
VM specimens

130
120
110
100
90
0.00

0.02

0.04

0.06

0.08

0.10

Porosity (Vol. Fraction)
Figure 5.5. The Young’s modulus, E, decreases linearly with porosity for the set of 13
specimens in this study.

118

Table 5.4. The Young’s modulus, E, shear modulus, G, and density, ρ, for the specimens
in this study, as compared to the range of E, G and ρ in a previous study on three Mg2Si
specimens produced by the same vendor.
Specimen
E (MPa)
G (MPa)
ρ (g/cm3) Reference
PM-0SiC
113.6 ± 0.3 48.3 ± 0.1
2.03
This study
PM-0.5SiC
112.9 ± 0.3 47.5 ± 0.1
2.02
This study
PM-1SiC
111.2 ± 0.3 46.1 ± 0.1
2.02
This study
PM-1.5SiC
105.8 ± 0.4 43.3 ± 0.1
2.01
This study
PM-2SiC
118.1 ± 0.2 50.3 ± 0.1
2.06
This study
PM-3SiC
116.7 ± 0.2 49.7 ± 0.1
2.04
This study
PM-4SiC
114.5 ± 0.6 49.7 ± 0.2
2.02
This study
VM-0SiC-1 110.4 ± 0.2 46.9 ± 0.1
2.00
This study
VM-0SiC-2 90.4 ± 0.3
37.3 ± 0.1
1.93
This study
VM-0.5SiC 107.6 ± 0.4 44.7 ± 0.1
2.01
This study
VM-1SiC
113.4 ± 0.2 48.3 ± 0.1
2.03
This study
VM-1.5SiC 113.0 ± 0.2 48.1 ± 0.1
2.03
This study
VM-2SiC
111.3 ± 0.3 47.5 ± 0.1
2.03
This study
Mg2Si
116.9 –
48.92 – 50.09 2.07 –
[Schmidt 2012]
117.7
2.09

119

described relatively well the resulting change in Young’s modulus where the Hashin
model can be written as

 E V  Er Vr  1

EC  Em  m m
 ErVm  Em Vr  1

(4)

where EC is the Young’s modulus of the composite, Em is the Young’s modulus of the
matrix material, Er is the Young’s modulus of the reinforcing phase, and Vm and Vr are
the volume fraction of the matrix and the reinforcing phase, respectively. Applying the
Hashin model (equation (4)) to the materials in this study, using the Young’s modulus of
the reinforcing phase SiCNP, Er, at 450 GPa [Schreiber 1966; Carnahan 1968] and the Em
of 112 GPa the Mg2Si measured in this study, the EC for the composite with the
maximum 4 vol% SiCNP is 117.5 GPa, which is similar to the measured E of 114.5 ± 0.6
GPa from specimen PM-4SiC (Figure 5.4a).
5.3.2.2 Elasticity and porosity
Small variations in density of the specimens in this study, from 2.00 to 2.06
g/cm3, is likely the dominant source of variation in E measured in this study (Figure 5.4a
– b, Figure 5.5). Typically, for small variations in porosity, P, the change in E with
porosity may be modeled by the empirical equation,
E  E0 1  bE P 

(5)

where E0 is the Young’s modulus of a fully dense material and bE is a materialdependent constant, typically between 2 and 6 for a wide range of materials [Rice 1998].
For TE materials YbAl3 [Schmidt 2013a] and lead-antimony-silver-tellurium (LAST) [Ni
2009], the experimentally determined values of bE were 2.34 and 3.5, respectively .
Assuming the matrix material contains 8% MgO [Schmidt 2012] (density 3.58 g/cm3
120

[Anderson 1966; Bogardus 1965]) and 92% Mg2Si (density 2.00 g/cm3 [Whitten 1965]),
the composite theoretical densities (matrix density, 2.126 g/cm3, SiCNP density, 3.16
g/cm3 [Aesar]) were calculated. The volume fraction porosity, P, was calculated for the
composite materials. The E versus P for the full set of 13 composite specimens in this
study were fit to equation (5), with the bE was 3.5 ± 0.5 and the E0 was 138 ± 5 GPa
(Figure 5.5). The linear relationship indicates that the E for the 14 specimens is a
function of P. The error on the E0 and bE are relatively large because of the restricted
range of P for the specimens this study.
A previous study on Mg2Si from lump material purchased from the same vendor
and processed by PM measured E of 116.9 GPa to 117.7 GPa [Schmidt 2012] (Table
5.4). The small (~4%) difference in elastic moduli between this study and the previous
study is likely due to the slightly higher density specimens in the previous study, 2.07
g/cm3 to 2.09 g/cm3 (Table 5.4).
5.3.3 Hardness and Toughness Results
Hardness, H, by Vickers indentation for specimens with SiCNP, excluding one
outlier, was relatively insensitive to vol% SiCNP, from 0 % to 4 vol% SiCNP, indentation
load, from 1.96 N to 4.9 N, or powder processing technique, averaging 4.76 ± 0.37 GPa
for the PM specimens (Figure 5.6a) and 4.83 ± 0.15 GPa for the VM specimens (Figure
5.6b). The outlier is specimen VM-0SiC-02 with a density of 1.93 g/cm3, lower than the
2.00 g/cm3 to 2.06 g/cm3 density of the other 12 specimens in this study. The H of the
outlier VM-0SiC-02 specimen is indicated by the open symbol in Figure 5.6b.
The fracture toughness, KC, is dependent on the powder processing conditions.
The KC of the PM composite reached a maximum at 1 vol% SiCNP, an increase of about
121

(a)

1.96 N load
2.94 N load
4.9 N load

7

Hardness (GPa)

6
5
4
3
2

1/2

1.5

(c)

Planetary milled

1.96 N load
2.94 N load
4.9 N load

1.2
0.9
0.6
0.3
0.0
0

2

Vol. % SiCNP

4

Vibratory milled

1.96 N load
2.94 N load
4.9 N load

5
4
3

4

Vol. % SiCNP

(b)

6

0

2

4

Vol. % SiCNP

1/2

0

Fracture Toughness (MPa m )

Planetary milled

Fracture Toughness (MPa m )

Hardness (GPa)

7

1.5

(d)

Vibratory milled

1.96 N load
2.94 N load
4.9 N load

1.2
0.9
0.6
0.3
0.0
0

2

4

Vol. % SiCNP

Figure 5.6. The hardness, (a) and (b) is not a function of the milling procedure or the
vol% SiCNP, but less scatter was observed in the (b) vibratory milled specimens than the
(a) planetary ball milled specimens. The fracture toughness exhibited a maximum at 1
vol% SiCNP for the (c) planetary ball milled specimens, but the fracture toughness is not a
function of vol% SiCNP for the (d) vibratory milled specimens. Open symbols in (b) and
(d) indicate a specimen with lower density of 1.93 g/cm3, relative to the 2.00 to 2.06
g/cm3 for all other specimens in this study.

122

33% over the unreinforced PM material, and is relatively insensitive to SiCNP addition
between 1 vol% and 2 vol% SiCNP addition (Figure 5.6c). In contrast, the VM composite
material was relatively insensitive to any additions of up to 2 vol% SiCNP (Figure 5.6d).
The VM material also exhibited a much smaller variation in measured KC, with the
coefficient of variation, CV, averaging 0.08 and ranging from 0.04 to 0.14 (Figure 5.6d).
The CV of the PM material averages 0.16 and ranging from 0.11 to 0.34.
The smaller CV observed in the VM specimens relative to the PM specimens may
be related to the smaller GS of the VM specimens, leading to a more uniform crack
length and possibly more uniform distribution of bridging and stalling. The smaller CV is
particularly important when considering the distribution of strength, and the related
probability of failure at a given load. The strength of the material that may be used safely
in a design depends upon the scatter in strength [Wachtman 2009], and the smaller CV for
the strength values in the VM specimens indicates a smaller scatter of strength for VM
specimens than PM specimens.
In this study, KC is not a function of GS for the Mg2Si with no SiCNP addition
(Figure 5.6c – d). This result is expected for cubic materials such as Mg2Si, because KC
is largely independent of GS [Wachtman 2009], and specifically for Vickers indentation
crack length, “there should be a rather weak dependence of crack length on GS”
[Wachtman 2009, pg 217].
However, the effect of SiCNP addition on KC was influenced by the powder
processing technique. The difference in size between the added SiCNP particles and the
Mg2Si matrix may play a role in the behavior of KC. In a study on fracture toughness on
TE material specimens sintered from a blend of nanoparticles with microparticles of the
123

Figure 5.7. Crack bridging, in PM Mg2Si was commonly observed in radial cracks for
all the Mg2Si specimens in this study.

124

Figure 5.8. Crack bridges were commonly observed in VM specimens regardless of
SiCNP addition. Crack bridging in radial cracks was not eliminated by reducing grain size
through VM processing. Spotting is from oil residue on the surface of the specimen.

125

same composition, Co4Sb11.5Te0.5, the KC increased with additions of nanoparticles [Duan
2014]. Similar to the KC of Co4Sb11.5Te0.5 [Duan 2014], this study indicates that the
toughening due to addition of SiCNP may depend on GS of the matrix Mg2Si relative to
the SiCNP.
5.3.3.1 Crack bridging and toughness
Crack bridging and stalling was observed on all of the different Mg2Si specimens,
both with and without additions and regardless of processing by PM (Figure 5.7) or VM
(Figure 5.8). Both bridging and stalling are extrinsic toughening mechanisms, and not
beneficial to KC in a fatigue loading condition such as thermal cycling [Lathabai 1991;
Ritchie 1999]. In some cases, these may be controlled for through processing. Bridging
in monophase alumina material was eliminated by reducing the GS [Lathabai 1991],
although changing the powder processing of the Mg2Si in this study did not produce a
similar result.
5.4 Conclusions
Fracture toughness, KC, of Mg2Si increases for PM material by 33% with the
addition of 1 – 2 vol% SiCNP, but KC is independent of SiCNP addition for VM material.
As is typical of cubic materials such as Mg2Si, KC is independent of GS for specimens
with no addition of SiCNP. The coefficient of variation for the KC of the VM samples was
smaller, 0.08, than for the PM samples, 0.16, indicating a likely smaller scatter of
specimen strength for VM specimens than the PM specimens.
ACKNOWLEDGEMENTS
The authors acknowledge the financial support of the Department of Energy,
Revolutionary Materials for Solid State Energy Conversion Center, an Energy Frontiers
126

Research Center funded by the U.S. Department of Energy, Office of Science, Office of
Basic Energy Sciences under award number DE-SC0001054.

127

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128

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132

6 Influence of silver nanoparticle addition, porosity and processing technique on
the mechanical properties of Ba0.3Co4Sb12 skutterudites
Robert D. Schmidt1, Eldon D. Case1, Zayra Lobo1, Travis R. Thompson1, Jeffrey S.
Sakamoto1, Xiao-Yuan Zhou2, Ctirad Uher2
1
Chemical Engineering and Materials Science Department,
Michigan State University, East Lansing, MI, 48824
2
Physics Department, University of Michigan, Ann Arbor, MI, 48109
Published in: Journal of Materials Science (2014) DOI:10.1007/s10853-014-8427-5.
Abstract
The thermoelectric skutterudite Ba0.3Co4Sb12 is a promising candidate for waste
heat recovery applications. Recently, it was demonstrated that the addition of silver
nanoparticles (AgNP) to Ba0.3Co4Sb12 increases both the thermoelectric figure of merit and
electrical conductivity. This study is the first to examine the effect of AgNP addition on
the material’s mechanical properties. This study also found that the Young’s modulus, E,
shear modulus, G, and bulk modulus, B decreased linearly with increasing volume
fraction porosity, P. Resonant ultrasound spectroscopy (RUS) was employed to measure
the elastic moduli and Vickers indentation was used to determine the hardness, H, and
fracture toughness, KC. Trends in the mechanical properties as a function of grain size,
porosity and the AgNP are discussed in terms of the pertinent literature. While KC was
independent of AgNP addition, porosity and grain size, both E and H decreased linearly
with increasing porosity. In addition, this study is the first to identify (i) the Ag3Sb phase
formed and (ii) the enhanced densification that occurs when the AgNP is sintered with
Ba0.3Co4Sb12 powders, where both effects are consistent with the eutectic and peritectic
reactions observed in the binary phase diagram Ag-Sb. These eutectic/peritectic
133

reactions may also be linked to the enhancement of electrical conductivity previously
observed when Ag is added to Ba0.3Co4Sb12. Also, similar beneficial eutectic/peritectic
reactions may be available for other systems where conductive particles are added to
other antimonides or other thermoelectric systems.

Keywords: thermoelectric; skutterudite, porosity, elastic modulus, peritectic reaction
6.1 Introduction
The conversion of waste heat to electrical energy by thermoelectric (TE) materials
is typically characterized by the material’s figure of merit, ZT, such that
(1)
where S is the Seebeck coefficient, σ is the electrical conductivity, κ is the thermal
conductivity, and T is temperature [Ioffe 1960]. ZT values of up to 1.7 [Shi 2011] have
been reported for bulk skutterudite TE materials.
In-service conditions subject thermoelectric materials to stresses from thermal
gradients, thermal transients, thermal expansion mismatch, and applied external stresses.
Due to these challenges, the mechanical properties of thermoelectric materials are
important, especially in waste heat harvesting applications. The response of a material to
imposed stresses requires knowledge of the elastic properties; for example the Young’s
modulus and Poisson’s ratio are needed in order to construct the stiffness matrix for finite
element analysis [Segerland 1984; Hutton 2004; Zienkiewicz 2005]. Also, the fracture
toughness, KC, which measures the resistance to crack growth [Wachtman 2009], is

134

important to the mechanical integrity. In addition, hardness is related to wear
characteristics of the material [Ren 2008].
A key motivation for this study is the recent work on Ba0.3Co4Sb12 by Zhou et al.
[Zhou 2012] which showed the addition of 0.5 wt% silver nanoparticles (AgNP) lead to a
30% increase in ZT, which was attributed primarily to an increase in electrical
conductivity. Also, while carrier concentrations remain unchanged, a modest increase in
the Seebeck coefficient also was observed with the added AgNP [Zhou 2012].
In general, the nanostructural and microstructural details can be extremely
important for the transport properties of thermoelectric materials, and many previous
studies have used nanostructures to reduce thermal conductivity by enhancing phonon
scattering [Androulakis 2007; Zhao 2012; Zhou 2008; Alleno 2009; Ji 2007; Toprak
2004; Mi 2008], which can lead, in turn, to increases in ZT. Also, reducing the grain size
or increasing porosity can enhance phonon scattering and thus increase ZT [Yoon 2013;
Tokiai 1997].
Although in this study, an increased porosity leads to decreases in the elastic
moduli, an increase in porosity also has the potential to increase the resistance to thermal
fatigue damage [Case 2012b; Case 2012a], which is important due to the inevitable
thermal cycling that thermoelectrics are subjected to during waste heat harvesting. In
addition to affecting mechanical properties, porosity also impacts transport properties. In
thermoelectrics such as nanoporous GeSi alloys [Lee 2010], porosity decreases both the
electrical and thermal conductivity, although the decrease in electrical conductivity
overwhelms the decrease in thermal conductivity, resulting in a net lowering of ZT due to
porosity. However, in skutterudites including La0.75Fe3CoSb12 [Yang 2004],
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Co0.9Ni0.1Sb3 , Co0.8Ni0.2Sb3 [He 2008] and a TiN nanoparticles-Co4Sb11.5Te0.5 composite
[Wen 2013], enhancements in ZT have been reported for porosity levels between P =
0.003 and 0.15. For example, Wen et al. [Wen 2013] densified a 0.01 volume fraction
TiN nanoparticles -Co4Sb11.5Te0.5 skutterudite and subsequent thermal annealing at 773 K
for 120 hours in vacuum led to bloating (the formation of internal porosity) and a 10
percent increase in porosity which Wen et al. ascribed to a reaction between the TiN
nanoparticles and the Co4Sb11.5Te0.5 matrix phases. Wen et al. noted that “The electrical
conductivity and the thermal conductivity of the annealed sample decline simultaneously
due to the higher porosity, but the thermal conductivity reduces more remarkably”,
leading to a 20 percent increase in ZT compared to the denser specimens (prior to
annealing and bloating) [Wen 2013]. Thus, in addition to having the potential to boost
thermal fatigue resistance, in some skutterudites porosity can increase ZT making it
important to also assess the mechanical properties such as elastic moduli, hardness and
toughness for porous thermoelectrics.
In this study, we examine the Young’s modulus, E, shear modulus, G, bulk
modulus, B, Poisson’s ratio, , hardness, H, and fracture toughness, KC, of Ba0.3Co4Sb12
with and without the addition 0.5 wt% AgNP. We further explore the effects of
microstructure/nanostructure and processing pursuing two processing routes: (i) planetary
milling (PM), then hot press (HP) sintering and (ii) vibratory milling (VM) followed by
pulsed electric current sintering (PECS). In this way, we produced specimens with a
range of porosity and grain size while using the two most common milling techniques
(planetary milling and vibratory milling) and densification techniques (HP and PECS)
used to process thermoelectric materials.
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6.2 Experimental procedure
6.2.1 Materials and Specimen Preparation
To fabricate Ba0.3Co4Sb12, elemental Ba (pieces, 99.9% pure), Co (powder 99.5%
pure), and Sb (shot 99.999% pure) in stoichiometric ratio were placed inside evacuated
carbon coated quartz ampoules, heated to 1100°C and held at that temperature 5 hours,
then quenched into a supersaturated salt water solution. The resulting ingots were then
annealed at 750°C for 7 days. Finally, the ingots were planetary ball milled.
In this study, two different processing techniques were used to fabricate two sets
of specimens with differing microstructures. First, AgNP powders, which had a vendor
specified purity of 99.9% and a size range of from 20 nm to 40 nm (45509, Alfa Aesar,
Ward Hill MA), were dispersed into the Ba0.3Co4Sb12 powder by planetary ball milling at
300 rpm for 15 min [Pilchak 2007]. Then specimens approximately 10.5 mm in diameter
and 10 mm in height were fabricated by hot pressing Ba0.3Co4Sb12 powders (with and
without the added AgNP) in a graphite die for 20 minutes in an argon atmosphere with 50
MPa pressure at temperatures of 673 K, 773 K or 873 K in order to produce specimens
with a range of volume fraction porosity, P, from 0.30 to 0.05 (Table 6.1). The hot
pressed specimens were then cut into discs approximately 1.7 mm thick using a slow
speed saw (Isomet, Buehler, Lake Bluff IL) with 0.3 mm thick diamond blade (801-137,
Leco Corp., St. Joseph, MI).
A second set of specimens was fabricated by reprocessing the specimens hot
pressed without AgNP additions by first grinding the hot pressed specimens without Ag
addition in an automated mortar and pestle (PM100, Retch) and then sieving with a 75
µm sieve, where the grinding and sieving steps were performed in an argon-filled glove
137

box containing less than 10 ppm oxygen. Using Viton gaskets (WC mill jar set 8004,
WC media 5004A, Viton gasket 39322, SPEX Sample Prep, Metuchen, NJ) the resulting
7.1 g ground powder batches were sealed in a WC mill jar with a total of six spherical
WC milling media (two WC spheres 11.2 mm in diameter and four WC spheres 7.9 mm
in diameter). In order to perform vibratory milling outside the glove box, prior to
removing the mill jar from the glove box, the mill jar and end cap were wrapped with
electrical tape (Super 88, 3m, St. Paul, MN) and Parafilm “M” (PM-996 Pechiney Plastic
Packaging, Menasha WI). The powders were milled for 10 minutes in a vibratory mill
(8000M SPEX SamplePrep) then the mill jar was returned to the glove box. The reading
of the oxygen meter on the glove box did not change when the mill jar was opened in the
glove box. The oxygen meter is sensitive to changes within ± 0.1 ppm, implying that the
sealing of the mill jar was effective. The vibratory milled powder then was sintered in an
argon atmosphere by PECS (SPS Model 10-3, Thermal Technology LLC, Santa Rosa,
CA) in a grafoil-lined graphite die at 673 K, 723 K or 773 K for 10 minutes with 50 MPa
pressure (Table 6.1), producing disk-shaped specimens approximately 12.6 mm in
diameter and 2.6 mm thick.
6.2.2 Elasticity Measurements
Resonant ultrasound spectroscopy (RUS) elasticity measurements were performed
using a tripod arrangement of piezoelectric transducers. A driving transducer which was
swept through a range of frequency from 35 kHz to 485 kHz excited mechanical
resonances in the specimen which were detected via the two pickup transducers. The
peaks in the intensity versus frequency output of the pickup transducers (Figure 6.1)

138

Table 6.1. Specimens of skutterudite Ba0.3Co4Sb12 used in this study varied based on
AgNP addition, sintering procedure and temperature, resulting porosity, and powder
processing. Specimens VM-PECS-673, VM-PECS-723 and VM-PECS-773 were
reprocessed from specimens PM-HP-673, PM-HP-773 and PM-HP-873 by grinding and
powder processing by vibratory milling, and sintering by PECS.
Specimen

AgNP
Powder
addition processing

Sintering
procedure

Sintering
temperature

PM-HP-673

No

HP

673K

Vol.
fraction
porosity
0.30

773K
873K
673K
773K
873K
673K
723K
773K

0.21
0.16
0.27
0.18
0.05
0.16
0.13
0.09

PM

PM-HP-773
No
PM
HP
PM-HP-873
No
PM
HP
PM-HP-673-Ag Yes
PM
HP
PM-HP-773-Ag Yes
PM
HP
PM-HP-873-Ag Yes
PM
HP
VM-PECS-673 No
VM
PECS
VM-PECS-723 No
VM
PECS
VM-PECS-773 No
VM
PECS
PM: Planetary milling, VM: Vibratory milling,
HP: Hot pressed, PECS: Pulsed electric current sintering

Intensity (a.u.)

45

30

15

0
0

200

400

600

Frequency (KHz)
Figure 6.1. RUS spectrum from specimen PM-HP-873-Ag, P = 0.05 with AgNP. The
elastic moduli of each of the specimens in this study are calculated from the specimen
mass, dimensions, shape, and resonant frequencies. Each peak in the spectrum represents
a mechanical resonance at that frequency

139

represent the mechanical resonance frequencies of the specimen. From the resonant
frequencies, specimen mass, dimensions and geometry, the elastic moduli of the disk
spaced specimens were calculated using commercial software (RUSpec and CylModel,
Quasar International, Inc., Albuquerque, NM). Additional details of the RUS procedure
are provided elsewhere [Ren 2009; Ni 2010; Schmidt 2010; Migliori 1997; Schmidt
2013].
6.2.3 Hardness and toughness measurements
Prior to indentation measurements of H and KC, and prior to energy-dispersive Xray spectroscopy measurements, the specimens were polished with diamond paste with
grit sizes ranging from 30 µm to 1 µm. At least ten indentations per load for loads of
1.96 N, 2.94 N, 4.9 N and 9.8 N were made on the polished surface of each specimen,
with a loading time of 5 seconds for each indentation. Prior to the hardness
measurements, the Vickers indenter was calibrated using a steel standard calibration
block (Yamamoto Scientific Tools Lab Co. LTD, Chiba, Japan). The hardness
calibration factor, ζranged from 0.95 to 0.97 for the indentation loads used in this study.
The hardness, H, for indentation was calculated from [Lawn 2012]
H=

1.8544 F

(2)

( 2 a )2

where F is the applied indentation load and a is half of the diagonal length of the
indentation impression.
The fracture toughness, KC, was calculated from

KC 

 ( E / H ) 0.5 F

(3)

c3/ 2
140

where ξ is a dimensionless calibration constant equal to 0.016 [Wachtman 2009], E is the
Young’s modulus measured by RUS, H is the hardness value and c is half of the radial
crack length and F is the applied load [Wachtman 2009] .
6.2.4 Energy-dispersive X-ray spectroscopy and microscopy
Except for specimen PM-HP-673-Ag, each of the sintered specimens was first
polished and then examined by energy-dispersive X-ray spectroscopy (EDS). However,
polishing was unsuccessful for PM-HP-673-Ag, so the examined surfaces were those cut
by a low speed diamond saw.
The microstructure and nanostructure of the powders and sintered specimens was
observed by scanning electron microscope (SEM, JEOL 6610LV or JSM-7500F, JEOL
Ltd., Japan) at a 15 kV accelerating voltage and either a 15 mm or 8 mm working
distance. Using SEM micrographs of the fracture surfaces of sintered specimens, the
grain size of sintered specimens was determined using the linear intercept method with at
least 200 intercepts per micrograph and a stereographic projection factor of 1.5
[Underwood 1969; Case 1981]. The microstructure of the polished specimen surfaces
was observed using the secondary electron image (SEI) mode. Atomic number contrast
was observed in the backscattered electron image (BEI) mode. Compositions were
determined in the BEI mode using EDS. For SEM observation, all specimens were
mounted on aluminum stubs, where the silver nanoparticles were adhered to the stubs
using carbon paint (05006-AB, SPI Supplies, West Chester, PA) and the sintered
specimens were mounted using carbon tape.

141

Figure 6.2. Silver nanoparticles exhibited agglomerates of 10 µm or greater (a-c), but
consisting of individual grains or particles consistent with the manufacturer claimed
average particle size of 20-40 nm (d)

142

Figure 6.3. Polished surfaces of specimen PM-HP-873-Ag, both in secondary electron
images (a) and backscatter images (b). Porosity is observed between larger grains (a and
b), but also with areas of Ag visible in backscatter as bright areas (b), due to the higher
average atomic weight of the silver rich regions. The abundance of Ag and the relative
deficiency of Co or Sb in the bright areas of the backscatter image (b) is confirmed by
energy-dispersive x-ray spectroscopy maps (c-e)

143

Counts per Second

300

(b)

Sb
Co
Ag

PM-HP-673-Ag
Ag

200

Sb
100

Co
0

0

10

20

30

Counts per Second

Distance (µm)
Sb
Co
Ag

(d) PM-HP-773-Ag
600

Ag

Sb

400

200

Co
0

0

1

2

3

4

Distance (µm)
Sb
Co
Ag

Counts per Second

(f) PM-HP-873-Ag
600

Ag
Sb

400

200

Co
0

0

1

2

3

4

5

Distance (µm)
Figure 6.4. For each of the hot pressed specimens with AgNP additions, an EDS line scan
was performed and point ID locations were chosen. For PM-HP-673-Ag, a cut surface
was used (a) because the specimen was not successfully polished. For PM-HP-773-Ag
and PM-HP-873-Ag, polished surfaces were examined (c and e). The line scan for PMHP-673-Ag (b) indicated only silver present except for two regions in the silver where
antimony and cobalt were present in concentrations consistent with skutterudite particles.
In contrast, the line scan for PM-HP-773-Ag (d) and PM-HP-873-Ag (f) indicated the
presence of antimony in the silver-rich locations. No silver was observed in the matrix
outside of the silver-rich locations

144

Figure 6.5. The microstructure of Ba0.3Co4Sb12, without Ag addition, changed as a
function of sintering temperature. For (a) a sintering temperature of 673 K,
microstructure and porosity, P, are consistent with a specimen with little to no observed
sintering or densification. After sintering at 773 K (b), only minimal densification and
neck formation are observed. Hot pressing at 873 K (c) enhanced both grain growth and
densification in the specimen without Ag nanoparticles, however, the microstructure still
is observed to be very porous, consistent with measurement of P = 0.16

145

Figure 6.6. The microstructure of Ba0.3Co4Sb12 with 0.5 wt% AgNP addition changed as a
function of sintering temperature. At 673 K (a), little to no sintering is observed in the
microstructure. Hot pressing at 773 K (b) resulted in limited grain growth and
densification, with necks observed between the grains but significant porosity observed,
consistent with early stage sintering. The porosity for the specimen with Ag
nanoparticles sintered at 873 K (c) is the lowest (P = 0.03) of all the specimens in this
study

146

Figure 6.7. Fracture surface images of reprocessed material sintered by PECS exhibit
dense regions surrounded by regions of higher porosity. All regions of the specimens
exhibit similar grain sizes. The porous areas decrease as the sintering temperature
increased from (a) 673 K, to (b) 723 K, to 773 K

147

Figure 6.8. After reprocessing by SPEX milling and sintering by PECS, the samples
exhibit a unimodal, sub-micron grain size distribution.

148

6.3 Results and Discussion
6.3.1 Microstructural and chemical analysis
The addition of AgNP resulted in a greater change in density at the higher sintering
temperature than the specimen without AgNP addition (Table 6.1). When HP sintered at
673 K, the porosity was nearly identical for the specimen without (P = 0.30) and with
AgNP (P = 0.27), but when sintered at 873 K, the specimen without AgNP addition (P =
0.16) was significantly less dense than the specimen with AgNP addition (P = 0.05). The
density difference for specimens sintered at the same temperature requires a close
examination of the microstructural features of the AgNP addition, examined in two parts.
The microstructural and nanostructural features examined in this study included:
(i) the as-received AgNP powders (Figure 6.2), and for the sintered Ba0.3Co4Sb12
specimens the micron-sized Ag inclusions (Figures 6.3 and 6.4) in section 6.3.1.1, and
(ii) porosity (Figures 6.5 – 6.7) as well as grain size and size distribution (Figure 6.5 –
6.8) in section 6.3.1.2.
6.3.1.1 Microstructure of the AgNP and Ag agglomerates
The as-received AgNP powders consisted of (i) large, irregularly-shaped
agglomerates up to 30 µm across, with most agglomerates being between 0.5 µm and 10
µm in diameter, (ii) individual spherical nanoparticles with diameters 30 nm (Figure
6.2d) and (iii) small clusters of nanoparticles (Figure 6.2). Similar agglomerates, small
clusters and individual AgNP are visible in micrographs taken by Zhou (Figure 2a of Zhou
2012]) of AgNP powders received from the same vendor as in this study.
After hot pressing at 673 K, 773 K and 873 K, the consolidated, micron-size Ag
particles observed in the Ba0.3Co4Sb12 specimens with 0.5 wt% AgNP (Figures 6.3 and
149

6.4) had roughly the same dimensions as the original AgNP agglomerates present in the
as-received AgNP powders (Figure 6.2). In the sintered specimens, the typical dimension
of Ag particles observed in PM-HP-773-Ag and PM-HP-873-Ag was between 0.3 µm
and 10 µm, with a few Ag particles of 20 µm diameter or greater, as observed by
backscatter electron images of polished surfaces (Figures 6.3 and 6.4). Thus the AgNP
agglomerates may not have broken up significantly during mixing in the planetary mill
prior to hot pressing.
As a rough gauge of how easily the AgNP agglomerates can be broken apart by
milling, 0.0225g of AgNP was wet milled by hand for 60 sec in a porcelain mortar and
pestle (60310 and 60311, CoorsTek, Golden, CO) with 5 mL of ethanol. After milling,
the AgNP agglomerates were still present but some surfaces of the agglomerate surfaces
appeared to be deformed by the hand milling and some of the nanoparticles on the
deformed surfaces of the agglomerates appeared to be smeared (Figure 6.9). After hand
milling, the AgNP agglomerates typically ranged in diameter from sub-micron to 100 µm
(Figure 6.9), similar to or greater than the dimensions of AgNP agglomerates before
milling. Thus, based on both the SEM examination of the AgNP agglomerates before and
after hand milling, the hand milling process did not appear to significantly break up the
agglomerates.
While the hand milling conditions are likely different than those encountered
during the planetary milling, it is likely that some of the original AgNP agglomerates in
the as-received powders survived (at least partially intact) the mixing process with the
AgNP agglomerates powders to give the micron-sized consolidated Ag particles observed
in the as-sintered Ba-skuttterudite-AgNP specimens in this study. This is further
150

Figure 6.9. Hand milling of AgNP agglomerates in ethanol were not observed to reduce
the size of the nanoparticle agglomerates. After hand milling, silver nanoparticle
agglomerates of 10 µm or greater were typically observed, similar to the size of
agglomerates for the as received AgNP. Several faces of the agglomerates appear to be
deformed after hand milling

151

supported by the SEM-based observation that the size of the AgNP agglomerates in the
powders is similar to the size of the Ag particles in the sintered specimens. Thus, it does
not seem to be necessary to postulate an accretion of AgNP during milling to explain the
present of micron-sized Ag particles in the sintered specimens.
6.3.1.2 Porosity and grain size and relationship to the processing technique
The six hot pressed specimens included this study (Table 6.1) showed a bimodal
grain size distribution (Figures 6.5 and 6.6) consisting of a polycrystalline matrix with
grain sizes ranging from approximately 0.3 µm to 3 µm, with an average grain size (GS)
of roughly 1 µm. Also, grains approximately 5 µm to 20 µm across were observed in
each HP specimen, both without AgNP (Figure 6.5) and with AgNP (Figure 6.6) additions.
Pores with diameters of submicron to a few microns across were distributed through the
matrix, consisting of open, interconnected porosity when sintered at 673 K, and
consisting of partially to fully isolated porosity at 773 K and 873 K (Figures 6.5 and 6.6).
The observed pore morphologies for the specimens sintered at 673 K, 773 K and 873 K
agrees with the pore evolution in sintered powders [Barsoum 2003].
Each of the three reprocessed specimens (vibratory milled and then sintered via
PECS at 773 K, 723 K and 673 K) had a much different microstructure than those
obtained by planetary milling and hot pressing. Namely, the VM-PECS specimens a
unimodal GS distribution (Figure 6.8) with a significantly smaller average GS of 0.17
µm, 0.14 µm, and 0.15 µm, respectively, than the specimens that were planetary milled
and hot pressed. The reprocessed specimen VM-PECS-773 had a volume fraction
porosity of only 0.09, which included dense regions with clusters of pores (Figure 6.7c).
However, specimen VM-PECS-673 included clusters of pores with islands of denser
152

material (Table 6.1, Figures 6.7a). The microstructure of specimen VM-PECS-723 was
intermediate in between specimens VM-PECS-773 and VM-PECS-673 (Table 6.1,
Figures 6.7b).
The addition of AgNP results in an increased density of hot pressed specimens at a
sintering temperature of 873 K, where the specimen without AgNP had a P value of 0.16
while the specimen sintered with 0.5 wt% AgNP had P = 0.05 (Table 6.1). At a hot press
sintering temperature of 773 K, the porosities of the specimens with and without 0.5 wt%
AgNP were 0.18 and 0.21, respectively (Table 6.1). Also, for a sintering temperature of
673 K, the porosities of the specimens with and without 0.5 wt% AgNP were 0.27 and
0.30, respectively (Table 6.1). Thus, hot press sintering at 773 K and 673 K resulted in
similar porosities for specimens with and without 0.5 wt% AgNP additions. However, the
AgNP addition resulted in considerably enhanced densification for hot press sintering at
873 K. The enhanced sintering is likely related to a reaction between the 0.5 wt% AgNP
addition and the Ba0.3Co4Sb12 matrix, as discussed in section 6.3.2.
6.3.2 Chemical analysis
6.3.2.1 Chemistry of the AgNP and Ag agglomerates
EDS analysis showed the as-received AgNP powder to be 99.5 at% Ag, with
oxygen and Al impurities (Table 6.2). The Al in the EDS analysis likely originated from
the aluminum stub on which the specimens were mounted.
Polished surfaces of specimens PM-HP-873-Ag and PM-HP-773-Ag were
examined by EDS, with matrix region and Ag-rich regions in each specimen examined
separately at the points indicated in Figures 6.4c and 6.4e, and line scans extending

153

Table 6.2 Results of EDS scan using Point ID mode on two as-received AgNP
agglomerates.
Location Ag
Al
O
Ag:Al
label
AgNP-1
85.15
0.60
14.25
99.3:0.7
AgNP-2
99.5
0.5
Not
99.5:0.5
Detected

Table 6.3 Results of EDS scan using Point ID mode on specimen PM-HP-873-Ag.
Spacing between spots is approximately 5 to 10 µm (Figure 6.4e). Ag areas examined are
1-3 µm in diameter.
Location Ba
Co
Ag
Sb
O
label
Matrix
1.69
21.54
Not Detected 76.78
Not Detected
Ag-873-1 Not Detected 1.28
73.96
24.76
Not Detected
Ag-873-2 Not Detected Not Detected 76.78
23.22
Not Detected
Ag-873-3 Not Detected 1.37
71.82
22.54
6.78

Table 6.4 Results of EDS scan using Point ID mode on specimen PM-HP-773-Ag.
Spacing between spots is approximately 4 µm (Figure 6.4c). Ag area examined
approximately 1-3 µm in diameter.
Location Ba
Co
Ag
Sb
O
label
Matrix
2.14
23.96
Not Detected 73.89
Not Detected
Ag-773-1 Not Detected 2.49
70.01
27.50
Not Detected

Table 6.5 Results of EDS scan using Point ID mode on specimen PM-HP-673-Ag.
Spacing between spots is approximately 5 to 10 µm (Figure 6.4a). Ag area examined is
approximately 20 µm in diameter.
Location Ba
Co
Ag
Sb
O
label
Matrix
1.44
21.01
Not Detected 77.56
Not Detected
Ag-673-1 Not Detected 6.80
72.21
20.99
Not Detected
Ag-673-2 Not Detected Not Detected 92.99
7.01
Not Detected
Ag-673-3 Not Detected Not Detected 94.21
5.79
Not Detected

154

across both matrix material and Ag-rich regions (Figure 6.4c – 6.4f). As determined by
EDS, the elemental composition of the matrix region is consistent with Ba0.3Co4Sb12
(Tables 6.3 and 6.4, Figure 6.4c – 6.4f). In the Ag-rich regions, the composition is
consistent with primarily Ag3Sb phase material. In specimen PM-HP-873-Ag, the Ag:Sb
ratio was 3.0:1 to 3.3:1 in the silver-rich regions (Table 6.3, Figure 6.4e), and in
specimen PM-HP-773-Ag, the ratio was 2.5:1 (Table 6.4, Figure 6.4c). Less than 2 at%
Co was detected in each of the silver-rich regions, consistent with little to no skutterudite
phase present in the silver-rich regions.
In contrast to the preparation of specimens PM-HP-873-Ag and PM-HP-773-Ag,
specimen PM-HP-673-Ag was cut on a low speed diamond saw because the high porosity
of the specimen (P = 0.27, Table 6.1) made it too friable for polishing. The elemental
composition of the matrix region is consistent with Ba0.3Co4Sb12 (Table 6.5, Figure 6.4a
and 6.4b). In the Ag-rich regions of PM-HP-673-Ag, the Ag:Sb ratio was highly
variable, with ratios of 3.4:1, 13.3:1 and 16.3:1 (Table 6.5), which is more indicative of a
mixture than a single phase. In the Ag-rich location with the highest concentration of Sb,
Ag-673-1, a significant concentration of Co was also detected, 6.80 at%, and in a Co:Sb
ratio of 1:3.1 (Table 6.5), consistent with a particle or particles of Ba0.3CoSb3 (matrix
material) embedded in otherwise pure Ag. Particles of Ba0.3CoSb3 may have become
embedded in the Ag-rich region during cutting. The presence of small, discrete
skutterudite particles embedded in the silver in specimen PM-HP-673-Ag is further
supported by the line scan (Figure 6.4b), in which there are two dips in the counts of
silver at distances of 5 µm and 10 µm, with corresponding increases of both Co and Sb
counts at each location. The EDS results from the other two Ag-rich locations, Ag-673-2
155

and Ag-673-3 (Table 6.5), are primarily pure Ag material, with no indication of
embedded Ba0.3CoSb3 particles.
6.3.2.2 Sintering behavior changes and scavenging of Sb
Although the Ba0.3Co4Sb12-Ag composition is within a quaternary Ba-Co-Sb-Ag
system for which no phase diagram is available, the Ag-Sb binary phase diagram may
provide important guidance to understanding the formation of Ag3Sb particles. In the
binary phase diagram for Ag-Sb, there are only two intermediate compounds, Ag3Sb and
Ag6Sb [Voronin 2013; Cipriani 1996; Feschotte 1992]. Upon cooling, Ag3Sb forms via a
peritectic reaction Ag6Sb + L  Ag3Sb at 835 + 2 K and an initial Sb concentration of
21.2 at% [Feschotte 1992]. Also, the eutectic reaction L  Ag3Sb + Sb occurs at 757 K
with a eutectic composition reported as 38 at% Sb [Voronin 2013; Okamoto 2007;
Hassam 2001] or 41 at% Sb [Okamoto 1993].
In the present research, the Sb that reacts with the AgNP may be scavenged from
the Ba0.3Co4Sb12 matrix. Scavenging of excess Sb can aid thermal stability in
skutterudites. For example, Zhang and Sakamoto found that the Sb deficient specimens
of Fe3.5Co0.5Sb12-based skutterudites were more dimensionally stable than specimens
with excess Sb [Zhang 2013].
The presence of a transient liquid phase is known to greatly enhance densification
during sintering [Barsoum 2003], thus the enhanced densification for the Ba-skutteruditeAgNP specimens observed in this study (section 3.1, Table 6.1) may be due to a transient
liquid phase during sintering associated with the peritectic and eutectic reactions in the
Ag-Sb system. Also, if the liquid phase wets the grain boundaries, the electrical
conductivity of the grain boundaries could be greatly enhanced, by a surface film rather
156

than only point contacts due to discrete AgNP or Ag particles, as was suggested by Zhao
et al. [Zhou 2012]. A similar binary and ternary eutectic in lead-free Sn-Ag-Cu solders
aids in wetting the surfaces of electrical wires, pins or pads [Bukat 2011; Dharma 2009].
6.3.2.3 Possible significance to other thermoelectric material systems
The proposed reaction of Ag with Sb in Ba-filled skutterudite Ba0.3Co4Sb12 has
important implications for other skutterudites, other antimonides and even other
thermoelectric systems. In this study the Ba-filled skutterudite is CoSb3-based, but more
generally unfilled skutterudites have the general composition TX3, where T is a transition
metal element (Co, Fe, Ni) and X is a pnicogen element (Sb, As, and P) [Yoshizawa
2004]. “Filler” atoms, often a rare earth element or mischmetal added to the skutterudite
composition, scatter phonons to make them an important class of thermoelectric materials
[Slack 1994; Morelli 1995; Nolas 1999; Nolas 2000; Uher 2001]. Many CoSb3-based and
FeSb3-based compositions have been studied in the literature [Zhang 2010], so in
addition to the particular Ba-filled skutterudite included in this study, adding AgNP to
other antimonide skutterudites may well lead to the same type of Ag-Sb reaction and thus
liquid phase sintering, the formation of Ag3Sb, enhanced densification and improvements
in the ZT and electrical conductivity. Also, for an antimonide thermoelectric that is not a
skutterudite, a recent study by [Xiong 2013] shows that Ag added to ZnSb leads to the
formation of Ag3Sb particles and a higher electrical conductivity.
This type of reaction may not be limited to Ag and antimonides. In fact, there
may be other conductive metal-thermoelectric material combinations in which similar
peritectic/eutectic reactions occur, accompanied by similar beneficial effects. One guide
to searching for such systems would be appropriate binary or ternary phase diagrams.
157

6.3.3 Elasticity results
The measured elastic moduli are essentially independent of the AgNP addition and
the processing/grain size, but are strong functions of porosity (Figure 6.10a-c).
6.3.3.1 Elasticity as a function of AgNP addition
In order to determine whether or not the elastic moduli are functions of the AgNP
addition, for the set of specimens (with and without AgNP addition) included in this study,
we examined the porosity dependence of Young’s modulus, shear modulus and bulk
modulus (Table 6.1, Figure 6.10). There are no significant differences between the slope
and intercept for the least squares fit to the data (i) with and (ii) without AgNP additions,
with coefficient of determination, R2, values of 0.955 to 0.998 for E and G, and R2 of
0.857 and 0.947 for B (Figure 6.10).
To put the elasticity dependence on AgNP addition into context, the literature
shows that the elastic modulus as a function of the overall composition depends on the
physical nature of the material system itself, where compositional changes can occur
when one has (i) a composite system in which discrete particles are added to a matrix of
differing composition or (ii) a solid solution system or (iii) a solid solution system that
includes micro- or nano scale particles. Changes in elastic moduli of a particulate
composite as a function of the addition of a given volume percent of particulate phase has
been modeled by a number of researchers [Hashin 1962; Halpin 1992; Bedolla 2012;
Couturier 1997] (Appendix A). The four composite models given in Appendix A predict
a decrease in the elastic modulus of the composite, EC of about 0.39% with the 0.5 wt%
AgNP addition to the Ba-skutterudite in this study.

158

Without AgNP
150

(a)

Without AgNP

(b)

With AgNP
Without AgNP, reprocessed

60

G (GPa)

E (GPa)

120
90
60

With AgNP
Without AgNP, reprocessed

30

30
0
0.0

0.1

0.2

0
0.0

0.3

0.1

Porosity

0.2

0.3

Porosity

Without AgNP
90

(c)

0.25

With AgNP

Poisson's Ratio

Without AgNP, reprocessed

B (GPa)

60

30

0
0.0

0.1

0.2

(d)

0.20
0.15
0.10

Without AgNP
0.05
0.00
0.0

0.3

Porosity

With AgNP
Without AgNP, reprocessed
0.1

0.2

0.3

Porosity

Figure 6.10. The (a) Young’s modulus, E, (b) shear modulus, G, and (c) bulk modulus,
B, are each a function of porosity. In each figure, the solid lines represent a least-squares
fit to equation (5b). The Poisson’s ratio (d) is observed to be a weak function of porosity.
The elastic moduli were not observed to be a function of the addition of 0.5 wt% AgNP or
of reprocessing

159

Table 6.6. The linear decrease in elastic moduli, E, G, and B, according to equation (5b),
for this study of Ba0.3Co4Sb12 is consistent with the limited information available in the
literature for porosity dependence of elastic moduli for thermoelectric materials [Schmidt
2013; Ni 2009].
Material
A0 (GPa)
b
N Prange
R2
Reference
Ba0.3Co4Sb12 + 0.5 143 ± 4 (E0)
wt% AgNP, E
Ba0.3Co4Sb12 , E
146 ± 9 (E0)
YbAl3 , E
174.0 ± 2.5
(E0)
LAST, E
58.3 ± 0.3 (E0)
Ba0.3Co4Sb12 + 0.5 59 ± 2 (G0)
wt% AgNP, G
Ba0.3Co4Sb12 , G
60 ± 3 (G0)
YbAl3, G
73.6 ± 0.9 (G0)
LAST, G
Ba0.3Co4Sb12 + 0.5
wt% AgNP, B
Ba0.3Co4Sb12 , B
YbAl3 , B

3.11 ± 0.08

3

0.05-0.27

0.998 This study

3.00 ± 0.16
2.34 ± 0.06

6
7

0.09-0.30
0.03-0.23

3.6 ± 0.1
3.07 ± 0.08

12 0.01-0.14
3 0.05-0.27

0.955 This study
0.994 [Schmidt
2013]
0.994 [Ni 2009]
0.998 This study

2.96 ± 0.15
2.38 ± 0.06

6
7

0.09-0.30
0.03-0.23

22.9 ± 0.1 (G0) 3.5 ± 0.1
82 ± 2 (B0)
3.25 ± 0.05

12 0.01-0.14
3 0.05-0.27

87 ± 10 (B0)
3.14 ± 0.31
91.3 ± 2.9 (B0) 2.22 ± 0.14

6
7

160

0.09-0.30
0.03-0.23

0.962 This study
0.995 [Schmidt
2013]
0.991 [Ni 2009]
0.999 This study
0.857 This study
0.947 [Schmidt
2013]

6.3.3.2 Elastic moduli and porosity
The elastic moduli of the skutterudite Ba0.3Co4Sb12 in this study are linear
functions of porosity over the range of volume fraction porosity included in this study
(between 0.05 and 0.30, Table 6.6, Figure 6.10). In addition, the elastic modulus versus
porosity data is independent of either the presence or absence of the 0.5 wt% AgNP (Table
6.6, Figure 6.10). Also, the powder processing technique (planetary milling or vibratory
milling) and the densification method (hot pressing or PECS (Table 6.1)) does not affect
the elastic modulus versus porosity behavior (Table 6.6, Figure 6.10).
The elastic moduli of TE materials are porosity dependent [Schmidt 2013; Ni
2009]. An empirical expression frequently used to describe the porosity dependence of
Young’s modulus, E, shear modulus, G, and bulk modulus, B [Schmidt 2013; Ni 2009]
of brittle materials [Rice 1998], including TE materials [Schmidt 2013; Ni 2009]
A = A0(exp-bAP)

(5a)

where A represents the property E, G, or B [Rice 1998] and bA is a unitless, materialdependent parameter that measures the rate of decrease in property A with increase P . If
bAP is small, the equation may be linearized by using the first two terms of the Taylor
series expansion of equation (5a) [Schmidt 2013].
A = A0(1 - bAP)

(5b)

For the nine Ba0.3Co4Sb12 specimens in this study (with and without AgNP
addition), a least-squares fit of the modulus data to equation (5b) yielded P = 0 intercept
values of E0 = 145.1 ± 5.2 GPa, G0 = 59.8 ± 2.0 GPa, and B0 = 84.9 ± 5.9 GPa with
coefficients of determination, R2, of at least 0.90 for E, G, and B. There is no significant
difference between the P = 0 intercept for the three specimens with 0.5 wt% AgNP as
161

compared to the six specimens without AgNP addition (Table 6.6). Also, the rate of
decrease in modulus with porosity (given by bA in equation (5b)) was between 3.0 and 3.2
for the Ba0.3Co4Sb12 (Table 6.6), which is consistent with values of 2 to 6 for a wide
range of solid materials [Rice 1998].
Although the data for the porosity dependence of elastic moduli of thermoelectric
materials is relatively limited, modulus versus P data is available for YbAl3 [Schmidt
2013], LAST [Ni 2009] (Table 6.6) and several for Co4Sb12-based skutterudites other
than the Ba-filled skutterudite included in this study (Figure 6.11) [Zhang 2010]. The bA
values for the Ba-filled skutterudite for E, G, and B in this study are bracketed by the bA
values for YbAl3 and LAST for the corresponding moduli (Table 6.6). Also, the elastic
modulus-porosity behavior for Ba0.3Co4Sb12 in this study is quite similar to that reported
by Zhang [Zhang 2010] for other Co4Sb12-based skutterudites (Figure 6.11).
In this study, Poisson’s ratio is insensitive to P for porosities P < approximately
0.20, but there is considerable scatter in the data (Figure 6.10d). For two previous
studies of TE materials, the Poisson’s ratio for LAST [Ni 2009] and YbAl3 [Schmidt
2013] was essentially constant or weakly decreasing with increasing P, for P less than
0.15 or 0.12.
In this study, the scatter in Poisson’s ratio (Figure 6.10d) is typical of
observations for porous ceramics [Ramakrishnan 1993; Boccaccini 1994], and the
observed relative decrease in Poisson’s ratio at P greater than about 0.20 may be
reasonably expected. Ramakrishnan and Arunachalam developed a model using 2dimensional finite element simulation showing Poisson’s ratio approaches 0.25 as
porosity increases [Ramakrishnan 1993]. However, the model does not agree with the
162

Elastic Moduli (GPa)

Ba0.3Co3Sb12 (this study)
Ba0.075Sr0.025Yb0.1Co4Sb12 [Zhang 2010]

150
120
90

(BaYb)0.03Co4Sb12 [Zhang 2010]

E

Ca0.07Ba0.23Co3.95Ni0.05Sb12 [Zhang 2010]

B

60
30

G

0
0.0

0.1

0.2

0.3

Porosity
Figure 6.11. The elastic moduli for the exact composition of skutterudite in this study
are not recorded in literature, however the moduli for specimens of similar composition
[Zhang 2010] are consistent with the porosity dependent elastic moduli relationships
observed in this study. Filled symbols indicate specimens with 0.5 wt% AgNP, unfilled
for specimens without any AgNP, and half-filled symbols for reprocessed specimens
without any AgNP. The solid lines represent a least squares fit to equation (5b) of the data
in this study

163

available data on porous ceramics [Boccaccini 1994], and may be limited by the nature of
the model, ignoring the heterogeneity of porosity [Rice 1995]. Furthermore, Rice argues
that any model should converge to 0 for P = 1, and argues that Poisson’s ratio should
generally decrease when approaching higher values of P [Rice 1995]. In an examination
of both pore shape and P, Dunn and Ledbetter determine that Poisson’s ratio may
increase, decrease or remain unchanged, depending on pore shape and distribution [Dunn
2011]. Thus for a Poisson’s ratio in the range of about 0.20 to 0.25 (for the pore-free
material), the experimental observations [Ramakrishnan 1993; Boccaccini 1994; Rice
1995] and theoretical predictions [Ramakrishnan 1993; Dunn 2011] agree that Poisson’s
ratio is nearly independent of P (for spherical pores) over the interval from approximately
0 < P < 0.20, which agrees with behavior observed for the Ba-skutterudites in this study
(Figure 6.10d).
6.3.3.3 Elastic moduli and grain size/processing effects
There was no observed difference between porosity dependent modulus behavior
of the reprocessed specimens and the HP specimens (Figure 6.10). The elastic moduli of
the skutterudite Ba0.3Co4Sb12 in this study (Figure 6.10) are not functions of grain size
(Figures 6.5-6.8, Table 6.7) or processing (Table 6.1). Grain size varied from bimodal
with grains up to approximately 20 µm across (Figures 6.5 and 6.6, Table 6.7) to less
than 0.2 µm (Figures 6.7 and 6.8, Table 6.7), based on processing by PM and HP, or
reprocessed by VM and PECS (Table 6.1).
The bimodal grain size distribution is not expected to influence the elastic moduli
of the material, as the elastic moduli of materials with grain sizes greater than
approximately 20 nm are typically not a function of grain size [Kim 1999].
164

Table 6.7. For CoSb3-based thermoelectric materials, a comparison of the KC results
from this study with the literature, including the porosity, P, the grain size, GS, of the
specimens and the KC measurement technique [Ravi 2009; Eilertsen 2013; Rogl 2011].
Material
KC
P
GS
KC
Reference
(MPam0.5)
(µm)
measurement
method
Ba0.3Co4Sb12 0.8 - 1.3
0.09 Bimodal a, Vickers
This study
0.20
0.14-0.17 indentation
Ba0.3Co4Sb12- 1.0 - 1.3
0.05 Bimodal a Vickers
This study
0.5 wt% Ag
0.18
indentation
CoSb3
1.7
< 0.01
NA
Chevron notch
[Ravi 2009]
bend
CeFe31.1 - 2.8
< 0.01
NA
Chevron notch
[Ravi 2009]
bend
xRuxSb12
CoSb3
0.82 ±
Nearly
1-2 µm,
Vickers
[Eilertsen
0.11
dense
15 µm
indentation
2013]
CoSb3
0.52 ±
Nearly
1-2 µm,
Crack opening
[Eilertsen
0.04
dense
15 µm
displacement
2013]
CoSb3
0.51 ±
Nearly
15 µm
Single-edge vee- [Eilertsen
0.06
dense
notch bend
2013]
0.1In CoSb3
0.46 ±
Nearly
15-40 µm Vickers
[Eilertsen
0.13
dense
indentation
2013]
0.1In CoSb3
0.49 ±
Nearly
15-40 µm Crack opening
[Eilertsen
0.03
dense
displacement
2013]
0.1In CoSb3
0.57 ±
Nearly
15 µm
Single-edge vee- [Eilertsen
0.06
dense
notch bend
2013]
Fe4Sb12- and 1.5 to 2.2
Typically NA
Vickers
[Rogl 2011]
b
Fe3CoSb12< 0.02
indentation
based b
NA: Information not available
a
Bimodal specimens had matrix grain sizes of 0.3 µm to 3 µm, with larger grains
approximately 5 µm to 20 µm across
b
DD0.88Fe4Sb12, P = 0.014; Ca0.41DD0.41Fe4Sb12, P = 0.015; Ba0.44DD0.42Fe4Sb12, P =
0.018; Ca0.20Sr0.12DD0.39Fe3CoSb12, P = 0.011; Ca0.20Ba0.14DD0.38Fe3CoSb12, P not given;
Sr0.12Ba0.18DD0.39Fe3CoSb12, P = 0.010; Sr0.066Ba0.066Yb0.066Co4Sb12, P not given;
Mm0.78Fe3CoSb12, P not given

165

The distribution of porosity may be influenced by the microstructure, with associated
influences on elastic moduli, however previous studies of TE materials showed only a
relation based on the volume fraction porosity and no pore distribution or shape factor
required to describe the modulus-porosity relationship [Schmidt 2013; Ni 2009].
6.3.4 Hardness and fracture toughness results
Specimens PM-HP-673 and PM-HP-673-Ag, both hot pressed at 673 K, were too
fragile to polish, limiting the hardness and fracture toughness measurements for the HP
specimens to the two sintered at 773 K and the two sintered at 873 K. However, H and
KC measurements were made on each of the three reprocessed PECS specimens since all
of those specimens had sufficient mechanical integrity so that polishing and indentation
was not a problem. Also, for the toughness measurements, radial cracks were not present
at a Vickers indentation load of 1.96 N for any of the specimens except VM-PECS-673
and VM-PECS-773, nor at 2.94 N for specimen PM-HP-673, so no KC data is reported
for the 1.96 N indentations for any specimen, nor at 2.94 N for specimen PM-HP-673
(Figure 6.12).
6.3.4.1 Hardness and toughness as a function of Ag addition
As was the case for the elastic moduli, the hardness and fracture toughness of the
Ba-skutterudite in this study were not sensitive to the AgNP addition (Figure 6.12, Table
6.7). For H, much of the literature on micro-sized and nanosized metallic particles added
to brittle matrices has focused on higher volume percentages. For example, H of alumina
decreased from 18 GPa to 9.5 GPa with the addition of 0.20 volume fraction aluminum

166

(a)

Hardness (GPa)

6

9.8 N
4.9 N
2.94 N
1.96 N
VM fit
BM fit

Vib
ra

tory
mil
led

4

Plan
e

2

0
0.00

0.05

tary

0.10

mill
ed

0.15

0.20

Porosity

1/2

Kc (MPa m )

2.0

9.8 N
4.9 N
2.94 N
Average KC

(b)

1.5

StDev KC

1.0

0.5

0.0
0.00

0.05

0.10

0.15

0.20

Porosity
Figure 6.12. The (a) hardness and (b) fracture toughness for the hot pressed specimens
with AgNP, filled symbols, the hot pressed specimens without AgNP, open symbols, and
the reprocessed PECS specimens without AgNP, half-filled symbols, from Vickers
indentation at four loads, 9.8 N, 4.9 N, 2.94 N, and 1.96 N. Full radial cracks were not
observed on the specimens at 1.96 N load and therefore no fracture toughness values are
available at 1.96 N load. The hot pressed specimens sintered at 673 K were not able to be
polished and were not tested. The solid lines in the figure (a) represent hardness for the
reprocessed specimens were fit to equation (6) separately from the hot pressed specimens
because hardness is a function of grain size. Fracture toughness, figure (b), was not
observed to be a function of either porosity or load, as plotted by the average (solid) and
standard deviation (dotted) lines, with an average KC for all 7 specimens of 1.0 ± 0.2
MPa-m½
167

particles (average XRD crystallite size of 25 nm, TEM grain size 26 ± 3 nm) [Zawrah
2012], and from 8.2 GPa to 7.3 GPa in hydroxyapatite with the addition of 5 wt%
irregularly-shaped 67%Ti-33%Fe particles which were less than 200 µm across [Chang
2010].
However, the choice of PtNP or AgNP additions strongly effected the observed
change in the hardness and fracture toughness of porcelain. The H and KC were 4.94 ±
0.33 GPa and 1.36 ± 0.03 MPa·m½, respectively, for the porcelain matrix itself. The
addition of AgNP raised the H and KC to 6.10 ± 0.14 GPa and 1.54 ± 0.05 MPa·m½, 23%
and 13% greater, respectively, than the H and KC of the matrix. In contrast, after the
addition of 26 wt% PtNP the hardness and fracture toughness were essentially unchanged
from that of the dental porcelain matrix with H = 5.05 ± 0.15 GPa and KC = 1.42 ± 0.02
MPa·m½. Thus, while the addition of PtNP left both the H and KC values essentially
intact, the addition of an equivalent weight % of AgNP to the same porcelain matrix
material resulted in large changes in both H and KC [Fujieda 2012]. For dilute
concentrations of nanoparticles, changes in the elastic modulus are typically on the order
of a few percent or less.
6.3.4.2 Hardness and fracture toughness as function of porosity
6.3.4.2.1 Hardness as function of porosity
In this study, the hardness, H, of Ba0.3Co4Sb12 and Ba0.3Co4Sb12-AgNP decreased
linearly with increasing porosity (Figure 6.12a). In general, hardness is a function of
porosity for ceramics or brittle semiconductors [Fan 2013; Ramadass 1983; Mangalaraja
2009]. A least-squares fit of the H versus volume fraction porosity, P, data was done to
the relationship
168

H = H0(1 – bHP)

(6)

where H0 = the value of hardness at P = 0 and bH is a unitless constant that describes the
rate of decrease in H with increasing P. For the four HP specimens, a least-squares fit of
the hardness-porosity data to equation (6) yielded H0 = 4.3 ± 0.2 GPa and bH = 3.6 ± 0.2
with the coefficient of determination R2 = 0.84 (Figure 6.12a). For the three reprocessed
specimens, H0 = 6.0 ± 0.5 GPa and bH = 3.0 ± 0.4, with R2 = 0.67 (Figure 6.12a). The
low R2 is likely due to the small data set (three reprocessed specimens) and scatter in the
data.
6.3.4.2.2 Fracture toughness as function of porosity
The fracture toughness of the specimens in this study is independent of porosity,
averaging 1.0 ± 0.2 MPa-m½ over the entire range of porosity for which KC was measured
in in this study, namely from P = 0.05 to 0.21 (Figure 6.12b, Table 6.1). Note that
fracture toughness was not measured for specimens PM-HP-673 (P = 0.30) or PM-HP673-Ag (P = 0.27) since these specimens were too fragile to be polished. In the literature,
it has been noted that KC can increase, decrease, or remain unchanged with increasing P
[Rice 1995; Shao 2013].
In a comprehensive review of the effects of porosity on the mechanical properties
of brittle materials [Rice 1995], Rice noted, especially for the intermediate porosity range
from roughly P = 0.1 to P = 0.15, there are a number of examples of materials in the
literature (including Al2O3, B4C, Si3N4) showing “that KIC values for some of these
porous bodies were clearly at least as high or higher than bodies with little or no
porosity”. Proposed mechanisms for an increasing or constant KC with increasing

169

porosity include crack-pore interactions, where pores can blunt or deflect a growing crack
[Case 2012b; Case 2012a].
6.3.4.3 Hardness and fracture toughness as a function of load
Over the indentation load range of 1.96 N to 9.8 N that is included in this study,
both H and KC were independent of the load for Ba-skutterudite (Figure 6.12). The H,
while independent of load, varied between specimens, but the KC was essentially constant
for all seven specimens examined. The average KC of the seven specimens in this study
is 1.0 ± 0.2 MPa-m½, which is comparable to the KC range of 0.46 MPa-m½ to 1.7 MPam½ measured for similar skutterudites (Table 6.7) [Ravi 2008; Eilertsen 2013; Rogl
2011].
For KC, the fracture toughness should ideally be independent of load. In order to
test this load independence, the c3/2 (where c = radial crack length) versus indentation
load, F, behavior was examined for each of the Ba-skutterudite specimens included in
this study. A plot of c3/2 versus F yielded a straight line plot with R2 > 0.98 in each case,
as demonstrated by plots from specimens VM-PECS-673 and PM-HP-873-Ag (Figure
6.13). Thus, the radial crack length versus indentation load behavior is consistent with
equation (3) for each specimen in this study, where equation (3) can be rewritten as
c3/ 2 

 ( E / H ) 0.5 F

(7)

KC

For a given specimen, we assume the ξ, E, H and KC are constant, thus equation
(7) is a straight line. The high value of R2 for the least-squares fit to equation (7)
supports the use of equation (3) to calculate KC.

170

(a) Specimen VM-PECS-673
2

R = 0.997

3/2

500

c

1000

3/2

( m )

1500

0

0

2

4

6

8

10

F (N)
1500 (b) Specimen PM-HP-873-Ag
2

1000

500

c

3/2

3/2

( m )

R = 0.998

0

0

2

4

6

8

F (N)

10

Figure 6.13. For each of the specimens, a plot of c3/2 versus load, F, was used to
determine the suitability of the fracture toughness by Vickers indentation. For 5 of 7
specimens, the coefficient of determination, R2, for a linear regression to equation (7)
through the data points is 0.99 or greater, with an R2 of 0.98 for specimen VM-PECS773, and 0.84 for specimen PM-HP-773. Note specimen PM-HP-773 also has a low
fracture toughness measurement at 2.94 N load. All specimens were measured at three
loads, except VM-PECS-673 and VM-PECS-773 with a fourth measurement at a Vickers
indentation load of 1.96 N

171

In contrast to KC, hardness is frequently observed to be a function of the applied
load. From the literature, for both metals [Pharr 2010; Nix 1998] and brittle solids [Bull
1989; Sangwal 2009], the measured hardness can be a function of the applied indentation
load. The indentation size effect (ISE) [Nix 1998], where H decreases as the applied load
increases, has been ascribed to elastic recovery and working hardening during indentation
[Bull 1989; Sangwal 2009] while an observed reverse indentation size effect (RISE)
[Sangwal 2000], where H decreases with decreasing load has been attributed to stress
relaxation during unloading [Sangwal 2000].
6.3.4.4 Hardness and fracture toughness results as a function of grain size
The hardness varied as a function of grain size, as observed by the fit to equation
(6) in Figure 6.12a, while the fracture toughness is independent of grain size, averaging
1.0 ± 0.2 MPa-m½ (Table 6.7). For the bimodal grain size HP specimens (matrix grain
sizes of 0.3 µm to 3 µm, with larger grains approximately 5 µm to 20 µm across), the H0
is 4.3 ± 0.2 GPa, while for the reprocessed specimens with average grain sizes of 0.17
µm, 0.16 µm and 0.14 µm, the H0 is 6.0 ± 0.5 GPa (Figure 6.12a).
6.3.4.4.1 Hardness results as a function of grain size
The difference in H0 between planetary milled and HP specimens and the
vibratory milled and PECS processed specimens likely is related to the grain size
dependence of H. A Hall-Petch type relationship between H and grain size, GS, available
in the literature is [Rice 2000]

H  H 0  kGS1 / 2

(8)

172

where H0 is considered as the H value in the single crystal limit and k is called the Petch
parameter. While Hall-Petch behavior is very common in metals [Lawn 1993], the nature
of the H versus GS dependence is uncertain for many ceramics [Rice 2000; Armstrong
2011]. Hall-Petch behavior is common for relatively soft ceramics such as alkaline
halides, but there is a great deal of scatter in the H versus GS data for most hard ceramics
[Rice 2000; Armstrong 2011]. Furthermore, the H0 obtained from H versus GS data if
not always a good predictor for the H of single crystals (as is typically assumed for
equation (8)) [Rice 2000]. In addition, for some ceramics, such as ZrO2 and AlMg2O4, H
is independent of grain size [Rice 2000]. Also, minima in H versus GS data are often
observed for intermediate grain sizes (GS on the order of several µm) such that the Petch
parameter k can take on both negative and positive values (with unequal magnitudes) for
a given data set [Rice 2000; Armstrong 2011]. Nevertheless, a well-accepted alternative
to equation (8) is not available in the literature and thus, in general, the H versus GS
behavior for brittle materials is not clear from the standpoint of the available data or the
available functional relationship (equation (8)).
6.3.4.4.2 Fracture toughness results as a function of grain size
In this study, fracture toughness, KC, is essentially independent of grain size, GS,
averaging 1.0 ± 0.2 MPa-m½ (Figure 6.12b).
This result may be counterintuitive, since fracture strength is typically a function
of grain size [Barsoum 2003]. However, fracture strength is based on the stress required
for failure of a specimen and is typically dependent on the largest flaw, and the intrinsic
flaw size typically scales with GS [Barsoum 2003]. In contrast, KC is based on the work

173

necessary to extend a crack [Barsoum 2003], which may or may not be related to grain
size.
Thus, grain size engineering alone will not likely improve fracture toughness
either for Ba-skutterudite or other cubic thermoelectric materials. Although no studies
are currently available in the literature for the grain size dependence of KC for
thermoelectric materials, KC has been observed to be essentially independent of grain size
for various cubic materials, tested using a variety of test methods, including Y2O3
(notched beam test [Monroe 1978] and double cantilever beam technique [Rhoades
1986]), MgO (Chevron notch method [Yasuda 1990]), NiZn ferrite (notched beam
[Veldkamp 1979]), and MgAl2O4 (double cantilever bean and Vickers indentation [Rice
1996]).

In addition, for noncubic materials with small grain size, KC can be independent

of grain size as was the case in a study by Yao et al. who found that KC was independent
of grain size for PECS-processed, fully dense polycrystalline alumina with grain sizes
ranging from 0.3 µm to 3.3 µm for KC measured by the surface crack in flexure technique
[Yao 2011].
In contrast to cubic materials, for noncubic materials with intermediate grain sizes
(roughly on the order of 10 to 100 µm), a maximum in KC has been observed as a
function of grain size [Wachtman 2009]. Lawn and co-workers ascribed the observed
increase in KC with increasing grain size to grain bridging [Vekinis 1990; Swanson 1987;
Foulk III 2007], with the principle mechanism responsible for grain bridging being the
clamping forces generated by thermal expansion anisotropy [Bennison 1989]. After the
maximum in KC, KCMAX, is reached, the subsequent decrease in KC with further increases
in grain size has been linked to thermal expansion anisotropy-induced microcracking in
174

noncubic materials, where the grain size at KCMAX coincides roughly with the critical
grain size for microcracking [Rice 1998]. Thus, while for noncubic materials, a grainsize dependent maximum in KC has been observed, the insensitivity of KC to grain size
for the cubic Ba-skutterudite in this study is consistent with the literature. In addition to
the grain size and porosity trends, the value of KC for the Ba-skutterudite measured in this
study is comparable to KC values in the literature for other CoSb3 systems [Ravi 2008;
Eilertsen 2013; Rogl 2011] (Table 6.7).
6.4 Summary and conclusions
In this study, the elastic moduli (Figure 6.10), hardness (Figure 6.12a), and
fracture toughness (Figure 6.12b) of Ba0.3Co4Sb12 were insensitive to the addition of 0.5
wt% AgNP. Both the elastic moduli and hardness were functions of porosity (Figures
6.10, 6.12a), which agrees with previous literature results for elasticity (Figure 6.11)
[Zhang 2010] and hardness [Ramadass 1983; Mangalaraja 2009; Shao 2013]. Fracture
toughness (Figure 6.12b) was not a function of porosity (Figure 6.12b), which may
indicate an interaction between the pores and the growing cracks.
The study by Zhou [Zhou 2012] demonstrated that Ag addition results in
important changes in thermoelectric properties (increasing electrical conduction) for Baskutterudite. However, this study indicates that the addition of silver also affects the
densification process which in turn can affect changes in mechanical properties. At a
sintering temperature of 873 K, the specimen without AgNP had a P value of 0.16 while
the specimen sintered with 0.5 wt% AgNP had P = 0.05. The increased densification with
the addition of Ag was likely due to a liquid phase sintering from the pertitectic reaction
that formed the Ag3Sb phase observed in the specimen.
175

Based on the results of this study, a similar peritectic reaction may explain the
formation of Ag3Sb and an enhanced ZT when Ag was added to ZnSb [Xiong 2013].
Similar peritectic or eutectic reactions may take place in other antimonide thermoelectric
systems when Ag or another conductive material is added to enhance electrical
conductivity. More generally, this type of eutectic or peritectic reaction to enhance
densification and improve electrical conductivity may operate in a number of
thermoelectric systems in addition to antimonides. Although a set of ternary or
quaternary phase diagrams may not be available for many thermoelectric systems, a
search of binary phase diagrams (such as the Ag-Sb phase diagrams used in this study)
may act as a guide to discover potential beneficial peritectic or eutectic reactions.
ACKNOWLEDGEMENTS
The authors acknowledge the financial support of 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 Science, Office of
Basic Energy Sciences under award number DE-SC0001054.

176

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186

7 High temperature elastic moduli of thermoelectric SnTe1+X –y SiC
nanoparticulate composites
Robert D. Schmidt 1, Eldon D. Case 1, Jennifer E. Ni1, Rosa M. Trejo 2, Edgar LaraCurzio2, Rachel J. Korkosz3, Mercouri G. Kanatzidis3
1

Chemical Engineering and Materials Science Department,
Michigan State University, East Lansing, MI, 48824
2
High Temperature Materials Laboratory,
Oak Ridge National Laboratory, Oak Ridge, TN 37831
3
Department of Chemistry,
Northwestern University, Evanston, IL, 60208
Published in: Journal of Materials Science 48 (2013) 8244 – 8258.
Abstract
In waste heat recovery applications, thermoelectric (TE) generators are subjected
to thermal gradients and thermal transients, creating mechanical stresses in the
thermoelectric legs. Such stresses are functions of the elastic moduli of the TE material.
For SnTe1+X matrices (where x = 0.0 or 0.016) composite specimens with 0 to 4 vol.%
SiC nanoparticle (SiCNP) additions, the elastic moduli (Young’s modulus, shear modulus,
bulk modulus and Poisson’s ratio) were measured by resonant ultrasound spectroscopy
(RUS) from room temperature to 663 K. The effects of matrix composition and the
SiCNP additions on the room temperature intercepts and the slopes of the elastic modulus
as a function of temperature are also discussed.

Keywords: thermoelectrics; elastic modulus; SnTe; SiC nanoparticles

187

7.1 Introduction
A number of thermoelectric (TE) materials, including SnTe are candidates for
harvesting waste heat from a variety of sources, including incinerators and automotive or
truck exhaust. The energy conversion efficiency, η, of a thermoelectric device can be
written as [Bux 2010]

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










(1)

where TH and TC are, respectively, the hot and cold side temperatures of the
thermoelectric device and T is the average device temperature. ZT is the dimensionless
figure of merit which is given by

ZT 

S 2 eT

(2)



where S = the Seebeck coefficient, σe = the electrical conductivity, S2 σe = the power
factor and κ = the thermal conductivity. As shown by equation (1), as ZT increases the
conversion efficiency increases.
However, in addition to the thermal and electrical transport properties, the
mechanical properties of the thermoelectric material are also important. Especially in the
context of harvesting waste energy, as the heat source (say an automobile engine or an
industrial furnace) is cycled on and off, the TE elements that are in place to capture waste
heat will also experience thermal transients. The maximum surface thermal stress, max,
induced by a thermal transient on a flat plate of uniform thickness is a function of the

188

temperature-dependent elastic modulus, E(T), and Poisson’s ratio, (T), and thermal
expansion coefficient, (T) such that [Lu 1998; Zhao 2000; Manson 1966]

max 

E T 
αT   T  f(Bi)
1   T 

(3)

The function f(Bi) increases monotonically with increasing Biot modulus Bi, where Bi =
ah/κ [Kreith 1973] and a is the characteristic dimension of the specimen, h is the surface
heat transfer coefficient and κ is the thermal conductivity of the specimen . In the
thermal transient case, T is the difference between the initial and final temperature
during the temperature excursion and the function f(Bi) depends on the dimensionless
parameter Bi. Also, T = Ti  T  is the quench temperature difference, where Ti is the
initial temperature of the specimen and T∞ is the temperature of the ambient medium.
In addition to stresses induced by thermal transients (equation 3), there are
thermal gradients imposed between the hot and cold plates of a thermoelectric device that
are essential for current to flow [D’Angelo 2011]. Also, the thermoelectric elements will
be subjected to stresses due to thermal expansion mismatch within the thermoelectric
module as well as to various external, mechanical stresses. Regardless of the mechanism
that generates the stress, calculations via both finite element [Martin 1973; Kaliakin
2002] and analytical techniques [Manson 1966] require knowledge of the elastic modulus
and Poisson’s ratio in order to analyze the stress-strain response of the material. Also, if
microcracks are induced by either mechanical or thermal loading, then the microcrackinduced changes in elastic moduli provide a means of monitoring the extent of
microcrack damage [Fan 2012; Case 1993; Chotard 2008].

189

In this study, the Young’s modulus, shear modulus, Poisson’s ratio, acoustic
wavespeed and Debye temperature were measured over the temperature range from 298
K to 663 K for six bulk SnTe1+X -SiC nanoparticle composites specimens with the SiC
nanoparticle (SiCNP) loading from 0 to 4 volume percent. Also, the effects of an offstoichiometric SnTe composition on the elastic moduli are discussed.
7.2 Experimental procedure
7.2.1 Specimen Preparation
To fabricate each SnTe1+X ingot, high purity powders of Sn (Plasmaterials, purity
99.999%) and Te (5N Plus Inc., purity 99.999%) with no added dopants were flame
sealed in a quartz tube under vacuum. For ingot SnTe(x=0) , stoichiometric amounts of
each powder were placed into quartz tubes (21.2499 g of Sn and 22.8462 g of Te in first
batch, 21.2478 g of Sn and 22.8486 g of Te in second batch). The sealed tubes were
heated to 1273 K in 10 hours, held at 1273 K for 10 hours then air quenched to room
temperature (RT).
For ingot SnTe(x=0.016), a non-stoichiometric amount of powder was added
(44.9274 g of Sn and 49.0715 g of Te) to a quartz tube to produce SnTe1.016. The sealed
tube was heated to 1148 K in 12 hours, held for 12-13 hours at temperature, then
quenched into water.
The resulting ingot was crushed and ground in a WC-lined mechanical mortar and
pestle. The ground powder was passed through a 53 µm sieve on a shaker table for 5 to
15 minutes. Powder that did not pass through the sieve was reground and re-sieved.
Additional details on the crush-grind-sieve-regrind (CGSR) procedure are provided
elsewhere [Pilchak 2007].
190

Table 7.1. For each of the six SnTe-SiCNP specimens included in this study, the volume
fraction SiCNP addition, specimen mass, dimensions, mass density, porosity, P, and mean
grain size. Specimens were prepared from one of two starting ingots, designated A or B
in the specimen label.
Mass
(g)

Dimensions
(cm)

Mass
P
Density
(g/cm3)

SnTe(x=0)V0
SnTe(x=0)V0.01
SnTe(x=0)V0.02

SiC
Nanoparticle
Volume
Fraction
0.00
0.01
0.02

7.7749
7.4952
7.3529

6.27
6.09
6.21

SnTe(x=0)V0.03

0.03

3.4264

6.13

0.034 1.0

SnTe(x=0)V0.04 0.04
SnTe(x=0.016)V0 0.00
a
Not available

7.6725
7.5693

Ø 1.984 × 0.401
Ø 1.973 × 0.403
Ø 1.989 × 0.31
1.162 × 1.249 ×
0.385
Ø 1.968 × 0.416
Ø 1.987 × 0.387

Mean
Grain
Size
(µm)
0.028 N.A. a
0.051 2.7
0.026 1.0

6.07
6.30

0.039 1.2
0.022 1.8

Temperature
Pressure

Temperature (K)

700

60

600
40
500
400

20

300
0

100

200

300

Pressure (MPa)

Specimen label

0

Time (min)
Figure 7.1. Processing parameters (temperature and die pressure) as a function of time
for the PECS densification of the SnTe-SiCNP specimens included in this study.

191

After grinding, the CGSR powder was milled in a planetary ball mill in 20 g to 30
g batches with 100 g of 10 mm diameter spherical alumina media at 150 RPM for 3 h
(PM100, Retsch GmbH, Haan, Germany). For specimens with SiC nanoparticle (SiCNP)
additions, 95% purity silicon SiCNP with a vendor –specified particle size of 50-60 nm
(SiCNP, 4621HW, Lot #4621-110209, Nanostructured & Amorphous Materials Inc.,
Houston, TX) was added to an 8 g batch of milled SnTe1+X powder and mixed at 110
RPM for 6 h with 100 g of 10 diameter mm alumina media. From 0 to 4 vol% SiCNP was
added to the SnTe1+X powders (Table 7.1).
Sintering of the milled powder was performed by pulsed electric current sintering
(PECS) in a 20 mm diameter graphite die lined with two layers of grafoil (SPS Model 103, Thermal Technology LLC, Santa Rosa, CA). For each specimen included in this
study, the PECS sintering was performed using an argon-filled chamber at 673 K and at a
die pressure of 60 MPa for 20 minutes, followed by 210 minutes at 573 K. Details of the
time-temperature and pressure-temperature profiles are given in Figure 7.1. The resulting
disk-shaped specimens were from about 3 to 4 mm thick, although one specimen (A-043) was cut into a rectangular parallelepiped prior to testing (Table 7.1).
7.2.2 Specimen characterization
The microstructure of the specimens was examined using the following scanning
electron microscopes (JEOL 6400, JEOL 6610LV or JSM-7500F, JEOL Ltd., Japan). All
SEM images taken with the JEOL 6400, JEOL 6610LV used 15 mm working distance
with a 15 kV accelerating voltage. For the JSM-7500F (high resolution SEM) a 4.5 mm
working distance and 2 kV accelerating voltage was used when imaging powder, 4.5 mm
working distance and 5 kV when imaging bulk specimens by secondary electron only,
192

and 8 mm working distance and 15 kV accelerating voltage on specimens imaged by
backscatter electron and for energy-dispersive X-ray spectroscopy (EDS).
The JSM-7500F was used to image fractured and polished surfaces of the SnTe1+X
bulk specimens along with the as-received and as-ground SiCNP. The fractured surfaces
of the specimens were not coated prior to SEM observation. However, the polished
surfaces and the SiCNP powders themselves were sputter coated with osmium since
without coating the specimens exhibited localized charging.
In order to attempt to break up extensive clumping in the as-received SiCNP, a 5
gram batch of the as-received SiCNP powders was mixed with 5 ml of ethanol and then
hand ground for 5 minutes with an alumina mortar and pestle. While the grinding
process in the mortar and pestle is certainly not identical to the grinding process
experienced during planetary milling of the SiCNP and SnTe1+X powder mixture that was
subsequently sintered, the hand grinding gives a rough gauge of the how easy it is to
break-up the agglomerates.
The milled powder was examined by XRD (Miniflex II, Cu Kα radiation, Rigaku,
Tokyo, Japan) to verify the phase composition and lattice parameter of the SnTe1+X
material.
7.2.3 High temperature Resonant Ultrasound Spectroscopy measurements
The elastic moduli were measured by Resonant Ultrasound Spectroscopy (RUS)
in a furnace with a flowing Ar-4% H atmosphere. The elastic moduli were measured at
RT before turning on the furnace. The specimen was heated to 333 K for the first
measurement at higher temperature, then the furnace temperature was increased in 30 K
increments to 663 K. The specimen was then cooled in 30 K increments from 663 K to
193

333 K. After the furnace was turned off and the specimen cooled to RT, the specimen
was measured one final time by RUS. Dimensional changes during heating were
calculated using a coefficient of thermal expansion of 22.2 x 10-6 K-1 (Schmidt et al.,
unpublished data). Additional details of the HT-RUS procedures are provided elsewhere
[Ren 2008; Ren 2009b; Ren 2009a].
7.3 Results and Discussion
7.3.1 Microstructural analysis
Both fracture surfaces (Figure 7.2a) and polished surfaces (Figure 7.2b) of the
SnTe1+X -SiCNP composite specimens were examined. No surface-breaking cracks were
observed for either the fractured surfaces (Figure 7.2a) or the polished surfaces (Figure
7.2b) of the specimens. The polished surfaces of the SnTe1+X specimens showed
occasional isolated, quasi-spherical pores with submicron diameters (Figure 7.2b). In
addition, the grains were relatively equiaxed with a mean grain size of roughly 1 – 3 µm
(Figure 7.2a, Table 7.1), as evaluated by the linear intercept technique on SEM
micrographs of fractured surfaces [Case 1981b]. Also, the fractures were predominantly
intergranular with transgranular fracture observed for some of the larger grains (Figure
7.2a). The mass, mass density, grain size and volume fraction porosity for each specimen
included in this study is listed in Table 7.1.
Room temperature X-ray diffraction showed that only the SnTe cubic phase
was present in the specimens from both ingots SnTe(x=0) and SnTe(x=0.016) (Table
7.1), however there was a systematic shift in the XRD patterns that was likely due to
compositional differences in SnTe1+X solid solution. The lattice parameter was a0 =
6.3130 + 0.0056 Å for the planetary-milled powders used to fabricate specimens each of
194

Figure 7.2. For SnTe specimen A-06 (0 vol% SiCNP), (a) fractured specimen surface and
(b) polished specimen surface.

Figure 7.3. The as-received SiCNP consisted of particles roughly 50 nm across
agglomerated into clusters ranging in size from approximately 100 nm to 20 µm.

Figure 7.4. (a) After grinding in an alumina mortar and pestle for 5 min in ethanol, the
SiCNP exhibited agglomerations of particles ranging from sub-micron to ~10 µm
diameter. (b) The agglomerations consisted primarily of nanoparticles with diameter less
than 100 nm, but with an occasional micron-scale particle. The size distribution of the
agglomerates after manual grinding was similar to that observed prior to manual grinding
(Figure 7.3).
195

the “SnTe(x=0.0)” specimens, of nominal composition SnTe. For the planetary-milled
powders used to fabricate the “SnTe(x=0.016)” specimen, of composition SnTe1.016, the
lattice parameter was 6.3014 + 0.0056 Angstroms. The literature value for lattice
parameter of SnTe given by is 6.313 Angstroms [Wyckoff 1963]. As Te is added to the
SnTe structure, Sn vacancies are created in the rock salt lattice, so that the shift in
stoichiometry results from the creation of cation vacancies [Rogacheva 1991].
The compositional difference between ingots SnTe(x=0) and SnTe(x=0.016) has
important implications for mechanical properties of the SnTe1+X specimens since in
general the elastic moduli are known to be sensitive to changes in composition within
solid solution systems [Ravinder 2001; Srinivas Rao 2003; Ren 2007] including
thermoelectric solid solutions [Ren 2007]. The composition-related changes in elastic
moduli are discussed further in following section.
The as-received SiCNP powders were not discrete nanoparticles but instead
consisted of clumps with diameters from roughly 100 nm to 20 µm across (Figure 7.3),
with individual particles roughly 100 nm across (Figure 7.3). Manual grinding in a mortar
and pestle did not noticeably reduce the clump size from the original several hundred nm
diameter (Figure 7.4). The manual grinding only provides a rough gauge of the ease of
breaking up the SiCNP powder agglomerates and does not approximate the grinding
action of the planetary mill used to process the bulk specimens in this study.
Fracture surfaces of specimens SnTe(x=0)V0, SnTe(x=0)V0.01,
SnTe(x=0)V0.02, SnTe(x=0)V0.03 and SnTe(x=0)V0.04 were examined (Figure 7.5a –
7.5e). Each specimen with SiCNP addition showed fine-grained clusters on the fracture
surface that likely represented SiCNP clumps on the surface that ranged from about
196

Figure 7.5. Fractured specimen surface images for (a) specimen SnTe (x = 0)V0 with no
SiCNP added, and for (b) SnTe (x = 0)V0.01, (c) SnTe(x = 0)V0.02, (d) SnTe(x =
0)V0.03, and (e) SnTe(x = 0)V0.04. In (b) – (e), the location of SiCNP clusters is
indicated by arrows.

197

200 nm to 2000 nm in across (Figure 7.5b – 7.5e). The SiCNP clumps are indicated by
arrows in Figures 7.5b – 7.5e. The fracture surface of the SnTe(x=0)V0 was free of such
clusters.
In order to determine whether or not the clusters observed on the specimen
fracture surfaces of the composites were composed of SiCNP, pairs of secondary electron
and backscattered images were taken at high resolution (Figures 7.6a – 7.6d). For
specimen SnTe(x=0)V0, with no SiCNP addition, the secondary electron image (Figure
7.6a) and the backscattered image (Figure 7.6b) were similar in appearance. However,
for SnTe(x=0)V0.04 (with 0.04 volume fraction of SiCNP), the backscattered image of the
specimen exhibited dark regions that indicate a lower atomic mass, which is consistent
with the presence of SiCNP at or just below the surface of the specimen in the dark
regions (Figure 7.6d). However, for the secondary electron image (Figure 7.6d), there
was much less atomic number contrast in the image. From measurements on SEM
micrographs taken at two different magnifications, the area fraction of SiCNP clusters was
estimated as roughly 2.1–2.5 % (Table 7.2).
EDS measurements on specimen SnTe(x = 0)V0.04 indicated a silicon content of
about 13 at% within dark region (the box-labeled ‘‘Spectrum 2’’ in Figure 7.7). In
contrast, a Si content of <1 at% was indicated by EDS in the light region marked by the
box-labeled ‘‘Spectrum 1’’ in Figure 7.7. Thus, there is a very strong indication that
SiCNP clusters ranging from roughly 100 to 1000 nm are distributed within specimen
SnTe(x = 0)V0.04.

198

Figure 7.6. Specimen SnTe(x = 0)V0, with no added SiCNP, shows no surface features
other than surface debris in both (a) a secondary electron image (SEI) and in (b) a
backscattered electron image. Specimen SnTe(x = 0)V0.04 with 0.04 vol fraction SiCNP
addition shows a difference between the (c) secondary electron image and (d) the
backscattered electron image, with the image in the backscattered electron mode showing
dark regions indicating likely SiCNP clusters at or near the specimen surface.

199

Table 7.2. For SiCNP clusters identified by electron backscatter images for specimen
SnTe(x = 0)V0.04 (Fig. 6), the SEM magnification, the area of the field of view of the
micrograph, along with the number, number density, and size range of the SiCNP clusters
Magnification Area
Number
Areal
Average
Range
Area
(µm2)
of SiC
number diameter
(nm)
fraction
spots
density
(nm)
SiC
(#/µm2)
X 25000
17.0
12
0.71
160
54 – 560 0.025
X 50000
4.2
16
3.8
68
21 – 120 0.021

Figure 7.7. A backscattered electron image of a polished surface of specimen SnTe(x =
0)V0.04 indicates darker regions with a lower average atomic weight, likely composed
primarily of the SiCNP. Using EDS, silicon was detected at the location of spectrum one,
at approximately 13 at%, but not at spectrum two, with <1 at%, confirming that the dark
regions contain a high concentration of the SiCNP. The specimen was osmium coated
prior to imaging to reduce localized charging.

200

7.3.2 Elastic modulus as a function of temperature, matrix composition and SiCNP
volume fraction
For the six SnTe1+X -ySiCNP (0 < y < 4 vol %) composite specimens included in
this study, the Young’s modulus (Figure 7.8) and shear modulus (not shown) decreased
approximately linearly with increasing temperature over the entire temperature range
from room temperature to 663 K. Equations (4a) and (4b) were fitted to the high
temperature Young’s modulus, E, and shear modulus, G, data, respectively, for
temperature T
E = ERT (1 - bTE(T-TRT) )

(4a)

G = GRT (1 - bTG(T-TRT) )

(4b)

where ERT and GRT are the RT intercepts, bTE and bTG are measures of the changes in E
and G, respectively, with temperature, T, and RT TRT (295 K). The values of the leastsquares parameters ERT, GRT, bTE and bTG are listed in Table 7.3 for each SnTe1+X -SiCNP
specimen included in this study.
The near- superposition of the heating and cooling curves for the elastic moduli
(Figure 7.8) indicates the absence of either (1) significant microcracking or (2) bloating.
Microcracking, if present, can reduce the elastic modulus of a material [Fan 2012; Case
1993; Chotard 2008]. Moreover, for materials that are microcracked at room
temperature, heating to a homologous temperature of about 0.6 can induce microcrack
healing, which in turn leads to a hysteresis in the modulus versus temperature curve
[Chotard 2008; Case 1981a]. Bloating, which refers to the generation of porosity during
heating, is often associated with solid phase decomposition reactions within a specimen
[Ni 2011].
201

SnTe(x=0)V0 Heating
SnTe(x=0)V0 Cooling

(a)

60

55

50
300

400

500

600

700

Young's Modulus (GPa)

Young's Modulus (GPa)

65

65

60

55

50
300

SnTe(x=0)V0.02 Heating
SnTe(x=0)V0.02 Cooling

(c)

60

55

50
300

400

500

600

700

65

55

50
400

500

600

700

Young's Modulus (GPa)

Young's Modulus (GPa)

60

300

600

700

60

55

50
300

400

500

600

700

Temperature (K)

SnTe(x=0)V0.04 Heating
SnTe(x=0)V0.04 Cooling

(e)
(c)

500

SnTe(x=0)V0.03 Heating
SnTe(x=0)V0.03 Cooling

(d)
(c)

Temperature (K)
65

400

Temperature (K)

Young's Modulus (GPa)

Young's Modulus (GPa)

Temperature (K)
65

SnTe(x=0)V0.01 Heating
SnTe(x=0)V0.01 Cooling

(b)

(f)
60

SnTe(x=0.016)V0 Heating
SnTe(x=0.016)V0 Cooling

55

50

45
300

400

500

600

700

Temperature (K)
Temperature (K)
Figure 7.8. The Young’s modulus versus temperature for the six SnTe–SiCNP specimens
included in this study. For each specimen, there is no observable hysteresis between the
heating and cooling curves indicating the lack of significant microcracking or bloating
over the test temperature range (room temperature to 663 K). The error bars are smaller
than the plotting symbols for each modulus value in (a–f).

202

Table 7.3. For the six SnTe-SiCNP specimens included in this study, results of a least
squares fit to equation (4a) for the Young’s modulus, E, versus temperature, T, data and
to equation (4b) for the shear modulus, G, versus T, data. The coefficients of
determination for the fit of the E versus T and the G versus T data are given by
and
, respectively.
Specimen

SnTe(x=0)V0

Vol.
fraction
SiC
0.00

SnTe(x=0)V0.01

0.01

SnTe(x=0)V0.02

0.02

SnTe(x=0)V0.03

0.03

SnTe(x=0)V0.04

0.04

Young's Modulus (GPa)

SnTe(x=0.016)V0 0.00

ERT

bTE
(K-1)×10-4

R2

62.87 ±
0.13
60.84 ±
0.10
63.40 ±
0.12
64.48 ±
0.09
61.04 ±
0.07
55.31 ±
0.15

5.83 ±
0.09
5.33 ±
0.07
5.82 ±
0.08
5.38 ±
0.06
5.44 ±
0.05
5.07 ±
0.12

0.993 25.27 ±
0.05
0.995 24.54 ±
0.05
0.994 25.33 ±
0.05
0.996 25.42 ±
0.05
0.998 24.41 ±
0.03
0.995 21.70 ±
0.07

GRT

bTG
(K-1)

R2

6.14 ±
0.09
5.62 ±
0.09
6.20 ±
0.08
5.72 ±
0.08
5.37 ±
0.05
5.29 ±
0.14

0.994
0.992
0.995
0.994
0.998
0.980

ERT
bEL
RT
TKINK

bEU

Temperature (K)

Figure 7.9. Schematic representation of the bilinear Young’s modulus, E, versus
temperature, T, behavior showing TKINK and the associated slope change in the E versus T
curve.

203

(a)

1.0

SnTe(x=0)V0 Heating
SnTe(x=0)V0 Cooling

0.5

Residual (GPa)

Residual (GPa)

1.0

0.0
-0.5
-1.0

(b)

0.5
0.0
-0.5
-1.0

300

400

500

600

700

300

Temperature (K)
(c)

1.0

SnTe(x=0)V0.02 Heating
SnTe(x=0)V0.02 Cooling

0.5
0.0
-0.5
-1.0

(d)

600

700

SnTe(x=0)V0.03 Heating
SnTe(x=0)V0.03 Cooling

0.5
0.0
-0.5

400

500

600

700

300

Temperature (K)
(e)

400

500

600

700

Temperature (K)
1.0

SnTe(x=0)V0.04 Heating
SnTe(x=0)V0.04 Cooling

0.5

Residual (GPa)

Residual (GPa)

500

-1.0
300

1.0

400

Temperature (K)

Residual (GPa)

Residual (GPa)

1.0

SnTe(x=0)V0.01 Heating
SnTe(x=0)V0.01 Cooling

0.0
-0.5
-1.0

(f)

SnTe(x=0.016)V0 Heating
SnTe(x=0.016)V0 Cooling

0.5
0.0
-0.5
-1.0

300

400

500

600

700

300

400

500

600

700

Temperature (K)
Temperature (K)
Figure 7.10. The residuals (equation 5) representing the difference between the
experimental Young’s modulus data and the modulus values predicted from the leastsquares fit of the E versus T data to equation (4). The dashed lines at 0.05 GPa are a
guide, representing roughly ± 0.01 ERT, where ERT is defined as the room temperature
intercept of the modulus–porosity relationship given by equation (4a). A change in the E
versus T slope occurs at approximately 543 K (TKINK).

204

7.3.2.1 Bilinear model of elastic modulus versus temperature
Although in this study the decrease in Young’s modulus for SnTe1+X is
approximately linear with increasing T, we will consider (1) a bilinear model of the
elastic modulus versus temperature behavior and (2) composition-dependent differences
and subsequent elastic modulus differences between ingots SnTe(x=0) and
SnTe(x=0.016) in this study. A schematic of the bilinear model for the E versus T
behavior is shown in Figure 7.9.
The motivation for the bilinear model comes from examining the residuals
obtained from the least-squares fit of the linear model (equation (4a)) to the SnTe1+X E
versus T data. For a given Young’s modulus, temperature data pair (Ej, Tj) the jth
residual, residj is defined as
residj = (Ej - Epred)

(5)

where Epred = the E value predicted by the least-squares fit to equation (4a) for T = Tj.
Thus, for a given data set including a total of N data pairs (Ej, Tj), the least-squares
procedure yields N residuals, which measure the differences between the data and the
curve obtained by the least-squares fit. Using the Epred values obtained from the linear
model, the residuals for each of the six specimens (Figures 7.10a – 7.10f) show maxima
in the vicinity of 543 K.
In contrast to the linear model, for the bilinear model for the E versus T behavior,
equation 4a is applied separately for the two contiguous temperature segments: (i) T <
TKINK and (ii) T > TKINK (Tables 7.4 and 7.5, Figure 7.9). At the temperature T = TKINK ,
the E versus T slope change is characterized by Δb, such that

205

Table 7.4. For two separate temperature ranges, RT – 543 K, and 543 K – 663 K, the E
versus T was fit to equation (4a).
Specimen

Temperature
range (K)
SnTe(x=0)V0
RT to 543
543 to 663
SnTe(x=0)V0.01 RT to 543
543 to 663
SnTe(x=0)V0.02 RT to 543
543 to 663
SnTe(x=0)V0.03 RT to 543
543 to 663
SnTe(x=0)V0.04 RT to 543
543 to 663
SnTe(x=0.016)V0 RT to 543
543 to 663

Fitted parameters
ERT
bTE (×10-4 K-1)
62.6 ± 0.1
5.4 ± 0.1
66.0 ± 0.3
7.1 ± 0.2
60.7 ± 0.1
5.1 ± 0.1
61.9 ± 0.7
5.8 ± 0.3
63.2 ± 0.1
5.5 ± 0.1
65.5 ± 0.6
6.7 ± 0.2
64.3 ± 0.1
5.1 ± 0.1
66.0 ± 0.3
6.1 ± 0.1
61.0 ± 0.1
5.3 ± 0.1
62.0 ± 0.1
5.9 ± 0.1
55.0 ± 0.1
4.5 ± 0.1
56.6 ± 1.2
5.8 ± 0.6

R2
0.999
0.995
0.993
0.972
0.993
0.987
0.995
0.996
0.996
0.991
0.991
0.907

Table 7.5. Comparison of Δb, equation (6), for this study and LAST [Ren 2010].
Specimen
SnTe(x=0)V0

Material Type
SnTe
SnTe – 1 vol%
SnTe(x=0)V0.01
SiCNP
SnTe – 2 vol%
SnTe(x=0)V0.02
SiCNP
SnTe – 3 vol%
SnTe(x=0)V0.03
SiCNP
SnTe – 4 vol%
SnTe(x=0)V0.04
SiCNP
SnTe(x=0.016)V0 SnTe1.016
155A (5K/min)
Ag0.86Pb19Sb1.0Te20
155B (5K/min)
Ag0.86Pb19Sb1.0Te20
155B (2K/min)
Ag0.86Pb19Sb1.0Te20

TKINK
543 K
543 K

Δb
-0.31
-0.14

Reference
This study
This study

543 K

-0.22

This study

543 K

-0.20

This study

543 K

-0.11

This study

543 K
523 K
523 K
523 K

-0.27
+0.47
+0.51
+0.47

This study
[Ren 2010]
[Ren 2010]
[Ren 2010]

206

b 

bEL  bEU
bEL

(6)

where bEL is the slope of the lower temperature region, T < TKINK and bEU is the slope of
the region upper temperature segment, T > TKINK (Table 7.5 and Figure 7.9). If, as
suggested above, we let TKINK = 543 K and apply equation 4a in a bilinear (piecewise)
manner from TRT to TKINK and from TKINK to TMAX then the residuals for the bilinear model
are reduced in magnitude (Figure 7.11) compared to the linear model and the maximum
near T = 543 K largely disappears (Figure 7.10). This result indicates that the bilinear
model is useful and that 543 K is a reasonable estimate for TKINK.
Based on a work by Hoang et al.[Hoang 2005], Ren et al. [Ren 2010] derived a
model for the similar bilinear E versus T behavior observed for a lead-antimony-silvertellurium thermoelectric material (LAST, Ag0.86 Pb19Sb1.0Te20), where a change in the
slope of E, versus was attributed to an order-disorder transition. The change in slope, Δb
with increasing temperature (equation (6)) was positive in the Ren et al. study [Ren 2010]
while in this study Δb is negative (Table 7.5). However, the values of TKINK are similar
for the two studies, namely 523 K for LAST [Ren 2010] and 543 K for this study.
In terms of the possible mechanism for the bilinear behavior of SnTe in this study,
it is important to note that the LAST materials studied by Ren et al. [Ren 2010] are
essentially silver and tin-doped PbTe and that PbTe is quite similar to SnTe in many
respects. For example, both SnTe and PbTe are IV-VI tellurides that crystallize in the
rocksalt structure [Lawson 1951; Noda 1987; Beattie 1969]. Other physical properties
for SnTe and PbTe that also are similar include the lattice constants, a0 (SnTe a0 = 0.6304
nm, PbTe a0 = 0.6454 nm) [Noda 1987; Mariano 1967; Seddon 1976], hardness, H (SnTe
207

1.0

SnTe(x=0)V0 Heating
SnTe(x=0)V0 Cooling

(a)

0.5

Residual (GPa)

Residual (GPa)

1.0

0.0
-0.5
-1.0

0.5
0.0
-0.5
-1.0

300

400

500

600

700

300

Temperature (K)
1.0

SnTe(x=0)V0.02 Heating
SnTe(x=0)V0.02 Cooling

(c)

0.5
0.0
-0.5
-1.0

600

700

SnTe(x=0)V0.03 Heating
SnTe(x=0)V0.03 Cooling

(d)

0.5
0.0
-0.5

400

500

600

700

300

Temperature (K)
1.0

SnTe(x=0)V0.04 Heating
SnTe(x=0)V0.04 Cooling

(e)

400

500

600

700

Temperature (K)

0.5

Residual (GPa)

Residual (GPa)

500

-1.0
300

1.0

400

Temperature (K)

Residual (GPa)

Residual (GPa)

1.0

SnTe(x=0)V0.01 Heating
SnTe(x=0)V0.01 Cooling

(b)

0.0
-0.5
-1.0

SnTe(x=0.016)V0 Heating
SnTe(x=0.016)V0 Cooling

(f)

0.5
0.0
-0.5
-1.0

300

400

500

600

700

300

400

500

600

700

Temperature (K)
Temperature (K)
Figure 7.11. Unlike Figure 7.10, the residuals represent the difference between the
experimental data and the least-squares fit performed to equation (4) in a piecewise
manner, that is least-squares fits were performed separately for the two temperature
intervals (i) TRT to TKINK and (ii) TKINK to the maximum test temperature. As in Figure
7.10, the dashed lines at 0.05 GPa represent roughly ± 0.01 ERT, where ERT is defined as
the room temperature intercept of the modulus-porosity relationship given by equation
(4a). In (a) – (f), the vertical line at 543 K represents TKINK, the temperature at which the
change in the E versus T slope occurs.

208

H = 0.78 GPa, PbTe H = 0.76 GPa) [Cui 2003], thermal expansion coefficient, α (PbTe α
= 20.4 × 10-6 K-1, SnTe α = 21.3 × 10-6 K-1) [Houston 1968; Belson 1970] and melting
points, TMP (PbTe TMP = 1197 K, SnTe TMP = 1079 K) [Liu 2009]. In addition, the
elastic moduli of cubic materials such as SnTe and PbTe can be compared using the
mean of the Hashin-Strikman (H-S) bounds. (The H-S bounds, which are computed from
the single crystal elastic constants, can be used to estimate the elastic moduli of dense
polycrystalline materials without crystallographic texture). For SnTe, the mean of the
H–S bounds for the Young’s modulus, E, and shear modulus, G, is 55.6 and 21.7 GPa,
respectively [Beattie 1969; Simmons 1971]. For PbTe, the mean of the H–S bounds
Young’s moduli and shear moduli is 58.1 and 23.0 GPa, respectively [Houston 1968].
Thus, both the E and G values of SnTe and PbTe are similar.
Thus, given both the similarity between SnTe and PbTe (and LAST) and the
tendency of SnTe to crystallize with an off-stoichiometric composition (as will be
discussed in the following section), the order-disorder mechanism proposed by Ren et al.
[Ren 2010] may also apply to SnTe. However, it must be noted that in LAST, the Ag
precipitates as nanoparticles of Ag2Te [Pei 2011; Cook 2009], but the order–disorder
mechanism related to the modulus–temperature kink in LAST [Ren 2010] may be more
closely associated with the matrix rather than the Ag2Te nanoparticles. SnTe does not
have a similar nanostructure. Thus, further research is needed to explore the kink
behavior in the E versus T behavior of SnTe.

209

7.3.2.2 Effects of chemical composition and porosity on elastic moduli of the SnTe1+X
matrix
In addition to the E versus T slope discussed in the previous section, we shall also
consider the nature of changes in elastic modulus both as (i) a function of the chemical
composition and (ii) as a function of residual porosity in the specimens. We shall first
consider the possible effects on the elastic modulus due to compositional differences.
In this study, the composition of matrix may be written as SnTe1+x, where for
ingot SnTe(x=0), x = 0 and for ingot SnTe(x=0.016), x = 0.016. For specimens without
SiCNP addition, the room temperature Young’s modulus of specimen SnTe(x=0)V0 from
ingot SnTe(x=0) is 62.9 GPa (Table 7.2 and Figure 7.8) and the Young’s modulus of
specimen SnTe(x=0.016)V0 from ingot SnTe(x=0.016) is 55.3 GPa.
These differences in the elastic moduli between ingots SnTe(x=0) and
SnTe(x=0.016) may be related to differences in the chemical composition between the
two ingots since significant changes in Young’s modulus and bulk modulus have been
observed to accompany shifts in the chemical composition of solid solution systems [Ren
2007]. As an example, for 14 solid solution systems from the literature, Ren et al. [Ren
2007] characterized composition-induced changes in Young’s modulus, E, and bulk
modulus, K, in terms of Emax/Emin and Kmax/Kmin, where the subscripts “max” and “min”
refer to the maximum value in E or K, respectively, over the entire compositional range
of the solid solution. As reviewed by Ren et al., Emax/Emin and Kmax/Kmin values as large
as 3 have been observed in the literature [Ren 2007].
To further examine the numerical values of composition-related changes in
mechanical properties, Table 7.6 compares the observed changes in E with composition
210

Table 7.6. Fractional changes in Young’s modulus, E, shear modulus, G, and hardness H
as a function of changes in composition from n1 to n2 [this study, [Kawaharada 2004;
Ravinder 2001; Schenk 1998].
Material

SnTe1+x
NiZrSn1-xSbx
NiZrSn1-xSbx
Mn1xCdxFe2O4
Mn1xCdxFe2O4
Zn1-xCdxTe

Property Property at
composition
x = n1
E
x=0
62.9 GPa
E
x = 0.01
111 GPa
E
x = 0.01
111 GPa
E
x=0
352 GPa
G
x=0
140 GPa
H
x=0
700 MPa

Property at
composition
x = n2
x = 0.016
55.3 GPa
x = 0.02
89.2 GPa
x = 0.05
71.8 GPa
x = 0.2
256 GPa
x = 0.2
108 GPa
x = 0.04
930 MPa

211

Fractional References
change in
property
-0.12
This study
-0.20

-0.27

[Kawaharada
2004]
[Kawaharada
2004]
[Ravinder 2001]

-0.23

[Ravinder 2001]

+0.33

[Schenk 1998]

-0.35

for SnTe1+X in this study, with additional literature data on compositionally-related
changes in Young’s modulus, E, shear modulus, G, and hardness H for several tellurides,
antimonides and oxides [Ravinder 2001; Kosuga 2005; Kawaharada 2004; Schenk 1998].
In Table 7.6, the compositional change in SnTe1+X comes about from the creation of Sn
vacancies in the lattice [Rogacheva 1991] (Section 7.3.1) and each of the other examples
in Table 7.6 is substitutional systems. From Table 7.6 and the Ren et al. study [Ren
2010], it appears to be feasible that the 10% difference in the elastic moduli observed
between ingots SnTe(x=0) and SnTe(x=0.016) (Table 7.3) in this study might be
attributed to compositional differences. The lattice parameter measurements for ingots
SnTe(x=0) and SnTe(x=0.016) (Section 7.3.1) also are consistent with compositional
differences between ingots SnTe(x=0) and SnTe(x=0.016).
In addition to composition differences between the ingots SnTe(x=0) and
SnTe(x=0.016), differences in the volume fraction porosity, P, among the specimens can
also affect the elastic moduli of the specimens. In general, frequently used relationship
between the Young’s modulus, E, shear modulus, G, and P are given by [Rice 1998]
E = E0 exp(-bPEP)

(7a)

G = G0 exp(-bPGP)

(7b)

where E0 and G0 are the Young’s modulus or shear modulus at zero volume fraction
porosity, P. The mean of the H-S bounds (section 7.3.2.1) can be used to estimate E0 and
G0. The parameters bPE and bPG are material dependent constants [Rice 1998] that
characterize the rate of decrease in the elastic moduli with increasing P. The values of
bPE and bPG for SnTe1+X are not available in the literature and in fact modulus versus

212

porosity data is very limited in the TEs literature. The only two studies in the literature
for which the porosity dependence of E and G for TE materials are Ni et al. [Ni 2009]
study of LAST and Schmidt et al. [Schmidt 2013] study of YbAl3. For LAST, bPE = 3.5 ±
0.2 and bPG = 3.5 ± 0.2, and for YbAl3, bPE = 2.34 ± 0.06 and bPG = 2.38 ± 0.06.
In order to compare the single crystal of E0 and G0 from the literature for SnTe
[Beattie 1969; Simmons 1971] to the E and G of the polycrystalline specimens in this
study, we must account for the effect of porosity in the polycrystalline specimens
(Equations (7a), (7b)), since the single crystal data represent materials for which P = 0.
Beattie’s single crystal moduli [Beattie 1969] were corrected for the P for the specimens
without SiCNP additions (SnTe(x = 0)V0 and SnTe(x = 0.016)V0) using
( )

(

)

(7c)

( )

(

)

(7d)

where ECORR and GCORR are the porosity-corrected values of E0 and G0. Also, for

and

we use the range of values obtained from the LAST and YbAl3 studies [Ni 2009;
Schmidt 2013]. The experimentally measured RT values of Eexp and Gexp are compared
to the corrected single crystal values, ECORR and GCORR, in Table 7.7. Although the
measured Eexp and Gexp are consistently higher than these calculated values from Beattie’s
single crystal data [Beattie 1969; Simmons 1971], the Eexp and Gexp values for the
tellurium-rich specimen, SnTe(x = 0.016)V0, are in significantly better agreement (3–8 %
higher) with the porosity-corrected Beattie data than the Eexp and Gexp values for the
stoichiometric specimen, SnTe(x = 0)V0 (which are 21–26 % higher).
A key question is “Were Beattie’s [Beattie 1969] single crystal SnTe specimens
also Te rich?” According to Baughman [Baughman 1969], Beattie’s SnTe single crystal
213

Table 7.7. In order to compare the room temperature experimental values of Young’s
modulus, Eexp, and shear modulus, Gexp, for this study’s specimens without SiCNP
additions to the single crystal values of E0 and G0 values from SnTe from the literature
[Beattie 1969; Simmons 1971], equations (7c) and (7d) were used to calculate porosity
corrected values for the single crystal data using the modulus-porosity slope data for two
thermoelectric materials, namely YbAl3 (bPE = 2.34, bPG = 2.38) and LAST (bPE = 3.5,
bPG = 3.5) [Schmidt 2013; Ni 2009]. This study’s experimental Eexp and Gexp values for
the tellurium rich specimen, SnTe(x=0.016)V0, are in the best agreement with the range
of porosity corrected values ECORR and GCORR.
Specimen

SnTe
(x=0)V0
SnTe
(x=0.016)V0

P

Eexp
ECORR
(GPa) (bPE=2.34)
(GPa)
62.87
0.028 ± 0.13 52.03
55.31
0.022 ± 0.15 52.76

ECORR
(bPE=3.5)
(GPa)
50.36
51.43

214

Gexp
ECORR(GPa) (bPE=2.38)
(GPa)
25.27
± 0.05 20.68
21.70
± 0.07 20.97

ECORR(bPE=3.5)
(GPa)
20.04
20.46

specimens were likely Te-rich. Beattie’s specimens were grown by the Czochralski
technique, “from a stoichiometric mixture of the components” [Baughman 1969],
however, the resulting SnTe crystals had “an indication that the original crucible charge
was not exactly stoichiometric …” giving a tellurium-rich phase, as supported by
Baughman’s observation [Baughman 1969] that “The termination of the tin telluride
crystal … is a typical example of this occurrence” [Baughman 1969]. Thus, the SnTe
composition is likely off stoichiometry for the available single crystal elasticity literature
[Beattie 1969], so that in turn the polycrystalline aggregate values [Simmons 1971]
calculated from the Beattie single crystal data in turn also represents the elastic moduli
for non-stoichiometric SnTe. Unfortunately, the precise chemical composition of
Beattie’s SnTe specimens is not given by either Beattie [Beattie 1969] or Baughman
[Baughman 1969]. Thus this study is the first study in the literature to show the apparent
sensitivity of the elastic moduli of SnTe1+X to small changes in x, although in the
literature [Ren 2007] the elastic moduli of other compounds have a documented
sensitivity to small changes in composition.
7.3.2.3 Comparison of the Young’s modulus versus elasticity behavior of
polycrystalline SnTe1+X to the literature
The values of ERT and bTE found in this study for SnTe1+X are comparable to those
measured for PbTe and LAST [Ren 2010; Houston 1968], which are also chalcogenides
and have the same crystal structure as SnTe (Table 7.8). If we compare the ERT and bTE
values SnTe1+X -SiCNP more broadly with other thermoelectric materials, namely with
data for selected skutterudites (Table 7.8) we find generally smaller values of bTE, namely

215

Table 7.8. Comparison of the Young’s modulus, E, versus temperature behavior for a
variety of brittle materials, SnTe [this study], PbTe [Houston 1968; Simmons 1971; Ren
2010], and selected skutterudite TE materials [Schmidt 2012; Ravi 2008]. The
parameters ERT and bRT were obtained via a least-squares fit of each of the data sets to
equation (4a). The coefficient of determination, R2, was equal to or greater than 0.98 for
each data set, indicating that equation (4a) describes the E versus temperature behavior
well.
Data
Temp ERT
bTE
R2E
Tech- References
Material
points Range (GPa)
(× 10-4
nique
(K)
K-1)
SnTe1+x (PC) a,b 25 b
RT –
55.3 –
5.07 – 0.993 RUS This study
c
663
64.5
5.83
–
0.998
PbTe (SC) a
5
100 – 58.4
5.7
0.99
IE d
[Houston
303
1968;
Simmons
1971]e
Ag0.86Pb19
12 f
RT –
61 – 64 5.9 –
0.98
RUS [Ren 2010]
a
c
Sb1.0Te20 (PC)
523
6.6
Co0.95Pd0.05
13
295 – 140.4
1.9
0.99
RUS [Schmidt
c
Te0.05Sb3
573
2012]
doped with 0.1
at.% Ce (PC) a
Co0.95Pd0.05
13 g
295 – 128.2 – 1.6 to 0.99
RUS [Schmidt
a
c
Te0.05Sb3 (PC)
573
138.7
1.8
2012]
Ce0.9Fe3.5Co0.5 13
295 – 127.7
2.5
0.99
RUS [Schmidt
c
Sb12 (PC) a
573
2012]
CoSb3 – doped 60 –
293 – 137.3 – 2.1 –
0.99
IE d
[Ravi 2008] i
a
h
(PC)
64
597
140.8
2.2
CeFe3RuSb12
62 –
293 – 132.1 – 2.2 –
0.99
IE d
[Ravi 2008] i
a
j
(PC)
63
597
138.1
2.3
a
Single crystal denoted by SC, polycrystalline denoted by PC
b
Includes each of the six specimens included in this study (Table 7.1), measured with 25
data points per specimen
c
Resonant ultrasound spectroscopy
d
Impulse excitation
e
The Young’s modulus from Houston was obtained as the average of the Hashin and
Shtrikman bounds as calculated by Simmons and Wang [Simmons 1971]
f
Each of 3 specimens were measured, 12 data points per specimen
g
Each of 2 specimens were measured, 13 data points per specimen
h
Each of 4 specimens were measured, 60 to 64 data points per specimen
i
ERT and bTE from calculation in [Schmidt 2012]
j
Each of 4 specimens were measured, 62 to 63 data points per specimen

216

between 1.6 and 2.3 K-1 [Schmidt 2012; Ravi 2008] (Table 7.8) although the ERT values
for the skutterudites are higher than those for SnTe and PbTe.
7.3.2.4 Effect of volume fraction of SiCNP on the elastic moduli of the SnTe1+X -SiCNP
composites
Since the maximum surface thermal stress, max, produced by a thermal transient
is function of the Young’s modulus (equation 3), in order to be able to estimate the insevice max for TE composite, one must determine how the added changes in the makeup of the composite (such as adding SiCNP) change the Young’s modulus of the material.
To model the effect of the SiCNP on the Young’s modulus, EC, of the SnTe1+X SiCNP composites included in this study, where in this case Er is the elastic modulus of
the SiCNP reinforcement, Em is the Young’s modulus of the matrix phase, Vm is the
volume fraction of the SnTe1+X matrix and Vr is the volume fraction of the SiCNP
reinforcement, we will use the following four composite models (equations 8 – 12),
namely: the rule of mixtures (ROM) model
EC = Vm Em + Vr Er

(8)

the Reuss constant strain model [Hashin 1962],
V
V
1
 m  r
EC Em Er

(9)

the Hashin particulate composite model [Hashin 1962; Bedolla 2012; Couturier 1997],

 E V  Er Vr  1

EC  Em  m m
 ErVm  Em Vr  1

(10)

and the Halpin-Tsai composite model [Halpin 1992]

217

 1  2( a / b )qVr 

EC  Em 
 ErVm  Em Vr  1

(11)

where EC is a function of the boundary condition parameter, q,

 Er 

 1
Em 

q
 Er   a 

  2 
 Em   b 

(12)

and a/b is the length/thickness ratio of the reinforcing phase.
Note that each of the composite models above (equations (8)–(12)) is a function
of Vr, the volume fraction of the reinforcing phase. The particle size of the reinforcing
phase is not explicitly included in any of the models, although it is assumed that the
dimensions of the reinforcing particles are much smaller than the specimen dimensions.
For the calculations of EC from equations (8) – (12), the volume fractions of
SiCNP, Vr, in this study were 0.0, 0.01, 0.02, 0.03 and 0.04. Since the SiCNP are
approximately equiaxed, the particle aspect ratio, a/b, in the Halpin-Tsai equation was set
to unity. The value of the Young’s modulus for SnTe1+X matrix, Em, was set at 67.1 GPa,
which is the RT E value measured on specimen SnTe(x=0)V0 (without SiCNP addition)
and then corrected to zero porosity (Section 7.3.2.2). The Young’s modulus of SiCNP, the
reinforcing phase, Er, was set to 450 GPa, which is the Young’s modulus for bulk SiC [51
52]. Figure 7.12 includes the experimental values of the Young’s modulus of the
SnTe1+X - SiCNP, the experimental values corrected to zero porosity and the predictions of
the four composite models (equations (8) – (12)).
The porosity, P, of the specimens included in this study ranged over a relatively
narrow range, from 0.022 to 0.051 (Table 7.1). However, each composite specimen had a
218

Young's modulus (GPa)

80

Rule of Mixtures
Halpin-Tsai, a/b = 1

Measured
Adjusted to P = 0 by bPE = 2.34

Hashin model

Adjusted to P = 0 by bPE = 3.5

Reuss model

75
70
65
60
0.00

0.01

0.02

0.03

0.04

Volume fraction of SiCNP
Figure 7.12. Comparison of the experimental Young’s modulus, E, results for the
composites SnTe1+X –ySiC (y = 0.0 to 0.04) with the four composite models given by
equations (8) – (12). Also plotted are the values of E corrected to zero porosity using
equation (7a).

219

porosity that was different than the other specimens (Table 7.1), thus in order to compare
the experimental data with the four elasticity models, the Young’s modulus was corrected
to correspond to zero porosity. Figure 7.12 shows both (i) the experimental Young’s
modulus data and (ii) the data corrected to zero P (using equation 7a). The Reuss model
(equation (9)) and the Hashin model (equation (10)) correspond best with the
experimental data.
7.5 Summary and conclusions
The linear decrease in Young’s modulus, E, (Figure 7.8 and Table 7.3) and shear
modulus, G, (Table 7.3) with increasing temperature is relatively described well by
equations 4(a) and 4(b), respectively. The lack of significant hysteresis between the
heating and cooling curves for E and G indicates that no significant microcracking or
bloating occurred over the test temperature range (RT to 663 K).
However, there appears to be a bilinear behavior for the elastic modulus versus
temperature behavior (Figure 7.9), with a change in the modulus versus temperature
behavior at about 543 K. This behavior might be explained by an order–disorder
mechanism similar to that proposed by Ren et al. [Ren 2010].
The addition of up to 4 vol% SiCNP to the SnTe1+X matrix lead to relatively
modest changes in (1) the observed modulus versus temperature slope and (2) the RT
elastic moduli, ERT. Changes in ERT can be described relatively well by either the Reuss
[Hashin 1962]or the Hashin [Hashin 1962] composite models (Figure 7.12). In the study,
the elastic modulus changes due to (i) the possible order–disorder transition in offstoichiometric SnTe and (ii) the addition of up to 4 vol% SiCNP was small. However
compositional shifts in the SnTe matrix seem to represent a much larger source of
220

perturbation on the elastic moduli of the SnTe1+X – SiCNP composite materials than either
the SiCNP additions or the bilinear E versus T behavior.
For the SnTe1+X matrix, in the absence of SiCNP addition, the compositional
differences between SnTe(x = 0) and SnTe(x = 0.016) may be responsible for the
differences in the measured elastic moduli between the two ingots. Similar significant
changes in elastic moduli with composition of solid solution systems have been reported
in the literature for other materials (Table 7.6), but this study is the first to report the
sensitivity of the elastic moduli to compositional changes in SnTe. Future studies should
explore functional relationship of the elastic moduli of SnTe1+X and the Te composition,
especially since there are some questions about the stoichiometry of the SnTe elasticity
data currently available in the literature.
ACKNOWLEDGEMENTS
The authors acknowledge the financial support of 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 Science, Office of
Basic Energy Sciences under award number DE-SC0001054. The authors also
acknowledge the use of the equipment high-temperature RUS measurements through the
Oak Ridge National Laboratory’s High Temperature Materials Laboratory User Program,
which is sponsored by the U. S. Department of Energy, Office of Energy Efficiency and
Renewable Energy, Vehicle Technologies Program.

221

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8 Mechanical properties of lower-cost, earth-abundant chalcogenide thermoelectric
materials, PbSe and PbS, with additions of 0 to 4% CdS or ZnS
Robert D. Schmidt 1, Eldon D. Case 1, Li-Dong Zhao 2, Mercouri G. Kanatzidis 2
1
Chemical Engineering and Materials Science Department,
Michigan State University, East Lansing, MI, 48824
2
Department of Chemistry, Northwestern University, Evanston, IL, 60208
To be submitted to: Journal of Materials Science
Abstract
The thermoelectric (TE) properties of PbTe-based materials have been optimized
to the extent that the maximum figure of merit, ZT, achieved is greater than 2. However,
the tellurium content limits the application potential due to both availability and cost.
Replacing the tellurium with selenium or sulfur produces an analogous thermoelectric
material using strategies learned from PbTe-based materials to achieve ZT values of 1.3
to 1.6. In order to effectively incorporate these new materials into TE devices, it is
important to understand materials’ response to thermally and mechanically imposed
loads, which in turn requires knowledge of the mechanical properties. In this study, the
hardness was determined by Vickers indentation and elastic modulus and Poisson’s ratio
were measured using resonant ultrasound spectroscopy (RUS) on PbSe- and PbS-based
thermoelectric specimens as a function the addition of 0-4 at% of CdS or ZnS. The
hardness and moduli of PbSe-based or PbS-based TE materials are not strong functions
of the addition of CdS or ZnS. With 2.0 at% or 2.5 at% Na doping, the hardness of PbSebased or PbS-based TE materials increased by about 30% and the elastic moduli
decreased by 5-10%. In addition, PbS may be effectively sintered at 723 K when doped
with 2.5 at% Na, but requires a higher sintering temperature when undoped.
228

Keywords: thermoelectric; hardness; elastic modulus
8.1 Introduction
The figure of merit, ZT, of bulk thermoelectric (TE) materials is defined as [Tritt
2011]
(1)
where S is Seebeck coefficient, σ is the electrical conductivity, T is temperature, and κ is
thermal conductivity. The ZT has been increased using a variety of techniques, including
atomic scale doping or substitution [Gelbstein 2008; Zhu 2009; Zhao 2012b], creation of
nanostructured bulk materials [Toprak 2004; Mi 2008; Hsu 2004; Zhu 2009],
incorporation of nanoparticles [Androulakis 2007; Zhao 2012a; Zhou 2008; Alleno 2009;
Ji 2007], or a combination of atomic, nanostructural, and microstructural length scale
modifications [Biswas 2012].
The application of these techniques has been particularly successful with lead
telluride-based thermoelectrics, with ZT values near or greater than 2 reported [Zhao
2013; Biswas 2012; Heremans 2008]. A limitation on the application of these materials
is the use of tellurium, due to the relative scarcity of the element [Haxel 2002], but sulfur
or selenium may be substituted for tellurium to produce analogous compounds [Zhao
2011; Zhao 2012a; Zhao 2012b; Zhao 2013]. The thermoelectric properties of lead
sulfide and lead selenide have been optimized with the same techniques as the lead
telluride-based compounds, such that a ZT value of 1.6 has been achieved for lead
selenide [Zhao 2013]and 1.3 for lead sulfide [Zhao 2012a; Zhao 2012b]. Changing the
chemistry of the thermoelectric however, can dramatically alter the mechanical properties
229

of the material, as has been observed in lead telluride-based materials [Ren 2007; Ren
2008].
The elastic properties of the TE materials are required as well to determine the
material response to stresses, just as the transport properties are required to determine the
ZT of the material. In waste heat harvesting applications, the stresses that the TE material
must survive are not trivial, as TE materials are intended for an environment with thermal
gradients, thermal shocks, attached to materials with thermal expansion mismatches, and
subjected to external loads. In addition, a TE module is typically composed of tens or
hundreds of legs of TE material electrically connected in series and thermally in parallel.
This arrangement subjects each leg individually to the full thermal gradient and
associated stresses, but the failure of just one leg results in the electrical failure of an
entire TE module.
The mechanical properties of many undoped TE materials have been published,
including PbTe [Houston 1968], Mg2Si [Whitten 1965; Milekhine 2002], SnTe [Beattie
1969] and CdSe [Cline 1967], but the mechanical properties may be significantly
changed when the TE material is optimized for improved ZT. The hardness and/or elastic
moduli of a material have been shown to change by the addition of nanoparticles [Zhao
2008; Kvetková 2013], creation of nanoprecipitates in the bulk material [Ni 2010],
doping [Gelbstein 2008], or alloying [Gelbstein 2008; Darrow 1969].Therefore, to
understand the mechanical response of a TE material that may be incorporated into a
device, the mechanical properties need to be measured on a TE material with the addition
of dopants, with nanoparticle or nanoprecipitates.

230

8.2 Experimental procedure
8.2.1 Materials and Specimen Preparation
Two tellurium-free thermoelectric materials with analogous crystal structure to
PbTe-based TE materials were included in this study, using methods similar to those
employed to optimize the PbTe-based TE materials [Zhao 2012b; Zhao 2013]. Ingots
were fabricated from elemental materials (99.99+% purity) with nominal compositions of
PbS or PbSe with x% CdS/ZnS, where the at fraction x = 1, 2, 3 and 4. For PbS, 2.5 at%
Na dopant was added, and for PbSe, 2.0 at% Na dopant was added [Zhao 2012b; Zhao
2013]. In addition, ingots of PbS and PbSe without Na dopant, and an ingot of PbSe with
2.0 at% Na dopant were made. Carbon-coated fused silica tubes with the elemental
material were evacuated to approximately 10-4 torr before being flame-sealed [Zhao
2012b; Zhao 2013]. The tubes were heated to 723 K in 12 h, then to 1423 K in 7 h,
thermally soaked for 6 h at 1423 K and then water quenched to room temperature [Zhao
2012b; Zhao 2013]. The ingots produced were crushed into powders, sieved through a 53
μm sieve, then densified by Pulsed Electric Current Sintering (PECS, Thermal
Technology SPS-10-4 or SPS-DR 2050) at 723 K (PbS), 873 K (undoped PbS) or 823 K
(PbSe) for 10 min in a 20 mm diameter graphite die under 60 MPa axial pressure in an
argon atmosphere [Zhao 2012b; Zhao 2013]. Except for the undoped PbS sintered at 723
K, this produced highly dense disk-shaped billets 20 mm in diameter and 9 mm thick,
with volume fraction porosity less than 0.05. Using a low speed diamond saw, the billets
were cut into bars, ~ 2 mm × 3 mm in cross section and approximately 9-18 mm long
[Zhao 2012b; Zhao 2013].

231

8.2.2 Elasticity Measurements
In this study, the elastic moduli were determined by a standing acoustic wave
technique, resonant ultrasound spectroscopy (RUS). The elastic moduli of each specimen
are a function of the specimen geometry, dimensions, density and resonant frequencies.
Each of the specimens in this study was of rectangular bar geometry. The dimensions of
each specimen were measured by micrometers (293-832, Mitutoyo, Japan), and the mass
by electronic balance (Adventurer AR2140, OHAUS, Pine Brook IL). The resonant
frequencies were measured by RUS (RUSpec, Quasar International, Albuquerque, NM),
in which the specimen was placed so that the corners of the specimen contacted two
transducers along the specimen’s body diagonal. One transducer was swept across a
range of frequencies from 10 kHz to 760 kHz in 29,999 steps and the mechanical
response to the frequency was recorded in the second transducer. Each sharp peak in
second transducer’s response to the driving signal (Figure 8.1) represents a mechanical
resonance frequency of the specimen. The set of recorded resonant frequencies were fit
to a model by commercial software (RPModel version 2.68b, Quasar International) to
determine the elastic moduli. Details of the RUS procedure may be found elsewhere
[Ren 2009; Ni 2010; Schmidt 2010; Migliori 1997; Schmidt 2013a].
The elastic moduli of other thermoelectric materials have been measured by
RUS, including PbTe-based compounds [Ni 2013; Ni 2009a; Ren 2009; Ni 2011; Ren
2010; Morrison 2012], SnTe [Schmidt 2013b], tetrahedrite [Fan 2013], YbAl3 [Schmidt
2013a], Mg2Si [Schmidt 2012a], skutterudite [Rogl 2011; Zhang 2010; Schmidt 2012b;
Schmidt 2010; Salvador 2009; Möchel 2011] and Zn4Sb3 [Bhattacharya 2006].

232

Intensity (A.U.)
0

100

200

300

400

500

Frequency (kHz)
Figure 8.1. RUS scan of PbSe specimen

233

600

8.2.3 Hardness and toughness measurements
Hardness was measured by Vickers indentation at 1.98 N load on a microindenter
(HMV-2000, Shimadzu, Okinawa, Japan), using the equation
H 

1.8544 P
2a 2

(2)

where P is the indentation load and 2a is the length of the indentation diagonal
[Wachtman 2009]. The Vickers hardness values from indentation of a standard block
(Yamamoto Scientific Tools Lab Co. LTD, Chiba, Japan) were used to determine a
calibration constant, β, of 0.95.
8.2.4 Microscopy and X-ray diffraction
The PbS and PbSe specimens were examined by scanning electron microscope
(SEM) on both polished and fractured specimen surfaces at 15 kV accelerating voltage
and 15 mm working distance (6610LV SEM, JEOL, Tokyo, Japan). Polished surfaces
were examined by secondary electron images and backscatter images to examine
indentation impressions and the morphology of secondary phases with different average
atomic weight. Grain size analysis was performed by the lineal intercept method on
secondary electron images of fractured specimen surfaces, with a minimum of 200
intercepts per image and a stereographic projection factor of 1.5. Energy dispersive x-ray
spectroscopy (Oxford EDS) was performed in the SEM at 15 kV accelerating voltage and
10 mm working distance for elemental analysis.
Fracture surfaces of each specimen were examined for mode mixity, M, defined
here as
M = ATRANS/ATOTAL

(3)
234

where ATRANS is the area of transgranular fracture, and ATOTAL is the overall area of a
fractured surface.
X-ray diffraction (XRD) was performed at the Michigan State University Center
for Crystallographic Research with Cu Kα radiation and a step size of 0.008° 2θ (Bruker
Davinci Diffractometer) from 25° to 75° 2θ on a rotary stage. Two XRD scans were
performed on the sintered PbS material, (i) on the bulk densified specimen, and (ii) on
powder ground by hand from the bulk specimen in a mortar and pestle.
8.3 Results and Discussion
8.3.1 Microstructural analysis
Only isolated spherical porosity was observed which is consistent with dense
specimens. Except for 1 at% ZnS in PbSe (with precipitates up to 4 µm), the addition of
ZnS in PbS or PbSe resulted in ZnS precipitates with diameters up to 10 to 15 µm (Tables
8.1 and 8.2), observed primarily at the grain boundaries (Figures 8.2 – 8.4). The addition
of 1 at% to 4 at% CdS in PbS or PbSe resulted in precipitates with diameters of up to 1
µm to 4 µm (Tables 8.1 and 8.2), observed primarily embedded in the matrix material
(Figures 8.2 – 8.4). In backscatter SEM imaging, both the CdS and ZnS precipitates were
uniformly distributed through the specimen matrix, with up to 15 µm ZnS precipitates
observed in both the PbSe and PbS (Figure 8.4, Tables 8.1 and 8.2). No precipitates were
observed in the samples of either PbS or PbSe without CdS or ZnS additions. All the
precipitates observed in this study were faceted (Figures 8.4 and 8.5). In particular, the
precipitate morphology was rod or plate-like for the CdS additions in both PbS and PbSe

235

Table 8.1. Composition, theoretical density, theo, measured density, meas, volume
fraction porosity, P, average grain size, <GS>, typical observed inclusion size range,
Incl, and mode mixity, M (equation 3) for the PbS-based specimens included in this
study.
Composition

theoa

meas

P

<GS>
(µm)
5.9b
1.8
3.2

Incl
(µm)
NA
NA
0.2 to 1

M

PbS
7.5970
7.535
0.008
0.91
Pb0.975Na0.025S 7.5970
7.325
0.036
0.15
Pb0.975Na0.025S 7.5716
7.278
0.039
0.94
+ 1 at% CdS
Pb0.975Na0.025S 7.5462
7.315
0.031
5.4
0.2 to 1.5 0.98
+ 2 at% CdS
Pb0.975Na0.025S 7.5207
7.148
0.050
4.5
0.2 to 2c 0.92
+ 3 at% CdS
Pb0.975Na0.025S 7.4952
7.148
0.046
3.6
0.2 to 3c 0.93
+ 4 at% CdS
Pb0.975Na0.025S 7.5704
7.231
0.045
2.1
0.2 to 12 0.34
+ 1 at% ZnS
Pb0.975Na0.025S 7.5437
7.264
0.037
2.2
0.2 to
0.72
d
+ 2 at% ZnS
10
Pb0.975Na0.025S 7.5168
7.241
0.037
2.3
0.2 to
0.91
d
+ 3 at% ZnS
15d
Pb0.975Na0.025S 7.4898
7.245
0.033
2.8
0.2 to 10 0.76
+ 4 at% ZnS
NA: Not applicable. No inclusions because no addition of CdS or ZnS
a
The theo values are calculated in Table S1 from [Zhao 2012a]
b
The <GS> includes a distribution of several large grains, 5 µm to 30 µm, and smaller
grains, 0.2 µm to 2 µm
c
Inclusions were typically rod- or plate-like shape
d
Larger inclusions were typically stacked plate-like shapes

236

Table 8.2. Composition, theoretical density, theo, measured density, meas, volume
fraction porosity, P, average grain size, <GS>, typical observed inclusion size range,
Incl, and mode mixity, M (equation 3) for the PbSe-based specimens included in this
study.
Composition

theoa

meas

P

<GS>
(µm)
9.9
4.0
3.2

Incl
(µm)
NA
NA
0.2 to 3

PbSe
8.258
8.125
0.016
Pb0.98Na0.02Se
8.258
7.955
0.037
Pb0.98Na0.02Se
8.2243
8.112
0.014
+ 1 at% CdS
Pb0.98Na0.02Se
8.1906
8.048
0.017
3.6
0.2 to 2
+ 2 at% CdS
Pb0.98Na0.02Se
8.157
7.950
0.025
4.0
0.2 to 3b
+ 3 at% CdS
Pb0.98Na0.02Se
8.1232
7.966
0.019
18.7
0.2 to 4b
+ 4 at% CdS
Pb0.98Na0.02Se
8.2163
8.074
0.017
3.3
0.2 to 4
+ 1 at% ZnS
Pb0.98Na0.02Se
8.1746
8.005
0.021
3.2
0.2 to 10
+ 2 at% ZnS
Pb0.98Na0.02Se
8.1329
8.049
0.010
3.2
0.2 to 12
+ 3 at% ZnS
Pb0.98Na0.02Se
8.0912
7.880
0.026
7.0
0.2 to 15
+ 4 at% ZnS
NA: Not applicable. No inclusions because no addition of CdS or ZnS
a
The theo values are calculated in Table S1 from [Zhao 2013]
b
Inclusions were typically rod- or plate-like shape

237

M
0.07
0.28
0.17
0.92
0.81
0.98
0.27
0.73
0.83
0.51

Figure 8.2. Fracture surfaces of PbS specimens indicate primarily transgranular fracture
in undoped PbS (a) changing to intergranular fracture for the Na-doped PbS specimen
(b). With 1% to 4% addition of CdS, the fracture mode changes to primarily
transgranular fracture (b, d), and with 1% to 4% addition of ZnS, the fracture mode
changes to mixed, with majority transgranular and minority intergranular (c, e). Note the
bright areas in images (c) and (e) are the ZnS precipitates.

238

Figure 8.3. Fracture surfaces of PbSe specimens indicate primarily intergranular fracture
for the pure PbSe specimen, the Na-doped PbSe specimen, and the specimens with 1%
addition of CdS or ZnS (a-c). With 2% to 4% addition of CdS or ZnS, the fracture mode
changes to primarily transgranular fracture (d-f), although significant intergranular
fracture was also observed in the specimen with 4% ZnS (f). Note the bright areas in
images (d) and (f) are the ZnS precipitates.

239

Figure 8.4. Secondary images of the polished specimens show isolated, micron scale
spherical porosity and minor scratches from polishing. In the specimens with 4% CdS or
ZnS, precipitates of sub-micron up to approximately 15 μm were observed, particularly in
backscatter electron (BSE) mode. The images of polished PbS in both secondary electron
(SE) and BSE mode (a and b) only exhibit spherical pores ~1 µm, with no evidence of
precipitates, consistent with the material having no additions of CdS or ZnS.

240

Figure 8.4 (cont’d)

241

Figure 8.5. Observed in backscatter, precipitates of CdS were up to ~4 μm, with some
micron scale precipitates with geometry of rods or plates and sharp facets consistent with
crystallographic alignment.

Figure 8.6. Some ZnS inclusions in PbS resembled stacked plates.
242

(Figure 8.5). In addition, the ZnS precipitate morphology included stacked plates,
particularly in the PbS matrix (Figures 8.4 and 8.6).
The fracture mode changed from primarily intergranular fracture in Na-doped PbS
and PbSe to primarily transgranular fracture when additions of up to 4 at% CdS or ZnS
were added to either Na-doped PbS (Table 8.1, Figure 8.2) or PbSe (Table 8.2, Figure
8.3). Mode mixity, M, was examined to determine the fraction of transgranular fracture,
with M = 0 indicating pure intergranular fracture and M = 1 indicating pure transgranular
fracture. Undoped PbS exhibited primarily transgranular fracture, M = 0.91, while the
Na-doped PbS changed to primarily intergranular, M = 0.14. The PbSe specimens
without CdS or ZnS exhibited primarily intergranular fracture, with both Na doped and
pure PbSe specimen M values ranging from 0.07 to 0.28. M increased to 0.51 to 0.98 for
PbS and PbSe specimens with additions of 2 at% to 4 at% CdS or ZnS, as compared to
the doped PbS and PbSe specimens. Generally, M was higher for specimens with
additions of CdS than with additions of ZnS (Tables 8.1 and 8.2). In both the PbS with
ZnS (Table 8.1) and the PbSe with ZnS (Table 8.2), M reaches a maximum at 3 at% ZnS.
In contrast, there was no observed maximum in M for CdS additions to PbS and PbSe.
EDS analysis of the polished surface of PbS indicated a deficiency of S (Table 8.3). The
lattice parameter from XRD of the PbS specimen was 5.941 Å for the bulk, as-sintered
specimen (Figure 8.7). The measured lattice parameters for sintered PbS are larger than
the lattice parameter of 5.932 Å for the same PbS material prior to sintering [Zhao
2012a], and consistent with a change in the concentration of S, as indicated by EDS
analysis.

243

Table 8.3. EDS results from four area scans of a polished PbS specimen, indicating a
higher concentration of Pb than S.
Location ID

Pb
50.4
50.4
50.9
50.5
50.8

Intensity (AU)

1
2
3
4
5

Atomic %
S
49.6
49.6
49.1
49.5
49.2

25

50

75

Position (2)
Figure 8.7. XRD pattern of the sintered PbS specimen.

244

The undoped PbS specimen required a higher sintering temperature (873 K) than
the Na-doped PbS specimens (723 K). An undoped PbS specimen produced at a
sintering temperature of 723 K was too porous for comparison to the nearly dense Nadoped specimens, with a density of 6.27 g/cm3, and a P of 0.18, far exceeding the
maximum of P < 0.05 for all other specimens in this study. Therefore, the porous
undoped PbS specimen was excluded from the elasticity and hardness testing.
8.3.2 Elasticity results
For the PbS-based specimens, the elastic moduli, E and G, were not sensitive to
the addition of CdS or ZnS, with a mean and standard deviation of E of 63.38 ± 2.25 GPa
(Figure 8.8a) and G was 24.69 ± 0.93 GPa (Figure 8.8c). The undoped PbS specimen had
a much lower porosity, P = 0.008, than all the othere Na-doped PbS-based specimens, P
= 0.031 to 0.050 (Table 8.1), likely due to the higher sintering temperature of the PbS
specimen (see section 8.2.1 for sintering procedures). This difference in P likely explains
the higher E and G of the undoped PbS specimen relative to the other PbS-based
specimens (Figure 8.8a), and not a sensitivity to Na doping, as discussed in section 8.4.2.
In contrast, the moduli of the PbSe-based specimens are sensitive to Na doping,
but not CdS or ZnS additions. Both the E and G of the PbSe specimens decreased with
the addition of Na dopant, from 64.29 ± 0.16 GPa and 25.29 ± 0.02 GPa for pure PbSe, to
60.33 ± 0.26 GPa and 23.66 ± 0.04 GPa for Na-doped PbSe (Figure 8.8b and 8.8d). No
change in modulus was observed in the Na-doped PbSe specimens as a function of
increasing additions of 1 at% to 4 at% CdS or ZnS except for a slight decrease in G and a
corresponding increase in ν. The mean of E for the PbSe specimens with either CdS or
245

(a)

70

60

E with CdS
E with ZnS
E undoped
E Na-doped

50
0

1

2

3

PbSe E (GPa)

PbS E (GPa)

70

(b)

60

E with CdS
E with ZnS
E undoped
E Na-doped

50

4

0

G with CdS
G with ZnS
G undoped
G Na-doped

26

24

28

PbSe G (GPa)

PbS G (GPa)

28

22

3

4

(d)

G with CdS
G with ZnS
G undoped
G Na-doped

26

24

22
0

1

2

3

4

0

% CdS/ZnS
0.40

0.35

0.30

0.25
0

1

2

3

1

2

3

4

% CdS/ZnS

Poisson's ratio with CdS
Poisson's ratio with ZnS
Poisson's ratio undoped
Poisson's ratio Na-doped

(f)

Poisson's ratio with CdS
Poisson's ratio with ZnS
Poisson's ratio undoped
Poisson's ratio Na-doped

0.40

PbSe Poisson's ratio

(e)

PbS Poisson's ratio

2

% CdS/ZnS

% CdS/ZnS
(c)

1

0.35

0.30

0.25
0

4

1

2

3

4

% CdS/ZnS

% CdS/ZnS

Figure 8.8. The E and G of the undoped PbS and PbSe were higher than the Na-doped
PbS and PbSe. The E and G of undoped PbS are likely higher due to reduced porosity
(pure PbS P = 0.008, all other PbS P = 0.031 to 0.050), while the E and G of undoped
PbSe are likely higher due to doping effects. Only small changes in E and G were noted
in Na-doped PbS and PbSe with addition of up to 4% CdS or ZnS, with. Only small
variability in the ν noted in PbS with addition of CdS or ZnS. The ν of PbSe increased
with the addition of CdS or ZnS. Solid line is average and dotted line is standard
deviation of the specimens with 1% to 4% CdS or ZnS addition.

246

(b)

(a)
1.0

H with CdS
H with ZnS
H undoped
H Na-doped

0.5

PbSe H (GPa)

PbS H (GPa)

1.0

0.0

0.0
0

1

2

3

H with CdS
H with ZnS
H undoped
H Na-doped

0.5

0

4

1

2

3

4

% CdS/ZnS

% CdS/ZnS

Figure 8.9. The hardness of both PbS and PbSe increased with the addition of Na dopant.
No measurable change in hardness was noted in PbS with addition of up to 4% CdS or
ZnS. Hardness of PbSe increased from 0.6 GPa to 0.8 GPa with the addition of either
CdS or ZnS.

247

ZnS was 61.03 ± 0.79 and the mean of G was 23.35 ± 0.35 GPa) (Figure 8.8b, 8.8d, 8.8f).
(Note: each of the specimens with additions of CdS or ZnS were Na-doped.)
8.3.3 Hardness results
The hardness of PbS and PbSe increased with 2.5 at% or 2.0 at% Na-dopant
additions, respectively, but were largely unaffected by the addition of 0 to 4 at% CdS or
ZnS (Figure 8.9). The hardness of the pure PbS was 0.72 ± 0.10, and the average of the
Na-doped PbS with additions of 0 to 4 at% CdS or ZnS was 1.12 ± 0.05 (Figure 8.9a).
Similarly, the hardness of the pure PbSe was 0.44 ± 0.02 GPa, but increased to 0.62 ±
0.02 GPa when doped with 2.0 at% Na, and averaging 0.74 ± 0.08 GPa for specimens
with 0 to 4 at% CdS or ZnS (Figure 8.9b).
8.4 Discussion
8.4.1 Microstructural analysis
The observation of ZnS precipitates of up to 10 µm to 15 µm in diameter (Tables
8.1 and 8.2), as compared to CdS precipitates of up to 1.5 µm to 4 µm in both the PbS
matrix (Table 8.1, Figure 8.4) and the PbSe matrix (Table 8.2, Figure 8.4), may be related
to the much lower solubility limit of ZnS in the matrix [Zhao 2013]. More specifically for
PbSe, “no solid solubility of Zn in PbSe was observed” [Zhao 2013]. Zhao et al.
expected a continuous change in band gap up to the solubility limit for additions of CdS
or ZnS in PbSe [Zhao 2013]. The band gap increased with up to 2% addition of CdS in
PbSe, but with ZnS in PbSe, “no band gap changes are observed, suggesting a much
lower solubility limit” of ZnS in PbSe [Zhao 2013].
Transmission electron microscopy observations of nanoprecipitates of CdS and
ZnS in PbS and PbSe matrices have shown endotaxial crystallographic alignment with
248

the matrix [Zhao 2013; Zhao 2012a]. The morphology of the observed micron-scale
precipitates with rod or plate geometry and sharp facets (Figure 8.4), particularly in the
samples with CdS addition (Figure 8.5), are consistent with the observations of
nanoprecipitate morphology.
The change in fracture mode observed between specimens with and without CdS
or ZnS addition (Tables 8.1 and 8.2) is often associated with a change in fracture
toughness. A change from intergranular to transgranular fracture has been associated
with either an increase [Mukhopadhyay 2010; Kawabata 1977; Karakasidis 2011] or
decrease [Yamada 2010; Jang 2010]. The fracture toughness of the material was not
determined in this study, but may be an area for future studies of PbS and PbSe with
additions of CdS or ZnS.
For PbS-based specimens sintered at 723 K, the P for the undoped material was
0.18, while the P of each of the Na-doped specimens was less than 0.05. A nearly dense
(P = 0.01) undoped PbS specimen was sintered for this study, but only by increasing the
sintering temperature to 873 K. The enhanced densification of the Na-doped PbS
specimens may indicate the Na dopant acts as a sintering aid. A previous study on a
different TE material, Ba0.3Co4Sb12, showed the addition of metal particles, specifically
0.5 wt% Ag nanoparticles, may act as sintering aid [Schmidt 2014]. In Ba0.3Co4Sb12, the
Ag had a eutectic or peritectic reaction with Sb in the Ba0.3Co4Sb12 [Schmidt 2014] and a
similar eutectic reaction may explain the enhanced densification in the Na-doped PbS
specimens.
The Na-S system has eutectics at 513 K and 61.5 at% Na, 522 K and 70 at% Na,
and at 525 K and 72.5 at% Na [Sangster 1997]. All three of these eutectic points are well
249

below the sintering temperature used for the Na-doped PbS samples, 723 K. In the
closely related PbTe material system, the Na in Na-doped PbTe partially segregates in a
layer less than 10 nm thick at the grain boundaries [Biswas 2012]. A similar Na-rich
layer may also form during sintering in the PbS-based material in this study, and this Narich layer may act as a liquid-phase sintering aid for the PbS-based system that accounts
for the enhanced sintering. The sintering behavior of Na-doped PbS has not been
explored and may be a topic for future work.
8.4.2 Elasticity analysis
For the PbS-based specimens, the undoped PbS specimen exhibited higher E and
G relative to the other PbS-based specimens (Figure 8.8a). The difference in elastic
moduli between PbS-based specimens likely a function of porosity, as the porosity of the
undoped PbS specimen is P = 0.008, much lower than all the other Na-doped PbS-based
specimens, P = 0.031 to 0.050 (Table 8.1), and not because of a sensitivity to the Na
doping.
In general, the elastic modulus of TE materials and other brittle materials is a
linear function of porosity [Schmidt 2013a; Ni 2009b; Rice 1998; Ni 2011],
E  E0 1  bE P 

(4)

where E0 is the Young’s modulus at P = 0, and bE is a measure of the decrease in E with
increasing P. For two previously studied TE materials, YbAl3 and LAST (lead–
antimony–silver–tellurium), bE is 2.34 [Schmidt 2013a] and 3.6 [Ni 2009b]. Based on
these values of bE, the difference between the undoped PbS and the Na-doped specimens
with 0 to 4 at% addition of CdS or ZnS is expected to be between 4 GPa and 11 GPa, and
consistent with the measured difference of approximately 6 GPa (Figure 8.8a).
250

The elastic moduli for the doped TE materials with nanoprecipitates in this study
have not been reported, however the moduli of the undoped PbS [Dalven 1969;
Bhagavantam 1951] and PbSe [Lippmann 1971; Dalven 1969; Hellwege 1979] are
known for single crystal specimens. The aggregate average of the Hashin and Shtrikman
bounds, <H-S>, [Simmons 1971] allow a direct comparison of the single crystal
specimen moduli to the moduli of a dense polycrystalline specimen (Table 8.4).
Comparing this study to the <H-S> averages, the polycrystalline PbS specimen in this
study (which has a volume fraction porosity, P of 0.008) were lower than the single
crystal values by 12% to 18%, with the measured E of 68.95 ± 0.10 GPa in this study,
and the single crystal <H-S> E of 78.05 GPa [Dalven 1969] and 83.61 GPa
[Bhagavantam 1951] (Table 8.4). The elastic moduli of PbSe in this study (P = 0.016),
with E of 64.29 ± 0.16 GPa, generally agrees with previous studies, with <H-S> E
between 61.68 GPa and 70.69 GPa [Lippmann 1971; Dalven 1969; Hellwege 1979]
(Table 8.4).
The reader may ask, “why are the moduli of PbS lower than those reported in
literature?” The two most likely causes would be (i) porosity and (ii) doping or
composition differences.
Porosity is not sufficient by itself to explain the difference between the literature
values of <H-S> E and the measured E in this study. The contribution from porosity may
be estimated using equation 4 and applying the measured bE from two previously studied

251

Table 8.4. The Young’s modulus, E, the shear modulus, G, and the Poisson’s ratio
measured in this study for the polycrystalline undoped PbSe and undoped PbS specimens
compared with the aggregate average values of E and G computed from the Hashin and
Shtrikman bounds, <H-S> [Simmons 1971] for single crystal elasticity from the literature
[Dalven 1969, Bhagavantam 1951, Lippmann 1971, Hellwege 1979].
Material Bulk material
form
PbS
Polycrystalline
PbS
Single crystal

E
(GPa)
68.95
78.05

G
(GPa)
27.16
29.98

Poisson’s
ratio
0.269
0.302

PbS

Single crystal

83.61

32.53

0.277

PbSe
PbSe
PbSe

Polycrystalline
Single crystal
Single crystal

64.29
66.83
70.69

25.29
23.76
24.11

0.271
0.298
0.466

PbSe
Single crystal
61.68
NA: Not available from literature

23.76

0.294

252

Density
(g/cm3)
7.53
7.5
(P=0.01)
NA

Reference
This study
[Dalven 1969]
[Bhagavantam
1951]
This study
[Lippmann 1971]
[Dalven 1969]

8.13
8.26
8.16
(P=0.01)
NA
[Hellwege 1979]

TE materials, YbAl3 (bE = 2.34) [Schmidt 2013a] and LAST (bE = 3.6) [Ni 2009b].
Based on these values of bE and the observed porosity in the PbS specimen (P = 0.046),
the E0 of PbS in this study would likely be in the range of 70.3 GPa to 71.0 GPa, which is
still 12% to 15% less than the average of literature values (Table 8.4).
After accounting for porosity, the remaining differences between the moduli of
the polycrystalline PbS specimen in this study and the literature may be related to
composition or doping and vacancies. To examine this possibility, a cut surface of the
PbS specimen was examined by EDS to determine an approximate composition (Table
8.3). The EDS surface composition of a polished surface of the specimen was PbS0.98,
averaged over 5 separate sites, where the area of each site was approximately 0.05 mm2.
The surface composition of the PbS specimen is thus consistent with sulfur vacancies
(Table 8.3). In this study, the PbS was densified by PECS in an argon atmosphere using
a starting powder milled from an ingot. During the initial stage of sintering before
densification occurs, the surfaces of the PbS powder particles are exposed to the sintering
atmosphere at elevated temperature, 873 K, providing a pathway for S loss. Prior to
sintering, the powder was single phase in XRD, with a lattice parameter of 5.932 Å [Zhao
2012a]. After sintering, the specimen was single phase in XRD, but with a lattice
parameter of 5.941 Å for the sintered specimen (Figure 8.7). The increase in lattice
parameter is consistent with a change in vacancy concentration. The observed reduction
in the elastic moduli by roughly 12% to 15% in this study may be caused by sulfur
vacancies introduced during sintering, as indicated by EDS analysis.
A change in elastic moduli by roughly 12% to 15% due to vacancies is not unique
to PbS. Another thermoelectric, SnTe1+x, exhibits a decrease of E by 12% with
253

increasing Te content from x = 0 to 0.016 and a subsequent rise in the number of cation
vacancies [Schmidt 2013b]. In addition, the elastic modulus of a set of nitrides decreases
with increasing N vacancies. The E of TiNx coatings decreases by 23% [Shin 2003] or
41% [Portnoi 1968] for a change in x from 1 to 0.67, decreases ~20% [Jiang 1991] or
50% [Portnoi 1968] for x from 1 to 0.5, and by 5% for a small change of x from 0.98 to
0.94 [Portnoi 1968]. Similarly, the E of ZrNx decreased 12% for a change in x from 1 to
0.85 [Portnoi 1968]. For CeO2-x-based compounds, increasing O vacancies (x from
approximately 0 to approximately 0.11, at O2 partial pressure of 0.22 atm and 4.50 × 10-22
atm) reduced the E of ceria by 11% and gadolinium doped ceria by 6% [Wang 2007].
8.4.3 Hardness analysis
Hardness values for single crystal PbS [Bloem 1955] and polycrystalline
specimens of PbS and PbSe [Darrow 1969] are available in the literature (Table 8.5), but
no hardness data is available in the literature for PbS and PbSe specimens optimized as
TE materials by the inclusion of Na dopant and CdS or ZnS nano/micro precipitates.
The hardness of PbS specimens included in this study was not observed to be a
function of addition of precipitates or the dopant (Table 8.5, Figure 8.9a). The hardness
of PbS is higher than reported in the literature [Bloem 1955; Darrow 1969], but hardness
is known to be a function of grain size, and would be expected to be higher for the
powder processed specimens in this study than for single crystal specimens of the same
composition [Rice 1994].

254

Table 8.5. In general, hardness, H, is grain size dependent, and the single crystal
hardness results from Bloem and Kr ger [Bloem 1955] are expected to have a lower
hardness than the other, polycrystalline specimens in this table. The grain size for the
PbS and PbSe was not listed by Darrow [Darrow 1969]. Average grain sizes for all
specimens in this study are between 1.8 µm and 18.7 µm, listed in Tables 8.1 and 8.2.
Material Bulk material
form
PbS
Polycrystalline
PbS
Single crystal
PbS
PbS
PbSe
Na-doped
PbSe
PbSe

Indentation Reference
Load (N)
1.96
This study
0.98
[Bloem 1955]

Polycrystalline
Polycrystalline
Polycrystalline
Polycrystalline

H
(GPa)
1.09 ± 0.14
0.4 to 0.7 (dependent on
vacancy concentration)
0.72 to 0.92
0.73
0.44 ± 0.02
0.62 ± 0.02

1.41
3.92
1.96
1.96

[Darrow 1969]
[Darrow 1969]
This study
This study

Polycrystalline

0.56 to 0.57

1.41

[Darrow 1969]

255

Although the hardness was not observed to be a function of Na doping in this
study, the hardness of PbS is a function of the vacancy concentration [Bloem 1955]. On
single crystal specimens of PbS, Bloem and Kroger reported a minimum hardness of 0.4
GPa is reported when there is a minimum of vacancies [Bloem 1955]. In this study, the
PbS was S-deficient (Table 8.3), implying S vacancies were present, regardless of the Na
doping and regardless of whether or not CdS or ZnS was added to the matrix. The
difference between the constant H in this study and the minimum reported by Bloem and
Kroger [Bloem 1955] is likely because there are likely a large number of S vacancies
(Table 8.3) in each of the PbS specimens in this study. For future work with different
processing conditions or Na doping concentrations, the vacancy concentration may
approach a value where a minimum in H is possible, and the value of H should be
reexamined.
For PbSe, there may be a similar relationship between vacancies and hardness as
was observed by Bloem and Kroger in PbS [Bloem 1955]. Without CdS or ZnS
additions, the hardness increased from 0.44 ± 0.02 GPa to 0.62 ± 0.02 GPa with the
addition of 2.0 at% Na dopant (Table 8.5, Figure 8.9b). After the addition of Na, the
hardness was only a weak function, if any, of CdS or ZnS addition, averaging 0.75 ± 0.07
GPa for all the specimens with CdS or ZnS addition (Figure 8.9b).
Fracture toughness was not measured in this study. For each of the specimens
included in this study, Vickers indentation produced an impression with a set of
typically 8 to 15 or more cracks surrounding and extending out from the sides of the
indentation impression, rather than a set of radial or Palmquist cracks that extend from
the corners of the indentation impression. The lack of well-defined radial cracks
256

precluded making an estimate of the fracture toughness for the materials in this study.
These cracks may develop as a result of many mechanisms, such as the environment,
microstructural toughening, surface stress, or preferred crystallographic cleavage planes
[Cook 2003]. Future studies may examine fracture toughness by a method other than
Vickers indentation.
8.5 Conclusions
For PbS + x at%(CdS, ZnS), neither the elastic moduli, with E averaging 63.38 ±
2.25 GPa, nor the H, averaging 1.12 ± 0.05 GPa, are a function of addition of 2.5 at% Na
dopant and 0 to 4 at % CdS or ZnS, but the elastic moduli of the sintered pure PbS is
lower than previous reports. The lower elastic modulus is partially accounted for by
porosity, but may also be related to S vacancies.
For PbSe + x at%(CdS, ZnS), the elastic moduli and hardness of PbSe are a
function of 2.0 at% Na dopant, but not a function of addition of 0 to 4 at% CdS or ZnS.
Without Na dopant, the E was 64.29 ± 0.16 GPa and H was 0.44 ± 0.02 GPa. With the
Na dopant, the E averaged 61.03 ± 0.79 and the H averaged 0.75 ± 0.07 GPa.
The elastic moduli are required material properties to model stresses of a TE
material in a module or device, and stress modeling is necessary for designing or
fabrication of a mechanically reliable device. Hardness is related to wear characteristics
for a material. As the transport properties of a TE material are optimized, the mechanical
properties may change, potentially requiring a redesign of a module or device.
The continuing work on optimization of PbS- [Zhao 2012a] or PbSe-based [Zhao
2013] TE materials carries implications on changing the mechanical properties of these
materials required for designing and modeling a TE module or device. The effects on
257

mechanical properties from two aspects of optimization were examined in this study, (i)
addition of a precipitate phase, namely CdS or ZnS, and (ii) changes based on Na doping
or S deficiency. Optimizing either PbS or PbSe by addition of up to 4 at% CdS or ZnS
may be performed without concern for changing elastic moduli or H, nor the mechanical
design of TE devices reliant upon the elastic moduli or H, although a change in fracture
mode may indicate a change in fracture toughness.
The addition of 1 at% to 4 at% CdS or ZnS to either a PbS or PbSe matrix
changes the fracture mode of the specimen, from primarily intergranular fracture to
primarily transgranular fracture. A change in mode mixity is often associated with a
change in fracture toughness. Fracture toughness could not be determined by Vickers
indentation in this study, but may be measured by an alternative method in future work.
The CdS and ZnS additions were observed as precipitates, with the range of precipitate
diameter generally not a function of concentration or if the matrix was PbS or PbSe. The
maximum diameter of CdS precipitates is up to 4 µm, and the maximum size of ZnS
precipitates up to 15 µm.
ACKNOWLEDGEMENTS
The authors acknowledge the financial support of 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 Science, Office of
Basic Energy Sciences under award number DE-SC0001054.

258

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266

9 Summary and Conclusions
9.1 Porosity dependence and processing method independence of elastic moduli
From the results of Chapter 3 on properties of YbAl3 and Chapter 6 on
Ba0.3Co4Sb12 skutterudites, we conclude that the Young’s modulus, E, shear modulus, G,
and bulk modulus, B, of bulk porous YbAl3 and Ba0.3Co4Sb12 are a function primarily of
the volume fraction of natural porosity, P. In this work, natural porosity refers to
porosity that occurs when powder processing and sintering a brittle material, as opposed
to introduced porosity such as that formed when a second material is mixed and then
burned out during sintering or when pores are formed via bloating. Two powder
processing and sintering methods, (i) grinding and sieving and hot press (HP) sintering,
and (ii) vibratory milling and pulsed electric current sintering (PECS), were used to
produce sets of specimens with a range of porosity for each of YbAl3 and Ba0.3Co4Sb12.
The powder processing method, sintering method, or different natural porosity size and
distribution are not a significant factor in determining the mechanical properties of E, G,
and H for YbAl3 and Ba0.3Co4Sb12. The properties may be accurately estimated with only
a knowledge of P.
The elastic moduli, E, G, and B, of many brittle materials have been shown follow
the empirical relationship [Rice 1998]
A = A0(exp-bAP)

(1)

where A represents E, G, or B, A0 represents E0, G0 and B0 , the P = 0 intercepts, and bA is
a unitless, material-dependent parameter. If bAP is small, equation (1) may be linearized
[Ni 2009b] by using the first two terms of the Taylor series expansion of equation (1).
267

A = A0(1 - bAP)

(2)

For both YbAl3 and Ba0.3Co4Sb12, the linear form has been used.
Rice [Rice 1998] has shown that the porosity dependence, bA, of the elastic
moduli for a variety of brittle materials typically lies between 2 and 6. Prior to this work,
the bE and bG values for only one TE material was in the literature, LAST (lead–
antimony–silver–tellurium) [Ni 2009a].
9.1.1 Grain size and processing method independence of elastic moduli
Processing conditions may lead to a change in grain size (GS), but a change in GS
does not change the elastic moduli for specimens with GS greater than approximately 20
nm [Kim 1999]. This was consistent with the results for the Ba0.3Co4Sb12 specimens,
where processing method changed the Ba0.3Co4Sb12 GS from bimodal, with most grains
>1 µm in diameter for the HP, to unimodal with an average GS of 0.14 – 0.17 µm. The
elastic moduli results for the different GS Ba0.3Co4Sb12 specimens in section 6 further
support the result that only the P dependence is required to predict the E, G, or B of a TE
material.
9.2 Sintering aids and TE materials
Sintering aids have generally not been considered for TE materials, despite the
numerous benefits, such as reduced sintering time, temperature and cost [German 1985].
A new possible sintering aid was determined for Sb-based skutterudites and other Sbcontaining TE materials, as well as a method to identify possible sintering aids for other
TE materials (chapter 6).
In examining the increased density of Ba0.3Co4Sb12 with 0.5 wt% Ag additions,
the Ag in the composite was determined to react with excess Sb and form an Ag3Sb phase
268

(chapter 6). Examining the binary phase diagram, this Ag3Sb phase likely formed in a
eutectic/peritectic reaction during sintering, and a liquid was likely present at 873 K, and
possibly at 773 K. This liquid acted as a sintering aid, and the reaction to form the Ag3Sb
phase may also act as a beneficial scavenger of excess Sb. The use of Ag as a sintering
aid may likely be expanded to other Sb-containing TE materials. Furthermore, the use of
a binary or ternary phase diagram between constituent elements of a TE material and a
possible addition may indicate materials with a possibly beneficial eutectic/peritectic
reactions.
9.3 Elastic moduli of TE materials with nanoparticle or nanoprecipitate additions
In general, if the addition of nanoparticles or nanoprecipitates does not change the
composition of the matrix TE material, the elastic moduli of the composite exhibits only
a weak dependence on the addition, and may be effectively modeled by the Hashin or
Halpin-Tsai models.
For nanoparticle or nanoprecipitate additions that are typically considered in TE
materials (less than 4 vol%), SiCNP additions in Mg2Si (chapter 5) or SnTe (chapter 7),
AgNP additions in skutterudites (chapter 6), or precipitates of CdS or ZnS in PbS or PbSe
(chapter 8), the elastic moduli are weak functions of the volume fraction of the additions.
The weak dependence of the elastic moduli is poorly described by a rule of mixtures
approximation (chapters 7 and 8),
EC = Vm Em + Vr Er

(3)

but may be reasonably described by either the Hashin particulate composite [Hashin
1962] (chapters 7 and 8)

269

 E V  Er Vr  1

EC  Em  m m
 ErVm  Em Vr  1

(4)

or the Halpin-Tsai model [Halpin 1992] (chapters 7 and 8)

 1  2( a / b )qVr 

EC  Em 
 ErVm  Em Vr  1

(5a)

where the boundary condition parameter, q, is

 Er 

 1
Em 

q
 Er   a 

  2 
 Em   b 

(5b)

These models for the Young’s modulus of the composite, EC, depend on the Young’s
modulus of the matrix material and reinforcing material (nanoparticle or
nanoprecipitates), Em and Er, and the volume fraction of the matrix and reinforcing
materials, Vm and Vr. For the Halpin-Tsai model, the length/thickness ratio, a/b, for
roughly equiaxed particles or precipitates was set to 1.
9.4 Fracture toughness and slow crack growth in Mg2Si and other TE materials
The fracture toughness, KC, of TE materials is low, typically less than 1.5 MPam1/2, and must be considered carefully when designing at TE module. Despite the
importance of KC, it has not been measured for many TE materials. The KC for both
unreinforced Mg2Si (chapter 4) and up to 4 vol% SiCNP-reinforced Mg2Si (chapter 5) was
measured, as well as for YbAl3 (chapter 3) and Ba0.3Co4Sb12 (chapter 6).
Fracture toughness is a function of both the reinforcing material and the powder
processing/sintering conditions. Planetary ball milled Mg2Si with addition of SiCNP
reached a maximum KC at 1 – 2 vol% SiCNP, increasing 33% over no addition, but
270

vibratory milled Mg2Si exhibited no improvement in KC with 0 – 2 vol% SiCNP addition
(chapter 5).
The ball milled Mg2Si with 1 – 2 vol% SiCNP may not be the best choice for
highest strength , despite having the highest KC, ~ 30% higher than without SiCNP or the
vibratory milled material (chapter 5). The fracture stress, σfract, is a function of KC, the
flaw size, a, and shape factor, Y, where [Rice 1998]
√

(6)

When fracture occurs, the critical flaw, acrit, is typically the largest flaw in a region of
high stress, and this flaw can be from a variety of sources, such as the pores and cracks
that form within a material or scratches and cracks at the surface from machining.
Typically, the largest flaw not caused by machining scales with GS. Vibratory milled
Mg2Si specimens exhibited an average GS (0.4 – 0.8 µm) roughly 1/5 the average GS of
planetary milled specimens (2 – 4 µm). If the critical flaw scales directly with GS, the
fracture stress would be ~70% higher with the vibratory milled Mg2Si than the ball milled
Mg2Si with 1 – 2 vol% SiCNP , even with the lower KC. If, however, the critical flaw does
not scale directly with GS, as might happen with flaws from machining or other external
sources, the highest KC would be the more desirable material.
In addition, slow crack growth is a particular concern for low fracture toughness
materials such as most TE materials. With slow crack growth, a flaw, such as from
cutting or grinding to fabricate a leg, may grow to a large flaw that leads to failure in the
minutes or hours after machining. Slow crack growth was examined for unreinforced
Mg2Si in dry room air and determined to not be a concern. However Mg2Si does react
with water and a humid or other environment may remain a concern (chapter 4).
271

REFERENCES

272

REFERENCES

[German 1985] German, R.M. Liquid phase sintering. Springer Science+Business Media,
Inc., Troy, New York, 1985.
[Halpin 1992] Halpin, J.C. Primer on composite materials analysis. Technomic
Publishing Company, Inc., Lancaster, Pennsylvania, 1992.
[Hashin 1962] Hashin, Z. The Elastic Moduli of Heterogeneous Materials. Journal of
Applied Mechanics 29 (1962) 143–150.
[Kim, Bush 1999] Kim, H.S., Bush, M.B. The effects of grain size and porosity on the
elastic modulus of nanocrystalline materials. Nanostructured Materials 11 (1999)
361–367.
[Ni, Ren, Case, Timm 2009a] Ni, J., Ren, F., Case, E., Timm, E. Porosity dependence of
elastic moduli in LAST (lead–antimony–silver–tellurium) thermoelectric materials.
Materials Chemistry and Physics(2009) .
[Ni, Ren, Case, Timm 2009b] Ni, J.E., Ren, F., Case, E.E.D., Timm, E.J.E. Porosity
dependence of elastic moduli in LAST (lead–antimony–silver–tellurium)
thermoelectric materials. Materials Chemistry and Physics 118 (2009) 459–466.
[Rice 1998] Rice, R.W. Porosity of Ceramics. Marcel Dekker, New York, 1998.

273

10 Future work
In the examination of the mechanical properties of YbAl3, there were considerable
differences between the experimental measurements of elastic moduli and published
models, and even between the models themselves (chapter 3). These were stated to
possibly be related to “complexities in modeling and understanding the nature of the
intermediate valence nature of the Yb ion in YbAl3.” As such, a closer examination of
the modeled and measured elastic moduli of other Yb-based materials may be
investigated.
For Mg2Si, slow crack growth in a dry environment does not occur (chapter 4).
However, machining fluids may be water-based or contain dissolved water or other polar
molecules required for slow crack growth, and storage of machined components may not
be in a dry environment. Additional measurements of Mg2Si and other TE materials in a
humid environment or with machining oil on the surface should be investigated to
determine if environmental assisted crack growth may occur in other common
environments in which the TE materials may be stored.
The fracture strength of Mg2Si specimens has shown improvement when SiCNP
was added to ball milled powder, but not vibratory milled powder (chapter 5). The
difference in the behavior between these two processing techniques may be related to
grain size, but requires further exploration. For non-cubic materials, KC may reach a
maximum at a critical grain size [Bennison 1989], although this is not shown for cubic
materials. The composite thermoelectric (TE) materials may warrant further

274

investigation to determine if an improved model for fracture toughness of cubic matrix
materials with addition of nanoparticles may be observed.
Additional work on discovery and use of sintering aids can benefit both the cost
and development of TE materials (chapter 6). Use of AgNP in other Sb-containing TE
materials may enhance sintering, and the use of binary or ternary phase diagrams should
be employed to discover other candidate materials for liquid phase sintering aids.
The functional relationship between elastic moduli of SnTe1+X as a function of x
has only been partially addressed (chapter 7), especially since the stoichiometry of the
SnTe is not in the previous elasticity literature [Beattie 1969; Baughman 1969].
The differences between the measured PbS (chapter 8) and the literature values
are a concern and should be further explored. The doping effect of contaminants and/or
excess Pb on the elastic moduli of PbS is significant in the measured results.

275

REFERENCES

276

REFERENCES

[Baughman, Lefever 1969] Baughman, R., Lefever, R. Czochralski encapsulation growth
of GeTe, SnTe and PbTe single crystals. Materials Research Bulletin 4 (1969) 721–
726.
[Beattie 1969] Beattie, A.G. Temperature Dependence of the Elastic Constants of Tin
Telluride. Journal of Applied Physics 40 (1969) 4818.
[Bennison, Lawn 1989] Bennison, S.J., Lawn, B.R. Role of interfacial grain-bridging
sliding friction in the crack-resistance and strength properties of nontransforming
ceramics. Acta Metallurgica 37 (1989) 2659–2671.

277

APPENDICES

278

APPENDIX A. Effect of nanoparticle addition on the elastic modulus of a
composite material
The effect of the nanoparticle additions on the Young’s modulus, EC, of a
nanocomposites material can be predicted from numerous models. In this appendix, we
list relationships for four composite models, namely rule of mixtures (ROM), Reuss
constant strain (RCS), Hashin particulate (HP) and Halpin-Tsai (HT) [Schmidt 2013].
For each model, the Young’s modulus of the composite, EC, is the based on Er, the elastic
modulus of the nanoparticle reinforcement phase, Vr, the volume fraction reinforcement
phase, Em, the Young’s modulus of the matrix phase, and Vm, the volume fraction matrix
phase. Expressions for the four models can be written as:
ROM: EC = Vm Em + Vr Er
RCS:

(9)

V
V
1
 m  r
EC Em Er

(10)

 E V  Er Vr  1

HP: EC  Em  m m
 ErVm  Em Vr  1

(11)

 1  2( a / b )qVr 

HT: EC  Em 
 ErVm  Em Vr  1

(12)

In the HT model, a/b is the aspect ratio (length/thickness) for the reinforcing
phase and q is a boundary condition parameter given by
 Er 

  1
E
q  m
 Er   a 

  2 
E
m

 b

(13)

279

Table A.1. For spherical metallic particle additions to brittle matrices [Fujieda 2012;
Hasselman 1965], comparison of the measured composite modulus, EC, with the values
predicted by the four models given in this appendix (rule of mixtures, ROM, Reuss
constant strain, RCS, Hashin particulate, HP, and Halpin-Tsai, HT [Schmidt 2013]). Em
is the Young’s modulus of the matrix material [Fujieda 2012; Hasselman 1965]and Er is
the Young’s modulus of the reinforcing material [Lowrie 1967; Macfarlane 1965;
Neighbours 1958; Chang 1966].
Material
[Reference]
Sodium borosilicate glass + W
[Hasselman 1965]

Dental porcelain
+ PtNP [Fujieda
2012]

Em
(GPa)
80.5
[Hassel
man
1965]
80.5
[Hassel
man
1965]
80.5
[Hassel
man
1965]
80.5
[Hassel
man
1965]
80.5
[Hassel
man
1965]
60.1
[Fujieda
2012]

Dental porcelain
+ AgNP [Fujieda
2012]

60.1
[Fujieda
2012]

Sodium borosilicate glass + W
[Hasselman 1965]
Sodium borosilicate glass + W
[Hasselman 1965]
Sodium borosilicate glass + W
[Hasselman 1965]
Sodium borosilicate glass + W
[Hasselman 1965]

Er
Vr
(GPa)
(%)
409.8
10
[Lowrie
1967]

EC
ROM RCS HP
(GPa) (GPa) (GPa) (GPa)
90.9
113.4 87.5
92.1
± 1.4

HT
(GPa)
96.2

409.8
20
[Lowrie
1967]

105.5
± 1.1

146.4

95.9

105.5

114.1

409.8
30
[Lowrie
1967]

118.0
± 0.2

179.3

106.1

121.1

134.7

409.8
40
[Lowrie
1967]

137.5
± 0.3

212.2

118.6

139.6

158.7

409.8
50
[Lowrie
1967]

159.9
± 0.5

245.2

134.6

161.9

186.8

177.6
11.7
[Macfar
lane
1965]
82
21.4
[Neigh
bours
1958;
Chang
1966]

67.2
± 1.6

73.9

65.2

67.5

69.7

67.8
± 4.3

64.8

63.7

64.2

65.0

280

Table A.1 summarizes the Young’s modulus change due to the addition of both
micron-sized and nanosized-metallic particles to brittle matrices in studies by Hasselman
[Hasselman 1965] and by Fujieda et al. [Fujieda 2012]. Table A.1 gives the measured
composite modulus, EC, for the addition of 0.10, 0.20, 0.30 and 0.40 volume fraction of
tungsten particles with diameters of approximately 30 µm to a borosilicate glass
[Hasselman 1965], along with the predicted values of modulus calculated by the ROM,
RCS, HP, HT models and the modulus of tungsten [Lowrie 1967]. In addition, Table A.1
lists the measured EC, for composite specimens from Fujieda et al. [Fujieda 2012], who
measured the elastic modulus change induced by adding either 26 wt% platinum
nanoparticles (PtNP) [Macfarlane 1965] or 26 wt% AgNP [Neighbours 1958; Chang 1966]
to a dental porcelain, where the mean diameters of the PtNP and AgNP nanoparticles were
5 nm and 10 nm, respectively. The measured composite moduli, EC, (Table A.1) [Fujieda
2012; Hasselman 1965] agree quite well with the moduli calculated in this study using
the Halpin-Tsai model (HT). Since the metal particles were spherical in both the
Hasselman [Hasselman 1965] and Fujieda et al. [Fujieda 2012] studies, for the purposes
of the calculations we set a/b = 1 in equation 12, where a/b is the particle aspect ratio.
The amounts of particle addition in the studies by Fujieda et al. [Fujieda 2012]
and Hasselman [Hasselman 1965] were significantly greater than the 0.0068 volume
fraction (0.5 wt%) AgNP added in this study. The four composite models given in this
Appendix predict a decrease in EC of about 0.39% with the 0.5 wt% AgNP addition to the
Ba-skutterudite in this study. In recent research by Schmidt et al. [Schmidt 2013] applied
the four modulus-composite models to a thermoelectric system consisting of a brittle
matrix and a brittle reinforcing phase, namely with 0.00, 0.01, 0.02, 0.03, and 0.04
281

volume fraction of added SiC nanoparticles (SiCNP) in the brittle thermoelectric matrix
SnTe1+X, (where x = 0.0 or 0.016), Hashin and the Halpin-Tsai models best described the
elastic modulus data. Thus, for the Hasselman [Hasselman 1965] and Fujieda et al.
[Fujieda 2012] studies in which the volume percentage of micro and nano particles added
was relatively high (from 0.10 to 0.40 volume fraction), as well as the SnTe1+X (with 0.00
to 0.04 volume fraction SiCNP added), the Haplin-Tsai model agrees with the
experimental modulus data relatively well. In particular, for 0.5 wt% AgNP in this study,
the Haplin-Tsai model predicts a change in E of only 0.35%, which is consistent with the
E values measured in this study for the Ba-skutterudite with and without added AgNP.

282

APPENDIX B. Standard operating procedure for HT-RUS furnace
Note: This SOP describes operation of the furnace, not the operation of the RUS
computer or software. The furnace controller and power supply was designed and constructed
by Brian Wright and Gregg Mulder of the Electrical and Computer Engineering Shop.
Precautions
Do not operate the furnace with the bell jar removed and the heating element leads
exposed. When the bell jar has been removed, if the high voltage is turned on, the line volage
leads and the ends of the SiC heating elements are exposed and are are an electrocution harzard.

Figure B.1. The top of the furnace has exposed leads to power the heating elements
with up to 120 VAC electricity. Do not operate the furnace with these leads exposed.

The furnace cools through the outside of the bell jar. When in operation, the bell jar may
get extremely hot and cause burns. Additional cooling for the bell jar may be required.
The specimen will be exposed to elevated temperatures. Verify that there are no
concerns with specimen decomposition or reaction at the temperatures it will be exposed to.
1 Furnace Preparation
1.1 Wear gloves and do not use oils. Oils, especially in the inner furnace, will be burned
off during operation. For this reason, do not introduce oils to the furnace. Keep the inner

283

furnace clean, remove any finger oils from the specimen and wear gloves when adjusting furnace
components to keep them clean.

Figure B.2. Note feedthroughs for the thermocouples (left arrow) and heating element power
(right arrow). These feedthroughs and the wires from them should not touch the base or the sides
of the bell jar when closed.

Figure B.3. Braided insulation must be in place around the conductors to the
heating elements to prevent a short.

284

1.2 Clean dust and debris. The furnace is composed of several refractory bricks that let
off a significant amount of abrasive dust and debris. For this reason, a thorough cleaning is
required prior to operation to ensure the proper sealing and operation of the furnace. Particular
attention is required with the feed-through connections for the power and thermocouples, to
ensure no shorts are created. Power is supplied through a feed-through with two copper
conductors, capable of handling the 20A current to the furnace heating elements (Figure B.3).
These copper conductors are shielded with high temperature braided ceramic insulator material,
and the insulator must be in place to protect from a potentially dangerous short between the bell
jar and the power supply. There are two types of thermocouples, one K-type thermocouple for
the lower temperature sensing near the transducers to sense if the transducers are over the
maximum design temperature, and a pair of R-type thermocouples to measure the temperature
within the furnace. All the thermocouples make connections to the bare wires of the feedthroughs.

Figure B.4. The o-ring and the base of the bell jar may have some debris, particularly from the
furnace refractories. The debris is abrasive, and may inhibit a proper seal between the bottom
and side of the bell jar. The debris should be removed and appropriate grease reapplied to the oring prior to operation.
285

1.3 Clean and reapply vacuum grease. Clean off the centering ring and o-ring at the base
of the bell jar (Figure B.4). The o-ring will have Apiezon or equivalent low volatile organic
compound (VOC), high temperature vacuum grease on it that may have debris embedded that
should be removed. Reapply a thin layer of Apiezon or equivalent low VOC, high temperature
vacuum grease.
1.4 Check for electrical shorts. Verify the power connections are properly shielded with
braided insulation (Figure B.3) and that they will not be touching the bell jar or any uninsulated
components when closed. Turn on the 120 V power for the temperature controllers (NOT the
high voltage for the heating elements) and check for room temperature readings from each of the
three thermocouples (Figure B.5). Inspect all cables for any damage.

Low voltage
power switch

High voltage
power switch

Figure B.5. Controls and power supply for furnace. Note the high voltage power supply is
activated with the red button, and indicated with a red light. Power for the transducers is
provided by a 110 VAC circuit, turned on with a toggle switch and indicated with a green light.

286

1.5 Inspect the hoses. Check the coolant lines to and from the RUS mount assembly
(Figure B.6). Check the chiller for proper operation, and to verify the tank is properly filled with
water. Turn on the chiller pump to verify no leaks. Turn off after inspection to avoid a buildup
of condensation inside the furnace. Inspect the compressed gas hoses for any damage (Figure
B.6). Verify the compressed gas cylinder has sufficient pressure to run for the duration of the
experiment. Verify the pressure regulator setting does not exceed the pressure rating of the hoses
and connectors, typically set much less than 100 psi (for example, 30 psi).
1.6 Set up the bubbler for proper operation. Verify the end of the gas out line that is in
the bubbler is below the liquid level (Figure B.7). Adjust the end of the gas out line if necessary
to be near the bottom of the bubbler. Refill with water if necessary.

Figure B.6. Blue hoses for gas in and gas
out (front bottom) and for coolant water in
and out (behind valves) should be inspected
for damage such as abrasion or holes.

Figure B.7. The bubbler (arrow), with the
hose extending out, should be filled to cover
the end of the hose with liquid to prevent air
from entering the hose.

287

1.7 Check the roughing pump. Verify oil is at proper level and is clean. Check for
obstructions at inlet and outlet. Note the inlet at the base of the furnace has a screen to catch
large debris before it may reach the pump (Figure B.8).
1.8 Check any additional equipment that may be attached or required for the experiment.

Figure B.8. Debris can be seen on the screen in the feed-through leading to the vacuum pump.

2 Furnace and sample preparation
The sample should be an appropriate specimen for RUS, either parallelepiped or cylinder
and with no major chips or flaws. Small chips or flaws may be acceptable. Note the large buffer
rods on the RUS transducer will limit the signal available and RUS signal will diminish with
increasing temperature, thus a heavier specimen is typically required than for the room
temperature setup to ensure sufficient signal. Specimens have been examined with mass of
0.80 g, however a mass of at least 2 g would improve the signal. A higher specimen mass will
help keep the RUS signal transferring through the buffer rods.
288

2.1 Measure the specimen mass, dimensions, and determine the thermal expansion for the
desired temperature range. The thermal expansion is required to calculate dimension changes for
RUS analysis.
2.2 Note any apparent defects on the specimens.
2.3 Verify the RUS transducer rods do not touch the furnace and may be adjusted to the
proper angle without hitting the furnace or any other components.

Figure B.9. The three transducers are mounted to copper blocks on the chiller plates underneath
the furnace. The mount swivels to allow the angle of the transducer to be adjusted.

2.4 DO NOT MOVE TRANSDUCERS BY THE BUFFER ROD. Adjust the RUS
transducers to support the edges of the specimen by adjusting the angle of the copper mount
that holds the base of the transducer. The mount should allow rotation of the transducer with
reasonable hand pressure. If the mount is (a) too difficult to move or (b) does not have sufficient
tension to prevent movement, the screw on the swivel mount may be adjusted. Note there is a
wave washer to maintain tension on the swivel mount without tightening the screw to fully tight.

289

2.5 Check for RUS signal. Place the specimen on the transducer and run a RUS scan to
check for proper signal. Adjust specimen placement and transducer angle to maximize RUS
signal. See RUS guide for setup of the RUS software and specimen placement.

Figure B.11. Molybdenum baffle being
inserted around buffer rods.

Figure B.10. Molybdenum sheets to be used
as baffles.

2.6 Place molybdenum baffle sheets around the transducers (Figures B.10 and B.11).
The specimen may need to be removed during baffle sheet placement. The molybdenum sheets
are placed on the second (of three) shelf on the furnace and RUS support, under the insulators
that support the heating elements. These should be placed as near as reasonably possible to the
RUS transducer rods without touching the transducer rods in order to deflect heat from the
furnace before it reaches the transducer base. Verify the RUS signal is maintained.
2.7 Close the front of the furnace with refractories. Fit the front SALI board into position
(Figures B.12 and B.13). Fit the front refractory bricks into position (Figures B.14 and B.15).
The top of the furnace may need to be slightly lifted to allow the refractories to fit. Verify the
RUS signal is maintained.

290

Figure B.12. Front SALI board of inner
furnace.

Figure B.13. Front SALI board of inner
furnace, inserted into position

Figure B.14. Front refractory bricks of outer
furnace.

Figure B.15. Front refractory bricks of outer
furnace, inserted into position

291

2.8 DO NOT PLACE HANDS OR BODY UNDER SUSPENDED BELL JAR. Place the
bell jar on the furnace. This is a two-person job. Use the hoist to lift the bell jar higher than the
furnace, then slide the bell jar into position with the gantry. One person must guide the bell jar
by the sides while the second person operates the hoist. Operate the hoist up or down with the
remote control wired to the hoist. Guide the bell jar down on the furnace o-ring seal. Bring the
hoist down sufficiently that there is some slack in the chain. Verify the RUS signal is maintained.

Figure B.16. Hoist and controls to operate
up and down. Note the hoist is mounted to a
rail for movement left and right, and that the
chain has some slack when the bell jar is in
position.

292

3 Evacuation of furnace
3.1 Clamp the bell jar to the base with the 12 clamps (Figure B.17) and tighten with a
wrench.

Figure B.17. Clamps for the bell jar. The same clamps are used to secure the top and base of
the bell jar.

3.2 Verify all gas inlet and outlet valves are closed.
There are three high vacuum gas valves mounted to the
underside of the table, two of which are for inlet and
outlet. Close the gas inlet and outlet to snug against the
valve seat. The middle valve is for use with a pressure
gauge. This middle valve should be left open. Currently,
there is no oxygen monitor on the furnace. If a different
configuration of the furnace is used that employs an
oxygen monitor, then the valve should be closed.

293

Figure B.18. High vacuum
valves below the furnace. The
gas in and gas out valves should
be closed before pumping down
the bell jar chamber.

3.3 Pump down the bell jar. Turn on the pump and run until the vacuum chamber has
been evacuated, typically about 10 minutes. Verify with pressure gauge.

Figure B.19. Flow control panel, with flow controls and
bypass for the inert gas in and out of the bell jar and the
coolant water from the chiller to the base of the
transducers.

3.4 Backfill the bell jar with inert gas. Open the cylinder valve for the compressed gas
cylinder containing inert gas and verify the pressure reading on the regulator is less than 100 psi.
Verify the gas in bypass valve, located on the flow control panel to the right of the furnace, is
closed. Open the high vacuum inlet valve below the furnace. If desired, the chamber may be
refilled by opening the refill bypass valve, being careful to avoid disturbing the RUS specimen
by the gas. Backfill with inert gas until the chamber is at atmospheric pressure. Verify the RUS
signal is maintained.
3.5 Repeat steps 3.3 and 3.4 until at least three inert gas purges of the furnace chamber
have been performed.

294

4 Operation of furnace
4.1 Turn on chiller. On the chiller unit, set to appropriate temperature (typically 20°C)
and flow (typically 0.5 gal/min).
4.2 Set gas flow. Fill bell jar with gas to slightly above atmospheric pressure to prevent
back flow. Open the high vacuum valve below the furnace for outlet gas to the bubbler. Open
the gas out valve on the flow control panel. Verify bubble flow through the bubbler. Adjust
inlet gas flow control to desired gas flow.
4.3 Set monitor. If an oxygen monitor is attached, open valve to monitor and set oxygen
monitor for operation according to manufacturer instructions. (No oxygen monitor is currently
attached).
4.4 Set temperature limit controllers. Both temperature controllers are Omega CN3101
series controllers with temperature limits that may be set with the arrow keys. If the controller is
tripped, the controller may be reset with the RESET button. The furnace temperature limit
controller is typically set to 25° to 50° above the maximum temperature for the experiment. The
transducer temperature limit controller is typically set to 80°C. Do not allow the transducers to
exceed 80°C to avoid irreparable damage to the transducers or cabling.

Figure B.20. From left, the furnace over temperature limit controller, furnace
temperature controller, and the transducer over temperature limit controller.
295

Figure B.21. Furnace temperature controller, from left, in run mode, selecting set point 1,
and setting set point 1 to 60°C.

Figure B.22. 208 VAC power switch with
red indicator light on, and 110 VAC power
switch with green indicator on.
4.5 Set first desired temperature. Set the furnace temperature controller for the desired
first temperature. Use the scroll key on the controller to change to set point 1, use the enter key
to select, then use the arrows to choose the desired temperature and enter the selected
temperature with the enter key. Use the scroll key to return to run mode. Turn the variac all the
way to the left. Turn on the 208/240VAC supply for the heating elements. Increase the variac
up to a maximum of 60 V. Verify the amperage on the ammeter to the heating elements is less
than 20 A. If the heating rate is insufficient, the variac may be increased up to a maximum of 20
A current. The voltage may be increased up to 120 V for older heating elements until a
maximum of 20 A of current. If a higher voltage is required, the heating elements must be
replaced (see section 6). Note two set points may be set on the controller at a time, although set
point 1 (SP1) is set up to run currently.
296

Figure B.23. Ammeter and voltmeter for
heaters. Resistance decreases with
temperature, and the current should be
monitored to not exceed 20 A. Operate
heater elements at less than 60 V for new
elements, less than 120 V for elements that
have aged due to use.

Figure B.24. Heater ammeter,
heater voltmeter, and variac
output knob on control box.

4.6 Hold at desired temperature. Allow the specimen to soak at the desired temperature
until it is uniformly heated, typically 5 minutes soak. Run a RUS scan. Record the settings and
time. Do not hold at high temperatures for excessively long time to avoid heating the top of the
bell jar excessively.
4.7 Set next desired temperature. Set the temperature controller for the desired next
temperature. Verify the amperage to the heaters does not exceed 20 A. Note the resistance of
the heating elements changes with temperature so that as the furnace temperature changes, the
current through the heating elements changes even when the voltage is fixed.
4.8 Repeat steps 4.6 and 4.7 until RUS scans are gathered for all desired temperatures.
4.9 Turn off 208/240 VAC power to heating elements. Allow furnace to cool below
50°C. Turn off oxygen monitor, if applicable. Turn off gas at regulator. The gas out valve
should remain open to allow for excess pressure to escape. Note that the gas will initially have
some pressure to continue a flow through the bubbler unit, but as the furnace cools the pressure

297

inside the furnace will drop which could cause the water from the bubbler to be drawn back into
the furnace. There is excess hose to reduce the chance of water from the bubbler reaching the
furnace, but monitor the bubbler to verify no water reaches the furnace.
5 Opening of furnace
5.1 Turn off chiller and turn off power to the temperature controllers. To prevent a
buildup of condensation on the transducers once the furnace is open, the chiller should be turned
off just before opening the chamber. To eliminate the chance of electrical energy in the
chamber, turn off power to the temperature controllers.

Figure B.25. Bell jar at rest on side table and furnace
opened. There should be some slack in the chain, allowing
all the weight of the bell jar to rest on the table.
5.2 Open chamber. When the bell jar is cooled sufficiently to safely handle, detach the
clamps from the bottom of the bell jar with care. Even with the outlet open, there may be a small
amount of pressure in the chamber. With one person to guide the bell jar, raise the hoist to lift
the bell jar above the top of the furnace. Slide the bell jar to the side table and lower onto the
table.

298

5.3 Verify the furnace is cool, then open the furnace. With gloves, remove the front
refractory bricks on the furnace and the front SALI inner furnace board.
5.4 Measure the specimen mass and dimensions.
5.5 Note any apparent defects on the specimens.
5.6 Verify all furnace equipment is properly turned off and stowed.

299

6 Replacement of service parts
6.1 Replacement of RUS transducer. If the RUS transducer is no longer providing a
proper signal, it may require replacement. Turn all power off. Disconnect the cable from the
transducer. Move molybdenum baffle sheets away from the transducer to allow the transducer to
be removed. Remove the transducer from the copper mounting block by loosening the clamp
screw on the swivel mount, then carefully lift the transducer out of the mounting block. Remove
the cold cap from the transducer (Figure B.26). Apply Apeizon or equivalent low VOC vacuum
grease to transducer near the top of the brass body to allow heat transfer between the body and
the cold cap. Apply a thin layer of grease to the base of the cold cap to allow heat transfer
between the cold cap and the swivel mount. Insert the replacement transducer into furnace
through the furnace chamber and seat into the swivel mount. Tighten the swivel mount screw.
Reconnect the transducer cable.

Cold cap on
transducer

Swivel mount
clamp screw
Transducer
cable

Figure B.26. RUS transducer mount components.

300

6.2 Replacement of heating elements. The heating elements should be changed only as a
full set, as the resistance of the elements changes as they are used. Do not replace individual
heating elements. Disconnect the clamps and the flat braided cables from the four heating
elements. Lift the heating elements out of the furnace. Replace with new heating elements.
Reconnect the flat braided cable and clamps to the new heating elements. The elements should
be wired together in series, supported on the base by an insulating material, and the hot zone
should be completely within the inner furnace.

Figure B.27. The spiral cut hot zone of the heating elements should be completely
contained within the furnace. The power connections to the heating elements should be
outside the furnace.

6.3 Replacement of furnace thermocouples. The furnace thermocouples are bare wire
type R platinum thermocouples and should only be handled with gloves. Disconnect the old
thermocouple from the terminal strip and remove. Thread the new thermocouple through the
holes, noting which is the positive and which is the negative side. Connect to the appropriate
terminal and trim the excess wire.

301

Figure B.28. Terminal strip on back of
furnace for R-type thermocouples, with
thermocouple wires extending into the
furnace.

302

APPENDIX C. Machine drawings of the HT-RUS equipment

Figure C.1. Gantry and full assembly.
303

Figure C.2. Gantry and full assembly BOM

304

Figure C.3. Gantry.
305

Figure C.4. Gantry BOM.

306

Figure C.5. Full assembly.
307

Figure C.6. Full assembly BOM.

308

Figure C.7. Bar clamp.
309

Figure C.8. Base mount weldment.
310

Figure C.9. Bell jar base.
311

Figure C.10. Bell jar base assembly.
312

Figure C.11. Bell jar base assembly BOM.
313

Figure C.12. Bell jar base weldment.
314

Figure C.13. Bell jar base weldment BOM.

315

Figure C.14. Bell jar top.
316

Figure C.15. Cold plate mount 1.
317

Figure C.16. Cold plate mount 2.
318

Figure C.17. Flange tube.
319

Figure C.18. Furnace box.
320

Figure C.19. Furnace box BOM.
321

Figure C.20. Furnace support plate.
322

Figure C.21. Heater support 2.
323

Figure C.22. Heater support.
324

Figure C.23. Inner furnace back SALI board.
325

Figure C.24. Inner furnace base SALI board.
326

Figure C.25. Inner furnace front SALI board.
327

Figure C.26. Inner furnace side SALI board.
328

Figure C.27. Inner furnace top SALI board.
329

Figure C.28. Inner furnace.
330

Figure C.29. Inner furnace BOM.
331

Figure C.30. Outer furnace base center.
332

Figure C.31. Outer furnace base left.
333

Figure C.32. Outer furnace base right.
334

Figure C.33. Outer furnace base.
335

Figure C.34. Outer furnace base BOM.
336

Figure C.35. Outer furnace front 2.
337

Figure C.36. Outer furnace front.
338

Figure C.37. Outer furnace side 2.
339

Figure C.38. Outer furnace side.
340

Figure C.39. Outer furnace top center.
341

Figure C.40. Outer furnace top left.
342

Figure C.41. Outer furnace top right.
343

Figure C.42. Outer furnace top.
344

Figure C.43. Outer furnace top BOM.
345

Figure C.44. Bell jar top.
346

Figure C.45. RUS and furnace.
347

Figure C.46. RUS clamp.
348

Figure C.47. RUS mount assembly.
349

Figure C.48. RUS mount assembly BOM.

350

Figure C.49. RUS mount.
351

Figure C.50. RUS support leg.
352

Figure C.51. RUS support plate.
353

Figure C.52. RUS support.
354

Figure C.53. Splash shield mount.
355

Figure C.54. Splash shield.
356

Figure C.55. Standoff.
357

Figure C.56. Table top.
358

Figure C.57. Transducer cold cap.
359

Figure C.58. Valve assembly.
360

Figure C.59. Valve mount.
361

REFERENCES

362

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[Schmidt, Case, Ni, Trejo, Lara-Curzio, Korkosz, Kanatzidis 2013] Schmidt, R.D., Case,
E.D., Ni, J.E., Trejo, R.M., Lara-Curzio, E., Korkosz, R.J., Kanatzidis, M.G. Hightemperature elastic moduli of thermoelectric SnTe1±x – y SiC nanoparticulate
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