ADVANCED BULK NANOCOMPOSITE MATERIALS
FOR THERMOELECTRIC APPLICATIONS
BY
Chen Zhou

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILSOPHY
Materials Science and Engineering
2011

ABSTRACT
ADVANCED BULK NANOCOMPOSITE MATERIALS
FOR THERMOELECTRIC APPLICATIONS
BY
Chen Zhou
Thermoelectric materials have received rejuvenated interest for the past two decades due to the
theoretical predictions that a high dimensionless thermoelectric figure of merit ZT > 1 can be
obtained in materials with complex structures and reduced dimensions, termed “nanostructured
materials”. The underlying benefit of nanostructuring is the possibility of at least partially
decoupling the interdependent relation between the Seebeck coefficient and electrical
conductivity so that one has the flexibility to tune them individually. The thermal conductivity is
expected to be reduced at the same time due to the phonon scattering from the nanoscopic
interfaces.
In this work, we investigate the thermoelectric properties of bulk nanocomposite
materials, which boast both ease of synthesis and enhanced thermoelectric performance
originating from the reduced dimension. Two material systems are of our interest: bismuth
telluride and p-type skutterudite.
For bismuth telluride and its alloys based nanocomposites, we select Bi2Te2.85Se0.15 as
the n-type matrix and Bi0.4Sb1.6Te3 as the p-type matrix respectively. The nanocomposite
materials were prepared by a solution based incipient wetness impregnation method. Adding
PbTe nanoparticles can effectively reduce the lattice thermal conductivity at low temperature.

But the doping effect from the excess Pb ion plays a dominant role compared to nanostructuring.
This results in creating a two carrier system for the n-type nanocomposites, and decreased power
factors for p-type nanocomposites.
For skutterudite based nanocomposites, we focus our attention on the under-developed ptype skutterudites. We start from the primitive Fe-doped binary skutterudite nanocomposite
Co0.9Fe0.1Sb3 with in-situ formed FeSb2 as nanoparticles and demonstrate 100% enhancement
in the overall thermoelectric performance. The success encouraged us to re-develop an Yb-filled
skutterudite as the matrix material and explore the thermoelectric properties over a wide range of
Yb filling fraction with various amount of antimonide based impurities (presumably FeSb2). We
achieve an enhanced thermoelectric performance up to 23% in optimized nanocomposites
compared to the control sample.
Last

but

not

least,

we

investigated

the

double

filled

p-type

skutterudite

Yb0.6GazFe2Co2Sb12. The unique role of Ga inducing a deep defect level in band structure
enhances the Seebeck coefficient without affecting the electrical resistivity. The best performing
sample demonstrates 46% enhancement of thermoelectric performance compared to
Yb0.6Fe2Co2Sb12 with only Yb filler.
Overall, our study indicates that nanostructuring does provide significant benefits when
applied to thermoelectrics under certain conditions. Time and more research will tell if this
approach is ultimately a viable one.

Copyright by
Chen Zhou
2011

To Wen, my parents
and
paternal grandparents

v

ACKNOWLEDGEMENTS

I feel fortunate to have found Prof. Donald Morelli as my advisor, the person who
introduced me to the field of thermoelectricity and experimental materials physics. I knew little
about thermoelectrics and had limited laboratory experience when I first joined him. It is Prof.
Morelli who taught and advised me from the very basics of equipment operations and material
synthesis all the way to data interpretation, conference presentation and journal publication. I
still remember the first time when he showed me how to mount a sample on a cryostat and the
days when we kneeled on the floor to fix the broken vacuum pump. I am very impressed by his
keen intuition and foresight, extreme patience and kindness to students, and his optimistic and
altruistic characters. Pursuing a PhD degree is not an easy task. But with the guidance and
encouragement from my advisor, my PhD life has been a memorable and pleasant journey.
I would also like to thank my other PhD committee members for their guidance and
contribution. Prof. Sakamoto introduced me the novel material synthesis techniques and
generously allowed me to use some of his equipment for my research. He is always full of ideas
and offers constructive critique on my work. Prof. Subramanian’s class on crystal anisotropy is
one of the best classes that I have had in the graduate school. Prof. Hogan generously shared his
thermal measurement instrument with us and offered many good suggestions.
I am blessed to have the opportunity to work with renowned professors and very talented
colleagues from other institutions in the framework of the RMSSEC Energy Frontier Research
Center. They are Prof. Brock and Dr. Shreyashi Ganguly from Wayne State University; Prof.
vi

Ctirad Uher and Dr. Xiaoyuan Zhou, Dr. Guoyu Wang, and Mr. Hang Chi from University of
Michigan.
Many thanks go to my colleagues Dr. Yanzhong Pei (former post-doctoral associate in
our group), Dr. Long Zhang, Dr. Ponnambalam Vijayabarathi, Mr. Eric Skoug, Mr. Chang Liu,
Mr. Hui Sun, Mr. Xu Lu, Mr. Hao Yang, Miss Gloria Lehr and Mr. Steve Boona, with whom I
built and shared the laboratory. I am especially thankful to technician Brian Wright for assisting
me with thermal measurement; technician Gary Keeney for gladly taking the extra effort to help
me machine parts; and the MSU Physics machine shop manager Tom Palazzolo and other
technicians for their fast handling of my machining requests.
I also benefited tremendously from fruitful discussion with Prof. Joseph Heremans from
the Ohio State University on the topic of Nernst coefficient measurement.
Last but not least, I want to thank my beloved wife Wen for her unconditional support,
warm encouragement, tender care and endurance during the past three years. I feel to be a better
person with her in my life. I am also indebted to my parents and paternal grandparents for
nurturing me, educating me through my youth and the sacrifices they made. Their noble
characters are beacons in my soul. I am grateful to all of my relatives, home and abroad, who
have consistently supported me and encouraged me. This dissertation is also dedicated to them.

vii

TABLE OF CONTENTS

LIST OF TABLES ....................................................................................................................... x
LIST OF FIGURES .................................................................................................................... xi
Chapter 1 Introduction to Thermoelectricity ............................................................................... 1 
1.1 The thermoelectric effect ...................................................................................................... 1 
1.2 The efficiency for thermoelectric device .............................................................................. 3 
1.3 Electron transport .................................................................................................................. 7 
1.4 Thermal transport ................................................................................................................ 11 
1.5 The effect of low dimensional materials............................................................................. 17 
1.6 The state-of-the-art thermoelectric materials ...................................................................... 19
Chapter 2 Measurement Technique and Equipment Setup........................................................ 22 
2.1 Seebeck coefficient measurement ....................................................................................... 22 
2.2 Electrical resistivity measurement ...................................................................................... 24 
2.3 Thermal conductivity measurement .................................................................................... 24 
2.4 Hall effect measurement ..................................................................................................... 25 
2.5 Nernst-Ettingshausen effect measurement .......................................................................... 26 
2.6 Automatic data acquisition process using Labview program ............................................. 28 
2.7 Sample synthesis ................................................................................................................. 31
Chapter 3 Bismuth Telluride Based Nanocomposites ............................................................... 32 
3.1 Synthesis and characterization of PbTe nanoparticles (NP) ............................................... 32 
3. 2 Synthesis and TE properties of n-type Bi2Te2.85Se0.15 .................................................... 37 
3.3 Synthesis and TE properties of n-type Bi2Te2.85Se0.15/xPbTe nanocomposite (NC) ....... 46 
3.4 Synthesis and TE properties of p-type Bi0.4Sb1.6Te3 ........................................................ 52 
3.5 Synthesis and TE properties of p-type Bi0.4Sb1.6Te3/xPbTe nanocomposite (NC) .......... 56 
3.6 Summary of the chapter ...................................................................................................... 68
Chapter 4 Unfilled P-type Skutterudite Based Nanocomposite................................................. 69 
4.1 Experiment .......................................................................................................................... 71 
viii

4.2 Results ................................................................................................................................. 72 
4.4 Summary of the chapter ...................................................................................................... 80
Chapter 5 High Temperature Thermoelectric and Magnetic Properties of P-type Yb filled
skutterudite YbxFeyCo4-ySb12 ................................................................................. 82 
5.1 Experiment .......................................................................................................................... 83 
5.2 Results and discussion ........................................................................................................ 84 
5.3 Summary of the chapter ...................................................................................................... 94
Chapter 6 Thermoelectric Properties and Galvanomagnetic Properties of P-type Yb-filled
Skutterudite Nanocomposites with FeSb2 Nanoinclusions....................................... 96 
6.1 Sample synthesis ................................................................................................................. 97 
6.2 Results ................................................................................................................................. 99 
6.4 Summary of the chapter .................................................................................................... 115

Chapter 7 Thermoelectric Properties of Double Filled P-type Skutterudite YbyGazFexCo4xSb12 ....................................................................................................................... 116 
7.1 Sample synthesis ............................................................................................................... 118 
7.2 Results ............................................................................................................................... 119 
7.3 Discussion ......................................................................................................................... 124 
7.4 Summary of the chapter .................................................................................................... 128

Chapter 8 Conclusions and Future Work ................................................................................. 130
Bibliography ............................................................................................................................ 134 

ix

LIST OF TABLES

Table 1 Scattering parameter s and temperature dependence of carrier mobility for different
scattering mechanisms. ................................................................................................. 11 
Table 2 Sample identification and some room temperature physical properties of
Bi0.4Sb1.6Te3/xPbTe NC ............................................................................................. 57 
Table 3 Some physical properties of Yb filled Fe compensated p-type skutterudite sample
YbxFeyCo4-ySb12 at room temperature. ...................................................................... 85 
Table 4 Some physical properties of Yb filled Fe compensated p-type skutterudite sample
YbxFeyCo4-ySb12 at room temperature. The lower and upper boundaries of estimated
number of carrier/formula unit are calculated assuming a variant Yb valence of +2 and
+3. Minus sign in estimated number of carrier/formula unit indicates the major carrier
is electron. .................................................................................................................... 94 
Table 5 Sample ID and nominal chemical composition for YbyFexCo4-xSb12/zFeSb2 included
in this study. ................................................................................................................. 98 
Table 6 Some room temperature physical properties of Yb0.6Fe2Co2Sb12/xFeSb2 samples . 107 
Table 7 Sample designation of double filled skutterudite YbyGazFexCo4-xSb12. .................. 118 

x

LIST OF FIGURES

Figure 1 Schematic illustration of the Seebeck voltage induced by the temperature gradient.
For interpretation of the references to color in this and all other figures, the reader is
referred to the electronic version of this dissertation. ................................................. 1 
Figure 2 Schematic illustration of Peltier effect ........................................................................ 2 
Figure 3 Themoelectric uni-couple for power generation (a) and cooling (b) .......................... 3 
Figure 4 Efficiency ϕmax as a function of ZT for an ideal TE power generator operating
between a heat source of 600K, 700K, 800K and a sink of 300K. ............................. 6 
Figure 5 Schematic illustration of the interdepedent relations among the Seebeck coefficient S,
electrical conductivity σ, the thermal conductivity κ, and the resulting ZT for
insulators, semiconductors and metals. ....................................................................... 7 
Figure 6 Seebeck coefficient as a function of reduced Fermi energy for different scattering
mechanisms. .............................................................................................................. 11 
Figure 7 Schematic illustration of different phonon scattering mechanisms as a function of
temperature ................................................................................................................ 17 
Figure 8 Electronic density of states (DOS) for a bulk 3D crystalline semiconductor, a
2Dquantum well, a 1D nanowire or nanotube, and a 0D quantum dot[13] .............. 18 
Figure 9 Milestones of ZT in the history of thermoelectrics. 1. CsBi4Te6;[28, 29] 2.
Bi2Te3;[30-35] 3. PbTe;[36] 4. Zn4Sb3;[37] 5. Yb0.2Co4Sb12;[38] 6. CeFe4Sb12;[39]
7. MM/DDFe4Sb12;[40, 41] 8. SiGe;[42] 9. Yb14MnSb11;[9] 10. YbxGa8xGa16Ge30 (clatharates);[43] 11. Hf0.6Zr0.4NiSn0.98Sb0.02 (half-Heusler);[44] 12.

Ba0.08La0.05Yb0.04Co4Sb12 (triple filled skutterudite);[22] 13. NaPb20SbTe22
(SALT);[45] 14. AgPb18+xSbTe20 (LAST);[23] 15. Ag(PbSn)mSbTe2+m
(LASTT);[24] 16. AgSbTe2-GeTe (TAGS);[46] 17. PbTe-PbSe;[25] 18. TlPbTe.[26] ................................................................................................................... 20 
Figure 10 Photograph of the flow cryostat used to measure the low temperature transport
properties. .................................................................................................................. 22 
xi

Figure 11 Schematic illustration of sample setup for low temperature transport properties
measurement ............................................................................................................. 23 
Figure 12 Hall coefficient measurement setup and wiring on a standard sample puck for
Quantum Design Versalab system. ........................................................................... 25 
Figure 13 (a) Schematic illustration of the Nernst effect and (b) the sample setup for
measurement. ............................................................................................................ 27 
Figure 14 Schematic illustration of the Nernst field under typical charge carrier scattering
mechanisms. .............................................................................................................. 28 
Figure 15 Screenshot of the labview based automatic data acquisition program. ..................... 29 
Figure 16 Flow chart of the labview based automatic data acquisition program ...................... 30 
Figure 17 X-ray diffraction of PbTe NPs. ................................................................................. 33 
Figure 18 TEM image of PbTe NPs. We estimate the particle size to be about 13nm ............. 34 
Figure 19 IR spectroscopy of PbTe NPs sintered at 350°C (a) and 410°C (b) in inert gas
environment for two hours. ....................................................................................... 35 
Figure 20 X-ray diffraction shows that PbTe NPs heated at 410°C for 2 hours still retain the
altaite phase (the fine lines shown at the bottom is the reference) with no impurity
phase. The crystallite size is estimated to be about 17-22nm using Scherrer formula.
................................................................................................................................... 36 
Figure 21 Seebeck coefficients as a function of temperature for Bi2Te2.85Se0.15 annealed at
different temperatures. .............................................................................................. 39 
Figure 22 Temperature dependence of electrical resistivity for Bi2Te2.85Se0.15 annealed at
different temperatures. .............................................................................................. 40 
Figure 23 Lattice thermal conductivity as a function of temperature for Bi2Te2.85Se0.15
annealed at different temperatures. ........................................................................... 41 
Figure 24 Dimensionless FOM ZT as a function of temperature .............................................. 42 
Figure 25 Carrier concentration as a function of temperature for samples annealed at different
temperatures. ............................................................................................................. 43 
Figure 26 Pisarenko relation (the room temperature Seebeck coefficient as a function of carrier
concentration) for samples annealed at different temperatures. ................................ 44 
Figure 27 Room temperature ZT as a function of annealing temperature. ................................ 45 
xii

Figure 28 Hall coefficient as a function of temperature for Bi2Te2.85Se0.15/PbTe NCs .......... 47 
Figure 29 Thermopower as a function of temperature for Bi2Te2.85Se0.15/PbTe NCs ............ 48 
Figure 30 Electrical resistivity as a function of temperature Bi2Te2.85Se0.15/PbTe NCs ........ 49 
Figure 31 Power factor as a function of temperature Bi2Te2.85Se0.15/PbTe NCs .................... 50 
Figure 32 Thermal conductivity as a function of temperature for Bi2Te2.85Se0.15/PbTe NCs 51 
Figure 33 ZT as a function of temperature for Bi2Te2.85Se0.15/PbTe NCs .............................. 51 
Figure 34 Seebeck coefficient and electrical resistivity as a function of temperature for
Bi0.4Sb1.6Te3 hot pressed at 350°C, 380°C and 410°C............................................ 52 
Figure 35 Power factor as a function of temperature for Bi0.4Sb1.6Te3 hot pressed at 350°C,
380°C and 410°C....................................................................................................... 53 
Figure 36 Carrier concentration as a function of temperature for Bi0.4Sb1.6Te3 hot pressed at
350°C, 380°C and 410°C .......................................................................................... 54 
Figure 37 Carrier mobility as a function of temperature for Bi0.4Sb1.6Te3 hot pressed at 350°C,
380°C and 410°C....................................................................................................... 55 
Figure 38 Thermal conductivity as a function of temperature for Bi0.4Sb1.6Te3 hot pressed at
350°C, 380°C and 410°C .......................................................................................... 55 
Figure 39 ZT as a function of temperature for Bi0.4Sb1.6Te3 hot pressed at 350°C, 380°C and
410°C......................................................................................................................... 56 
Figure 40 IR spectroscopy of hydrazine PbTe NPs with oleate ligands, hydrazine treated PbTe
NPs and thermal treated PbTe NPs. .......................................................................... 58 
Figure 41 TGA of oleate capped PbTe NPs heat treated under N2 atmosphere ........................ 59 
Figure 42 PXRD patterns of NCs with 1wt% and 10wt% PbTe NPs loading. Asterisk indicates
the PbTe impurity phase............................................................................................ 60 
Figure 43 TEM images of PbTe NPs and NCs with 1 %, 0.5 % and 0.1 wt% discrete PbTe NPs
inside the Bi0.4Sb1.6Te3 matrix ................................................................................ 61 

xiii

Figure 44 Seebeck coefficient, electrical resistivity and power factor as a function of
temperature for Bi0.4Sb1.6Te3/xPbTe NC ................................................................ 62 
Figure 45 Thermal conductivity as a function of temperature for Bi0.4Sb1.6Te3/xPbTe NC. The
inset shows the lattice thermal conductivity as a function of temperature................ 63 
Figure 46 ZT as a function of temperature for Bi0.4Sb1.6Te3/xPbTe NC. ................................ 65 
Figure 47 Temperature dependence of carrier concentration for Bi0.4Sb1.6Te3/xPbTe NC..... 66 
Figure 48 Pisarenko relation of NCs. The fitted line is constructed as an aid to the eye. All
matrix bismuth antimony telluride of various carrier concentrations were synthesized
in our lab.................................................................................................................... 67 
Figure 49 Unit cell of a filled skutterudite. R: filler atom, M: transitional metal, A: pnicogen
atom ........................................................................................................................... 70 
Figure 50 X-ray diffraction patterns of samples x=0, 0.05, 0.1, 0.2 and control sample
Co0.75Fe0.25Sb3 ........................................................................................................ 72 
Figure 51 High resolution FESEM images on the fractured surface of nanocomposite samples
Co0.9Fe0.1+xSb3+2x and control sample Co0.75Fe0.25Sb3. (a) x=0.05, the inset
image zooms in the circled area to reveal the nanoscopic feature; (b) x=0.1; (c)
x=0.2; (d) Co0.75Fe0.25Sb3. ...................................................................................... 73 
Figure 52 Seebeck coefficient as a function of temperature. Ref data are excerpted from
reference.[87] ............................................................................................................ 74 
Figure 53 Electrical resistivity as a function of temperature ..................................................... 75 
Figure 54 Temperature dependence of the power factor ........................................................... 76 
Figure 55 Thermal conductivity as a function of temperature................................................... 77 
Figure 56 ZT as a function of temperature ................................................................................. 78 
Figure 57 Lattice constant with respect to the Fe/metal ratio. The square at x=0 on the abscissa
corresponds to CoSb3 with a lattice constant of 9.0385Å[47] .................................. 79 
Figure 58 Seebeck coefficient as a function of hole concentration. Reference data are from
Reference [88] on FexCo4-xSb12. The fitted line is calculated based on the reference.
................................................................................................................................... 80 
Figure 59 X-ray diffraction patterns for all samples. (a) x=0.4; (b) x=0.6; (c) x=0.8; (d) x=1 . 84 
xiv

Figure 61 Temperature dependence of Seebeck coefficient. Ref data are the Seebeck
coefficients of YbFe4Sb12 measured by Kuznetsov et al[91]................................... 86 
Figure 62 Electrical resistivity as a function of temperature. Ref data are YbFe4Sb12 measured
by Kuznetsov et al[91] .............................................................................................. 87 
Figure 63 Power factors as a function of temperature. Ref1 are data calculated based on
YbFe4Sb12 measured by Kuznetsov et al[91]. Ref2 is the power factor for
Ce0.9Fe3.5Co0.5Sb12 synthesized by us as a control sample. ................................... 88 
Figure 64 Thermal conductivity as a function of temperature. The inset graph shows the lattice
thermal conductivity. 1/T relation is plotted as an aid to understand the graph. ...... 89 
Figure 65 TE dimensionless figure of merit ZT as a function of temperature. Ref1 is the
estimated highest ZT of YbFe4Sb12 by Kuznetsov et al[91]. Ref2 (Yb0.8Fe4Sb12)
and Ref3 (Yb0.5Fe2Co2Sb12) are near room temperature ZT reported by Bauer et
al[94]. ........................................................................................................................ 90 
Figure 66 Magnetization of YbxFeyCo4-ySb12 for sample x=0.4, x=0.6, x=0.8 and x=1 at 60K,
80K, 100K, 150K, 200K, 250K and 300K. ............................................................... 91 
Figure 67 χT vs T ....................................................................................................................... 93 
Figure 68 1/(χ- χ0) vs T............................................................................................................... 93 
Figure 69 X-ray diffraction of Yb0.6Fe2Co2Sb12/zFeSb2 (a) 12.12 0.6R 0.2FS2 (b) 12.11 0.6R
0.1FS2 (c) 12.10 0.6R 0.05FS2 (d) 12.5 0.6R. Trace antimony was also observed in
(a) .............................................................................................................................. 99 
Figure 70 Zoomed in x-ray diffraction of two Yb0.6Fe2Co2Sb12/0.1FeSb2 samples synthesized
under the same condition. The major impurity phase is FeSb2 while another closely
related CoSb2 and some Sb is also observed. ......................................................... 100 
Figure 71 Zoomed in x-ray diffraction of Yb0.4FeCo3Sb12/zFeSb2 (a) 12.4 0.4R (b) 14.9 0.4R
0.1FS2 (c) 14.18 0.4R0.05FS2 (d) 14.10 0.4R 0.2FS2 (e) 14.11 0.4R 0.3FS2. The
expansion of the primary skutterudite peak around 31 degree 2θ indicates the
existence of FeSb2. .................................................................................................. 101 
Figure 72 FESEM images on the fractured surface of sample 13.9 0.6R0.05FS2(1) which
demonstrate the existence of FeSb2 nanoparticle. Images from (a) to (d) are in
increasing magnification. ........................................................................................ 102 
xv

Figure 73 Power factors of nanocomposite samples and control samples as a function of
temperature. The samples are grouped according to the Yb filling ratio “y” (a) y=0.4;
(b) y=0.5; (c) y=0.6; (d) y=0.7; (e) y=0.8; (f) y=0.9; (g) y=1. Generally,
nanocomposite samples could exhibit enhanced power factors when y≤0.7 as
shown from (a) to (d). Once y>0.7, most nanocomposite samples show comparable
or smaller power factors compared to control samples as shown from (e) to (g). .. 106 
Figure 74 Seebeck coefficient and electronic resistivity as a function of temperature for
Yb0.6Fe2Co2Sb12/xFeSb2....................................................................................... 107 
Figure 75 Temperature dependence of thermal conductivity for Yb0.6Fe2Co2Sb12/xFeSb2. The
inset graph displays the lattice thermal conductivity. ............................................. 109 
Figure 76 ZT as a function of temperature for Yb0.6Fe2Co2Sb12/xFeSb2. ............................. 110 
Figure 77 Pisarenko relation of nanocomposites and regular skutterudite samples at room
temperature. Blue diamond (skutterudite) points represent regular skutterudite
samples of various carrier concentrations prepared in our lab. The fit line serves as
an aid to the eye....................................................................................................... 111 
Figure 78 DOS effective mass m* and carrier scattering parameter s as a function of reduced
Fermi energy EF. ..................................................................................................... 114 
Figure 79 (a) 3D graph of the projected Seebeck coefficient S as a function of electrical
resistivity ρ and lattice thermal conductivity κl. (b) Cross section of κl = 0.2W/mK
from (a) which is used to identify the minimum Seebeck coefficient needed to attain
certain ZT. ............................................................................................................... 117 
Figure 80 Powder x-ray diffraction patterns of samples included in the study. (a) Y60; (b)
Y60G10; (c) Y60G15; (d) Y60G20; (e) Y65. The major peaks of all samples are
indexed to the skutterudite phase CoSb3 PDF# 01-073-7899. Trace amount of Sb
phase can also be detected in (a) but unidentifiable in the graph. Trace amount of Yb
can be found in (b), (c), and (d) and are labeled in the graph accordingly. ............ 119 
Figure 81 Lattice constant as a function of Ga filling fraction. ............................................... 120 
Figure 82 Temperature dependence of the Seebeck coefficient and the electrical resistivity. 121 
Figure 82 Power factor as a function of temperature............................................................... 122 
Figure 83 Total thermal conductivity and lattice thermal conductivity as a function of
temperature. ............................................................................................................. 123 
Figure 84 ZT as a function of temperature. Ref represents ZT of YbFe4Sb12 reported by
Kuznetsov and Rowe[91] ........................................................................................ 124 
xvi

Figure 85 Pisarenko relation of single filled Yb based p-type skutterudite and Yb Ga double
filled skutterudite at 300K. Circles in the figure represent additional Yb filled
skutterudite samples. Fit line represents the logarithmic relation expressed by
Equation 74 and serves as an aid to the eye. ........................................................... 125 
Figure 86 (a) DOS effective mass as a function of Fermi energy EF at 300K. Circle represents
Yb filled skutterudite and serves as supplemental datum. (b) Carrier scattering
parameter s as a function of temperature. ............................................................... 127 
Figure 87 Carrier concentration as a function of temperature. ................................................ 128 

xvii

Chap 1 Intro
pter
oduction to Thermoel
o
lectricity

e
ectric effect
t
1.1 The thermoele
The discov
very of the thermoele
e
ectric (TE) effect dat back in 1821 whe Seebeck
tes
n
en
k
reported to the Pr
d
russian Aca
ademy of Science that he had ob
S
t
bserved a p
potential difference by
y
heating the junctions between two dissim
n
milar conduc
ctors.[1] The Seebeck c
coefficient, also known
n
hermopowe S, is defin as the ra of poten
er
ned
atio
ntial differe
ence and tem
mperature gr
radient.
as the th
V
S  lim
T 0 T

1

Figure 1 is a schem
matic explan
nation for th Seebeck coefficient where carri with hig
he
iers
gher kinetic
c
energy on the hot side migrate to the col side, resu
ld
ulting in a v
voltage diffe
erence. The sign of the
e
e
k
nt
mined by the dominant carrier in the materia and it is p
e
t
al
positive for
r
Seebeck coefficien is determ
holes an negative for electron
nd
ns.

Figure 1 S
Schematic il
llustration o the Seebe voltage induced by the temper
of
eck
y
rature
gradient. For interpret
tation of the references to color in this and a other fig
e
s
n
all
gures,
the reader i referred to the electro version of this dissertation.
is
o
onic
n
Thirteen ye
ears later, th French w
he
watchmaker Peltier discovered a second the
ermoelectric
c
shown in Figure 2): wh a current passes th
hen
hrough a jun
nction of di
ifferent met
tals, there is
s
effect (s
an abso
orption or ge
eneration of heat, whic is distinc from the Joule heating and depends on the
ch
ct
e

1

directio of curre
on
ent. The Pe
eltier coeff
ficient Πab is defined as the ra of reve
d
ate
ersible heat
t
generation Q over the current I passing th
hrough the j
junction.
 ab 

Q
I

2

Figur 2 Schem
re
matic illustra
ation of Pelt effect
tier
From therm
modynamic arguments, Thomson derived the Kelvin relations and discovered
,
e
d
the thir thermoelectric effe now te
rd
ect,
ermed “Tho
omson effect”. Thoms
son effect is the heat
t
generation or abso
orption in a homogen
neous condu
uctor besid Joule he
des
eating when a current
n
t
passes t
through a te
emperature g
gradient. Th Thomson coefficien γ is define as:
he
n
nt
ed



Q
lim
T  0 I T

3

where Δ is the ra of rever
ΔQ
ate
rsible heat g
generation. The import
tance of Ke
elvin relatio is that it
ons
t
not only connects the Seebeck and Peltie coefficien as show in Equati 4, but a offers a
y
k
er
nts
wn
ion
also
way of calculating the absolu Seebeck coefficient using Equ
g
ute
t
uation 5. Eq
quation 5 als indicates
so
s
beck coeffic
cient for all material is zero at zero kelvin.
l
s
o
the Seeb
 ab  SabT
b
2

4

T
dS 
 ; S   dT
0 T
dT T

5

1.2 The efficiency for thermoelectric device
The basic thermoelectric device is a uni-couple that consists of a p-type material coupled
with an n type material. The device is capable of converting heat into electricity thus working as
a power generator [Figure 3(a)], or transfering heat from one end to the other under electric
current thus working as a heat pump [Figure 3(b)]. Here we use the generator model to discuss
the parameters that govern the efficiency of thermoelectric devices.
 

Hot
p

Cold

Heat release
n

p

T

n

Heat absorption
I

RL
(a)

(b)

Figure 3 Themoelectric uni-couple for power generation (a) and cooling (b)
The efficiency ϕ is the ratio of power W delivered to the load to the heat supply Q from
the source. The current I generated by the thermal electromotive force (EMF) can be expressed
as:
I

 S p  Sn  Th  Tc 
R p  Rn  RL

3

6

where Th and Tc are temperature of the heat source and sink; and Rp, Rn and RL represent
electrical resistance of the p-type leg, n-type leg and load respectively. The heat supply Q
comprises the Peltier effect, the heat conductance and half of the Joule heating that is returned to
the source.











1
Q  S p  S n ITh  K p  K n Th  Tc   I 2 R p  Rn
2



7

Thus



I 2 RL
W

1
Q
S p  Sn ITh  K p  K n Th  Tc   I 2 R p  Rn
2
T T
r
 h c
Th
1  r 2  1 Th  Tc
1  r  
Z pnTh 2 Th












8

where r=RL/(Rn+Rp). It can be seen that ϕ is a function of r. The maximum efficiency can be
obtained by setting dϕ/dr=0, which yields:

r  1  Z pnT ; T 

Th  Tc
2

9

So the maximum efficiency ϕmax is:

max 

Th  Tc 1  Z pnT  1
T
Th
1  Z pnT  c
Th

10

Similarly, the coefficient of performance (COP) for thermoelectric refrigeration can be derived
as:

4

COPmax 

1  Z pnT  1 1
T

Th  Tc 1  Z pnT  1 2

11

The first term in both equations of ϕmax and COPmax is the Carnot efficiency and the
second term is related to the material properties Zpn. For fixed Th and Tc, ϕmax increases with an
increasing Zpn towards the Carnot limit. For optimized geometries of the p-type and n-type
elements, Zpn is
Z pn 

S2
pn
 
 p


 p


1/2






1/2 

 
 n 
n 

2

12






where κ is the thermal conductivity and σ the electrical conductivity.
The requirement for high conversion efficiency translates to separately seeking p-type or
n-type materials with high Seebeck coefficient, electrical conductivity and low thermal
conductivity. Therefore we define the thermoelectric figure of merit (FOM) Z for a given
material as:

Z

S 2



13

Since Z itself is usually a function of temperature and has dimension of inverse temperature, it is
more practical to use the dimensionless FOM ZT in place of Z. For most thermoelectric devices
at their operational temperature, the p and n-type elements have nearly identical thermoelectric
properties, so Zpn can be approximated by the average of Zp and Zn.

5

Figure 4 Efficiency ϕmax as a function of ZT for an ideal TE power generator
operating between a heat source of 600K, 700K, 800K and a sink of 300K.
Figure 4 plots the maximum power generation efficiency as a function of average ZT for
a fixed sink temperature of 300K and various heat source temperatures of 600K, 700K and 800K
based on Equation 10. In order to gain a conversion efficiency of 20%, thus capable of
competing with the conventional heat engines, a ZT greater than 2 is needed. Unfortunately, the
best known TE materials prior to 1990s have a ZT around unity. The definition of FOM is very
deceptive as the three seemingly independent physical quantities are intricately related to each
other as shown in Figure 5. For example, insulators may have a large Seebeck coefficient and
low thermal conductivity, but have low electrical conductivity; on the other hand, metals are
good electrical conductors, but they also conduct heat well and suffer a low Seebeck coefficient,
typically only a few μV/K. It is found that semiconductors have the best compromise and
tunability among S, σ, and κ in order to yield a high FOM, which explains why most good
6

thermoe
electric mat
terials are h
heavily dope semicond
ed
ductors. We will briefl discuss th transport
e
ly
he
t
theories in the next sections.
s
t

Figure 5 Schema illustrati of the in
atic
ion
nterdepeden relations among the Seebeck co
nt
oefficient S,
electrical conducti
ivity σ, th thermal conductivit κ, and the resultin ZT for insulators,
he
ty
ng
nductors an metals.
nd
semicon
1.3 Elec
ctron trans
sport
The probab
bility of an electron occ
e
cupying the level of en
e
nergy E is d
described by the Fermiy
Dirac d
distribution f
function f(E
E):
f (E) 

1
 E  EF 
1  exp 

 kT 

14
4

where EF is the F
Fermi energ k the Bo
gy,
oltzmann co
onstant. Th number o available states at a
he
of
e
energy level E is g
given by the density of states func
e
f
ction g(E). F a simpl parabolic band, g(E)
For
le
c
)
expressed a
as:
can be e

7

g E 



where m*   2  2 E k 2



1

 

3/2

4 2m*
h

E1/2

3

15

is the effective mass, h is the Planck constant. The carrier

concentration is obtained by multiplying f(E) and g(E) and integrate over the all possible energy
levels:


n   f ( E ) g ( E )dE 



4 2m*kT



3/2

h3

0

F1/2  

16

here   EF kT ,   E kT is the reduced Fermi energy and kinetic energy of carriers

respectively. Fr(η) is the Fermi-Dirac integral defined as:




0

0

Fr ( )    r f   d  

 r d
1  exp     

17

The Equation 14 describes the electron distribution under no applied electric field.
Suppose an electric field is applied and a steady state is set up. If the field is small, f(E) can be
replaced by a new distribution function f1(E) and the rate of change is

f E  f E
df
 1
dt


18

where τ is the relaxation time of the system. Two processes are involved in calculating the
electrical conductivity: 1) the electrons will acquire a drift velocity under the electric field E and
2) the electrons will be scattered by lattice vibrations, other electrons, and crystal imperfections.
In the steady state, the two processes are balanced so we have:

8

 df  E  
 df  E  

0



 dt drift  dt  scattering

19

 df  E  
 df  E   dv
eE df  E 



  *
dv
m
 dt drift  dv  dt

20

 df  E  
f E  f E
 1



 dt  scattering

21

The drift term is:

and the scattering term is:

Combining Equation 19-21, we have the new distribution function f1(E):

eE df  E 

dv
m*

f1  E   f0  E  

22

The one dimensional current density is:

 g

df E
 e2 E
v
*
0
dv



j  e  vf1  E  g  E dE   
0

m

 E dE

23

Hence we obtain the expression for the electrical conductivity σ according to its definition.



j 16 2 m*1/2e 2 
3/2 df  E 

0   E  E dE dE
3
E
3h

24

The average energy of electrons in the current is


Ej  E  dE


E  0
0 j  E  dE

 df



0

E l

dE
 E  l E EdE
 
dE

 df

0

 E  E 2dE

25

where the electron mean free path l(E)=τv. From the thermodynamic perspective, the Seebeck
coefficient is the flow of entropy per passing electron, so

9

E 
1 E E  k  E
   F  B
 F 
e
eT
T  e  kBT kBT 
  df   

l    2 d 
 0

k
d
 B
 
e   df   

l    d 
 0

d



k   s  2  Fs 1  
 B
 

e   s  1 Fs  



S

Sentropy

26

-s

s is the power for the square of the matrix element of the scattering transition W(E)∝E , also
referred to as the carrier scattering parameter. Although we use electrons as an example to derive
the Seebeck coefficient, the case for holes is identical. The positive sign in Equation 26
represents the case for holes and negative sign for electrons. The above equation is the most
general expression for the Seebeck coefficient which is valid for both non-degenerate and
degenerate semiconductors and metals. In some texts, s’=s-1/2 is used in place of s. This comes
1/2

from the fact that for simple parabolic bands g(E)∝E

, so τ(E)∝W

-1

(E)g

-1

s-1/2

(E)=E

. We

will use the notation of s throughout this dissertation. When this is the case, the carrier mobility
has a temperature dependence of μ∝T
and μ∝T

s-1/2

s-3/2

for scattering by lattice vibration (thermal fluctuation)

for scattering by ionized and neutral lattice defects. Table 1 lists the values of s for

common scattering mechanisms, together with corresponding s’ and the temperature dependence
of mobility μ. Figure 6 plots the Seebeck coefficient as a function of reduced Fermi energy η for
different scattering mechanisms.

10

Scattering mechanism
Phonon

s
0
1/2

Ionic impurity

0

2

Neutral impurity

s’
-1/2

μ

3/2

μ ∝T

-3/2

μ∝T
μ∝T

0

3/2

Seebeck coefficient (μV/K)

Table 1 Scattering parameter s and temperature dependence of
carrier mobility for different scattering mechanisms.

600
s=0
s=1/2
s=2

500
400
300

s=2

200

s=1/2

100

s=0

0
-3

-2

-1
0
1
2
3
4
Reduced Fermi Energy η

5

Figure 6 Seebeck coefficient as a function of reduced
Fermi energy for different scattering mechanisms.
1.4 Thermal transport

The thermal conductivity κ comprises two parts, the electronic thermal conductivity κe
and the lattice thermal conductivity κl:

   e  l
κe is usually calculated by Wiedemann-Franz law κe=LσT , where the general expression for
Lorenz number L is given by[1]:
11

27

L

1  s  3  s  Fs F2 s   2  s 2 F2 s   k 2
1
1  s 2 Fs2

28

 
e

where F and s are Fermi integral and scattering parameters defined in the previous section. For
metals and strongly degenerate semiconductors, the Lorenz number takes the value

L

2 k 

2

8
2
   2.4453  10 W K
3 e

29

For intrinsic semiconductors, the Lorenz number takes the value
2

k
L  2    1.4866  108 W K 2
e

30

The Lorenz number of partially degenerate semiconductors falls between the above mentioned
two extreme cases and could be calculated using Equation 28, although for a material whose
-8

-2

lattice thermal conductivity κl is of major importance, assuming L=2.4453×10 WΩK will not
incur a huge error.[2]
A special case that should catch one’s attention is the bipolar thermal diffusion, in which
electrons in the conduction band and holes in the valence band both contribute to the electronic
thermal conductivity. In this case, κe is not a simple addition of κe1 from electron and κe2 from
the hole, but has a more complex form:
2

E 
k   T 
 e   e1   e 2    1 2  4  G 
kT 
 e  1   2 

2

31

The additional last term on the right hand side of Equation 31 arises from the transportation of
ionization energy of approximately equal number of electrons and holes created at the hot end

12

and recombined at the cold end. Thus this phenomenon will be most noticeable in intrinsic
semiconductors where both electrons and holes have high mobility.[2, 3]
The lattice thermal conductivity κl is related to the transport of phonons, which are
quanta of the vibrational energy of the lattice analogous to photon. The average number of
phonons with energy ħω is given by:

N0  q  

1
  
exp 
 1
 kT 

32

The total heat current Q due to all modes is:

Q   N  q  vG  q 

33

where vG(q)=dω/dq is the group velocity of propagation. Similar to the electron transport, the
phonon drift under the temperature gradient will be balanced by the phonon scattering so that at
equilibrium one has:
 N 
 N 

0



 t drift  t  scattering

34

N
 N 
   vG  T 


T
 t  drift

35

where

In the relaxation time method, it is assumed that the rate of the scattering process is proportional
to the departure of the distribution from the equilibrium so that:
N N
 N 
 0



 t  scattering

13

36

If we further assume N is not too greatly different from N0, then ∂N/∂T in Equation 35 can be
replaced by ∂N0/∂T. Thus we have the following equation for one dimensional case.
N N
N 0 T
N
 N 
 0
  vG  T 
 v zG


T
T z

 t  scattering

37

The lattice thermal conductivity κl is defined as:

l  

Q
2 N 0
   vG
T / z
T

38

z2

2

If we replace the summation by integral over ω and write (vG ) =1/3(vG) , we obtain

l 

N0
1 max
2
0 vG f   T d
3

39

where f(ω)dω is the number of phonon modes between ω and ω+dω per unit volume:
f   d  

3 2
2 2 v3

d

40

so that Equation 39 transforms into

l 

1
2 2 v

max

0

  / kT 2  exp   / kT d
 
3

exp   / kT   1



2

41

If we let x=ħω/kT and write ωmax=ωD=θ(k/ħ), where the Debye temperature θ is chosen to be
such that there are just 3N distinguishable modes:
3N  

D

0

f  d 

then

14

42

3

 /T
x4 e x
k
l  2   T 3    x 
dx
2
0
x
2 v   
e 1

k





43

Equation 43 is the Debye approximation for the lattice thermal conductivity. The heat capacity is

C  x 

3

4 x
k 3 x e
T
 
2 2 v3   
ex  1

3k





2

44

and the conductivity given by Equation 43 can be simplified as
1
3

l  v2 

 /T

0

1
3

  x  C  x dx  v 

 /T

0

l  x  C  x dx

45

where l(x)=vτ(x) is the mean free path of the phonon. [3, 4]
Equation 43 is often used to analyze and predict the experimental data. This is done by
calculating the relaxation time τ(x) for various phonon scattering mechanisms τi(x), the inverse of
which are additive.

 1   i1  x 

46

i

For phonon-phonon normal scattering (N-process), the relaxation rate:

 N1  B aT b

47

where B is a constant independent of ω and T. a and b are empirical constants for specific groups
of elements or crystal structures. The N-processes do not directly contribute to the thermal
resistance but have great effect on transferring phonons between different modes.
For phonon-phonon Umklapp scattering (U-process), Slack[5] proposed the following
form:

15


 U1 

 2
2

Mv  D

 2T exp   D 3T 

48

where γ is the Gruneisen parameter and M the average atomic mass. At sufficiently high
temperature, U-processes become the dominant phonon scattering mechanism and κl is
proportional to 1/T.
For point defect scattering:
1
 PD

 m  mi 
  fi 


3
 m 
4 v
i
V

4

2

49

where V is the volume per atom, mi is the mass of an atom, fi the fraction of atoms with mass mi,
and m is the average mass of all atoms.
For boundary scattering:

 B1 

v
d

50

where d is the grain size for polycrystals or sample size for single crystal. Figure 7 plots the
schematic illustration of the temperature dependence of typical phonon scattering mechanisms in
polycrystalline semiconductors.

16

κl Arb. unit

κ l ∝ T3

κl =1/3 CVvl

κl ∝1/T
Boundary Defects

Umklapp processes

Temperature (K)
Figure 7 Schematic illustration of different phonon
scattering mechanisms as a function of temperature
1.5 The effect of low dimensional materials

The optimization of ZT can be artificially divided into two routes according to its
2

definition: 1) to reduce the lattice thermal conductivity κl , 2) to increase the power factor S σ
with the caution that compromises have to be made so that the overall ZT is enhanced. The first
route of κl reduction appears easier as only one parameter is involved and over the years
researchers have discovered a few successful methods to lower κl such as increasing the average
atomic mass,[6] making alloys and solid solutions,[7, 8] seeking materials with intrinsic complex
structures,[9] and creating phonon scattering by inserting foreign atoms into an open void.[10]
However, κl cannot be indefinitely reduced as the minimum κl is estimated to be 0.1-0.2
W/mK by using κl=1/3Cvl where the phonon mean free path l is assumed to be on the order of
17

interatomic spacing. Thus for even higher ZT, it is critical to enhance the power factor portion of
2

the FOM. Traditionally, increasing S σ relies on properly doping the material so that the Fermi
level is positioned in the optimal region to yield the maximum value.[1] The limitation for this
method is that 1) the maximum attainable value is very likely pre-set by the nature of the
material and 2) it is very hard to independently tune S and σ.
In 1993, Hicks and Dresselhaus first predicted theoretically that the ZT in a 2D quantum
well structure could be increased by several fold over the same 3D bulk materials, if superlattice
multilayers are properly oriented and their size is comparable to the interatomic spacing. This
work was soon expanded to quantum wires and quantum dots as they can offer more quantum
confinement[11, 12].

Figure 8 Electronic density of states (DOS) for a bulk 3D crystalline semiconductor,
a 2Dquantum well, a 1D nanowire or nanotube, and a 0D quantum dot[13]
The following proof of principle experiments demonstrated that the enhancement of ZT in
2

nanostructured materials comes from both the reduction of κl and the enhancement of S σ. The
reduction of κl is not hard to understand as the reduced dimension caps the mean free path l. To
2

understand the enhancement of S σ, it is helpful to express the Seebeck coefficient according to
the Mott and Jones equation[14]:
18

S

 2k 2T  d ln   E  



3e

dE


 EE


F

 2k 2T  d ln g  E 
3e





dE



d ln v 2  E 
dE



d ln   E  


dE
 E  EF

51

where v is the average electron drift velocity, and  is the relaxation time. For free electrons,
g(E)∝E

1/2

2

s

, v ∝E, and τ∝E . The first term d ln g  E  dE suggests that a large thermopower is

possible if the Fermi level is positioned near a sharp spike in the density of state (DOS).
Theoretical calculation indeed shows that the DOS becomes discontinuous when the dimension
of the constituent is reduced as illustrated in Figure 8. This mechanism has been corroborated by
the large power factor enhancement in PbTe quantum well structures[15, 16], Si/Ge
superlattice[17], PbSeTe based quantum dot superlattice (ZT~1.3-1.6 ) [18] and Bi2Te3/Sb2Te3
superlattice (ZT~2.4) [19]. The third term d ln   E  dE indicates that it is also possible to
enhance the Seebeck coefficient by tweaking the scattering parameter s (also known as the
energy filtering effect[20]). In fact, this method has been proposed by Ioffe and his coworkers as
a way to search for new TE materials with ionic bonding.[1] Heremans et al has demonstrated in
PbTe nanostructures[21] that the enhanced Seebeck coefficient is the result of a greater
scattering parameter s caused by resonant scattering.

1.6 The state-of-the-art thermoelectric materials

Figure 9 plots the ZT as a function of temperature for selected materials that mark the
milestones on the advancement of TE materials. By discovering materials with intrinsic complex
structures,[9, 22] utilizing phase decomposition to create imbedded nanostructures,[23, 24] band

19

structure engineering[25, 26] and advanced materials processing techniques (such as melt
spinning[27]), many material systems exhibit a ZT above unity and some even get close to 2.

2
1.8

14

1.6
13

1.4

16
7

4

1

10

9

11

2

0.8

12

18
15

1.2
ZT

17

3

6
8

1

0.6
0.4
5

0.2
0
0

200

400

600

800

1000

1200

1400

Temperature (K)

Figure 9 Milestones of ZT in the history of thermoelectrics. 1. CsBi4Te6;[28, 29] 2.
Bi2Te3;[30-35] 3. PbTe;[36] 4. Zn4Sb3;[37] 5. Yb0.2Co4Sb12;[38] 6. CeFe4Sb12;[39]
7. MM/DDFe4Sb12;[40, 41] 8. SiGe;[42] 9. Yb14MnSb11;[9] 10. YbxGa8-xGa16Ge30
(clatharates);[43] 11. Hf0.6Zr0.4NiSn0.98Sb0.02 (half-Heusler);[44] 12.
Ba0.08La0.05Yb0.04Co4Sb12 (triple filled skutterudite);[22] 13. NaPb20SbTe22
(SALT);[45] 14. AgPb18+xSbTe20 (LAST);[23] 15. Ag(PbSn)mSbTe2+m
(LASTT);[24] 16. AgSbTe2-GeTe (TAGS);[46] 17. PbTe-PbSe;[25] 18. Tl-PbTe.[26]
The pioneering results inspired us to investigate bulk nanocomposite materials that
incorporate the relative ease of synthesis with the possible enhancement of TE properties due to
the reduced dimension of the nanoparticles. We expect the myriad nanoscopic interfaces
20

produced by these nanoparticles can effectively scatter the phonons, thus reducing the lattice
thermal conductivity. We are also interested in finding out if these nanoparticles can at least
partially preserve the feature of DOS as that exhibited by 0D quantum dots or act as an energy
filter at the grain boundaries, thus improving the Seebeck coefficient without affecting the
electrical conductivity too much. With these hypotheses in mind, we start our exploration to the
nanocomposite TE materials.

21

Chapter 2 Measurement Technique and Equipment Setup

2.1 Seebeck coefficient measurement

The Seebeck coefficient is calculated as the ratio of the potential difference ΔV and
temperature difference ΔT across the sample as shown in Equation 52.
S

V
T

52

For low temperature from 80K to room temperature, this is measured under vacuum in a
continuous flow cryostat (see Figure 10) using steady state technique with liquid nitrogen as the
refrigerant.

Figure 10 Photograph of the flow cryostat used to
measure the low temperature transport properties.

22

The setup for measuring low temperature Seebeck coefficient is shown in Figure 11. A
rectangular parallelepiped shape sample with dimensions of approximately 2.4mm × 2.4mm ×
8mm is cut out of the ingot or the consolidated pellet. The sample is usually anchored to a copper
base using a conducting silver epoxy. A 800Ω resistor wrapped by copper foil is attached to the
top of sample to work as a mini heater and generate the temperature gradient for Seebeck
coefficient and thermal conductivity measurement. Two copper-constantan thermocouples are
anchored to the middle of the sample to measure the temperature difference. The copper leads
also serve to measure the voltage difference at the same time.
Heater made of a resistor
wrapped by copper foil

Thermocouple 1

Sample

Thermocouple 2

Copper base

Figure 11 Schematic illustration of sample setup for low
temperature transport properties measurement
The high temperature Seebeck coefficient (from room temperature up to 800K) is
measured in a commercial equipment ULVAC ZEM-3. The principle of measurement is
identical to that of the low temperature except the Seebeck coefficient is calculated as the slope
of a set of different ΔV vs ΔT.

23

2.2 Electrical resistivity measurement

The electrical resistivity ρ is measured by standard four-point method and calculated by
using Ohm’s law. The resistivity measurement is carried out in parallel with the Seebeck
coefficient measurement in the cryostat (for low temperature) and in ZEM3 (for high
temperature).
Care must be paid to the influence of Peltier effect on the accuracy of voltage
measurement. The as-measured voltage consists of the voltage drop due to the sample resistance
and Seebeck voltage, Vtotal=VIR+VSeebeck=VIR+SΔT. Since TE materials usually have large S,
it is possible to incur a large error during the measurement. To minimize the Seebeck induced
voltage, the measurement must be completed in short time (usually less than 5 seconds). In
addition, it is better to use an AC resistance bridge or the polarized DC current (providing a
current from both positive and negative direction) to subtract the VSeebeck part.[47]
VIR 

VI   S T   VI   S T 
2

53

Another source of error for ρ is from the accuracy of measuring the cross sectional area a
and the distance between thermocouple leads l. The error of geometry, however, does not
influence ZT as the errors from ρ and κ usually cancel out each other.

2.3 Thermal conductivity measurement

The low temperature thermal conductivity is measured in the cryostat and calculated as:

 K

l
Ql
VI l



a Ta T a

24

54

where K is the thermal conductance, l is the probe separation between the two thermocouples and

a is the cross-sectional area. The radiation loss is corrected by subtracting the thermal
conductance to the ambient Kloss from the total thermal conductance K.
High temperature thermal conductivity is obtained by the laser flash thermal diffusion
technique, in which thermal conductivity is related to thermal diffusivity D, isobaric specific heat

Cp, density d by κ=dDCp. Thermal diffusivity D and specific heat Cp were measured in
commercial equipments Netzsch LFA 457 and Netzsch DSC 200F3 respectively. Density d was
measured at room temperature by Archimedes method with 200 proof ethanol as the medium.

2.4 Hall effect measurement

Bz

Ey
jx

I+

V+

V-

I-

CH1

I+ V+ V- I-

CH2

Figure 12 Hall coefficient measurement setup and wiring on a
standard sample puck for Quantum Design Versalab system.

25

Hall coefficients and electrical resistivity from 60K to 400K were carried out using AC
current in a varying magnetic field from -3T to 3T in a Quantum Design Versalab system. A thin
slab with approximate thickness of 1mm was cut out of the same ingot or sample that is used for
low temperature transport measurement. The sample mounting and wiring are illustrated in
Figure 12, where the four contacts of CH1 are assigned for measuring the Hall resistance and
CH2 is used to measure the electrical resistivity. Since the majority of materials studied in this
project are heavily doped semiconductors, we assume a single carrier model with a scattering
parameter of unity to calculate the Hall coefficient, hence the carrier concentration given by
Equation 55.
RH 

Ey
j x Bz



Vyt
I x Bz



Rxy t
Bz



1
ne

55

2.5 Nernst-Ettingshausen effect measurement
The Nernst-Ettingshausen effect is another galvanomagnetic effect that provides very
important information to the transport properties of TE materials. The Nernst effect [Figure 13(a)]
is very analogous to the Hall effect (Figure 12) except that the driving force of charge carriers is
the thermal gradient rather than the electric field in the Hall effect. The Nernst coefficient is
measured in the cryostat under the magnetic field capable of -2T to 2T. The sample setup is
virtually the same as that for low temperature cryostat measurement with a third thermocouple to
measure the transverse temperature gradient and transverse voltage incurred by the Nernst effect.
The calculation of Nernst coefficient N is given in Equation 56.

26

Heater

Hz

TC3

Bz

TC1

T

Ey

Δx

Δy

- ∇xT

TC2

(b)

(a)

Figure 13 (a) Schematic illustration of the Nernst
effect and (b) the sample setup for measurement.

N 

Ey
Tx Bz



V y / y 1
V y x

T / x Bz
TBz y

56

The Nernst field is highly dependent on the scattering mechanisms of the charge
s-1/2

carriers.[48] As shown in Chapter 1, the relaxation time τ(E)∝ E

s’

=E . The deflection angle

φ depends on the relaxation time τ. If τ is smaller, the arc length of the charge orbit is shorter,
hence φ is smaller. Conversely, a larger τ means a larger deflection angle φ. For ionized impurity
scattering s’>0, τ is larger for more energetic electrons from the hot side than the less energetic
electrons from the cold side. Hence φ1>φ2, the Nernst field points to the right. This gives a
positive Nernst coefficient. Similarly, for acoustic phonon scattering, s’<0, τ is larger for the less
energetic electrons from the cold side. Hence φ1<φ2, the Nernst field points to the left and
Nernst coefficient is negative. For neutral impurity scattering, s’=0, φ1=φ2, Nernst coefficient is
zero.
27

Bz
ENernst
hot

Bz
ENernst

e-

hot

φ2

Enernst=0
e-

φ1

Bz

hot

φ1

φ1

φ2

cold
Ionized
impurity
s’>0
τ1> τ2
φ1 > φ2

e-

φ2

cold
Acoustic
phonons
s’<0
τ1<τ2
φ1<φ2

cold
Neutral
impurity
s’=0
τ 1 = τ2
φ1 = φ2

Figure 14 Schematic illustration of the Nernst field
under typical charge carrier scattering mechanisms.
Combining the Nernst coefficient N with the Seebeck coefficient S, electrical
conductivity σ, and the Hall coefficient RH, one is able to calculate the DOS effective mass m*
and the carrier scattering parameter s. This method is known as the “method of four coefficients”
[21, 48-51], which is well documented in the literature and will be discussed in details in the
later chapter.

2.6 Automatic data acquisition process using Labview program
The labview based automatic data acquisition program was developed in our laboratory
in the summer of 2009 and has been continually upgraded/expanded to refine the operating
parameters and accommodate more testing capabilities. The PC based program controls the
temperature controllers, magnets, and meters etc. via National Instruments GPIB card and
28

Standard Commands for Programmable Instruments (SCPI) language. At the present, the
program is able to fully control every aspect of the measurement, perform measurements that
otherwise cannot be performed by manual operation, has a user friendly input and output panel,
real time data graphing and instant data saving capability. The key operational functions have
been compacted to subVIs to improve the readability of the program and facilitate the ease of
future expansion. Now, the only things that still need to be done manually are mounting samples
in the instruments, turning on the vacuum pump and liquid nitrogen supply. Everything else can
be adjusted and controlled by program from any place in the world where there is internet
connection. This greatly improves the research productivity in our laboratory from 1 sample/2
days to 2 samples/day or even 3 samples/day if needed. Figure 15 displays the screenshot of the
program interface which can measure the Seebeck coefficient, electrical resistivity, thermal
conductivity, Hall coefficient and Nernst coefficient simultaneously. Figure 16 displays the flow
chart of the program.

Figure 15 Screenshot of the labview based automatic data acquisition program.

29

Sample info
& parameters
Set temperature &
wait for steady state
N
|T-Tset|<0.5K
Y
Measure ρ
Y
Sweep magnetic field

Hall switch
N

Measure transverse ρ

Activate heater

N

Y
Hall loop
end?

Measure S & κ

Y
Nernst switch

data
output

Sweep magnetic field

Measure Nernst V

S, ρ & κ
data output

Y
N
Nernst
loop end?

Turn off heater

data
output

N

Y
Program end

T>Thigh?

Figure 16 Flow chart of the labview based automatic data acquisition program
30

2.7 Sample synthesis
Since the methods for synthesizing our samples are different for each material system,
details of sample synthesis will be given in the corresponding chapters covering each material.

31

Chapter 3 Bismuth Telluride Based Nanocomposites
Bismuth telluride based nanocomposites use bismuth telluride and its alloys as the matrix
material and lead telluride nanoparticles (NPs) as the nanoinclusions. We select bismuth telluride
and lead telluride because both materials are well-known good TE materials in their bulk form
with comparable TE properties, thus making them more likely to enhance the overall properties
of the composites.[52] As a first step, we prepare our matrix materials and lead telluride
nanoparticles separately. N-type Bi2Te2.85Se0.15 and p-type Bi0.4Sb1.6Te3 were prepared and
characterized at Michigan State University; PbTe NPs were prepared through wet chemistry
method by our collaborators at Wayne State University. The well characterized matrix material
and NPs were mixed together using incipient wetness impregnation method, consolidated into
the bulk materials and characterized at Michigan State University. The following sections offer
detailed descriptions of our study.

3.1 Synthesis and characterization of PbTe nanoparticles (NP)
The PbTe NPs were synthesized by our collaborators Shreyashi Ganguly and Prof.
Stephanie Brock at Wayne State University. Discrete PbTe nanoparticles were prepared by
combining lead acetate trihydrate (Pb(OAc)2·3H2O) (1.317 g, 3 mmol) with oleic acid (OA) (3
mL, 6 mmol) and 1-octadecene (ODE) (6 mL, 18 mmol) and heating this mixture under inert
atmosphere on a Schlenk line at 170 °C for 30 min to obtain a colorless solution [53]. The
temperature of the solution was then reduced to 150 °C followed by rapid injection of 3 mL of
1M trioctylphosphine (TOP) tellurium, which was formed by dissolving 1.27 g of Te in 10 mL of
32

trioctylphosphine solution in a glove box. The resultant solution was left at 150 °C for 5 min and
then the reaction was quenched by plunging the flask into a cold-water bath. The NPs were
precipitated inside a glove box by adding hexane as the solvent and acetone as the antisolvent,
and isolated by centrifugation.
X-ray diffraction (Figure 17) has confirmed the phase purtiy of our PbTe NPs. We
applied the Scherrer analysis to estimate the crystallite size to be around 13-19 nm based on the
characteristic peak broadening of the NPs, which agrees very well with the NP size given TEM
image (Figure 18).

____ PbTe nanoparticles
____ PDF#38-1435 corresponding to
altaite phase of PbTe nanoparticles

100

Intensity (arb.units)

80

60

40

20

0
20

30

40

2( )

50

60

Figure 17 X-ray diffraction of PbTe NPs.

33

70

5 nm
Figure 18 TEM image of PbTe NPs. We estimate the particle size to be about 13nm
Thermogravimetric (TGA) analysis was performed at Wayne State University to test the
thermal stability of PbTe NPs. PbTe NPs were heated in a nitrogen protected environment. At
500°C, TGA result shows 15 % weight loss in the PbTe NPs but x-ray diffraction confirms that
the characteristic peaks match the diffraction pattern of cubic PbTe (altaite phase), with no other
peaks observed. The size of the nanoparticles increased slightly from 16 nm to 24 nm which was
estimated by Scherrer formula. At 600C, TGA result shows 25 % weight loss. An extra impurity
phase indexed to Pb was also observed along with the PbTe phase. We conclude that the PbTe
NPs are thermally stable below 500°C. Such a finding has been confirmed by TEM images on
the heated PbTe NPs.
In order to remove the organic ligands that encapsulate the PbTe NPs, we sintered the
PbTe NPs in inert gas protected environment for 2 hours at various temperatures below 500°C.
IR spectroscopy analysis shows that for sintering temperature of 350°C as shown in Figure 17(a),

34

(a)

(b)
Figure 19 IR spectroscopy of PbTe NPs sintered at 350°C
(a) and 410°C (b) in inert gas environment for two hours.
the organic groups are still present (peak at 1512 cm-1 and 1394 cm-1 for the symmetric and
asymmetric stretching vibrations of COO- and 2918 cm-1 and 2840 cm-1 corresponding to

35

aliphatic –CH stretches). Figure 19(b) shows that for sintering temperature of 410°C, no peak
was observed, suggesting that the organic ligands have been completely removed.

Figure 20 X-ray diffraction shows that PbTe NPs heated at 410°C for 2 hours still retain
the altaite phase (the fine lines shown at the bottom is the reference) with no impurity
phase. The crystallite size is estimated to be about 17-22nm using Scherrer formula.
In conclusion, we have successfully synthesized PbTe NPs which are thermally stable up
to 500°C. X-ray powder diffraction has confirmed the phase purity of the NPs and the particle
size is estimated to be about 13nm based on Scherrer analysis and TEM image. IR spectroscopy
suggests that heating PbTe NPs at 410°C in inert gas protected environment for two hours is an
effective way to remove the surface organic ligands encapsulating the PbTe NPs.

36

3. 2 Synthesis and TE properties of n-type Bi2Te2.85Se0.15

Bismuth telluride (Bi2Te3) has a rhombohedral unit cell of space group R3m , which can
often be envisioned more conveniently as a hexagonal primitive cell with quintuple layers of
Te(1)  Bi  Te(2)  Bi  Te(1)  along c-axis.[47] Bi2Te3 can be made both p-type and n-type by
alloying with Sb2Te3 or Bi2Se3 of similar tetradymite structure. Single crystalline Bi2Te3 have
been grown successfully using the Bridgman method[54], travelling heater method (THM)[32]
and zone melting[55]. In spite of the high FOM they present, these single crystals suffer
inevitable drawback of poor mechanical properties due to the weak Van der Waals bonding
between Te(1)  Te(1) basal planes[56, 57]. Thus polycrystalline Bi2Te3 fabricated by powder
metallurgy are sought for their improved mechanical properties. However, their thermoelectric
properties are very sensitive to processing procedures and have been shown to be quite widely
varying.[58-62] This is especially true for n-type Bi2(Te, Se)3, which may largely be contributed
to the electronically active point defects[63] and inhomogeneity of selenium[64].
In order to obtain reproducible TE properties for our n-type Bi2Te2.85Se0.15, we first
investigated the influence of annealing on the TE properties of undoped Bi2Te2.85Se0.15. High
purity starting materials of Bi, Te, and Se of stoichiometric ratio were charged into a carbon
-6

coated quartz ampoule and sealed under vacuum of 10

Torr. The quartz ampoule was slowly

heated to 750°C and held for 12 hours to melt all constituents before being quenched in a water
bath. The glossy ingot was milled for 15 min. into fine powders in a Spex mill/mixer.
37

The milled powders were cold pressed under the load of 1 ton in an 8mm stainless steel
die. Cold pressed pellets were re-sealed under vacuum, and annealed at temperatures of 350°C,
400°C, 450°C, 500°C, 520°C, 540°C, 560°C, and 580°C respectively. All samples were annealed
for 2 days except that of 450°C sample due to an unexpected fuse break. We estimate the actual
time is 2-3 days at 450°C. An individual type-K thermocouple was used to calibrate the
temperature inside the furnace. The annealed samples were sliced to rectangular parallelepiped
of approximately 3mm × 3mm × 7.5mm for transport property measurement and 1mm × 2.2mm
× 7.6mm for Hall measurement. The relative density of our samples is estimated to be about 80%
of theoretical density.
X-ray diffraction was performed on the surface perpendicular to the pressing direction.
The characteristic peaks match the indices of PDF reference 01-085-0439, which indicates we
successfully obtained Bi2Te2.85Se0.15. We also calculated the F factor for the degree of
orientation and observe no apparent anisotropy.[62]
Figure 21 shows the Seebeck coefficient as a function of temperature. Here for the sake
of simplicity in discussion, we arbitrarily divide the annealed samples into two categories:
samples annealed at 520°C and above are referred to as high temperature group while those
annealed at 500°C and below are referred to as low temperature group. As shown in Figure 21,
the Seebeck coefficient for as-pressed unannealed sample is slightly positive, which implies the
actual chemical composition is Bi rich and falls in the p-type region. Upon annealing, all samples
were converted to n-type and Seebeck coefficients generally become more negative with
increasing annealing temperatures. For samples annealed at high temperatures (520°C and
above), all Seebeck coefficients achieve their negative peaks below room temperature and then
38

rise with increasing temperature. The marginal effect of annealing on maxima is reduced at
higher temperature with the exception of the sample annealed at 580°C, which is only 5°C below
the melting point.

Figure 21 Seebeck coefficients as a function of temperature
for Bi2Te2.85Se0.15 annealed at different temperatures.

39

Figure 22 Temperature dependence of electrical resistivity
for Bi2Te2.85Se0.15 annealed at different temperatures.
Figure 22 reveals the temperature dependence of electrical resistivity. Samples annealed
at lower temperatures (500°C and below) have a smaller resistivity compared to that of the
higher temperature group. Increasing the annealing temperature increases the resistivity in
general. Resistivity for samples annealed at higher temperature region, on the contrary shows a
decreasing trend and its peak shifts to higher temperature as annealing temperature increases
with the sample annealed at 520°C on top of all the other samples. The emergence of the
resistivity peaks indicates the loss of selenium.

40

Figure 23 Lattice thermal conductivity as a function of temperature
for Bi2Te2.85Se0.15 annealed at different temperatures.
Figure 23 shows the lattice thermal conductivity as a function of temperature. The
electronic thermal conductivity has been subtracted by Wiedemann-Franz Law. Apart from
samples annealed at the highest and lowest temperatures, all samples have similar values with a
difference less than 25% at room temperature. The deviation for these samples can be attributed
to the difference in porosity and measurement error. The large separation for samples annealed at
both ends can be understood by considering the content and homogeneity of Bi2Se3 as a solid
solution.

41

Figure 24 is the temperature dependence of dimensionless FOM ZT. The sample
annealed at 450C has the highest ZT=0.51 at 300K and has not reached its full potential due to
the limit of our measurement capability.

Figure 24 Dimensionless FOM ZT as a function of temperature
For bismuth telluride, the transport properties are very sensitive to the carrier
concentration which is largely influenced by electronically active point defects and stoichiometry.
The chalcogen elements Te and Se can segregate along the grain boundaries during solidification
[64, 65]. The deficiency of chalcogen makes the actual stoichiometry Bi rich, which results in a
p-type material. Upon annealing, segregated Se and Te are re-introduced into the material where
most Se replaces Te(2) because of its higher diffusion coefficient and larger electronegativity.
42

This process converts the material to n-type. When the annealing temperature is high, chalcogens
can evaporate and leave behind electronically active antisite defects and vacancies [66, 67]:

/
//

Bi2Te3  2 BiTe  2VBi /  VTe  3 / 2Te2 ( g )  8h

57


/
1.5/

3Bi2 Se3  4 BiBi  2 BiSe  2VBi  7VSe  9 / 2 Se2 ( g )  2e /

58

Figure 25 Carrier concentration as a function of temperature for
samples annealed at different temperatures.
We believe the process described by Equation 57 of major importance because of the
/
abundance of tellurium and a stronger bond between Bi-Se(2) [68]. The holes generated by BiTe
///
and VBi reduce the carrier concentration through compensation as illustrated in Figure 25. As

43

we increase the annealing temperature, the number of charge carriers is reduced and we start to
observe the advent of extrinsic to intrinsic conversion in 500°C annealed sample. It is worth
noticing that for samples annealed above 520°C, the carrier concentration increases slightly in
the extrinsic region which suggests larger amount of Se loss may contribute some extra electrons
as described by Equation 58.

Figure 26 Pisarenko relation (the room temperature Seebeck coefficient as a
function of carrier concentration) for samples annealed at different temperatures.
Figure 26 is the so-called Pisarenko relation of our samples, depicting the relation
between Seebeck coefficient and electron concentration at room temperature. As annealing
temperature is increased, the carrier concentration decreases; the absolute value of Seebeck

44

coefficient increases as a result until it hits the extrinsic-intrinsic border where it starts to drop
off.
In order to seek the optimal temperature range for annealing, we plot the room
temperature ZT as a function of annealing temperature as shown in Figure 27. We find the
annealing temperature in the vicinity of 440°C offers the best TE performance at 300K.
0.6
350C
400C

0.5

450C
500C

ZT

0.4

520C
540C

0.3

560C

0.2
0.1
0
300

350

400

450

500

550

600

Annealing temperature °C

Figure 27 Room temperature ZT as a function of annealing temperature.
In summary, undoped n-type polycrystalline Bi2Te2.85Se0.15 has been successfully
fabricated by cold pressing and annealing. The transport properties, determined primarily by
carrier concentration, are very sensitive to processing parameters. Annealing could be visualized
as a dynamic equilibrium between homogenization through solid state diffusion and formation of
antisite defects and vacancies induced by chalcogen evaporation. If the annealing temperature is
45

too low, the homogenization is incomplete resulting in inferior properties. If the temperature is
too high, the excessive holes generated by electronically active defects will compensate the
electrons and shift the carrier concentration out of the optimized zone. Thus a proper
combination of annealing temperature and time is crucial to fine tune the carrier concentration.
For our undoped n-type Bi2Te2.85Se0.15 polycrystals, the sample annealed at 450°C for 2-3 days
exhibits the highest ZTmax=0.51 at 300K.

3.3 Synthesis and TE properties of n-type Bi2Te2.85Se0.15/xPbTe nanocomposite (NC)

The synthesis of nanocomposites involved dispersion of an appropriate mass of PbTe
nanoparticles into a minimum amount of solvent, hexane. The resulting solution was sonicated
for 10 minutes to make a colloidal suspension. The PbTe nanoparticle sol was then added
dropwise to Bi2Te2.85Se0.15 powders with constant stirring. The slurry was continuously stirred
to facilitate incorporation of the PbTe nanoparticles throughout the matrix, then left to dry under
ambient temperature and pressure inside Ar purged glovebox. This process is a variant of the
incipient wetness impregnation technique. The resultant composite was placed inside a carbon
crucible and heated at 410°C for two hours to pyrolyze organic ligands encapsulating the PbTe
nanoparticles. The heat treated powder was then hot pressed inside a 12 mm graphite die under a
pressure of 60 MPa at an approximate temperature of 350°C for 5 minutes. A total of five
samples have been prepared with PbTe NP weight percentage of 0wt%, 0.1wt%, 1wt%, 5wt%
and 10wt% respectively. The 0wt% sample represents the pure Bi2Te2.85Se0.15 with no added
PbTe NPs which serves as the control sample. All Bi2Te2.85Se0.15 powders come from the same
46

batch which eliminates the influence of property deviation from the matrix material. The pressed
disks all have densities greater than 90% of the theoretical density. Here for the sake of
simplifying the discussion, we use the weight percentage of PbTe NPs to designate our samples.

X-ray diffraction scans were performed on all samples confirming that Bi2Te2.85Se0.15 is
the major phase with trace amount of PbTe phase observed around 39 degree 2θ. Figure 28 is
the Hall coefficient as a function of temperature. As it can be seen from Figure 28, the matrix
x=0 is n-type; upon adding PbTe NPs, the RH is first reduced a little for x=0.1 sample, and
gradually converted to positive region at low temperature. Sample x=5 and x=10 have
overlapping temperature dependence of RH, which starts from about 1 × 10

-7

ΩmT

-1

at 60K,

gradually decreases crossing over 0 at 350K and falls into the negative region.
4.00E-07

KZ15PbTe0
KZ15PbTe0.1
KZ15PbTe1
KZ15PbTe5
KZ15PbTe10

RH RHm T -1T-1 )
(Ω (Ωm )
RH (Ωm T -1)

3.00E-07
2.00E-07
1.00E-07
0.00E+00
-1.00E-07
-2.00E-07
-3.00E-07
-4.00E-07
50

150

250
350
Temperature (K)

450

Figure 28 Hall coefficient as a function of temperature for Bi2Te2.85Se0.15/PbTe NCs

47

Such a behavior can be explained by the two carrier system as shown in Equation 59, where
c=μe/μp is the mobility ratio between electrons and holes. Adding PbTe NPs into the n-type
Bi2Te2.85Se0.15 matrix introduces holes, which even converts the n-type matrix into p-type
semiconductor at higher PbTe weight percentages. As temperature increases, the higher mobility
of electrons leads to their dominance over the holes and brings RH for x=5 and x=10 into the ntype region.

Seebeck Coefficient (μV K-1) )
Seebeck coefficient(μV K-1

RH  

3 nc 2  p
8e  nc  p 2

100

59

KZ15PbTe0
KZ15PbTe0.1
KZ15PbTe1
KZ15PbTe5
KZ15PbTe10

50
0
-50
-100
-150
-200
50

150

250
350
Temperature (K)

450

Figure 29 Thermopower as a function of temperature for Bi2Te2.85Se0.15/PbTe NCs
Figure 29 displays the Seebeck coefficient as a function of temperature for NCs. The
behavior of the Seebeck coefficients confirms the result of the Hall measurement that the

48

existence of two carriers leads to the reduction of the absolute value of thermopower as
described in Equation 60
S

Se e  S h h
e  h

60

Figure 30 shows the electrical resistivity as a function of temperature for NCs. Resistivity
for all samples except x=0.1 exhibits a metallic behavior. Resistivity ρ first increases with the
addition of PbTe NPs from 0.1wt% up to 5wt% then decrease in 10wt% sample. The increase of
ρ in NCs may be attributed to the reduced mobility from increasing carrier scattering between
electrons and holes. The facts that x=10 has a lower resistivity than x=5 and x=0.1 exhibits an
activated behavior above room temperature once again suggest that PbTe NPs generate holes in
the n-type matrix and electrons in Bi2Te2.85Se0.15 have a higher mobility than the holes.

Electrical resistivity (Ω cm)

0.0035

KZ15PbTe0
KZ15PbTe0.1
KZ15PbTe1
KZ15PbTe5
KZ15PbTe10

0.003
0.0025
0.002
0.0015
0.001
0.0005
0
50

150

250
Temperature (K)

350

450

Figure 30 Electrical resistivity as a function of temperature Bi2Te2.85Se0.15/PbTe NCs

49

Because of the decrease of the absolute Seebeck coefficient and increase of electrical
resistivity, the power factors (Figure 31) in the NCs are lower than the pure matrix
Bi2Te2.85Se0.15. The reduction of power factor is evident even in the smallest PbTe NPs loading
amount at 0.1wt%.

-1
Power Factor (10-6 W cm-1 -1 -2 -2
Power Factor (10 W cm K K
Power Factor (10-6 -6 W cmK-2)) )

40

KZ15PbTe0
KZ15PbTe0.1
KZ15PbTe1
KZ15PbTe5
KZ15PbTe10

30

20

10

0
50

150

250
Temperature (K)

350

450

Figure 31 Power factor as a function of temperature Bi2Te2.85Se0.15/PbTe NCs
The temperature dependence of the thermal conductivities κ is plotted in Figure 32.
Lower PbTe containing samples x=0.1 and x=1 have a comparable thermal conductivity with the
matrix material x=0. NCs x=5 and x=10 with higher PbTe NPs addition indeed show a reduced
thermal conductivity below 300K but it rises faster and eventually exceeds the thermal
conductivity of matrix material at 380K due to the much stronger influence from the bipolar
thermal diffusion.

50

Thermal conductivity (W(W cmK-1) )
Thermal conductivity cm-1 -1 K-1

0.04
0.035
0.03
0.025
0.02
0.015

KZ15PbTe0
KZ15PbTe0.1
KZ15PbTe1
KZ15PbTe5
KZ15PbTe10

0.01
0.005
0
50

150

250
Temperature (K)

350

450

Figure 32 Thermal conductivity as a function of temperature for Bi2Te2.85Se0.15/PbTe NCs

0.45

KZ15PbTe0
KZ15PbTe0.1
KZ15PbTe1
KZ15PbTe5
KZ15PbTe10

0.4
0.35

ZT

0.3
0.25
0.2
0.15
0.1
0.05
0
50

150

250
Temperature (K)

350

450

Figure 33 ZT as a function of temperature for Bi2Te2.85Se0.15/PbTe NCs

51

Because of the strongly degraded electronic properties, ZT (Figure 33) in NCs are not
enhanced compared to the matrix material. Because of the intrinsic p-type doping behavior of the
PbTe NPs, we shifted our focus to the p-type bismuth telluride based NCs in order to avoid the
two carrier system.

3.4 Synthesis and TE properties of p-type Bi0.4Sb1.6Te3

0.004

pBiTeKZ7.1 350hp
pBiTeKZ7.2 380hp
pBiTeKZ7.3 410hp

200

0.0035
0.003
0.0025

150

0.002
100

0.0015
0.001

50

0.0005
0

Electrical resistivity (Ω cm)

-1
Seebeck coefficient (μV K )
Seebeck Coefficient (μV K -1)

250

0
50

150

250
350
Temperature (K)

450

Figure 34 Seebeck coefficient and electrical resistivity as a function of
temperature for Bi0.4Sb1.6Te3 hot pressed at 350°C, 380°C and 410°C
P-type bismuth antimony telluride with nominal composition Bi0.4Sb1.6Te3 was
employed as the matrix material for making p-type nanocomposites. This matrix is a solid
solution of 20% Bi2Te3 and 80% Sb2Te3 and can be seen more explicitly if we writte the
chemical formula as (Bi2Te3)0.2(Sb2Te3)0.8. The synthesis procedure is identical to the
52

preparation of n-type matrix except the annealing temperature is set at 540°C for three days in
order to homogenize the properties, and 1wt% excess Sb is added as a p-type dopant. The batch
is labeled as pBiTeKZ7. X-ray diffraction has been performed on pulverized powders and
confirmed the phase purity. The powders were hot pressed at 350°C, 380°C and 410°C
respectivley for 15 minutes in order to find the optimum processing parameter. All hot pressed
pucks have a density greater than 90% of the theoretical density.
Figure 34 shows the Seebeck coefficient and electrical resistivity as a function of
temperature for p-type matrix hot pressed at 350°C, 380°C and 410°C. Seebeck coefficient first
increases then decreases with the hot pressing temperature. The sample hot pressed at 380°C has
the highest Seebeck coefficient about 200 μV/K at 360K. Electrical resistivity shows a
monotonic reduction with the increase of hot pressing temperature.

Power Factor (10-6 W cm -1 K-2 )

40

pBiTeKZ7.1 350hp
pBiTeKZ7.2 380hp
pBiTeKZ7.3 410hp

30

20

10

0
50

150

250

350

Temperature (K)

Figure 35 Power factor as a function of temperature for
Bi0.4Sb1.6Te3 hot pressed at 350°C, 380°C and 410°C

53

450

Figure 35 shows the power factors of the hot pressed p-type matrix materials. The sample
hot pressed at 380°C has an overlapping power factor with sample hot pressed at 410°C. The
-1 -2

peak power factors for sample 7.2 and 7.3 are about 30 Wcm K at room temperature, well in
-1 -2

the range reported in the literature.[62] Sample 7.1 showed a lower peak factor of 18 Wcm K .

Carrier concentration (cm -3 )

8E+19
pBiTeKZ7.1 350hp
pBiTeKZ7.2 380hp
pBiTeKZ7.3 410hp

7E+19
6E+19
5E+19
4E+19
3E+19
2E+19
1E+19
0
50

150

250
350
Temperature (K)

450

Figure 36 Carrier concentration as a function of temperature
for Bi0.4Sb1.6Te3 hot pressed at 350°C, 380°C and 410°C
Figure 36 reveals the temperature dependence of the carrier concentration. The carrier
concentrations are identical for all samples at about 4×1019 cm-3 and are insensitive to the
pressing temperature, suggesting a successful extrinsic doping. The carrier mobility as a function
of temperature is plotted in Figure 37. Sample pBiTeKZ7.1 hot pressed at 350°C shows a lower
mobility compared to other two hot pressed at higher temperature. The difference may result
from a different degree of anisotropy due to the pressing temperature.
54

 
Carrier mobility (cm V s )

Carrier mobility (cm2 V-1 s-1)-1)
Carrier mobility (cm2 V-1 -1
2
-1 s

600

pBiTeKZ7.1 350hp
pBiTeKZ7.2 380hp
pBiTeKZ7.3 410hp

500
400
300
200
100
0
50

150

250
Temperature (K)

350

450

-1 -1
Thermal conductivity (W cm-1 K-1-1)
Thermal conductivity (W cm K
Thermal conductivity (W cm -1 K ))

Figure 37 Carrier mobility as a function of temperature for
Bi0.4Sb1.6Te3 hot pressed at 350°C, 380°C and 410°C
0.03

pBiTeKZ7.1 350hp
pBiTeKZ7.2 380hp
pBiTeKZ7.3 410hp

0.025
0.02
0.015
0.01
0.005
0
50

150

250
Temperature (K)

350

450

Figure 38 Thermal conductivity as a function of temperature for
Bi0.4Sb1.6Te3 hot pressed at 350°C, 380°C and 410°C

55

The thermal conductivity as a function of temperature plotted in Figure 38 corroborates
our assumption. Sample pBiTeKZ7.1 exhibits the lowest thermal conductivity, while those for
the other two samples are identical to each other.
Despite the difference between electronic properties and thermal conductivities, the ZT
(shown in Figure 39) for samples hot pressed at different temperatures are almost the same in the
whole temperature regime of the measurement, reaching ZTmax=0.73 at 360K.
0.8
pBiTeKZ7.1 350hp
pBiTeKZ7.2 380hp
pBiTeKZ7.3 410hp

0.7
0.6

ZT

0.5
0.4
0.3
0.2
0.1
0
50

150

250

350

450

Temperature (K)

Figure 39 ZT as a function of temperature for Bi0.4Sb1.6Te3
hot pressed at 350°C, 380°C and 410°C

3.5 Synthesis and TE properties of p-type Bi0.4Sb1.6Te3/xPbTe nanocomposite (NC)

The synthesis of p-type Bi0.4Sb1.6Te3/xPbTe NC follows the same procedure as that of
the n-type NC described in Section 3.3. The mixed composite powder was loaded into a graphite
crucible and heated at 410 °C for 2 hours in order to eliminate residual organics at the surface of
the PbTe NPs. The heat treated powder was then hot pressed between at 380 °C under a pressure
56

of 60MPa for 15 minutes to form a dense disk. A total of four samples with PbTe weight
percentage of 0%, 0.1%, 0.5% and 1% were prepared. The 0% sample was a pure Bi0.4Sb1.6Te3
fabricated in the same procedure as NCs to serve as a control sample. Densities for all hot
pressed samples are above 94% of the theoretical density. As in Section 3.3, we use the weight
percentage x of PbTe NPs to designate our samples in order to simplify the discussion. Table 2
lists the identification of the samples together with some room temperature physical properties.
Sample name

x=0
(control)

x=0.1

x=0.5

x=1

PbTe nanoparticles weight
percentage

0%

0.1%

0.5%

1%

Relative density

95.74%

97.09%

96.32%

94.15%

Seebeck coefficient (10 V/K)

186

136

110

84

Electrical resistivity (mΩ cm)

1.14

0.672

0.688

0.500

Wcm K )

-1 -2

30.15

26.48

18.11

15.37

-2

1.48

1.65

1.71

1.81

1.65

1.78

1.82

2.00

3.68

5.41

7.90

10.8

-6

Power factor (10

-6

Thermal conductivity (10 W/cmK)
-8

-2

Lorenz number (10 WΩ K )
-19

Carrier density (10

-3

cm )

Table 2 Sample identification and some room temperature
physical properties of Bi0.4Sb1.6Te3/xPbTe NC
The oleate groups terminating the surface of PbTe NPs can be expected to act as
insulating barriers, decreasing the overall electrical conductivity of the system [69, 70]. To
remove the oleate ligands, both thermal as well as chemical treatments were explored. For the
chemical treatments, PbTe NPs dispersed in hexane were stirred along with anhydrous hydrazine
followed by precipitation precipitated with acetonitrile [70]. The hydrazine-treated NPs retain the
57

cubic Altaite phase of the precursor NPs, but exhibit significant aggregation. A comparison of
Infrared spectroscopy (IR) spectra obtained before and after hydrazine treatment is shown in
Figure 40. The peak at 1512 cm-1 and 1394 cm-1are attributed to the presence of symmetric and
asymmetric stretching vibrations of oleate COO-, whereas those at 2918 cm-1 and 2840 cm-1
correspond to oleate aliphatic –CH stretches. While significant reduction in peak intensity is
observed complete removal of the oleate group was not achieved by hydrazine treatment.

Figure 40 IR spectroscopy of hydrazine PbTe NPs with oleate
ligands, hydrazine treated PbTe NPs and thermal treated PbTe NPs.
Thermal treatment was found to be more effective for oleate group removal. A suitable
temperature was determined by thermogravimetric analysis (TGA). As shown in Figure 41 the
TGA of the NPs revealed a 16 % weight loss overall between 255-455°C, which we attribute to
desorption/decomposition of surface oleate functionalities. Based on the TGA data, heat
58

treatment of the nanoparticles was carried out in a flow furnace at 410 °C for 2 h under nitrogen.
As it can be seen from Figure 40 both –COOH and the –CH stretching vibrations are absent after
thermal treatment suggesting successful removal of the organic groups.

Figure 41 TGA of oleate capped PbTe NPs heat treated under N2 atmosphere
Powder X-ray diffraction (PXRD) was collected on a Rigaku RU 200B (40kV, 150 mA,
Cu Kα radiation) diffractometer. Samples were deposited on a quartz holder coated with a thin
layer of grease and the data were acquired in the 2θ range 20-70° with a step size of 1.2°. PbTe
NPs in the NCs cannot be detected by PXRD at the low concentrations explored here (Figure 42)
due to sensitivity of the PXRD technique. In order to demonstrate that the PbTe phase can be
retained under conditions of composite formation, an additional 10wt% PbTe NC sample was
prepared. In this sample the most intense (220) plane of Altaite phase close to 40 degree 2θ is
visible.

59

Figure 42 PXRD patterns of NCs with 1wt% and 10wt% PbTe NPs
loading. Asterisk indicates the PbTe impurity phase.
Transmission electron microscopy (TEM) and energy dispersive spectroscopy (EDS)
were performed using a JEOL 2010 transmission electron microscope operated at a voltage of
200kV and a current of 106-108 μA with a coupled EDS detector (EDAX Inc). Figure 43 shows
the images of the precursor NPs as well as 1 wt %, 0.5 wt % and 0.1 wt % of PbTe nanoparticles
in Bi0.4Sb1.6Te3 matrix. The PbTe NPs were observed in all cases and showed no agglomeration,
suggesting good dispersion. The presence of 13 nm sized PbTe cubes approximately scale with
the nominal concentration of PbTe NPs added to the matrix. The elemental analysis (EDS) of the
as prepared nanoparticles gives a composition of Pb:Te of 1:0.94 close to the ideal value of
Pb:Te of 1:1, with a slight excess of Pb.

60

5 nm

5 nm

5 nm

5 nm

Figure 43 TEM images of PbTe NPs and NCs with 1 %, 0.5 % and
0.1 wt% discrete PbTe NPs inside the Bi0.4Sb1.6Te3 matrix

61

Seebeck coefficient(μV K-1)-1)
Seebeck Coefficient (μV K
Seebeck coefficient (μV K-1 )
Electrical resistivity (Ω cm)
Power Factor (10-6-6WW cm-1 -2 -2)
Power Factor (10 -6 cm-1-1K K )
Power Factor (10 W cm K-2

250

x=0
x=0.1
x=0.5
x=1

200
150
100
50
0
0
0.0016

x=0
x=0.1
x=0.5
x=1

0.0014
0.0012
0.001
0.0008
0.0006
0.0004
0.0002
35
0

x=0
x=0.1
x=0.5
x=1

30
25
20
15
10
5
0
50

100

150

200

250

300

350

400

Temperature (K)

Figure 44 Seebeck coefficient, electrical resistivity and power factor
as a function of temperature for Bi0.4Sb1.6Te3/xPbTe NC
62

Figure 44 displays the temperature dependence of electronic properties for our
nanocomposite samples as well as the control sample, x=0. The Seebeck coefficients of NCs
decrease monotonously with increasing concentration of PbTe NPs. The electrical resistivity
exhibits the same trend, except that x=0.1 and x=0.5 have nearly identical values. Despite the
2

decrease in resistivity the thermoelectric power factors (S σ) of nanocomposites are lower than

Thermal conductivity (W cm-1 K-1
Thermal conductivity (W cm -1 -1
Thermal conductivity (W cm-1 K-1)))

the control sample due to the much stronger reduction of the Seebeck coefficients.
0.05

x=0
x=0.1
x=0.5
x=1

0.045
0.04
0.035

0.02
0.01
0

0.03

50

150

250

350

0.025
0.02
0.015
0.01
0.005
0
50

100

150

200

250

300

350

400

Temperature (K)
Figure 45 Thermal conductivity as a function of temperature for Bi0.4Sb1.6Te3/xPbTe
NC. The inset shows the lattice thermal conductivity as a function of temperature.
Figure 45 shows the thermal conductivity as a function of temperature. The lattice
thermal conductivity κl shown in the inset of Figure 45 was calculated by subtracting the
electronic thermal conductivity κe from the total thermal conductivity. The electronic thermal
conductivity is estimated by using Wiedemann-Franz law κe=LσT, where L is the Lorenz number,
63

σ the electrical conductivity and T the absolute temperature. The choice of a reasonable Lorenz
number is a delicate issue as we cannot assume our samples to be degenerate semiconductors.
We also note that there is approximately a factor of three differences between the most resistive
and least resistive samples, so one Lorenz number may not fit all data equally well. To tackle this
problem, we first estimated the reduced Fermi energy η from the Seebeck coefficient by using

 5


  2  s '  F3 2  s '

k


S   
 
3
e 


 s '  F3 2  s '
 2





61

s’

where k is the Boltzmann constant s’ is the exponent of energy in the scattering law, τ~E and F
is the Fermi-Dirac integral defined in Equation 17. For this study, we use s’=-0.5, a value
typically used for acoustic phonon scattering of carriers in Equation 61 to estimate the reduced
Fermi energy η. From η, we calculated the Lorenz number by:

L

3F0 F2  4 F12  k 
 
e
F02

2

62

A more detailed description of the above analysis can be found in reference [1]. We repeated this
process for each sample in order to get a more accurate estimation about lattice thermal
conductivity. The calculated Lorenz number for different samples can be found in Table 2. We
found that, despite overall increase in total thermal conductivity, lattice thermal conductivities in
NCs are indeed reduced compared to the matrix sample due to the additional phonon scattering
resulting from the PbTe NPs. The lattice thermal conductivity of sample x=1 is reduced by close

64

to 50% compared to the control sample. The increase of thermal conductivity in NCs comes from
the increased electronic thermal conductivity κe.
0.8

x=0
x=0.1
x=0.5
x=1

0.7
0.6

ZT

0.5
0.4
0.3
0.2
0.1
0
50

100

150

200

250

300

350

400

Temperature (K)
Figure 46 ZT as a function of temperature for Bi0.4Sb1.6Te3/xPbTe NC.
Figure 46 shows FOM ZT as a function of temperature. ZTs of NCs are reduced
compared to matrix due to the decreased Seebeck coefficient. A noticeable ZT reduction starts at
PbTe loading as little as 0.5wt%.
Figure 47 shows the carrier concentration as a function of temperature. The hole
concentration increases with increasing PbTe concentration, suggesting a doping effect of PbTe
nanoparticles. This doping effect may come either directly from PbTe as an inclusion, since
PbTe is generally a p-type semiconductor, or from Pb

65

2+

leaching from the incorporated

3+

nanoparticles and occupying the Bi

site, generating a hole and thus increasing the overall hole

Carrier concentration (cmcm-3)
Carrier concentration ( -3 )

concentration. This hypothesis is consistent with the work by Kusano and coworkers, who have

1E+21
1021

x=0
x=0.1
x=0.5
x=1

1020
1E+20

1019
1E+19
50

150

250

350

450

Temperature (K)
Figure 47 Temperature dependence of carrier concentration for Bi0.4Sb1.6Te3/xPbTe NC.
attempted to mechanically alloy bulk bismuth antimony telluride and PbTe and consolidated the
powder by spark plasma sintering. The TE transport properties of such composite materials
exhibited a similar trend as in our study and they concluded the increase of carrier concentration
is due to the doping effect of PbTe.[71] Pb was also used as a p-type dopant for both Bi2Te3 and
Sb2Te3 as reported by Plachacek et al. where they concluded that the increase of hole
concentration was attributed to the interaction between Pb atom and native point defects in
Bi2Te3 and Sb2Te3. [72, 73]

66





-1
Seebeck Coefficient(μV KK-1))
Seebeck coefficient(μV K-1
Seebeck coefficient (μV
Seebeck coefficient(μV K-1) )

3/2 

2 2 m kT

k
S   s ' co nst  ln

3
e
h np




300

63

matrix
x=0.1
x=0.5
x=1
Log. (matrix)
Matrix fit

250
200
150
100
50
0
5x1018
5E+18

5x1019
5E+19

5x1020
5E+20

Carrier concentration (cm-3)
Carrier concentration (cm-3)
Figure 48 Pisarenko relation of NCs. The fitted line is constructed as an aid to the eye. All
matrix bismuth antimony telluride of various carrier concentrations were synthesized in our lab.
To elucidate the effect of PbTe NPs on the Seebeck coefficient of the matrix
Bi0.4Sb1.6Te3, we plot the Pisarenko relation of our p-type matrix Bi0.4Sb1.6Te3 and NCs
(shown in Figure 48). The fit line is created from a number of Bi0.4Sb1.6Te3 samples of various
carrier concentrations synthesized in our lab. From the approximate Equation 63, based on a
simplified one carrier model [36], for a series of samples that share the same exponent of
scattering s’ and approximately the same effective mass m*, the Seebeck coefficient is

67

proportional to the logarithmic inverse of the hole concentration np and should fall close to the
fitted line in a plot constructed as in Figure 48. The points representing NCs fall in the vicinity of
the fitted line in Figure 48. This suggests that the charge carrier scattering mechanism for NCs is
the same as for matrix materials if we assume the effective mass is not affected by a low
percentage of PbTe incorporation. As the doping effect of PbTe NPs has been confirmed, it is
reasonable to attribute part of the reduced lattice thermal conductivity to the phonon scattering
caused by the collateral PbTe doping. Such a behavior has been reported by Zhu et. al. in
antimony telluride doped with lead telluride [74].

3.6 Summary of the chapter
We systematically investigated the thermoelectric properties of bismuth telluride and its
alloys based nanocomposites with PbTe as nanoinclusions. The NCs were synthesized using a
novel incipient wetness impregnation method wherein nanosized PbTe NPs were encapsulated in
bulk bismuth telluride matrix. NCs that retain the nanosized PbTe inclusions have been
successfully synthesized. Introducing PbTe NPs inside the n-type matrix materials generates a
two carrier system which generally is not a favorable case for TE materials. For p-type NCs, the
Seebeck coefficients and electrical resistivity decrease with the addition of PbTe NPs. The lattice
thermal conductivity also decreases with the addition of PbTe NPs and the carrier concentration
increases with the increasing concentration of PbTe NPs. The Pisarenko relation reveals that the
carrier scattering mechanism in the nanocomposites does not deviate from that of the bulk
bismuth antimony telluride. Considering the presence of PbTe NPs found in hot pressed NC
samples, we conclude that the effect of doping from PbTe dominates that from nanostructuring.
68

Chapter 4 Unfilled P-type Skutterudite Based Nanocomposite
Skutterudite compounds were identified as good candidates for TE application almost
two decades ago.[75] Unfilled skutterudites are binary compounds of the form MA3 , where M is
a metal such as Co, Rh, or Ir, and A is As, P, or Sb.[76, 77] The high carrier mobility and large
effective mass [78, 79] found in some skutterudites endow them with power factors comparable
to and even exceeding Bi2Te3 and PbTe. Their thermal conductivities, on the other hand, are
relatively too large to make them useful TE materials.[10, 78] Previous attempts at reducing
thermal conductivity focused on inserting foreign atoms into the large voids in the unfilled
skutterudite structure, thus producing “filled” skutterudite compounds.[80-82] Figure 49
schematically shows the unit cell of a filled skutterudite. The foreign atom confined in the cage
exhibits an Einstein-like mode that provides additional phonon scattering to dampen the lattice
thermal conductivity.[10, 83, 84] This approach has achieved great success especially in
enhancing the ZT in n-type filled skutterudites, for instance, it is not unusual for double-filled
skutterudites to display[85] ZT greater than 1.3, and the melt-spun filled skutterudites containing
InSb nanoinclusions reaching[27] ZT in excess of 1.4. Recently, even p-type filled skutterudites
exceeded ZT of unity [40].
Another direction originating from a different train of thought for improving the TE
properties is to reduce the dimension of materials’ building block, also referred to as
“nanostructuring”. The physics is either to evoke quantum confinement in order to alter the
DOS[86] or to tweak the electron scattering parameter so that one may have the chance to boost
the Seebeck coefficient, and hence the power factor.[21] The thermal conductivity is also

69

expected to be reduced because of the extra phonon scattering from the myriad of nanoscopic
interfaces.

M
R

A
Figure 49 Unit cell of a filled skutterudite. R: filler atom, M: transitional metal, A: pnicogen atom
In this chapter, we report work on bulk p-type skutterudite nanocomposites of
Co0.9Fe0.1+xSb3+2x. This composition can be reformulated as a base composition of
Co0.9Fe0.1Sb3 and a variant part of FeSb2. It is our interest to initially demonstrate whether these
nanocomposites can be synthesized and, if so, whether the existence of nanoinclusions can offer
any positive influence. Four samples were synthesized with x = 0, 0.05, 0.1, and 0.2 respectively.
A fifth sample was fabricated with composition Co0.75Fe0.25Sb3 that has the same Fe/Co ratio as
that of x=0.2 sample. Here x = 0 and Co0.75Fe0.25Sb3 both serve as control groups to discern if
property changes are related to Fe substitution for Co or FeSb2 nanoinclusions.

70

4.1 Experiment
High purity starting materials of Co (powder), Fe (powder), and Sb (lump) were weighed
according to the stoichiometric ratio and charged into carbon coated ampoules. The ampoules
-6

were sealed under vacuum of 10

Torr, heated to 1373K to melt the materials, and rapidly

quenched in a cold water bath. The quenched samples were annealed at 973K for 3 days.
A disk was cut from the middle of each annealed ingot and further sectioned into
rectangular parallelepiped with dimensions of approximately 3mm × 3mm × 8mm for measuring
transport properties from 80K to 300K. Seebeck coefficient, electrical resistivity, and thermal
conductivity were measured from 80K to 300K under vacuum using a steady state technique in a
continuous flow cryostat with liquid nitrogen as a refrigerant. The accuracy of the electrical
resistivity and thermal conductivity measurement is limited by the precision in measuring
dimensions of samples, namely the distance between two thermocouple probes and the cross
sectional area. They are also affected by and the thermal and electrical contacts between
thermocouple probes and sample, which applies to Seebeck coefficient too. We estimated a 10%
uncertainty in transport properties measurement from 80K-300K. A thin slab of approximate
thickness of 1mm was cut out of the same low temperature measurement sample for Hall
measurement. Hall coefficients and electrical resistivity from 60K to 400K were carried out
using ac current in a varying magnetic field from -3T to 3T. The remnants from the disks were
pulverized to powders for x-ray diffraction analysis and/or mounted on conducting epoxy for
SEM imaging. X-ray diffraction patterns for all samples were collected from 2ranging from 20
to 90 degrees in a Rigaku MiniFlex 2 using Cu Kα radiation. SEM images were done in JEOL
JSM 7500 high resolution field emission microscope.
71

High temperature TE transport properties were measured by our collaborators at
University of Michigan. The electrical conductivity and the Seebeck coefficient in the interval
300K – 800K were measured in a home built apparatus under the protective atmosphere of argon
on the same rectangular samples measured at temperatures below the ambient. Separate disks
sectioned from individual ingots in proximity to where rectangular samples were cut were used
for high temperature thermal conductivity measurements. The details for thermal conductivity
measurement by laser flash technique have been described in previous experimental section.

4.2 Results

(deg)
Figure 50 X-ray diffraction patterns of samples x=0, 0.05, 0.1, 0.2 and
control sample Co0.75Fe0.25Sb3
72

Figure 50 displays the x-ray diffraction patterns, which show that the skutterudite phase
is the majority phase for all samples. A minute amount of Sb impurity phase is present in
samples with x=0, x=0.05, and the control sample Co0.75Fe0.25Sb3. As anticipated, the FeSb2
phase can be found in samples with high Fe content, x = 0.2 and Co0.75Fe0.25Sb3.

Figure 51 High resolution FESEM images on the fractured surface of nanocomposite samples
Co0.9Fe0.1+xSb3+2x and control sample Co0.75Fe0.25Sb3. (a) x=0.05, the inset image zooms in
the circled area to reveal the nanoscopic feature; (b) x=0.1; (c) x=0.2; (d) Co0.75Fe0.25Sb3.
Figure 51 shows high resolution FESEM images of all nanocomposite samples (x=0.05, x
=0.1, x=0.2), and control sample Co0.75Fe0.25Sb3. The amount of nanoparticles present in the
SEM images approximately scales with the FeSb2 we intentionally added to the base
composition Co0.9Fe0.1Sb3 as shown from Figure 51 (a)–(c). In Figure 51 (d), which retains the
73

same Fe/Co ratio as x=0.2 sample but has the normal skutterudite composition MA3, the
nanoparticles have almost disappeared and grain boundaries are much cleaner compared to
nanocomposite samples. This suggests that either Fe atoms were absorbed to form skutterudite or
some FeSb2 nanoparticles have grown up significantly to micron size. We also performed the
EDS analysis in the same region as shown in Figure 51(b). By using “Point and ID Analyzer”
function, we detected higher Fe but less Sb content in the regions with clusters of nanoparticles
compared to the skutterudite grains without such features. Combined with x-ray diffraction
results, we identified the nano-inclusions observed in our SEM images to be FeSb2.

Seebeck coefficient (μV K-1) )
Seebeck Coefficient (μV K-1

180

x=0

160

x=0.05

140

x=0.1

120

Co0.75Fe0.25Sb3

x=0.2
Ref17

100
80
60
40
20
0
0

200

400
600
Temperature (K)

800

Figure 52 Seebeck coefficient as a function of temperature.
Ref data are excerpted from reference.[87]
The Seebeck coefficient as a function of temperature is plotted in Figure 52. Here, in
order to compare their properties, we also include the results of Co0.9Fe0.1Sb3 from the
74

literature.[87] All Seebeck coefficients increase monotonously with increasing temperature. Our
base sample x=0 exhibits a very similar behavior to that of the reference. All nanocomposite
samples and the higher Fe content control sample Co0.75Fe0.25Sb3 exhibit higher Seebeck
coefficients than the x=0 sample between 160K and 565K. Samples x=0.05 and x=0.01 extend
the lead all the way up to the measurement limit at 788K. The Seebeck coefficients for the
nanocomposite samples first increase with the amount of FeSb2 (when x<0.1) and then start to
drop for samples with higher amount of FeSb2.

Electrical resistivity (Ω cm)

0.0025

x=0
x=0.05
x=0.1
x=0.2
Co0.75Fe0.25Sb3
Ref17

0.002

0.0015

0.001

0.0005

0
50

250

450

650

850

Temperature (K)

Figure 53 Electrical resistivity as a function of temperature
The electrical resistivity as a function of temperature is shown in Figure 53. The
resistivity for all samples exhibits a metallic behavior, increasing with temperature.
Nanocomposites have higher resistivity values than the control sample x=0 at lower temperature,
but, interestingly, they begin to saturate near room temperature, a behavior that is not observed in
75

the sample with x=0. The crossover happens around 423K. Above 500K sample x= 0 has the
largest electrical resistivity. Co0.75Fe0.25Sb3 has the lowest resistivity, a phenomenon to be
expected as the higher Fe substitution creates more holes, but it also exhibits the saturation
behavior similar to the nanocomposite samples. The temperature dependence of power factor is
displayed in Figure 54. All nanocomposite samples have higher power factors compared to
-1

-2

control sample x=0. Sample x=0.05 shows the highest value of 17×10-6 Wcm K at 788K.

-1
Power Factor (10-6 W cm-1 K-2-2)
Power factor (10-6 W cm K )

20

x=0
x=0.05
x=0.1
x=0.2
Co0.75Fe0.25Sb3

18
16
14
12
10
8
6
4
2
0
50

250

450

650

850

Temperature (K)

Figure 54 Temperature dependence of the power factor
The temperature dependence of the thermal conductivity is plotted in Figure 55. The
thermal conductivity in all nanocomposite samples is substantially reduced with respect to the
both control sample x=0 and Co0.75Fe0.25Sb3 over the whole temperature range of measurement,
and is even comparable to some filled skutterudites.[88]

76

-1 K
Thermal conductivity (W cm-1K -1
Thermal conductivity (W cm-1 K-1-1) )
Thermal conductivity (W cm
)

0.08

x=0

0.07

x=0.05
x=0.1

0.06

x=0.2
Co0.75Fe0.25Sb3

0.05
0.04
0.03
0.02
0.01
0
50

250

450

650

850

Temperature (K)

Figure 55 Thermal conductivity as a function of temperature
Mismatches between low and high temperature data sets at 300K for some samples do
exist in electrical resistivity as well as thermal conductivity as shown in Figure 53 and Figure 55
respectively. The difference in resistivity is less than 6% for all samples. The largest difference
in thermal conductivity is about 24% found in x=0 sample. We estimate the error is inherent to
the geometric factor used for computing electrical resistivity and, in the case of thermal
conductivity, due to different techniques used to determine thermal conductivity at low and high
temperatures. The overall effect on ZT, however, is insignificant as the errors from resistivity and
thermal conductivity partially cancel out each other. The combined enhancement of power
factors and the reduction in thermal conductivity in our nanocomposites increase the ZT values
compared to the control sample x=0 as shown in Figure 53. Sample x=0.05 displays a ZT=0.59 at
788K which is twice as large as that of sample x = 0, and shows no sign of reaching its peak at
the limiting temperature of these measurements.
77

0.7

x=0
x=0.05
x=0.1
x=0.2
Co0.75Fe0.25Sb3
Ref17

0.6
0.5

ZT

0.4
0.3
0.2
0.1
0
50

250

450

650

850

Temperature (K)

Figure 56 ZT as a function of temperature

4.3 Discussion
It is imperative to discern the influence of Fe substitution and justify that the
enhancement of Seebeck coefficient can be attributed to the FeSb2 nanoinclusions. To do so, we
have calculated the lattice constant as a function of Fe substitution ratio on the metal site. Upon
Fe replacement of Co, the lattice constant is expected to increase linearly with the Fe
concentration. This is indeed the case for our control samples that satisfy the skutterudite
formula MA3 as shown in Figure 57. The lattice constants for the nanocomposites, on the other
hand, first expand slightly compared to the control sample x=0, but eventually saturate with
additional Fe content. This is a strong indication of the formation of FeSb2 precipitates. For the
Co0.75Fe0.25Sb3 sample, the lattice constant is smaller than the value of 9.062Å reported on the

78

same composition.[89] So the actual amount of Fe going into the Co sites may be smaller than
the stoichiometric amount, with the remaining Fe atoms combining with excess Sb to form FeSb2.
9.065
Co1-xFexSb3+yFeSb2
Co1-xFexSb3
Linear (Co1-xFexSb3)

Lattice constant (Å)

9.06
9.055
9.05
9.045
9.04
9.035
0

0.1

0.2

0.3

Fe/M ratio

Figure 57 Lattice constant with respect to the Fe/metal ratio. The square at x=0 on
the abscissa corresponds to CoSb3 with a lattice constant of 9.0385Å[47]
We also plot the Seebeck coefficients at 300K as a function of hole concentration, known
as the Pisarenko relation, in Figure 58. As Fe has one less valence electron than Co, Fe
substitution for Co will increase the hole concentration. Thus given the similar DOS effective
mass m* and carrier scattering parameter s’ (which determines the energy dependence of the
s’

carrier scattering time via the relation ~  ), the Seebeck coefficient should decrease with an
increasing Fe substitution due to the increase of hole concentration. The data reported by Tang et

al on FexCo4-xSb12 supports this assumption quite well.[89] Our control sample x=0 also agrees
reasonably well with the fitted line based on Tang’s data. The thermopowers for the
79

nanocomposites obviously diverge from the fit line for regular Fe substituted samples, which
suggest the enhanced thermopower is due to an alteration either in the DOS effective mass m* or
the scattering parameter s’ brought about by the FeSb2 nanoinclusions. The other control sample
Co0.75Fe0.25Sb3 also diverges from the fit. Combining the analysis of the lattice constant and the
behavior of the thermopower described above, we conclude that small amount of FeSb2 must
have existed in this sample too, influencing its properties.

Seebeck coefficient (μV K )

Seebeck coefficient (μV K-1)
-1

80
70
60
50

x=0
x=0.05
x=0.1
x=0.2
Co0.75Fe0.25Sb3
Ref19
Fit line on Ref19

40
30
20
10
0
1019
1.00E+19

1020
1.00E+20

-3
Hole concentration (cm-3 )

1021
1.00E+21

Hole concentration (cm )

Figure 58 Seebeck coefficient as a function of hole concentration. Reference data are from
Reference [88] on FexCo4-xSb12. The fitted line is calculated based on the reference.

4.4 Summary of the chapter
We have successfully synthesized p-type skutterudite nanocomposites based on
Co0.9Fe0.1Sb3 with FeSb2 nanoinclusions. The existence of FeSb2 nanoparticles not only
provides extra phonon scattering that reduces the thermal conductivity, but also changes either
80

the DOS effective mass m* or the scattering parameter s’ resulting in an enhanced thermopower
and hence power factors. Further experimental work and theoretical calculation is needed to
determine which one plays a dominant role. The best nanocomposite sample displays a ZT=0.59
at 788K, which is a factor of two increase compared to the control sample x=0. Considering the
prototype of the base material is Fe doped binary skutterudite, nanocomposite synthesis is a very
promising approach for improving TE properties.

81

Chapter 5 High Temperature Thermoelectric and Magnetic
Properties of P-type Yb filled skutterudite YbxFeyCo4-ySb12

In the previous chapter, we have successfully synthesized the unfilled p-type skutterudite
nanocomposite and demonstrated a 100% enhanced thermoelectric performance. This inspired us
to extend the work to p-type filled skutterudite. To do so, we need to identify a p-type matrix
material upon which the nanocomposites can be created. Instead of using the Ce-filled p-type
skutterudite, whose performance is the best so far, we took some effort to explore a new p-type
system, the Yb-filled skutterudite.
Yb is an indispensible filling element in n-type filled skutterudites, but very little is
known about their p-type counterparts for potential applications as thermoelectric materials. In
this chapter, we report a systematic study of high temperature thermoelectric transport properties
of p-type Yb-filled Fe-compensated skutterudites YbxFeyCo4-ySb12 with the aim to complement
the knowledge base for the Yb-filled skutterudite family. The highest ZTmax=0.6 was found in
Yb0.6Fe2Co2Sb12 at 782K. YbFe4Sb12 exhibits the second highest ZTmax =0.57 at780K, which
is much higher than the previous estimate of 0.4 for the same composition. In addition, we also
measured the magnetic properties of these compounds and our results agree with what have been
reported previously.

82

5.1 Experiment
Pure element starting materials of Yb (pieces 99.9%), Fe (powder 99%), Co (powder
99.5%), and Sb (shot 99.999%) were weighed according to the stoichiometric ratio and placed
inside graphite crucibles covered by graphite lids. The graphite crucibles were placed inside
quartz ampoules and sealed under a vacuum of greater than 10-5 Torr. The graphite crucible
serves as a protection layer to deter the spontaneous reaction between Yb and the quartz ampoule,
which is otherwise very detrimental to TE properties especially at high rare earth filling fractions.
From our experience, this step is crucial in order to obtain high quality homogeneous
skutterudite ingots. The sealed ampoules were heated to 1373K at a rate slower than 0.5K/min
and held at that temperature for 6 hours before rapid quenching in a cold water bath. The
quenched samples were annealed at 923K for 3 days. The annealed ingots were ball milled into
fine powders and hot pressed at 873K for 15min. The densities of all hot pressed samples are
above 95% of the theoretical density.
A disk of approximately 1mm in thickness was cut from the as-pressed pellet for thermal
diffusivity measurements. The balance of the pellet was sectioned into a rectangular
parallelepiped with dimensions of approximately 2.4mm × 2.2mm × 8mm for Seebeck
coefficient and electrical resistivity measurements. Details of the high temperature TE transport
properties measurement techniques can be found in previous chapters. The magnetic properties
were measured by the vibrating sample magnetometer (VSM) module in the Versalab. X-ray
diffraction patterns for all samples were collected on powders in the range from 20 to 90 degrees
of 2θ in a Rigaku MiniFlex II using Cu Kα radiation.

83

5.2 Results and discussion

Figure 59 X-ray diffraction patterns for all samples. (a) x=0.4; (b) x=0.6; (c) x=0.8; (d) x=1
Four samples of YbxFeyCo4-ySb12 were prepared with x=0.4, y=1; x=0.6, y=2; x=0.8,
y=3; and x=1, y=4. Table 3 summarizes some basic physical properties of these samples. Here,
for the sake of simplicity, we identify our samples by their Yb filling fraction x. Figure 59 is the
x-ray diffractogram for all samples. The characteristic peaks were indexed primarily to
skutterudite phases with a trace of Sb impurity phase found in samples x=0.8 and x=1. The
diffraction pattern of x=0.4 best matches the reference phase of CoSb3 PDF#03-065-0671 and

84

Sample ID

x=0.4

Nominal composition

x=0.6

x=0.8

x=1

Yb0.4FeCo3Sb12 Yb0.6Fe2Co2Sb12 Yb0.8Fe3CoSb12

Estimated No. of carrier
per formula unit
Observed No. of carrier
per formula unit
Carrier density at 300K
20 -3
(×10 cm )
Carrier mobility at 300K
2 -1 -1
(cm V s )
Density
-3
(g cm )

YbFe4Sb12

-0.2~0.2

0.2~0.8

0.6~1.4

1~2

0.06

0.235

0.325

0.84

1.479

6.03

8.54

21.5

28.95

14

17.3

9.53

7.512

7.635

7.927

7.895

Table 3 Some physical properties of Yb filled Fe compensated p-type skutterudite sample
YbxFeyCo4-ySb12 at room temperature.

9.16

Lattice constant (Å)

9.14
9.12
9.1
9.08
9.06
9.04
9.02
9
0

0.2

0.4

0.6

0.8

1

x

Figure 60 Lattice constant as a function of filling fraction x. Sample x=0.4 best matches CoSb3
PDF#03-065-0671 while sample x=1 best matches Yb0.93Fe4Sb12 PDF#00-056-1123. Lattice
constants for x=0 and x=0.2 are from reference[47, 90]. Diffractions for other samples exhibit a
gradual transition.

85

sample x=1 best matches that of Yb0.93Fe4Sb12 PDF#00-056-1123, the skutterudite phase with
the highest Yb filling fraction found in the database. Diffraction patterns for the remaining
samples show a gradual transition from the binary CoSb3 phase to the Yb0.93Fe4Sb12 phase.
Figure 60 shows the lattice constant as a function of Yb filling fraction x. The lattice
constant increases nearly linearly with the increasing amount of Yb, which is another good sign
of successful rare earth filling. We must point out, however, that this linear expansion may not
be the sole result of Yb filling, but a combination of Yb filling and Fe substitution for Co as the
ionic radius for Fe

2+

3+

is larger than that of Co . Nevertheless, the lattice constant for our x=1

sample is 9.153Å which agrees well with 9.156Å reported by Kuznetsov and Rowe for
YbFe4Sb12[91] and 9.154Å by Berardan et al.[92].

Seebeck coefficient (μV K-1))
Seebeck Coefficient (μV K-1

180

x=0.4
x=0.6
x=0.8
x=1
Ref

160
140
120
100
80
60
40
20
0
250

350

450

550

650

750

850

Temperature (K)
Figure 61 Temperature dependence of Seebeck coefficient. Ref data are the
Seebeck coefficients of YbFe4Sb12 measured by Kuznetsov et al[91].
86

Figure 61 depicts the temperature dependence of the Seebeck coefficient. The Seebeck
coefficient decreases with increasing Yb filling fraction x as a result of higher hole concentration
induced by Fe compensation. The highest Seebeck coefficient was found in sample x=0.4 with
its peak of 158 μV/K at 710K. The Seebeck coefficient for x=1 agrees well with that reported by
Kuznetsov and Rowe for YbFe4Sb12.

Electrical resistivity (Ω cm)

0.0025

x=0.4
x=0.6
x=0.8
x=1
Ref

0.002

0.0015

0.001

0.0005

0
250

350

450

550

650

750

850

Temperature (K)
Figure 62 Electrical resistivity as a function of temperature. Ref
data are YbFe4Sb12 measured by Kuznetsov et al[91]
Figure 62 shows the electrical resistivity as a function of temperature. Resistivity also
decreases with increasing x as a result of the increasing carrier concentration. Our x=1 sample
shows a resistivity smaller by almost a factor of two compared to that measured by Kuznetsov
and Rowe. Therefore, as shown in Figure 63, the power factor in our x=1 sample is significantly
enhanced compared to YbFe4Sb12 previously reported and is even on par with the power factor of
87

Ce0.9Fe3.5Co0.5Sb12. Power factor decreases with decreasing x value and is mostly influenced
by the electrical resistivity as the Seebeck coefficients are comparable in all samples except
x=0.4.
-1
Power Factor (10 -6 W cm K -2
Power Factor(10-6-6W cm-1 -1 K-2)
Power Factor (10 W cm K-2 ))

40

x=0.4
x=0.6
x=0.8
x=1
Ref1
Ref2

35
30
25
20
15
10
5
0
250

350

450

550

650

750

850

Temperature (K)
Figure 63 Power factors as a function of temperature. Ref1 are data calculated
based on YbFe4Sb12 measured by Kuznetsov et al[91]. Ref2 is the power
factor for Ce0.9Fe3.5Co0.5Sb12 synthesized by us as a control sample.
Figure 64 is the temperature dependence of thermal conductivity. The lattice thermal
conductivity was obtained by subtracting the electronic part from the total thermal conductivity.
The electronic thermal conductivity was estimated by using Wiedemann-Franz law κe=LσT
-8

where the Lorenz number L=2.44×10

2

WΩ/K , a value reasonable for these degenerate

semiconductors. Lattice thermal conductivities follow the 1/T relation and decrease with
increasing Yb filling fraction except for sample x=0.8. The lowest lattice thermal conductivity
88

was found to be 0.48 W/mK in sample x=1 at 710K. This value is very close to the theoretical
limit of 0.2 W/mK that we have calculated assuming a phonon mean-free path equal to one
interatomic spacing. Interestingly, the partially filled sample x=0.6 exhibits a smaller lattice
thermal conductivity than the higher Yb filled sample x=0.8 and is very close to the fully filled
sample x=1. Such a trend was observed previously in Ce-filled skutterudites at low temperatures.
It seems to apply also in our case where a combination of different scattering processes (point
defect, mass and size defect, and valence difference upon Fe substituting for Co) all contribute to
the overall low lattice thermal conductivity.[78, 87, 93].

Thermal conductivity (W -1 -1-1 K-1
Thermal conductivity (W mcm-1K-1))
Thermal conductivity (W cmK )K -1)
Thermal conductivity (W cm-1

6

x=0.4
x=0.6
x=0.8
x=1
1/T

3

5.5

2

5

1

4.5

0
250

4

450

650

850

3.5
3
2.5
2
1.5
1
250

350

450

550

650

750

850

Temperature (K)

Figure 64 Thermal conductivity as a function of temperature. The inset graph shows the
lattice thermal conductivity. 1/T relation is plotted as an aid to understand the graph.

89

0.7

x=0.4
x=0.6
x=0.8
x=1
Ref1
Ref2
Ref3

0.6
0.5

ZT

0.4
0.3
0.2
0.1
0
250

350

450

550

650

750

850

Temperature (K)
Figure 65 TE dimensionless figure of merit ZT as a function of temperature. Ref1 is the
estimated highest ZT of YbFe4Sb12 by Kuznetsov et al[91]. Ref2 (Yb0.8Fe4Sb12) and
Ref3 (Yb0.5Fe2Co2Sb12) are near room temperature ZT reported by Bauer et al[94].
Figure 65 is the TE figure of merit ZT as a function of temperature. The maximum ZT
was found to be 0.6 in sample x=0.6 at 782K as a result of a moderately high power factor and
low thermal conductivity. Sample x=1 exhibits the next highest ZT of 0.57. Such ZT values,
although lower than observed in the Ce filled p-type skutterudites[95], are much higher than
previously reported ZT of 0.4 in YbFe4Sb12.[91] The room temperature ZT s for our x=0.6 and
x=0.8 samples also double the values reported by others in materials of similar compositions[94].
We believe that this difference is primarily due to the lower resistivity of our samples, which is a
consequence of the minimization of impurities and defects during the synthesis process.

90

0.08

0.07

x=0.4

0.06
0.05
0.04
0.03
0.02
0.01
0.00
0.00

0.05
0.04
0.03
0.02
0.01

1.00

2.00

3.00

0
0.00

4.00

Magnetic Field (Tesla)
0.25

1.00
2.00
3.00
Magnetic Field (Tesla)

0.9

x=0.8
Magnetization (emu/g)

0.15

0.1

0.05

4.00

x=1

0.8

0.2
Magnetization (emu/g)

x=0.6

0.06
Magnetization (emu/g)

Magnetization (emu/g)

0.07

0.7
0.6
0.5
0.4
0.3
0.2
0.1

0
0.00

1.00

2.00

3.00

0
0.00

4.00

Magnetic Field (Tesla)

1.00

2.00

3.00

Magnetic Field (Tesla)

Figure 66 Magnetization of YbxFeyCo4-ySb12 for sample x=0.4, x=0.6, x=0.8 and
x=1 at 60K, 80K, 100K, 150K, 200K, 250K and 300K.

91

4.00

The magnetizations for all samples are shown in Figure 66. The total magnetization
consists of the following three parts: diamagnetic contribution Mdia, paramagnetic contribution

Mpara, and ferromagnetic contribution Mferro. Mdia is linear in applied field and independent of

M  M dia  M para  M ferro

64

temperature. Mpara arises from the Yb filling and Fe substitution for Co. Mferro comes from the
Fe impurity and saturates at low magnetic fields below 1T. The different temperature and field
dependence allows one to separate these three contributions. From the linear slope at high
magnetic field (>1T), we estimate the susceptibility χ which includes both contributions from

Mdia and Mpara. Susceptibility χ follows the Curie-Weiss law given by Equation 65, where χ0 is
the diamagnetic contribution to the susceptibility and C is the Curie constant. The high

  0 

C
T

65

temperature slope of χT vs T (shown in Figure 67) gives the value of χ0. Subsequently, C is
determined from the slop of 1/(χ-χ0) vs T (shown in Figure 68). The effective moment μeff of
each formula unit (Yb and Fe) can be obtained from Curie constant C by using Equation 66
where k is the Boltzmann constant, NA is the Avogadro’s number, μB is the Bohr magneton.
Table 4 lists μeff together with other room temperature physical properties for all samples.

eff 

3kC
N A B

92

66

χTχT (emu Kmole-1Tesla-1) )
(emu K mole-1 Tesla-1

70000

x=0.4
x=0.8

60000

x=0.6
x=1

50000
40000
30000
20000
10000
0
0

200

400

Temperature (K)

Figure 67 χT vs T

1/ (χ-χ ) (mole Tesla emu-1)
1/(χ-χ0) 0( mole Tesla emu-1)

0.14

x=0.4
x=0.6
x=0.8
x=1

0.12
0.1
0.08
0.06
0.04
0.02
0
0

100
200
300
Temperature (K)

Figure 68 1/(χ- χ0) vs T

93

400

Sample ID
Nominal composition

x=0.4

x=0.6

x=0.8

Yb0.4FeCo3Sb12 Yb0.6Fe2Co2Sb12 Yb0.8Fe3CoSb12

Estimated No. of carrier
per formula unit
Observed No. of carrier
per formula unit
Carrier density at 300K
20 -3
(×10 cm )
Carrier mobility at 300K
2 -1 -1
(cm V s )

x=1
YbFe4Sb12

-0.2~0.2

0.2~0.8

0.6~1.4

1~2

0.06

0.235

0.325

0.84

1.479

6.03

8.54

21.5

28.95

14

17.3

9.53

μeff / formula unit

0.714

1.285

2.318

3.064

Density
-3
(g cm )

7.512

7.635

7.927

7.895

Table 4 Some physical properties of Yb filled Fe compensated p-type skutterudite sample
YbxFeyCo4-ySb12 at room temperature. The lower and upper boundaries of estimated number of
carrier/formula unit are calculated assuming a variant Yb valence of +2 and +3. Minus sign in
estimated number of carrier/formula unit indicates the major carrier is electron.

5.3 Summary of the chapter
We have systematically investigated the high temperature TE transport properties of ptype Yb-filled Fe-compensated skutterudite YbxFeyCo4-ySb12. With the aid of a graphite
crucible during synthesis, we are able to obtain high quality ingots with excellent reproducibility.
The lattice thermal conductivity is significantly reduced to the level near the theoretical limit
upon Yb filling. Fe substitution for Co also depresses the lattice thermal conductivity through
additional phonon scattering mechanisms. The highest ZTmax is 0.6 in sample x=0.6 at 782K.

ZTs for other samples have also been significantly enhanced compared to published results on
similar compositions. ZTs in high Yb filling fraction samples (x=0.8 and x=1) failed to exceed
94

that of Ce filled skutterudites due to the high electronic thermal conductivity κe, which, in the
case of YbFe4Sb12, accounts for 67% of the total thermal conductivity at room temperature and
up to 80% at 780K. The effective moments were measured and results agree with the values
reported in literature.[92]
Now that we have a well-characterized p-type skutterudite matrix material in hand, we
study the effect of FeSb2 nanoinclusions on the TE properties of this system.

95

Chapter 6 Thermoelectric Properties and Galvanomagnetic Properties of
P-type Yb-filled Skutterudite Nanocomposites with FeSb2 Nanoinclusions

In this chapter, we extend the work to Yb-filled p-type skutterudite nanocomposites with
in-situ formed FeSb2 as nanoinclusions. Such a composite configuration utilizes a new p-type
matrix YbyFexCo4-xSb12, which is analogous to CeyFexCo4-xSb12 but its high temperature TE
properties have only been systematically studied recently.[96] The FeSb2 nanoinclusion is the
most probable impurity phases found in Fe compensated p-type skutterudite. Thus YbyFexCo4xSb12/zFeSb2

nanocomposites

are

thermodynamically

favorable

and

stable.

These

nanocomposites can be easily synthesized by fine control of the starting stoichiometry and the
subsequent heat treatment process. A series of samples covering a wide range of ytterbium filling
and Fe/Co ratio have been systematically studied in order to reveal the influence of nanosized
FeSb2 on the overall TE properties of the bulk nanocomposites. By taking advantage of these
naturally occurring FeSb2 nanoparticles, we achieve a ZTmax=0.74 in Yb0.6Fe2Co2Sb12
/0.05FeSb2 at 780K. We also measured the Nernst coefficient on the best performing group
Yb0.6Fe2Co2Sb12/xFeSb2 and apply the method of four coefficients to calculate the DOS
effective mass and the carrier scattering parameter. We find that a larger effective mass induced
by the presence of nanoparticles is the origin of the enhanced Seebeck coefficient.

96

6.1 Sample synthesis

A series of YbyFexCo4-xSb12/zFeSb2 samples have been synthesized with Yb filling
fraction y=0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. The Fe composition x changes according to x=5y-1. The
nominal FeSb2 content z is set at 0.05, 0.1, and 0.2 for each combination of Yb filling y and Fe
composition x. Table 5 summarizes the sample denomination and nominal chemical composition.
Pure element starting materials of Yb (pieces 99.9%), Fe (powder 99%), Co (powder
99.5%), and Sb (shot 99.999%) were weighed according to the stoichiometric ratio, and placed
inside graphite crucibles. The graphite crucibles loaded with reactants were sealed under a
vacuum of 10-5 Torr inside quartz ampoules. The sealed ampoules were heated to 1373K at a rate
slower than 0.5K/min and held at that temperature for 6 hours before rapid quenching in a cold
water bath. The quenched samples were annealed at 923K for another 3 days to promote
homogeneity. The annealed ingots were ball milled into fine powders and hot pressed at 873K
for 15min. The densities of all hot pressed samples are above 95% of the theoretical density.
The sample geometries, and measurement techniques are the same as those described in
previous chapters. High temperature Seebeck coefficient and electrical resistivity (from room
temperature to 800K) were measured on all samples in an ULVAC ZEM-3 system. The same
rectangular bar sample was also used to measure the Nernst coefficient from 110K to 350K
under a magnetic field from -2.2T to 2.2T in a homemade device. Nernst coefficient
measurement were performed on the group of samples with Yb filling y=0.6. X-ray diffractions
were performed on all samples to confirm the phase constitution. The thermal conductivity and
Hall coefficient measurement were performed on selected sample groups of our interest.

97

Sample ID
12.4 0.4R
14.18 0.4R 0.05FS2
14.9 0.4R 0.1FS2
14.10 0.4R0.2FS2
14.11 0.4R0.3FS2
14.3 0.5R
14.12 0.5R 0.05FS2
14.13 0.5R 0.1FS2
14.14 0.5R0.2FS2
12.5 0.6R
12.10 0.6R0.05FS2(1)
13.9 0.6R0.05FS2(2)
12.11 0.6R0.1FS2
12.12 0.6R0.2FS2
12.9 0.7R
12.13 0.7R0.05FS2
12.14 0.7R0.1FS2
12.15 0.7R0.2FS2
12.6 0.8R
12.16 0.8R0.05FS2
12.17 0.8R0.1FS2
12.18 0.8R0.2FS2
12.8 0.9R
12.19 0.9R0.05FS2
12.20 0.9R0.1FS2
12.21 0.9R0.2FS2
12.7 1R
12.22 1R0.05FS2
12.23 1R0.1FS2
12.24 1R0.2FS2

Nominal chemical composition
Yb0.4FeCo3Sb12
Yb0.4FeCo3Sb12/0.05FeSb2
Yb0.4FeCo3Sb12/0.1FeSb2
Yb0.4FeCo3Sb12/0.2FeSb2
Yb0.4FeCo3Sb12/0.3FeSb3
Yb0.5Fe1.5Co2.5Sb12
Yb0.5Fe1.5Co2.5Sb12/0.05FeSb2
Yb0.5Fe1.5Co2.5Sb12/0.1FeSb2
Yb0.5Fe1.5Co2.5Sb12/0.2FeSb2
Yb0.6Fe2Co2Sb12
Yb0.6Fe2Co2Sb12/0.05FeSb2
Yb0.6Fe2.05Co2Sb12
Yb0.6Fe2Co2Sb12/0.1FeSb2
Yb0.6Fe2Co2Sb12/0.2FeSb2
Yb0.7Fe2.5Co1.5Sb12
Yb0.7Fe2.5Co1.5Sb12/0.05FeSb2
Yb0.7Fe2.5Co1.5Sb12/0.1FeSb2
Yb0.7Fe2.5Co1.5Sb12/0.2FeSb2
Yb0.8Fe3CoSb12
Yb0.8Fe3CoSb12/0.05FeSb2
Yb0.8Fe3CoSb12/0.1FeSb2
Yb0.8Fe3CoSb12/0.2FeSb2
Yb0.9Fe3.5Co0.5Sb12
Yb0.9Fe3.5Co0.5Sb12/0.05FeSb2
Yb0.9Fe3.5Co0.5Sb12/0.1FeSb2
Yb0.9Fe3.5Co0.5Sb12/0.2FeSb2
YbFe4Sb12
YbFe4Sb12/0.05FeSb2
YbFe4Sb12/0.1FeSb2
YbFe4Sb12/0.2FeSb2

Table 5 Sample ID and nominal chemical composition for
YbyFexCo4-xSb12/zFeSb2 included in this study.

98

6.2 Results

Figure 69 X-ray diffraction of Yb0.6Fe2Co2Sb12/zFeSb2 (a) 12.12 0.6R 0.2FS2 (b) 12.11
0.6R 0.1FS2 (c) 12.10 0.6R 0.05FS2 (d) 12.5 0.6R. Trace antimony was also observed in (a)
Figure 69 is the x-ray diffraction of Yb0.6Fe2Co2Sb12/zFeSb2 where skutterudite phase is
found to be the primary phase for all sample. The impurity phase FeSb2 was observed together
with trace amount of Sb impurity. Figure 70 is the zoomed in x-ray diffraction of two
Yb0.6Fe2Co2Sb12/0.1FeSb2 samples synthesized under the same condition where FeSb2 phase
could be identified at multiple positions. The CoSb2 which is isostructural with FeSb2 and Sb
were also observed.

99

Figure 70 Zoomed in x-ray diffraction of two Yb0.6Fe2Co2Sb12/0.1FeSb2
samples synthesized under the same condition. The major impurity phase is FeSb2
while another closely related CoSb2 and some Sb is also observed.

100

Figure 71 Zoomed in x-ray diffraction of Yb0.4FeCo3Sb12/zFeSb2 (a) 12.4 0.4R (b) 14.9
0.4R 0.1FS2 (c) 14.18 0.4R0.05FS2 (d) 14.10 0.4R 0.2FS2 (e) 14.11 0.4R 0.3FS2. The
expansion of the primary skutterudite peak around 31 degree 2θ indicates the existence of
FeSb2.
Figure 71 is the zoomed in x-ray diffraction of Yb0.4FeCo3Sb12/zFeSb2. The most
apparent indicator for FeSb2 is the expansion of the primary skutterudites peak near 31 degree 2θ.
X-ray diffractions of other Yb filling group show the similar results. Figure 72 shows high
resolution SEM images taken on the fractured surface of sample 13.9 0.6R0.05FS2(2). We
estimate the nanoparticle size to be about 20-40 nm based on Figure 2(b). From the results of our
101

previous work,[97] x-ray analysis and electron dispersive spectrum analysis, we believe the
majority of nanoparticles present in Figure 72(d) are FeSb2.

Figure 72 FESEM images on the fractured surface of sample 13.9
0.6R0.05FS2(1) which demonstrate the existence of FeSb2 nanoparticle. Images
from (a) to (d) are in increasing magnification.
Figure 73 (a)-(g) show the power factors as a function of temperature for the
nanocomposite samples and control samples synthesized in compositions listed in Table 5. The
materials are grouped based on the Yb filling ratio “y”. Generally, nanocomposite samples
exhibit enhanced power factors when y≤0.7 as shown from (a) to (d). Once y>0.7, most
nanocomposite samples show comparable or smaller power factors compared to control samples
as shown from (e) to (g).

102

Figure 73 Power factors as a function of temperature.

Power Factor (10-6 W cm-1 K-2 )
W cm-1 K-2 )
Power Factor (10-6 -6 W cm-1 K-2)
Power Factor (10

20

12.4 0.4R
14.18 0.4R 0.05FS2
14.9 0.4R 0.1FS2
14.10 0.4R 0.2FS2
14.11 0.4R 0.3FS2

18
16
14
12
10
8
6
4
2
0
250

350

450

550

650

750

850

Temperature (K)

(a)

Power Factor (10-6 W cm-1 K-2
Power Factor (10-6 W cm-1 K-2 ))

25

14.3 0.5R1.52.512
14.19 0.5R0.05FS2
14.20 0.5R0.1FS2
14.21 0.5R0.2FS2

20
15
10
5
0
250

350

450

550

650

Temperature (K)

(b)

103

750

850

Figure 73 continued

-1

-2

Power Factor (10 W cm
)
Power Factor (10-6 W cm -1KK-2 )

25

-6

20

15
12.5 0.6R
12.10 0.6R0.05FS2(1)
13.9 0.6R0.05FS2(2)
12.11 0.6R0.1FS2
12.12 0.6R0.2FS2

10

5
250

350

450

550

650

750

850

Temperature (K)

(c)

Power Factor (10-6 W cm-1 K-2) )
Power Factor (10-6 W cm-1 K-2

30

12.9 0.7R
12.13 0.7R0.05FS2
12.14 0.7R0.1FS2
12.15 0.7R0.2FS2

25
20
15
10
5
0
50

250

450
Temperature (K)

(d)
104

650

850

Figure 73 continued

-6 W cm-1 K-2
Power Factor (10-6 W cm-1 K-2))

30

12.6 0.8R
12.16 0.8R0.05FS2
12.17 0.8R0.1FS2
12.15 0.7R0.2FS2

25
20
15
10
5
0
250

350

450
550
650
Temperature (K)

750

850

(e)

Power Factor (10-6 W cm-1 K-2
Power Factor (10-6 W cm-1 K-2) )

30
25
20
15
10
12.8 0.9R
12.19 0.9R0.05FS2
12.20 0.9R0.1FS2
12.21 0.9R0.2FS2

5
0
250

350

450

550

650

Temperature (K)

(f)
105

750

850

-6 W cm-1 K-2
Power Factor (10-6 W cm-1 K-2))

40

12.7 1R4012
12.22 1R0.05FS2
12.23 1R0.1FS2
12.24 1R0.2FS2

35
30
25
20
15
10
5
0
250

350

450

550

650

750

850

Temperature (K)

(g)
Figure 73 Power factors of nanocomposite samples and control samples as a function
of temperature. The samples are grouped according to the Yb filling ratio “y” (a)
y=0.4; (b) y=0.5; (c) y=0.6; (d) y=0.7; (e) y=0.8; (f) y=0.9; (g) y=1. Generally,
nanocomposite samples could exhibit enhanced power factors when y≤0.7 as shown
from (a) to (d). Once y>0.7, most nanocomposite samples show comparable or
smaller power factors compared to control samples as shown from (e) to (g).
To seek the highest possible ZT and investigate the physical mechanisms for the
enhanced electronic properties in some of the nanocomposites, we focus on characterizing the
full TE transport properties, galvanomagnetic properties and applying the method of four
coefficients on the group with Yb filling ratio y=0.6. To further simplify our discussion, we use
the nominal FeSb2 content x to denote our samples. Sample x=0 with no intentionally added
FeSb2 serves as a control sample. Sample x=0.05(2) which is of identical composition of

106

Sample
ID

x=0
x=0.05(1)
x=0.05(2)
x=0.1
x=0.2

Corresponding
notation in Figure
70 (c)

Nominal composition

Seebeck
Density
-3 coefficient
(g cm )
(μV/K)

12.5 0.6R

Yb0.6Fe2Co2Sb12

7.635

87.67

Carrier
density
(1020
-3
cm )
6.03

12.10
0.6R0.05FS2(1)
13.9
0.6R0.05FS(2)
12.110.6R0.1FS2

Yb0.6Fe2Co2Sb12/0.05FeSb2

7.525

94.55

15.6

Yb0.6Fe2.05Co2Sb12

7.791

89.73

12.8

Yb0.6Fe2Co2Sb12/0.1FeSb2

7.759

85.63

9

12.12
0.6R0.2FS2

Yb0.6Fe2Co2Sb12/0.2FeSb2

7.788

75.36

3.83

Table 6 Some room temperature physical properties of Yb0.6Fe2Co2Sb12/xFeSb2 samples
2

140
120

1.5

100
80

1

60
x=0
x=0.05(1)
x=0.05(2)
x=0.1
x=0.2

40
20
0
250

350

450

550

650

750

0.5

Electrical resistivity (mΩ cm)

Seebeck coefficient (μV K-1)
Seebeck Coefficient (μV K -1)

160

0
850

Temperature (K)

Figure 74 Seebeck coefficient and electronic resistivity as a
function of temperature for Yb0.6Fe2Co2Sb12/xFeSb2.

107

x=0.05(1) was used to reproduce and cross-check the transport properties of x=0.05(1). Table 6
lists some room temperature physical properties of the Yb0.6Fe2Co2Sb12/xFeSb2 samples.
Figure 74 exhibits the Seebeck coefficient and electrical resistivity as a function of
temperature. Seebeck coefficients for all samples increase monotonously as a function of
temperature. Nanocomposite samples x=0.05(1), x=0.05(2) show consistent higher Seebeck
coefficients over the whole temperature range compared to x=0. At 780K, x=0.05(1) has a
Seebeck coefficient of 149μV/K, and x=0.05(2) has a Seebeck coefficient of 145 μV/K; while
the Seebeck coefficient for x=0 is 138 μV/K. When the FeSb2 content x>0.1, Seebeck coefficient
deceases with an increasing x. Electrical resistivity for all samples exhibit a metallic behavior.
x=0.05(1) and x=0.05(2) have electrical resistivity close to x=0 while x=0.1 and x=0.2 show
lower resistivity values.
The temperature dependence of power factors is plotted in Figure 73 (c) [please refer to
Table 6 for the corresponding notation in Figure 73 (c)]. Compared to x=0 at 780K, x=0.05(1)
and x=0.05(2) show 17-19% power factor enhancement as a result of enhanced Seebeck
coefficients; x=0.1 also shows a 15% enhancement due to the reduced electrical resistivity; while
x=0.2 shows a reduction because of the greater influence from the reduced Seebeck coefficient.

108

-1
Thermal conductivity (W cm-1 K-1 )
Thermal conductivity (W cm-1 K-1))
Thermal conductivity (W m-1 K

6

2

5

x=0
x=0.05(1)
x=0.05(2)
x=0.1
x=0.2

κl k l

1.5
1
0.5

4

0
250

450

650

850

3
2
1
0
250

350

450

550

650

750

850

Temperature (K)

Figure 75 Temperature dependence of thermal conductivity for
Yb0.6Fe2Co2Sb12/xFeSb2. The inset graph displays the lattice thermal conductivity.
The thermal conductivity for all samples is insensitive to the temperature change as seen
in Figure 75. To estimate the lattice thermal conductivity κl, we calculate the electronic thermal
conductivity κe using Wiedemann Franz Law κe=LσT, where L is the Lorenz number, σ the
electrical conductivity and T temperature, and subtract κe from total thermal conductivity κ. Here,
-2

we assume L=2.44×10-8 W Ω K , a value that is suitable for degenerate semiconductors. Lattice
thermal conductivities for all samples (inset of Figure 75) decrease with increasing temperature
and do not show much deviation from each other. κl for nanocomposite samples except x=0.2,
are slightly reduced compared to x=0 at higher temperature. As pointed out in our previous
-1 -1

work,[96] κl for x=0 is 0.49 Wm K

at 780K, which is already very close to the theoretical
109

-1 -1

limit of 0.2 Wm K we calculated assuming a mean free path equal to lattice spacing. So the
weak reduction of κl in nanocomposite samples suggests that the opportunity for further lattice
thermal conductivity reduction by nanostructuring is very limited. On the other hand, κe for
x=0.1 and x=0.2 is greater than that of x=0, which negates the benefit from lattice thermal
conductivity reduction if there is any. As a result, x=0.1 has a thermal conductivity similar to that
of x=0, and x=0.2 has an even larger thermal conductivity.
0.8
0.7
0.6

ZT

0.5
0.4
x=0
x=0.05(1)
x=0.05(2)
x=0.1
x=0.2

0.3
0.2
0.1
0
250

350

450

550

650

750

850

Temperature (K)

Figure 76 ZT as a function of temperature for Yb0.6Fe2Co2Sb12/xFeSb2.
Figure 76 displays the ZT as a function of temperature. As a result of an enhanced power
factor, x=0.05(1), x=0.05(2) and x=0.1 all demonstrate a higher ZTmax of 0.74, 0.72 and 0.68
respectively at 780K compared to ZTmax=0.6 of x=0.

110

6.3 Discussion

Seebeckcoefficient (μV K-1) )
Seebeck coefficient (μV K -1

120
110
100

skutterudite
0.05(1)
0.05(2)
0.1
0.2

90
80
70
60
1020
1E+20

1021
1E+21

Carrier concentration (cm-3)

1022
1E+22

Carrier concentration (cm-3)
Figure 77 Pisarenko relation of nanocomposites and regular skutterudite samples at room
temperature. Blue diamond (skutterudite) points represent regular skutterudite samples of
various carrier concentrations prepared in our lab. The fit line serves as an aid to the eye.
As shown in Figure 74, x=0.05(1) and x=0.05(2) show enhanced Seebeck coefficients
compared to x=0. x=0.1 has identical Seebeck coefficient but a lower electrical resistivity than
x=0, which could be perceived as an equivalent of an increase in the Seebeck coefficient. To
explain the mechanism for such an enhancement, we plot the room temperature Seebeck
coefficient as a function of carrier concentration, known as the “Pisarenko relation”,[36] in
Figure 77. For a semiconductor with only one type carrier, Seebeck coefficient can be expressed
as[36]




2 2 mkT
k
S
s  2  ln
e
h 3n



111

 




67

where, s is the carrier scattering parameter, m* the density of state effective mass, and n the
carrier concentration. For bulk semiconductors with similar composition, s and m* usually have
comparable values, thus the Seebeck coefficient is proportional to the logarithm of inverse
carrier concentration. This is exactly the case for the regular skutterudite samples shown in
Figure 74, where samples obey a linear relation as suggested in Equation 67. Nanocomposite
samples x=0.05(1) and x=0.05(2) show higher Seebeck coefficients than those projected by the
fit.
To understand the effects of nanostructuring on s and m*, we use four measured transport
properties, namely Seebeck coefficient S, the electrical conductivity σ, the Nernst coefficient N,
and Hall coefficient RH to directly calculate the scattering parameter s, and the density of state
effective mass m*. The derivation of equations is provided below following Heremans et al’s
work.[21, 51, 98] γ(E) describes the non-parabolic energy of carriers given by Equation 68,
where Eg is the bandgap.

 E 

2k 2
2mv*

 ' 1 2
 '' 


E 
 E 1 


Eg 



E
Eg

68

2
Eg

The carrier concentration, carrier mobility, Seebeck coefficient and Nernst coefficient can be
expressed by Equation 69-72.

 2m *  E  0    E  

n p  
2 3
3 
112

3

2



1
RH e

69

  RH  

S 

N 



70

n pe

2 k


 ''
 '' 
kT  s  1  2 
3 e 

 '

71

2 k


1  '
 '' 
kT  s    2 
3 e 
2 
 '

72

These equations can be fitted by using mathematical software or solved explicitly as a function
of measured parameters to yield Fermi energy EF, scattering parameter s and DOS effective
mass m*( EF) from Equation 73-75.


 2k 2T
 A 
eEg
Eg 

EF 
2







 2k 2T
A

eEg

A

2


 2k 2T
A
 2

eEg


, AS 

N



73

3N
4




2 2
E g  2 EF 
  Eg  k T



eEg
1 
EF 
s  

 EF  1 

EF
Eg 
2 



1 2
Eg









74

m *  EF   m *  E  0   '  E F 

75

In this study, we use the non-parabolic band model described by Equation 65, which has been
used to study the band structure of CoSb3.[99-101] The band gap Eg=0.5eV is adapted from
literature on YbFe4Sb12.[102, 103]

113

*
DOS effective mass m v*/m0
DOS effective mass m /m0
v

Scattering parameter
Scattering parameter s λ

15

x=0
x=0.05(1)
x=0.05(2)
x=0.1
x=0.2

12
9
6
3
2
0
0

2

4

6

8

0

1.5

2

4

6

8

1
0.5
0
-0.5
Reduced Fermi energy

Figure 78 DOS effective mass m* and carrier scattering parameter s
as a function of reduced Fermi energy EF.
It can be seen from Figure 78 that the DOS effective masses for x=0.05(1) and x=0.05(2)
are 3 to 4 times greater than the effective mass for x=0. The large effective mass implies that the
presence of nanoparticles could induce a localized sharp peak in the DOS that leads to enhanced
Seebeck coefficients. The scattering parameter s, on the other hand, has changed from acoustic
phonon scattering in x=0.05(1) and x=0.05(2) to neutral impurity scattering in x=0.1, and to
mixed neutral and ionized impurity scattering in x=0.2. Matrix skutterudite x=0 also has an s
indicating neutral impurity scattering. Thus, it is the effective mass rather than the scattering
114

parameter that results in an enhanced Seebeck coefficient, and hence, the power factor for our
nanocomposite samples.

6.4 Summary of the chapter
In conclusion, we investigated the high temperature TE properties of p-type skutterudite
nanocomposite YbyFexCo4-xSb12/zFeSb2. These nanocomposites can be easily formed in-situ
during solidification via fine control of starting stoichiometry and subsequent heat treatment
process. The presence of small amount of FeSb2 nanoparticles can increase the power factors in
a range of nanocomposites with Yb filling ratio y≤0.7 and FeSb2 content z≤0.1.
We thoroughly characterized the full TE transport properties, galvanomagnetic properties
and applied the method of four coefficients to calculate the scattering parameter s and DOS
effective mass m*. We found that an enhanced effective mass induced by the FeSb2
nanoparticles is the driving force for the enhanced Seebeck coefficient, hence the enhanced
electronic properties. The lattice thermal conductivity is slightly reduced in nanocomposites as
well but the reduction is insignificant to cause a dramatic enhancement in ZT due to the near
phonon glass lattice thermal conductivity in the matrix skutterudite. Sample x=0.05(1)
demonstrated the highest ZTmax=0.74 at 780K which is 23% enhancement over the matrix x=0.

115

Chapter 7 Thermoelectric Properties of Double
Filled P-type Skutterudite YbyGazFexCo4-xSb12

In previous two chapters, we have seen that filled p-type skutterudites that exhibit high
ZTs are generally very conductive, with an electrical resistivity typically below 1 mΩ cm. The
lattice thermal conductivity, on the other hand, is very close to the theoretical minimum. This
implies the room for further ZT enhancement by reducing the lattice thermal conductivity is very
limited and the electronic thermal conductivity is a significant contribution to the total thermal
conductivity, sometimes even exceeding 50%. Therefore it is important to seek new mechanisms
on improving the Seebeck coefficient S because 1) the square power will amplify any gain from
S; 2) increasing σ will also increase κe in the denominator which partially cancels out the gain.

ZT 

S 2
S 2
1
T
T  S     LT   l 
l   e
 l  L T
T 

76

To explicitly show what a Seebeck coefficient is needed for certain lattice thermal
conductivity and resistivity in order to get a ZT=1, we start from the definition of ZT and express
the Seebeck coefficient S as a function of electrical resistivity ρ and lattice thermal conductivity
κl as shown in Equation 76. If we assume ZT =1 at 800K and the Lorenz number L=2.44×10
2

-8

-2

V K , we plot the projected Seebeck coefficient a function of electrical resistivity ρ and lattice
thermal conductivity κl as shown in Figure 79(a). The cross section area at κl = 0.2W/mK shown
in Figure 79(b) is used to identify the minimum Seebeck coefficients needed to attain a certain
ZT. Taking ZT =1, for example, if we assume ρ=1 mΩ cm, then a S >164 μV/K is needed to
achieve the goal.
116

(a)

l WmK 1
0.8
0.6
0.4

 

0.2
2
220

200
S VK
180

160
0

0.5

1
1
1.5
Rho m cm  5

(b)

2

Seebeck coefficient (μV/K)

180

ZT=0.5

170

ZT=0.6

160

ZT=0.7
ZT=0.8

150

ZT=0.9

140

ZT=1

130
120
110
100
0

0.001

0.002

Electrical resistivity (Ω cm)
Figure 79 (a) 3D graph of the projected Seebeck coefficient S as a function of electrical
resistivity ρ and lattice thermal conductivity κl. (b) Cross section of κl = 0.2W/mK from
(a) which is used to identify the minimum Seebeck coefficient needed to attain certain ZT.

117

In this chapter, we report the high temperature thermoelectric properties of a new p-type
double filled skutterudite YbyGazFexCo4-xSb12. We choose Ga as the second filler atom because
1) theoretical calculation identified Ga and other group III elements In, Tl as impurities being
able to induce a deep defect state in narrow band semiconductors;[104] 2) Ga has been reported
as a filler atom for CoSb3, although discrepancy of the exact filling fraction exists.[105, 106]
We have also applied the method of four coefficients[48] to calculate the DOS effective mass m*
and carrier scattering parameter s, with the hope of elucidating the unconventional behavior of
electronic properties observed in some samples.

7.1 Sample synthesis

Sample ID
Y60

Nominal composition
Yb0.6Fe2Co2Sb12

Density
-3
(g cm )
7.635

Y60G10

Yb0.6Ga0.1Fe2Co2Sb12

7.807

Y60G15

Yb0.6Ga0.15Fe2Co2Sb12

7.726

Y60G20

Yb0.6Ga0.2Fe2Co2Sb12

7.758

Y65

Yb0.65Fe1.5Co2.5Sb12

7.57

Table 7 Sample designation of double filled skutterudite YbyGazFexCo4-xSb12.
High purity starting materials Yb (pieces 99.9%), Fe (powder 99%), Co (powder 99.5%),
Sb (shot 99.999%), and Ga (pieces 99.999%) were used to synthesize the skutterudite ingots. The
annealed ingots were pulverized into powders and consolidated by hot pressing. The details of
118

the synthesis can be found elsewhere.[96] A total of five samples have been prepared. Table 7
serves as a key to the sample designation. The first four samples are based on Yb0.6Fe2Co2Sb12
with a variant Ga filling fraction “z” ranging from 0 to 0.2. The fifth sample with a higher Yb
filling fraction and lower Fe/Co ratio is used to probe the transport behavior at a lower carrier
concentration.

7.2 Results

CoSb3
Yb

(e)

(d)
(c)
(b)

(a)

Figure 80 Powder x-ray diffraction patterns of samples included in the study. (a) Y60;
(b) Y60G10; (c) Y60G15; (d) Y60G20; (e) Y65. The major peaks of all samples are
indexed to the skutterudite phase CoSb3 PDF# 01-073-7899. Trace amount of Sb
phase can also be detected in (a) but unidentifiable in the graph. Trace amount of Yb
can be found in (b), (c), and (d) and are labeled in the graph accordingly.

119

Figure 80 displays the powder x-ray diffraction patterns of samples listed in Table 7.
Skutterudite phase was found to be the primary phase for all samples and the patterns match
PDF# 01-073-7899. Trace amount of Sb can be detected by x-ray analysis software JADE in
sample Y60, which is common for Sb based skutterudites. However the amount is so small that
the intensity is closer to the background noise and unobservable in the figure. A trace amount of
Yb can also be detected in sample Y60G10, Y60G15, and Y60G20.
 

9.081

Lattice constant (Å)

9.08
9.079
9.078
9.077
9.076
9.075
9.074
9.073
9.072
9.071
0

0.05

0.1

0.15

0.2

Ga filling fraction z

Figure 81 Lattice constant as a function of Ga filling fraction.
The filling fraction of Ga has been a matter of controversy in previous literature reports.
Su et al reported that Ga filling could reach as high as x=0.22 in GaxCo4Sb12;[105] on the other
hand

Harnwunggmoung and co-workers reported a Ga filling fraction at a miniscule

x=0.02.[106] The exact Ga filling fraction is out of the scope of this work and may be subject to
change with the complexity of another filler element and Fe substitution on the Co site. We plot
120

the lattice constant as a function of Ga filling fraction z as shown in Figure 81 and our result
agrees more with Su’s work. We cannot clearly detect Ga and its compounds in x-ray, nor could
we find the evidence in the EDS analysis. This suggests either we have successfully inserted Ga
into the skutterudite cages up to z=0.2 or the Ga impurity phase is below the detection limit of
our instruments considering that even the most Ga rich sample Y60G20 has a Ga concentration
of only 1.2at%. Further evidences for Ga filling can be sought in the difference of transport
properties.

Seebeck Coefficient (μV KK-1)
Seebeck coefficient(μV -1)

180

0.003

Y60
Y60G10
Y60G15
Y60G20
Y65

160
140

0.0025

120
0.002

100
80

0.0015

60
40

0.001

Electrical resistivity (Ω cm)

 

20
0.0005

0
200

400

600

800

Temperature (K)

Figure 82 Temperature dependence of the Seebeck coefficient and the electrical resistivity.
Figure 82 displays the temperature dependence of the electronic properties. Seebeck
coefficients for all samples exhibit the typical behavior for heavily doped semiconductors:
increasing monotonously with the increasing temperature before reaching the intrinsic region.
Sample Y65 has a higher Seebeck coefficient compared to Y60, which is what one would expect
from a reduced carrier concentration due to the combined effects of a higher Yb filling fraction
121

and a lower Fe/Co ratio. Ga filled samples also exhibit enhanced Seebeck coefficients compared
to sample Y60. But unlike Y65, their resistivities remain almost the same as Y60, a phenomenon
quite different from that expected for ordinary doping optimization. As a result, the power
factors in these Ga filled samples demonstrated an over 30% enhancement compared to Y60, as
shown in Figure 82. The power factor for the best performing sample Y60G10 reaches 25 Wcm1

K-2 at 810K.

-1
-2
Power Factor (10-6 W cm-1 K-2) )
Power Factor (10-6 W cm K

30

Y60
Y60G10
Y60G15
Y60G20
Y65

25
20
15
10
5
0
250

350

450

550

650

750

850

Temperature (K)

Figure 82 Power factor as a function of temperature.
Figure 83 shows the thermal conductivity as a function of temperature. The lattice
thermal conductivity κl is obtained by subtracting the electronic thermal conductivity κe=LσT
from the total thermal conductivity κ. Here, we use the Lorenz number L=2×10-8 V2 K-2, a value
typically used for filled skutterudites.[108] The lattice thermal conductivity is first reduced
slightly with Ga filling in Y60G10, and rises up with higher Ga filling in Y60G15 and Y60G20.
122

This can be understood as the actually Yb filling fraction may be affected by the extra filler Ga.
As it is seen from Figure 80, trace amount of Yb impurity phase is present in samples with Ga,
which indicates adding Ga indeed repels some Yb out of the skutterudite cages. The similar
phenomenon has also been reported by Xiong et al in n-type Yb filled skutterudite with Ga[107],
where actual Yb filling fraction decreases with increasing Ga. Thus, the lattice thermal
conductivity reflects the collateral effects of additional phonon scattering from second filler Ga

3
2.5
2

2

1.5

1.5

1

1

0.5

0.5

0

0
250

350

450

550

650

750

850

-1

2.5

-1

Y60
Y60G10
Y60G15
Y60G20

-1

-1

Thermal
Thermal conductivity (W cm -1 K)-1)
conductivity (W cm K

3

Lattice thermal conductivity (W cm K )
Lattice thermal conductivity (W cm -1 K-1)

and the loss of primary filler Yb.

Temperature (K)

Figure 83 Total thermal conductivity and lattice thermal
conductivity as a function of temperature.
Because of the enhanced power factors, Ga filled samples demonstrate enhanced ZTs
compared to that of Y60 as shown in Figure 84. Sample Y60G10 exhibits the highest ZTmax=0.83
at 736K, which is 46% enhancement compared to that of Y60, and over 100% enhancement
compared to ZTmax=0.4 in YbFe4Sb12 from an earlier report.[91]
123

0.9

Y60
Y60G10
Y60G15
Y60G20
Ref 22

0.8
0.7

ZT

0.6
0.5
0.4
0.3
0.2
0.1
0
250

350

450

550

650

750

850

Temperature (K)

Figure 84 ZT as a function of temperature. Ref represents ZT
of YbFe4Sb12 reported by Kuznetsov and Rowe[91]

7.3 Discussion
As we have seen repeatedly throughout this work, a good way to probe the behavior of
Seebeck coefficient is to plot the “Pisarenko relation”,[36] which is the Seebeck coefficient as a
function of carrier concentration. A series of control samples of various Seebeck coefficients and
carrier concentrations create a fit line based on Equation 77 which assumes comparable DOS
effective mass m* and scattering parameter s for compounds of similar compositions. If samples
significantly deviate from such a fit line, it is a good indication of either a different m* or s.
Figure 85 is the Pisarenko relation at room temperature for our skutterudite samples, where
sample Y60, Y65, and other single filled Yb samples create the fit line. It is obvious that at the

124

same carrier concentration, samples co-filled with Ga have a higher Seebeck coefficient
compared to those without Ga.




2 2 mkT
k
S
s  2  ln
e
h 3n



Seebeck coefficient(μV K-1
Seebeck Coefficient (μVK-1)

 

120

 

77





Y60
Y60G10
Y60G15
Y60G20
Y65
Skutterudite

110
100
90
80
70
60
0

1E+21
1021

2E+2121
2×10

3E+21
3×1021

-3
Carrier concentration (cm-3))
Carrier concentration

Figure 85 Pisarenko relation of single filled Yb based p-type skutterudite and
Yb Ga double filled skutterudite at 300K. Circles in the figure represent
additional Yb filled skutterudite samples. Fit line represents the logarithmic
relation expressed by Equation 74 and serves as an aid to the eye.
To understand which of m* and s is the dominant mechanism for the enhanced Seebeck
coefficient in Ga filled samples, we measured the Nernst coefficient and applied the method of
four coefficients to compute m* and s. Details of this method have already been mentioned in
previous chapter. In this study, we use the non-parabolic band model described by Equation 78,
125

2k 2
2mv*


E 
 E 1 


Eg 



78

which has been used to study the band structure of CoSb3.[99-101] The band gap Eg=0.5eV is
adapted from literature on YbFe4Sb12.[102, 103] Using this method, we calculate m*, s, and EF
3/2

for all our samples listed in Table 7. From classical physics, the DOS g(E) ∝ (m*)

, so the

energy dependence of m* can be viewed at least as a qualitative reflection of the shape of g(E).
As shown in Figure 86(a), at 300K, Ga filled samples exhibit a higher effective mass m*
compared to Y60 at a Fermi energy level closer to the valence band edge, between 35meV and
54meV in contrast to over 100meV for Y60. Sample Y65 is also pushed closer to the valence
band edge at approximately 30meV, which is expected due to the low carrier concentration. The
slightly increased m* appears to reflect the natural DOS of Yb-filled p-type skutterudite near the
valence band edge,[102, 103] but smaller m* for Y65 means it has less carriers and should enter
the intrinsic region at a lower temperature compared to Ga-filled samples. This agrees with
Figure 82 which shows that the Seebeck coefficient of sample Y65 reaches a maximum near
740K and begins to decrease above that temperature. The single filled Yb samples forms a
relatively flat slope while the much higher m* found in Ga co-filled samples suggests the
existence of spike like features in g(E) which translates to a larger Seebeck coefficient. This
finding is also corroborated by the carrier concentration data shown in Figure 87. When Ga is
inserted into the voids of skutterudites, it should contribute electrons. Su et al estimated that each
Ga donates 0.9 electrons.[105] If this is the case, the hole concentration should decrease instead
of increase in our Ga-filled samples. The anomalous increase of the hole concentration combined

126

(a)
12

Y60
Y60G10
Y60G15
Y60G20
Y65
Skutterudite

m*/me
e

10
8
6
4
2
0
0

0.05

EF (eV)

0.1

0.15

(b)

scattering parameter s

2

Y60
Y60G10
Y60G15
Y60G20
Y65

1.5
1
0.5
0
-0.5
-1
100

200

300

400

Temperature (K)

Figure 86 (a) DOS effective mass as a function of Fermi energy EF at 300K.
Circle represents Yb filled skutterudite and serves as supplemental datum. (b)
Carrier scattering parameter s as a function of temperature.
with the reduced Fermi level suggests the deep defect states induced by Ga alter the band
structure closer to the valence band edge. The scattering parameters s shown in Figure 86(b)
127

imply a neutral impurity scattering for Y60 and acoustic phonon scattering for other samples, so

-3
Carrier concentration (cm-3 -) ))
Carrier concentration(cm 3
Carrier concentration (cm

that s is not the driving force for the enhanced Seebeck coefficient.

1E+22

1022

Y60
Y60G10
Y60G15
Y60G20
Y65

1E+21
1021

1020
1E+20
50

150

250

350

450

Temperature (K)
Figure 87 Carrier concentration as a function of temperature.

7.4 Summary of the chapter
In conclusion, we have successfully synthesized double filled p-type skutterudite
Yb0.6GazFe2Co2Sb12. The results suggest that the second filler atom Ga induces a deep defect
level in the band structure which pins the Fermi level closer to the valence band edge. The
unique role of Ga greatly enhances the Seebeck coefficient without affecting the electrical
conductivity. The best performing sample has a ZTmax=0.83 at 736K which is 46% enhancement
compared to the control sample synthesized by ourselves, and over 100% enhancement
compared to ZTmax =0.4 in YbFe4Sb12 from an earlier report.[91] Although, such a ZT value is
still lower than ZT=0.9 in Ce0.9Fe3.5Co0.5Sb12 (synthesized in our laboratory) and the even higher
128

ZT in didymium-filled skutterudites[40, 109], it certainly narrows the gap and demonstrates the
potential for the once overlooked Yb-filled p-type skutterudites. Future theoretical calculations
on the band structure of partially filled skutterudite may improve our understanding of the
influence of defect states and guide the exploration for p-type skutterudites with higher ZT.

129

Chapter 8 Conclusions and Future Work
We have successfully employed multiple approaches to synthesize bulk nanocomposite
materials for thermoelectric applications. Two material systems are of our interest: they are
bismuth telluride and its alloy based nanocomposites, and p-type skutterudite based
nanocomposites.
For bismuth telluride and its alloys based nanocomposites, we select Bi2Te2.85Se0.15 as
the n-type matrix and Bi0.4Sb1.6Te3 as the p-type matrix respectively. Through careful process
optimization, we obtain matrix materials with reproducible TE properties. The nanocomposite
materials were prepared by a solution based incipient wetness impregnation method, followed by
burning off the organic ligands and consolidating the powders by hot pressing. TEM images
suggest that the PbTe nanoparticles retain their nano-sized feature after hot pressing. For n-type
nanocomposites, adding PbTe nanoparticles create a two carrier system which severely degrade
the electronic properties. For p-type nanocomposites, adding PbTe nanoparticles can more
effectively reduce the lattice thermal conductivity at lower temperature. But the doping effect
from the excess Pb ion plays a dominant role compared to nanostructuring which increases
electrical conductivity but decreases the Seebeck coefficient. This results in a decreased power
factor. The total thermal conductivity is not reduced for nanocomposites as well due to the
enhanced contribution from the electronic thermal conductivity.
For skutterudite based nanocomposites, we focus our attention on the under-developed ptype skutterudites. We start from the primitive Fe-doped binary skutterudite nanocomposite
Co0.9Fe0.1Sb3 with in-situ formed FeSb2 as nanoparticles to test the viability of this approach.
130

The best performing nanocomposites enhance the ZT by a factor two compared to the control
sample. The success led us to proceed with filled skutterudite with antimony impurities as the
nano-inclusions. A new Yb filled p-type skutterudite is developed as the matrix material. By
revising the synthesis procedure, we successfully reduce the spontaneous reaction between the
rare earth element and the quartz ampoule, thus enhancing the thermoelectric power factor by
100% and the ZT by 50% compared to the literature reported a decade ago. We explored the
thermoelectric properties of Yb filled p-type skutterudite nanocomposites for a wide range of Yb
filling fraction and FeSb2 amount.

We discovered enhanced power factors in these

nanocomposites when the Yb filling fraction is not greater than 0.7. The best performing
nanocomposites were found when Yb filling fraction is 0.6. These nanocomposite compositions
embody and exemplify all the theoretical and technical advancements in thermoelectrics: using
rattlers to scatter phonons, creating a solid solution by partially filling the voids and using Fe
substitution on Co site, and taking advantage of naturally occurring nanoscopic impurity phases
to further improve ZT. By combining our results with other literature reports, we find that the
marginal enhancement of nanocomposite tends to dwindle as the properties of the matrix
materials are enhanced, from a 100% enhancement in our prototype demonstration in binary
skutterudite nanocomposites, to 23% enhancement to p-type filled skutterudites to merely 14%
in advanced n-type skutterudites.[27, 107, 110].
Last

but

not

least,

we

investigated

the

double

filled

p-type

skutterudite

Yb0.6GazFe2Co2Sb12. The unique role of Ga inducing a deep defect state in band structure
greatly enhances the Seebeck coefficient without affecting the electrical resistivity. The best
performing sample has a ZTmax=0.83 at 736K which is 46% enhancement compared to
131

Yb0.6Fe2Co2Sb12 with only Yb filler and over 100% enhancement compared an earlier
report.[91] Such a ZT value certainly makes these double filled skutterudites an alternative to Cefilled skutterudite due to their reduced consumption of precious rare-earth elements.
Future work for preparing bulk nanocomposites should seek more compatible material
systems where the feasibility of the approach and the complexity of the possible interactions
between the matrix material and nano-inclusions should be given all-round evaluation before the
execution of the project. Nanostructuring should not be deemed as a preconceived elixir to the
enhancement of TE properties aforehand, not even for the reduction of thermal conductivity, but
as a high risk adventure where the property matching between matrix material and nanoinclusions is crucial. An abundant nano material supply and well-equipped characterization
facilities are needed to guarantee a thorough investigation. For in-situ synthesized bulk
nanocomposite materials, it remains a question if this approach is viable for mass production as
the cooling rate in a big ingot is quite different from a laboratory scale trial experiments. But the
melt-spinning technique at least opens a door to the possibility. In addition, there is still room for
improving the electronic properties through band structure engineering. More theoretical
calculations are needed to guide the experimental work.
While “nano” has been employed by many researchers as the ultimate solution to many
problems, it does seem to provide significant benefits when applied to thermoelectrics. Time and
more research will tell if this approach is ultimately a viable one.

132

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