COPPER-BASED DIAMOND-LIKE TERNARY SEMICONDUCTORS FOR
THERMOELECTRIC APPLICATIONS
By
Eric John Skoug

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

ABSTRACT
COPPER-BASED DIAMOND-LIKE TERNARY SEMICONDUCTORS FOR
THERMOELECTRIC APPLICATIONS
By
Eric John Skoug
Heightened global concern over greenhouse gas emissions has led to an increased demand for
clean energy conversion technologies. Thermoelectric materials convert directly between thermal
and electrical energy and can increase the efficiency of existing processes via waste heat recovery
and solid-state climate control applications. The conversion efficiency of available thermoelectric
materials and the devices comprised of them is unfortunately quite low, and thus new materials
must be developed in order for thermoelectrics to keep pace with competing technologies. One approach to increasing the conversion efficiency of a given material is to decrease its lattice thermal
conductivity, which has traditionally been accomplished by introducing phonon scattering centers
into the material. These scattering centers also tend to degrade electronic transport in the material,
thereby minimizing the overall effect on the thermoelectric performance. The purpose of this work
is to develop materials with inherently low lattice thermal conductivity such that no extrinsic modifications are required. A novel approach in which complex ternary semiconductors are derived
from well-known binary or elemental semiconductors is employed to identify candidate materials.
Ternary diamond-like compounds, namely Cu2 SnSe3 and Cu3 SbSe4 , are synthesized, characterized, and optimized for thermoelectric applications. It is found that sample-to-sample variations
in hole concentration limits the plausibility of Cu2 SnSe3 as a thermoelectric material. Cu3 SbSe4
is found to be a promising material that can achieve thermoelectric performance comparable to
state-of-the-art materials when optimized. This work uncovers anomalous thermal conductivity in
several Cu-Sb-Se ternary compounds, which is used to develop a set of guidelines relating crystal
structure to inherently low lattice thermal conductivity.

Copyright By
ERIC JOHN SKOUG
2011

DEDICATION
To my loving wife Shannon, who believes in me when I need it most.
To Dad, my hero and role model who taught me that I can achieve anything I set my mind to.
To Connie, Jennica, Evan, and Kryn, who encourage and support me in all that I do.
To Mom, who is with me in memory every day.

iv

ACKNOWLEDGEMENTS
I am extremely grateful to those who have contributed their time and effort to this project. I
would like to thank my advisor and mentor Dr. Donald Morelli for giving me the opportunity
to conduct this research, and my committee members Drs. Jeff Sakamoto, Tim Hogan, and K.
Subramanian for their guidance. I am indebted to my coworkers and lab-mates Jeff Cain, Kevin
Zhou, Chang Liu, Ponns, Hui Sun, Xu Lu, Hao Yang, Steve Boona, and Gloria Lehr for their hard
work and helpful discussions throughout the course of my graduate study. I would also like to
thank my collaborators Paul Majsztrik, Melanie Kirkham, Edgar Lara-Curzio, Chris Wolverton,
Yongsheng Zhang, Bhanu Mahanti, and Dat Do for their valuable contributions.
Finally I would like to acknowledge the funding sources for this project. This work was supported by the National Science Foundation under Award No. NSF-CBET-0754029. In addition,
sample synthesis efforts were partially supported as part of the Center for Revolutionary Materials for Solid State Energy Conversion, an Energy Frontier Research Center funded by the U.S.
Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number
DE-SC0001054. Research through the Oak Ridge National Laboratory’s High Temperature Materials Laboratory User Program was sponsored by the U. S. Department of Energy, Office of Energy
Efficiency and Renewable Energy, Vehicle Technologies Program.

v

TABLE OF CONTENTS

List of Tables

viii

List of Figures

ix

1 Introduction to Thermoelectrics
1.1 Thermoelectric Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Applications For Thermoelectric Devices . . . . . . . . . . . . . . . . . . . . . .
1.3 Thermoelectric Conversion Efficiency . . . . . . . . . . . . . . . . . . . . . . . .

1
1
3
4

2 Approaches to Increasing the Thermoelectric Figure of Merit
2.1 Substitutional Solid Solutions . . . . . . . . . . . . . . . .
2.2 Atomic Rattlers . . . . . . . . . . . . . . . . . . . . . . .
2.3 Low-Dimensional Materials . . . . . . . . . . . . . . . . .
2.4 Ternary Compounds Based on PbTe . . . . . . . . . . . .
2.5 Motivation For The Present Work . . . . . . . . . . . . . .

.
.
.
.
.

8
8
9
10
12
13

3 Synthesis and Characterization Methods
3.1 Materials Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Crystal Structure, Phase Purity, and Microstructural Analysis . . . . . . . . . . . .
3.3 Transport Property Measurements . . . . . . . . . . . . . . . . . . . . . . . . . .

15
15
16
16

4 Rocksalt-Like Cu-Based Ternary Compounds
4.1 Background and Motivation . . . . . . . . .
4.2 Experimental . . . . . . . . . . . . . . . .
4.3 Results and Discussion . . . . . . . . . . .
4.3.1 CuBiSe2 . . . . . . . . . . . . . . .
4.3.2 Cu3 BiSe3 . . . . . . . . . . . . . .
4.3.3 Other Cu-Bi-Se Ternary Compounds
4.4 Summary . . . . . . . . . . . . . . . . . .

.
.
.
.
.
.
.

21
21
22
22
22
26
32
34

.
.
.
.
.
.
.
.
.

36
36
36
38
39
40
41
41
41
48

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.

5 Diamond-Like Cu-Based Ternary Compounds
5.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Why Study Diamond-Like Cu-Based Ternary Compounds? . . . .
5.1.2 Third-Order Ternary Derivatives of II-VI: I2 -IV-VI3 Compounds .
5.1.3 Fourth-Order Ternary Derivatives of II-VI: I3 -V-VI4 Compounds .
5.1.4 Outline for the Present Work . . . . . . . . . . . . . . . . . . . .
5.2 Cu2 SnSe3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . .
5.2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vi

.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

5.3

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

49
49
49
59
60
60
60
63
65
65
65
77
79
79
80
88
90
90
91
104
107

6 The Effect of Lone Electron Pairs on the Lattice Thermal Conductivity of Group
VA Chalcogenides
6.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1 Phase Purity of CuSbSe2 and Cu3 SbSe3 . . . . . . . . . . . . . . . . . .
6.4 The Lattice Thermal Conductivity of CuSbSe2 , Cu3 SbSe3 , and Cu3 SbSe4 . . . .
6.5 The Effect of Lone-Pair Electrons on the Coordination Environment of Sb . . . .
6.6 Generalization to Group VA Chalcogenides . . . . . . . . . . . . . . . . . . . .
6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.
.
.
.
.
.
.
.

111
111
114
115
115
119
119
122
126

5.4

5.5

5.6

5.7

5.8

The Cu2 SnSe3 -Cu2 GeSe3 Solid Solution . . . . . . . . . . . . . . . . . . .
5.3.1 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Cu2 SnSe3 -Cu2 SnS3 Solid Solution . . . . . . . . . . . . . . . . . . . .
5.4.1 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Off-Stoichiometric Cu2 GeSe3 Compounds . . . . . . . . . . . . . . . . . . .
5.5.1 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cu3 SbSe4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.1 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Cu3 SbSe4 -Cu3 SbS4 Solid Soluiton . . . . . . . . . . . . . . . . . . . .
5.7.1 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cu-Based Diamond-Like Ternary Compounds: Conclusions and Future Work

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

7 Conclusions and Future Work

128

References

133

vii

LIST OF TABLES

Table 4.1 Average compositions (determined by EDS) of the light and dark phase regions in the slow cooled Cu3 BiSe3 sample shown above. . . . . . . . . . . . 28
Table 4.2 Average compositions (determined by EDS) of the light and dark phase regions in the quenched Cu3 BiSe3 sample shown above. . . . . . . . . . . . . 29
Table 4.3 Measured and reported room temperature thermoelectric properties of Cu3 BiSe3 29
Table 5.1 Reported thermal conductivities and band gaps for a series of diamond-like
semiconductors with increasing number of atoms per unit cell. . . . . . . . . 38
Table 5.2 EDS compositions of the majority phase for selected Cu2 Ge1+x Se3 compounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Table 5.3 Refined lattice constants for the Cu3 SbSe4-x Sx compounds, estimated standard deviation of the last digit is given in parentheses. . . . . . . . . . . . . . 91
Table 5.4 Phonon-impurity scattering parameters along with calculated (κcalc ) and measured (κexp ) thermal conductivities (in W/m*K) for the Cu3 SbSe4-x Sx compounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Table 5.5 Room temperature properties of the Cu3 Sb1-y Gey Se4-x Sx compounds. . . . 101
Table 6.1 Relative amounts of phases present in Cu3 SbSe3 samples quenched from
500◦ C and 900◦ C in room temperature water. . . . . . . . . . . . . . . . . . 116
Table 6.2 Properties of group VA chalcogenides taken from the literature (continues on
next page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

viii

LIST OF FIGURES

Figure 1.1

Figure 1.2

Figure 1.3

Figure 2.1

Schematic representation of a simple thermocouple composed of metals m1
and m2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

Schematic representation of a thermoelectric unicouple demonstrating the
Seebeck effect (left) and the Peltier effect (right). For interpretation of the
references to color in this and all other figures, the reader is referred to the
electronic version of this dissertation. . . . . . . . . . . . . . . . . . . . . .

3

Conversion efficiency versus hot side temperature for thermoelectric power
generation for several different values of ZT (reproduced from [6]). . . . . .

6

Compositional dependence of the thermal resistivity of GaAs-AlAs alloys.
Reproduced from [13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

Figure 3.1

Sample preparation for direct fusion synthesis. From left to right: stoichiometric quantities of the pure elements, pure elements in quartz ampoule,
evacuating quartz ampoule, sealing quartz ampoule, sealed quartz ampoule
ready to be placed in furnace. . . . . . . . . . . . . . . . . . . . . . . . . . 15

Figure 3.2

Schematic representation of experimental setup used for low temperature
measurements of Seebeck coefficient, electrical resistivity, and thermal conductivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Figure 3.3

Schematic representation of experimental setup used for low temperature
Hall measurements, pictured normal to the sample thickness. . . . . . . . . 20

Figure 4.1

Schematic representation of an as-synthesized CuBiSe2 sample after slowcooling and annealing at 400◦ C (left), XRD pattern of the top portion and
powder diffraction file (PDF) for Cu2 Se (upper right), and XRD pattern of
the lower portion and PDF for Cu1.78 Bi4.73 Se8 . . . . . . . . . . . . . . . . 23

Figure 4.2

XRD pattern of a quenched CuBiSe2 sample and PDF for Cu1.78 Bi4.73 Se8 . 25

Figure 4.3

XRD patterns from Cu3 BiSe3 samples that were (a) slow cooled from
750◦ C to 400◦ C and annealed for 4 days and (b) quenched in water from
750◦ C, along with the reported pattern for rocksalt Cu3 BiSe3 [47]. . . . . . 27

ix

Figure 4.4

EDS X-ray mapping of a slow cooled Cu3 BiSe3 sample. Upper left BSE
image shows the mapped region, remaining images show the distribution
of Cu, Bi, and Se as indicated. . . . . . . . . . . . . . . . . . . . . . . . . 28

Figure 4.5

BSE image of a quenched Cu3 BiSe3 sample, showing phase separation
at the grain boundaries. Dashed line indicates region selected for X-ray
mapping, shown in Figure 4.6 below. . . . . . . . . . . . . . . . . . . . . . 30

Figure 4.6

EDS X-ray mapping of a quenched Cu3 BiSe3 sample. Upper left BSE
image shows the mapped region, remaining images show the distribution
of Cu, Bi, and Se as indicated. . . . . . . . . . . . . . . . . . . . . . . . . 31

Figure 4.7

XRD patterns of CuBi3 Se5 compounds prepared with different starting
compositions as indicated. Lower plot shows the powder diffraction file
(PDF) for
Cu1.78 Bi4.73 Se8 , reported by Makovicky et al [52]. . . . . . . . . . . . . . 33

Figure 4.8

Low temperature thermoelectric properties of CuBi3 Se5 compounds. Compositions of the samples are: #1 - Cu1.6 Bi4.8 Se8 , #2 - Cu1.7 Bi4.7 Se8 , #3 Cu1.78 Bi4.73 Se8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Figure 5.1

X-ray diffraction pattern for Cu2 SnSe3 quenched in water from 900◦ C.
All peaks correspond to the cubic phase, shown at right, where the larger
spheres represent the random arrangement of Cu and Sn atoms on the cation
sublattice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Figure 5.2

X-ray diffraction pattern for Cu2 SnSe3 slow cooled and annealed at 400◦ C.
Inset shows low angle peaks corresponding to the monoclinic structure,
shown at right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Figure 5.3

Temperature dependence of the hole concentration of Cu2 Sn1-x Gax Se3
and
Cu2 Sn1-y Iny Se3 compounds. . . . . . . . . . . . . . . . . . . . . . . . . . 45

Figure 5.4

Low temperature thermoelectric properties of the Cu2 Sn1-x Gax Se3 compounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Figure 5.5

High temperature electronic properties of Cu2 Sn0.975 Ga0.025 Se3 . . . . . . 47

Figure 5.6

X-ray diffraction patterns of quenched Cu2 Sn1-x Gex Se3 compounds, 0 ≤
x ≤ 1.0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

x

Figure 5.7

X-ray diffraction patterns of slow cooled Cu2 Sn1-x Gex Se3 compounds, x
≤ 0.5. Lower plot shows close-up view of low angle peaks indicating monoclinic structure, vertical lines represent reported peak locations for monoclinic Cu2 SnSe3 [65]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Figure 5.8

X-ray diffraction patterns of slow cooled Cu2 Sn1-x Gex Se3 compounds, x
> 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Figure 5.9

Lattice spacing of the Cu2 Sn1-x Gex Se3 compounds with Cu2 SnSe3 -type
structure: (a) lattice parameter of the cubic (quenched) samples, (b) interplanar spacing of the (200) planes of the monoclinic (slow cooled) samples.

53

Figure 5.10 Temperature dependence of the Seebeck coefficient and electrical resistivity of the Cu2 Sn1-x Gex Se3 compounds for x < 0.5 . . . . . . . . . . . . . 54
Figure 5.11 Temperature dependence of the thermal conductivity of the Cu2 Sn1-x Gex Se3
compounds for x = 0 and 0.5. Dotted lines represent lattice thermal conductivity calculated from the Debye model (equation 5.2). . . . . . . . . . . 58
Figure 5.12 X-ray diffraction patterns of the Cu2 SnSe3-x Sx compounds. . . . . . . . . 61
Figure 5.13 Lattice thermal conductivity of the Cu2 SnSe3-x Sx compounds. . . . . . . . 62
Figure 5.14 High temperature thermoelectric properties of Cu2 Sn0.925 In0.075 Se2.1 S0.9

63

Figure 5.15 XRD patterns for slow cooled Cu2 Ge1+x Se3 compounds with negative values of x. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Figure 5.16 Temperature dependence of the electrical resistivity, Seebeck coefficient,
and thermal conductivity for slow cooled Cu2 Ge1+x Se3 compounds with
negative values of x. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Figure 5.17 XRD patterns for the Cu2 Ge1+x Se3 compounds with 0 ≤ x ≤ 0.55. . . . . 68
Figure 5.18 Temperature dependence of the thermoelectric properties of the Cu2 Ge1+x Se3
compounds with 0 ≤ x ≤ 0.55. . . . . . . . . . . . . . . . . . . . . . . . . 69
Figure 5.19 XRD patterns for the Cu2 Ge1+x Se3 compounds with 0.55 ≤ x ≤ 1.0, ”SC”
and ”Q” labels indicate slow cooled and quenched samples respectively. . . 70

xi

Figure 5.20 Temperature dependence of the thermoelectric properties of the Cu2 Ge1+x Se3
compounds with 0.55 ≤ x ≤ 1.0, ”SC” and ”Q” labels indicate slow cooled
and quenched samples respectively. . . . . . . . . . . . . . . . . . . . . . . 71
Figure 5.21 Measured thermal conductivity at 80K (a) and calculated lattice constant
(b) versus Ge content for the (Cu2 Ge1.55 Se3 )1-y Gey solid solution. The
dashed line in (b) represents the linear relation predicted by Vegard’s law.
The data for pure Ge are taken from [45] and [94]. . . . . . . . . . . . . . . 72
Figure 5.22 EDS X-ray mapping of a typical region of a Cu2 Ge1+x Se3 sample. Upper left BSE image shows the mapped region, remaining images show the
distribution of Cu, Ge, and Se as indicated . . . . . . . . . . . . . . . . . . 73
Figure 5.23 EDS composition (at% Ge) versus starting Ge content (x) for Cu2 Ge1+x Se3
compounds. Error bars indicate ±10% error associated with EDS measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Figure 5.24 EDS X-ray mapping of a typical region of a Cu2 Ge2.2 Se3 sample. Upper left BSE image shows the mapped region, remaining images show the
distribution of Cu, Ge, and Se as indicated . . . . . . . . . . . . . . . . . . 76
Figure 5.25 XRD pattern of a Cu3 SbSe4 sample slow cooled from 900◦ C to room temperature, along with the PDF data for Sb2 Se3 and Cu3 SbSe4 . . . . . . . . . 81
Figure 5.26 XRD pattern of a Cu3 SbSe4 sample quenched from 500◦ C to room temperature, along with the PDF data for Cu3 SbSe4 . . . . . . . . . . . . . . . 82
Figure 5.27 EDS X-ray mapping of a typical region of Cu3 SbSe4 (work completed at
ORNL). Upper left image shows a backscattered electron image of a 600µm
x 600µm region, and the distributions of Cu, Sb, and Se in the same region
are shown as indicated (white pixel indicates presence of element). . . . . . 83
Figure 5.28 Temperature dependence of the hole concentration and mobility for Cu3 SbSe4 ,
with and without the post-quench 300◦ C/48 hrs annealing step. Dashed line
indicates the T-3/2 temperature dependence characteristic of carrier scattering by acoustic phonons. . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Figure 5.29 Temperature dependence of the hole concentration and mobility of Cu3 Sb1-x Ax Se4
compounds (A = Ge or Sn). . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Figure 5.30 Temperature dependence of the electronic properties of the Cu3 Sb1-x Ax Se4
compounds (A = Ge, Sn). . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

xii

Figure 5.31 Temperature dependence of the thermal conductivity and dimensionless
thermoelectric figure of merit of the Cu3 Sb1-x Ax Se4 compounds (A = Ge,
Sn). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Figure 5.32 XRD patterns of Cu3 SbSe4-x Sx samples. . . . . . . . . . . . . . . . . . . 92
Figure 5.33 Refined lattice constants of the Cu3 SbSe4-x Sx samples (from Figure 5.32)
versus fractional occupation S (equal to x/4). Dashed lines indicate linear
relationship predicted by Vegard’s law. . . . . . . . . . . . . . . . . . . . . 93
Figure 5.34 Hole concentration and mobility of the Cu3 SbSe4-x Sx compounds. . . . . . 94
Figure 5.35 Temperature dependence of the thermal conductivity of selected Cu3 SbSe4-x Sx
compounds. Dashed lines are the calculated lattice thermal conductivities
obtained from the Debye model. Error bars indicate ±5% experimental error. 95
Figure 5.36 Compositional dependence of the lattice thermal conductivity (κL ) of the
Cu3 SbSe4-x Sx compounds at 80K and 300K. Dashed lines are the calculated lattice thermal conductivities obtained from the Debye model. Error
bars indicate ±5% experimental error. . . . . . . . . . . . . . . . . . . . . 97
Figure 5.37 Ratio of the weighted mobility (U) to lattice thermal conductivity (κL ) versus composition in the Cu3 SbSe4-x Sx system for x≤2. . . . . . . . . . . . 100
Figure 5.38 Temperature dependence of the Seebeck coefficient and Electrical resistivity of the Cu3 Sb1-y Gey Se4-x Sx compounds . . . . . . . . . . . . . . . . . 102
Figure 5.39 Temperature dependence of the thermal conductivity and dimensionless
thermoelectric figure of merit of the Cu3 SbSe4-x Sx compounds . . . . . . . 103
Figure 5.40 High temperature lattice thermal conductivity of the Cu3 SbSe4-x Sx compounds. Dashed line indicates κL calculated from the Debye model for
x=1.2 using γ=1.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Figure 6.1

Temperature dependence of the thermal conductivity of Cu3 SbSe3 (open
symbols) and Cu3 SbSe4 (closed symbols). The electronic contribution is
negligible for all samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Figure 6.2

Backscattered electron images of Cu3 SbSe3 quenched from (a) 900◦ C and
(b) 500◦ C into room temperature water with three phases labeled: A =
Cu2-x Se, B = Cu3 SbSe3 , C = CuSbSe2 . . . . . . . . . . . . . . . . . . . . 116

xiii

Figure 6.3

X-ray mapping on a similar region of the sample shown in Figure 6.2(b). . . 117

Figure 6.4

X-ray diffraction pattern of a Cu3 SbSe3 sample quenched from 900◦ C into
icewater and annealed at 400◦ C for 5 days. . . . . . . . . . . . . . . . . . 118

Figure 6.5

Temperature dependence of the lattice thermal conductivity of CuSbSe2 ,
Cu3 SbSe3 , and Cu3 SbSe4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Figure 6.6

Local coordination environment of Sb in CuSbSe2 , Cu3 SbSe3 and Cu3 SbSe4 .
Shaded lines represent bonds, dotted ovals represent the approximate morphology of the LEP orbital. . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Figure 6.7

Lattice thermal conductivity versus average X-M-X bond angle of the group
VA chalcogenides. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Figure 6.8

Lattice thermal conductivity versus average X-M-X bond angle of the group
VA chalcogenides, separated according to the coordination number (CN) of
the group V atom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

xiv

1
1.1

Introduction to Thermoelectrics
Thermoelectric Effects

The field of thermoelectricity has garnered considerable attention over the past two decades due to
growing concern about carbon-based fuel consumption and greenhouse gas emissions. The principal thermoelectric effects, however, have been known for almost two centuries. In 1821 Thomas
Seebeck discovered that heating a junction between two dissimilar metals produced a potential
difference, and in 1834 Jean-Charles Peltier noted that heat was either absorbed or liberated at said
junction when an electrical current was passed in different directions. These phenomena, known
respectively as the Seebeck and Peltier effects, can be explained qualitatively using a simple thermocouple composed of metals m1 and m2 shown in Figure 1.1 [1].

m1

B

A
m2

D

C

m2

Figure 1.1: Schematic representation of a simple
thermocouple composed of metals m1 and m2 .

If junction A is maintained at a different temperature than junction B, a voltage will develop between points C and D. This effect is quantified by expressing the voltage drop per unit temperature
change:

S=

∆V
∆T

(1.1)

where S is referred to as the Seebeck coefficient. If the circuit is closed at points C and D and an
1

electrical current flows through the loop, heat will be either absorbed or liberated at junctions A
and B depending on the direction of the current. The ratio of the exchanged heat (Q) to the current
in the loop (I) is defined as:

Π=

Q
I

(1.2)

where Π is the Peltier coefficient. The Seebeck and Peltier coefficients demonstrate the same basic
physical process and are related through the simple expression:

S=

Π
.
T

(1.3)

This macroscopic view of the thermoelectric effects is instructive, but it does not provide insight into the fundamental mechanisms behind the effects. For this purpose it is useful to consider
a thermoelectric unicouple composed of one n-type (charge carried by electrons) and one p-type
(charge carried by holes) material, shown in Figure 1.2(a). If one side of the couple is exposed to
a heat source as shown, the charge carriers in the materials become energized at the hot side and
diffuse toward the cold side. This causes a thermally induced voltage to develop across the couple
via the Seebeck effect, and an electrical current I will flow in the direction indicated when a resistive load is connected to the couple. Conversely, an applied clockwise current I will induce the
flow of electrons and holes and generate a temperature difference across the couple via the Peltier
effect, as shown in Figure 1.2(b). In this configuration, the thermoelectric couple acts as a solidstate heat pump. Connecting many thermoelectric couples electrically in series and thermally in
parallel forms a thermoelectric module, which can then be used in one of many applications for
thermoelectric devices.

2

Cooled Surface

Heat Source
_

_
_

_
n

+

_

+
p

n

Cold Side
I

+

_

+

+

+

_

+

_

_

_

+

+

+
p

Heat Dissipated
I

I

I
+ -

Figure 1.2: Schematic representation of a thermoelectric unicouple demonstrating the Seebeck
effect (left) and the Peltier effect (right). For interpretation of the references to color in this and all
other figures, the reader is referred to the electronic version of this dissertation.

1.2

Applications For Thermoelectric Devices

The Seebeck and Peltier effects suggest two distinct applications for thermoelectric devices: power
generation and climate control. The earliest and perhaps most successful application has been the
long-term use of radioisotope thermoelectric generators (RTGs) in NASA’s deep space probes.
RTGs utilize the heat produced by a decaying radioactive material (such as Plutonium-238) to
generate electrical power by way of many thermoelectric modules. These generators demonstrate
the stability and longevity of thermoelectric devices; several deep space probes still in operation
by NASA today (most notably the Voyager probes) were launched over 30 years ago. RTGs are
seldom used for remote power generation in terrestrial applications, mainly due to fears over radioactive contamination should the generator become damaged.
At present, thermoelectric climate control has been utilized only in small-scale applications.
The completely solid-state, motion free cooling provided by a thermoelectric module allows for
temperature regulation of electronic components that are sensitive to vibration. The module’s small
footprint has lead to small-scale refrigeration applications, such as portable picnic coolers that are

3

powered by the auxiliary port in a car. Most recently, thermoelectric devices are being used to
provide localized heating and cooling in automotive seats and cup holders, primarily in high-end
luxury models.
The driving force behind the renewed interest in thermoelectric research is not the specialized
applications mentioned above. Thermoelectrics have the potential to impact the world’s energy
crisis, namely by improving the efficiency of existing processes. In the United States alone, over
half of the energy produced every year is not utilized, but rather lost due to inefficient energy production [3]. In an automobile, for example, only 20-30% of the energy generated by the engine
is used for vehicle operation while the majority of the energy is lost as heat. In this instance, a
thermoelectric generator in contact with the exhaust stream or radiator could transform a portion
of the wasted heat into useable electricity. Calculations have shown that a suitable thermoelectric
generator used in this way could improve fuel economy by up to 4%, a substantial gain [4]. In
addition, current automotive air conditioning systems are required to cool the entire cabin quite
rapidly in order to achieve customer comfort, and therefore typically have enough cooling capacity to cool a small household. Thermoelectric modules strategically placed in the vehicle would
provide targeted cooling rather than full cabin cooling, while simultaneously requiring less power
to operate and eliminating the use of harmful refrigerants. Large-scale thermoelectric applications
are not limited to the automotive sector; other proposed applications include solar thermoelectric
generators (STEGs) which have recently been demonstrated as a promising new route towards solar power generation [5]. The use of thermoelectric technology on a large scale has been frustrated
mainly by the low conversion efficiencies of currently available thermoelectric materials.

1.3

Thermoelectric Conversion Efficiency

The conversion efficiency η of a thermoelectric device is limited to a fraction of its Carnot efficiency (∆T /Th ):

4

∆T
η=
·
Th

√
¯
1 + ZT − 1

(1.4)

¯
1 + Z T + Tc /Th

¯
where Z is a material dependent parameter and T , Th , and Tc are the average operating temperature,
hot side temperature, and cold side temperature, respectively. From equation 1.4 it is clear that the
parameter Z, termed the thermoelectric figure of merit, is the foremost quantity for improving
η. This quantity is commonly multiplied by the operating temperature T and expressed as the
dimensionless thermoelectric figure of merit ZT , given by:

ZT =

S2 σ
·T
κ

(1.5)

where S is the Seebeck coefficient, σ is the electrical conductivity, and κ is the thermal conductivity
of the material. For most applications, a conversion efficiency of more than 20% is required in
order for a thermoelectric device to be competitive with conventional technologies. Figure 1.3
shows that very large values of ZT are required for thermoelectrics to achieve greater than 20%
conversion efficiency. At present, the best thermoelectric materials have ZT on the order of 1 - 1.5,
but with continually increasing activity in thermoelectric materials research, materials with ZT =
2.0 are not out of the question. A material that has ZT ≥ 2 in addition to low raw material and
production costs would justify the large-scale use of thermoelectric power generation and cooling.
The problem with achieving very high values of ZT is that Z is comprised of contraindicated
physical parameters. That is, the constituents of Z cannot be independently varied; changing one
parameter will always affect another. For instance, the total thermal conductivity (κT ) of any
material is composed of contributions from the crystal lattice (κL ) as well as the charge carriers
(κe ):

κT = κe + κL .

5

(1.6)

80

Conversion Efficiency (%)

70

ZT = infinity
(Carnot limit)

60

ZT = 20

50
ZT = 4
40
ZT = 2
30
ZT = 0.7

20
10
0
300

400

500

600

700

800

900

1000

1100

1200

1300

Heat Source Temperature (K)

Figure 1.3: Conversion efficiency versus hot side temperature for thermoelectric power generation
for several different values of ZT (reproduced from [6]).

If the electrical conductivity of the material is increased, the electronic component of the thermal
conductivity will increase proportionally as defined by the Wiedemann-Franz law:

κe = L0 σT

(1.7)

where L0 is the Lorenz number, normally taken to be 2.44×10−8W ΩK −2 . The lattice component
can be reduced by introducing impurities or defects into the crystal lattice, but these will also scatter
electronic charge carriers and negatively affect electronic transport in the material. Furthermore,
there is a lower limit to the lattice thermal conductivity determined by the interatomic spacing.
If one choses to focus solely on the numerator of Z (S2 σ, termed the thermoelectric power fac-

6

tor), equally problematic contradictions are encountered. Assuming a single parabolic band model
with one type of strongly degenerate carrier present, the Seebeck coefficient can be expressed as
[7]:

S=

2
8π2 kB ∗ π 2/3
m T( )
3n
3eh2

(1.8)

where kB is Boltzmann’s constant, e is the electronic charge, h is Planck’s constant, m∗ is the
carrier effective mass, and n is the carrier concentration. Equation 1.8 is called the Pisarenko
relation and illustrates the dependence of the Seebeck coefficient on carrier concentration. The n
dependence of the electrical conductivity is given by:

σ = neµ

(1.9)

where µ is the carrier mobility. It is evident from equations 1.8 and 1.9 that increasing the carrier
concentration of a material (doping) will cause S to decrease and σ to increase, thus minimizing
the overall effect on Z. In addition, a large carrier effective mass will produce a large Seebeck
coefficient but will degrade the carrier mobility according to µ = eτ/m∗ , where τ is the carrier
scattering time.
Despite these challenges, numerous approaches to increasing the thermoelectric figure of merit
have been developed. The following review covers some of the most successful approaches and is
not meant to offer exhaustive coverage of all possible techniques. Most importantly, this review
will highlight a new approach to identifying materials with potentially large thermoelectric figure
of merit and provide motivation for the present work.

7

2
2.1

Approaches to Increasing the Thermoelectric Figure of Merit
Substitutional Solid Solutions

One of the earliest approaches to increasing the thermoelectric figure of merit was to introduce
electrically neutral impurity atoms into the crystal lattice of a given material. This practice is still
widely used today as it provides a fairly simple route to incremental enhancements in ZT . The
main principle behind this approach is that impurity atoms with atomic mass and radius different
than the host atoms will disrupt the periodicity in the crystal lattice and cause increased phonon
scattering, thus reducing the lattice thermal conductivity. The increase in ZT arises due to the fact
that the impurity atoms typically scatter phonons to a larger extent than charge carriers, causing a
larger disruption in thermal rather than electrical transport.
The thermal conductivity of solid solutions was studied extensively by Ioffe, who first applied the approach to thermoelectric materials [8], [9]. He noted that the presence of impurity
atoms always decreased the thermal conductivity more than the carrier mobility due to the shorter
wavelength of phonons as compared to electrons. Typically, two compounds with similar crystal
structures are chosen such that the composition can be varied continuously without inducing structural transformations or impurity phase formation. The thermal conductivity of the zincblende
Ga1-x Alx As alloys, shown as thermal resistivity (κ−1 ) in Figure 2.1, illustrates this concept. For
a mixture of GaAs and AlAs crystals, one would expect the thermal resistivity to follow a linear
relation, indicated by the dashed line, as defined a simple rule of mixtures. The disordered arrangement of Ga and Al atoms on the metal sublattice causes increased phonon scattering, leading to the
large increase in thermal resistivity for the intermediate compositions. Many of the best thermoelectric materials to date come from solid solutions of two compounds, including the PbTe-PbSe,
Si-Ge, and Bi2 Te3 -Bi2 Se3 systems [10] - [12].

8

Thermal Resistivity (cm*K/W)

10
9
8
7
6
5
4
3
2
1
0
0

0.2

0.4

0.6

0.8

1

AlAs Fraction
Figure 2.1: Compositional dependence of the thermal resistivity of GaAsAlAs alloys. Reproduced from [13].

2.2

Atomic Rattlers

Materials with large voids in their crystal structures are ideal candidates for thermoelectric applications, particularly because of their ability to accommodate heavy ”rattling” atoms. Here the
lattice thermal conductivity is again reduced by the presence of impurity atoms, but in this case the
impurity atoms reside in interstitial atomic sites rather than substituting for host atoms as in solid
solutions. This approach was first proposed by Slack [14], who noted that void-filling atoms in the
skutterudite crystal structure possessed large thermal vibration parameters [15] and postulated their
ability to scatter phonons and reduce κL . This idea prompted a vast undertaking of research on the
skutterudite material system, which has led to one of the most successful classes of thermoelectric
materials to date.

9

Skutterudites, typified by the naturally occurring mineral CoAs3 , had been known for many
years but were not seriously considered for thermoelectric applications until the mid-1990s when
Morelli et. al. showed that their lattice thermal conductivity could be reduced by more than an
order-of-magnitude by filling the atomic ”cages” with rare earth atoms[16]. It was later shown
that while the weakly-bound filling atoms effectively scatter phonons, the covalently-bound metalantimony framework maintains the high carrier mobility of the binary skutterudite antimonides,
leading to high ZT values at elevated temperatures [17]. Skutterudites can be doped both n and
p-type and are currently some of the best available thermoelectric materials for power generation,
with reported ZT values in excess of 1.7 [18].
Shortly after the discovery of filled-skutterudite thermoelectric materials, work began on another class of cage-structure compounds termed clathrates. These compounds are structurally similar to certain phases of ice where guest atoms reside in cages formed by the water molecules.
Nolas et. al. first realized the potential of semiconducting Ge clathrates for thermoelectric applications, and reported very low thermal conductivity for compounds of the form Sr8 Ge46 [19]. The
glass-like thermal conductivity in these compounds is attributed to strong phonon scattering from
the ”rattling” of the Sr2+ ion inside the Ge cage, much the same as the skutterudite compounds. ZT
values as high as 1.35 have been reported for Ge clathrate compounds; current research is focused
on clathrate compounds with Si or Sn as the group IV element to replace costly Ge [20], [21].

2.3

Low-Dimensional Materials

The effect of material dimensions on thermoelectric properties was first studied several decades
ago after Goldsmid and Penn noted that phonon scattering at grain boundaries can become appreciable in solid solutions, where heat is carried primarily by low frequency phonons [22]. Early
experimental studies focused on fine-grained Si-Ge alloys [23] and showed that ZT can be increased due to the reduction in κL . The problem is that both phonons and electrons are scattered
at grain boundaries, so typically only small ZT improvements can be achieved. In addition, for
10

high temperature materials, grain growth will likely occur due to long-term exposure to high operating temperatures. Thus, recent work is focused primarily on fine-grained Bi2 Te3 alloys for low
temperature applications [24], [25].
The most significant justification for low-dimensional thermoelectric materials came in 1993
when Hicks and Dresselhaus showed that carrier confinement in quantum structures could lead
to improved thermoelectric properties [26]. The basis of their theory relies on the fact that as the
dimensionality of a system decreases, carrier confinement produces sharp features in the electronic
density of states that can be exploited to effectively ”decouple” S, σ and κ, resulting in extremely
high ZT values. Positioning the Fermi level near one of these features leads to a high thermoelectric
power factor since S is proportional to the energy dependence of the density of states and σ is
proportional to the number of available states. The reduced dimensions and increased number of
interfaces will alter the phonon characteristics of the material and cause low κL in addition to the
high power factor.
This principle has been demonstrated on laboratory-scale quantum structures, most notably on
PbTe quantum-dot superlattices that were reported to have ZT values exceeding 3 at elevated temperatures [28]. Although this result is quite amazing, these structures are complicated and expensive to produce and are not practical for large-scale applications. Thus over the past several years
a major effort has been devoted to producing bulk thermoelectric materials with similar properties.
The most common method is to introduce nanoscale inclusions into a bulk thermoelectric material
thereby forming a nanocomposite that takes advantage of both the carrier confinement and phonon
scattering properties of low-dimensional materials [29]. Another approach is to search for bulk
materials that inherently have sharp features in their density of states. This has been demonstrated
in the intermetallic compounds CoSi and Fe2 VAl, both of which have high thermoelectric power
factors, although they are plagued by high thermal conductivity and thus low ZT values [30], [31].

11

2.4

Ternary Compounds Based on PbTe

To this point, the discussion on improving the thermoelectric figure of merit has focused on means
of modifying well known materials. The approaches mentioned above aim to decouple the thermal
and electrical transport properties of a given material in order to increase ZT . Most frequently, this
is accomplished by introducing phonon scattering centers into the material to reduce the lattice
thermal conductivity. Unfortunately, phonon and electron scattering centers are often one in the
same and only incremental improvements to ZT can be achieved. An alternative approach is to
search for materials with low intrinsic thermal conductivity; that is, they require no modification
in order to achieve lattice thermal conductivity in the range appropriate for thermoelectric applications. The ternary compounds AbSbTe2 and AgSbSe2 have demonstrated this quality and thus
received considerable attention for thermoelectric applications.
Schematically, these compounds are derived from PbTe by way of atomic substitution on the
cation sublattice. Consider two unit cells of PbTe (Pb2 Te2 ), now simply replace the Pb2+ ions with
Ag1+ and Sb3+ ions in equal proportions thereby forming the ternary compound AgSbTe2 . Since
charge balance is maintained, AgSbTe2 retains that rocksalt crystal structure of PbTe but with two
distinct atomic species Ag and Sb on the Pb sublattice. This method of deriving ternary compounds
was pioneered by Goodman and Douglas, who found that compounds of the form I-III-VI2 maintained a diamond-like crystal structure very similar to their binary II-VI and III-V counterparts
(This notation will be used in the text to refer to families of compounds; roman numerals indicate
the group of the periodic table and subscripts indicate stoichiometry) [32]. Subsequently, a host of
ternary [33], [34] and quaternary [35] compounds derived in this fashion were reported.
Early studies on AgSbTe2 and AgSbSe2 reported very low thermal conductivity [36], [37] and
ZT approaching 1.3 at 720K for the telluride [38], but these early samples were likely multiphase
[39]. Recent studies have reported single phase samples [40] with ZT values approaching 1.2 at
400K [41]. In addition, compounds in the AgSbTe2 -PbTe solid solution have shown ZT = 2.2 at
800K, the largest figure of merit for any bulk thermoelectric material [42], although it has since
12

been shown that these compounds are essentially nanocomposites rather than true solid solutions
[43].
Essential to the success of the thermoelectric AgSbX2 compounds is their low intrinsic thermal
conductivity. The low and temperature independent lattice thermal conductivity of AgSbTe2 (0.7
W/m*K at 300K) is characteristic of an amorphous material and has been the subject of several
investigations [37], [44]. The low thermal conductivity of AgSbTe2 arises due to intrinsic anharmonicity in the lattice caused by its crystal structure and interatomic bonding. AgSbTe2 has twice
as many atoms per unit cell (n) as its parent compound PbTe which, from the empirical relationship
κL ∝ n−2/3 derived by Slack [45], accounts for the difference in thermal conductivity between
these isostructural compounds. Octahedral coordination in the rocksalt structure contributes to the
anharmonicity in the lattice since each atom has 6 nearest neighbors, leaving little room for thermal vibration. Finally, the Sb ion is nominally in the trivalent state which means that the Sb 5s2
electrons are not involved in bonding. These ”lone-pair” electrons around adjacent Sb ions can
then interact with neighboring atoms, causing increased anharmonicity as compared to AgInTe2
where all of the valence electrons of In3+ form bonds with neighboring atoms.

2.5

Motivation For The Present Work

The recent triumphs of AgSbTe2 and its related compounds warrant further exploration in this
area. One major drawback of AgSbTe2 is a high raw material cost; both Ag and Te are very costly
and replacements are needed in order for cost effective production. In the present work, only
compounds that contain Cu as the group I element and Se or S as the group VI element are explored.
In the following chapters, a comprehensive study of three approaches to producing new Cu-based
ternary semiconductors for thermoelectric applications is presented. Chapter 4 covers Cu-based
rocksalt structure ternary compounds, essentially following the same approach used for AgSbTe2 .
Very few Cu-based rocksalt compounds have been reported, and none have been investigated for
thermoelectric applications.
13

In Chapter 5 this approach is expanded to diamond structure compounds, where there exists a
host of Cu-based diamond-like ternary semiconductors that have remained essentially unexplored
for thermoelectric applications. Another advantage of these compounds is that higher-order substitutions are possible, which means that diamond-like compounds with larger number of atoms per
unit cell can be formulated. This represents a potential for the discovery of ternary semiconductors
with very low lattice thermal conductivity.
Finally in Chapter 6 the influence of lone-pair electrons on lattice thermal conductivity is investigated. The wealth of Cu-based ternary compounds presents a unique opportunity to study
this effect, for which there is essentially no definitive evidence. A direct correlation between lonepair electrons and low lattice thermal conductivity could provide a new design criteria for high
efficiency thermoelectric materials.

14

3

Synthesis and Characterization Methods

The synthesis and characterization methods employed in this work were similar for all materials
studied. Characterization techniques are held constant for all materials systems in order to facilitate comparison, while small variations in the synthesis procedure will be described separately in
subsequent chapters.

3.1

Materials Synthesis

All materials were synthesized using direct fusion in evacuated quartz ampoules. Stoichiometric
quantities of the pure elements (typically >99.999%, Alfa Aesar Puratronic c ) were placed in
quartz ampoules (8mm inner diameter) and evacuated to <10-5 Torr. A methane-oxygen torch
was then used to seal the elements under vacuum, as shown in Figure 3.1.

Figure 3.1: Sample preparation for direct fusion synthesis. From left to right: stoichiometric
quantities of the pure elements, pure elements in quartz ampoule, evacuating quartz ampoule,
sealing quartz ampoule, sealed quartz ampoule ready to be placed in furnace.

The sealed ampoules were then hung vertically in a digitally-controlled furnace and subjected
to a precise temperature profile determined from phase diagrams (if available) or literature data.
All of the materials studied here were heated slowly (0.4◦ C/min, to accommodate the high vapor
pressure of Se and S) to 750 - 900◦ C, held for 12 hours, and cooled to room temperature. Cooling
was achieved by either maintaining a constant cooling rate in the furnace or quenching the ampoule
in water, the details of which will be discussed later. In some cases, powder processing was
15

used to produce high-quality samples for transport property measurements, as will be described in
subsequent chapters.

3.2

Crystal Structure, Phase Purity, and Microstructural Analysis

The first step in characterizing the samples was to determine the phase purity and the crystal
structures of the phases present. A portion of each sample was pulverized using a mortar and
pestle and deposited onto a glass slide for X-ray diffraction (XRD) analysis. A Rigaku Miniflex II
X-ray diffractometer (Cu Kα radiation, λ=0.154 nm) was used to evaluate the crystal structures of
the majority phases. XRD patterns were analyzed using the Jade 9.0 sofware package, equipped
with the JCPDS XRD pattern database. Differential scanning calorimetry (DSC 200 F3 Maia c
from Netzsch) was employed to detect impurity phases below the detection limit of XRD, and also
to measure the melting temperature and heat capacity of the samples.
Scanning electron microscopy (SEM) was used to investigate samples with complicated microstructures that could not be reliably evaluated by XRD or DSC. For certain samples, microscopy
was performed at Oak Ridge National Laboratory using a Hitachi S3400 environmental SEM
equipped with backscattered electron (BSE) and secondary electron (SE) detectors, as well as
energy dispersive x-ray spectroscopy (EDS) instrumentation and software for elemental analysis.
The majority of the SEM analysis was completed at the Michigan State University Center for Advanced Microscopy (MSU CAM) using a JEOL 6400V SEM with BSE, SE, and EDS capabilities.
The microscope used for each sample will be indicated in the text. Samples for microscopy were
polished flat and mounted using carbon tape.

3.3

Transport Property Measurements

Samples for thermal and electrical transport measurements were cut to the appropriate dimensions
using a diamond saw. Low temperature (80-300K) Seebeck coefficient, electrical resistivity, and

16

thermal conductivity measurements were conducted simultaneously on rectangular parallelepiped
samples (approximately 3×3×6 mm) in a Janis model ST-100 cryostat cooled with flowing liquid
nitrogen. A silver-filled epoxy was used to fix one end of the sample to a copper block, the
other end to a 800-1000 Ω metal-film resistor, and two thin copper strips along the length of the
sample (see Figure 3.2). Two thermocouples made from copper and constantan wires (<0.1mm
diameter) were soldered directly to the copper strips. Electrical resistivity (ρ) was measured using
a standard 4-point probe DC technique (IS represents current supplied to the sample), utilizing
the two copper leads of the thermocouples as the voltage probes. The Seebeck coefficient (S) and
thermal conductivity (κ) were measured simultaneously by passing a current through the metalfilm resistor (IH ), thereby generating a temperature gradient (∆T ) through the sample, and waiting
for the system to reach steady-state (∆T constant). The Seebeck coefficient was then calculated as
follows:

S=

∆V
∆T

(3.1)

where ∆V is the thermally induced voltage (Seebeck voltage) measured using the copper leads of
the thermocouples. The measured thermoelectric voltage includes a contribution due to the leads,
but because of the large Seebeck coefficients of the samples, this contribution is generally less than
1% of the total. The thermal conductivity was calculated according to:
I V l
κ= H H
∆T s

(3.2)

where VH , l, and s are the measured voltage across the resistor, distance between the thermocouples, and sample cross sectional area, respectively. All measurements were conducted under
vacuum (< 10-5 torr) to minimize radiation losses. A standard fused quartz sample was used as a
calibration standard for thermal conductivity, and the thermal conductivity data reported here have
been corrected for parasitic and radiation heat losses. Labview c software was used for automated

17

IH
800Ω
metal-film
resistor

coppe
r
IS

antan
const
coppe
r

sample

antan

const

copper block
Figure 3.2: Schematic representation of experimental setup used for low temperature measurements of Seebeck coefficient, electrical resistivity, and thermal conductivity.

data collection.
High temperature (300-1073K) electrical resistivity and Seebeck coefficient measurements
were performed using the ULVAC ZEM-3 measurement system. Parallelepiped samples (approximately 3×3×6 mm) were used for the measurements. The ends of the sample were clamped
between nickel electrodes, and two spring-loaded type R thermocouples were placed along the
length of the sample (approximately 3 mm apart). Resistivity was measured using a standard 4point probe DC technique, utilizing the thermocouples as voltage probes. The Seebeck coefficient
was measured by generating a localized temperature gradient through the sample and measuring
both the voltage drop and the temperature difference between the thermocouples. All measurements were performed under vacuum (backfilled with high purity He) to minimize conduction

18

and convection losses, and the instrumentation was calibrated using a standard constantan sample.
High temperature thermal conductivity data were calculated from thermal diffusivity (α, measured
using LFA-457 from Netzsch), specific heat capacity (c p , measured using DSC 200 F3 Maia from
Netzsch, ASTM E1269-05 method), and density (ρo , measured using Archimedes method) measurements according to:

κ = α · c p · ρ.

(3.3)

Thermal diffusivity measurements were conducted on thin plate samples (∼ 1mm thickness) and
density and specific heat measurements were conducted on small (<100 mg) sections of material.
Low temperature (50-300K) Hall effect measurements were carried out using one of two similar systems. In both cases thin plate samples (approximately 3×8×1 mm) were used, and all
connections were made using thin (0.127 mm diameter) silver wire and a silver-filled adhesive.
A constant magnetic field was applied in the direction normal to the sample plane while an AC
current was passed along the length of the sample, and the transverse voltage (Hall voltage, VH in
Figure 3.3) was measured across the width of the sample. The Hall coefficient (RH ) was calculated from the slope of the Hall voltage versus field curve. The electrical resistivity was measured
simultaneously by monitoring the sample voltage (VS ) in the absence of a magnetic field. The
carrier concentration (n) and mobility (µ) were then calculated from:
1
ne

(3.4)

1
neµ

(3.5)

RH =
and

ρ=
where e is the electronic charge 1.602×10-19 C.

The Versalab measurement system (Quantum Design) utilized a superconducting magnet (-3
19

VH

VS

IS

B
Figure 3.3: Schematic representation of experimental setup used for
low temperature Hall measurements, pictured normal to the sample
thickness.

to 3 Tesla) and a closed-loop He compressor to achieve the proper measurement environment. The
MultiView c software package was used for data collection. The other system utilized a liquid
nitrogen cooled Janis model ST-300 cryostat and a water-cooled electromagnet (-2.5-2.5 Tesla)
to achieve the measurement environment. A LakeShore model 370 AC resistance bridge and the
LabView c software package were used for data collection.

20

4
4.1

Rocksalt-Like Cu-Based Ternary Compounds
Background and Motivation

With the success of AgSbTe2 and its related compounds, the logical first step is to investigate
Cu-based ternary compounds with rocksalt-like crystal structures as a low cost alternatives to Agbased thermoelectrics. Although no Cu-based rocksalt-like ternary compounds have been reported
for thermoelectric applications, several have been mentioned in the literature. Zhuze et. al. [34]
reported that the compound CuBiSe2 had a rocksalt-like structure (similar to AgSbTe2 ) with a =
0.569 nm and later Spitzer [46] reported a low room temperature lattice thermal conductivity (1.1
W/mK) for the same compound. Subsequently, three separate investigations into the Cu-Bi-Se
ternary system have found no evidence of a CuBiSe2 phase [47]-[49].
Two of the three reports on the Cu-Bi-Se ternary system identified a different composition,
Cu3 BiSe3 , as having a rocksalt-like crystal structure with a = 0.587 nm [47], [48]. Spitzer [46]
and Pollak et. al. [50] reported a low room temperature lattice thermal conductivity (1.1 W/mK)
for this compound. In contrast, Karup-Moller found no evidence of a phase corresponding to
Cu3 BiSe3 . Karup-Moller and Garcia agree on the existence of the ternary compound with nominal composition CuBi3 Se5 (Garcia uses Cu1.6 Bi4.8 Se8 ), which was identified by Karup-Moller
as Cu1.7 Bi4.7 Se8 . Makovicky et. al. later refined the composition and crystal structure of this
compound as Cu1.78 Bi4.73 Se8 (monoclinic, space group C2/m [52]). Although this compound
does not have the rocksalt crystal structure, it is investigated here for completeness. The contradicting reports in the literature regarding rocksalt-like CuBiSe2 and Cu3 BiSe3 along with their
apparently low lattice thermal conductivities prompted the present investigation into the Cu-Bi-Se
ternary system.

21

4.2

Experimental

All samples studied here were synthesized by direct fusion at 750◦ C as described in section 3.1.
Since no synthesis information or phase diagrams are available for CuBiSe2 , samples were cooled
either by quenching in water from 750◦ C or by slow cooling from 750◦ C to 400◦ C at 0.3◦ C/min,
annealing for 48-96 hours, and cooling to room temperature at 0.3◦ C/min. The phase diagram
produced by Garcia et. al. indicates that Cu3 BiSe3 forms via a peritectic reaction at 588◦ C
[48], and thus samples were prepared by quenching in water to avoid the formation of secondary
phases. Samples were also prepared by slow cooling and annealing (as described for CuBiSe2 )
for comparison. Samples with composition CuBi3 Se5 (or Cu1.6 Bi4.8 Se8 ), Cu1.7 Bi4.7 Se8 , and
Cu
Bi
Se were prepared by slow cooling from 750◦ C to room temperature at 0.3◦ C/min.
1.78

4.73

8

All samples for SEM analysis were cut from the ingots, polished flat, and studied using the JEOL
6400V microscope (MSU CAM). Samples for transport property measurements were cut directly
from the ingots.

4.3

Results and Discussion

4.3.1

CuBiSe2

Samples prepared with the starting composition CuBiSe2 formed different phases depending on
the synthesis method. Upon slow cooling to 400◦ C and annealing, the samples solidified in two
separate regions of the ampoule as shown in Figure 4.1. XRD revealed the top portion to be single˚
phase α-Cu2 Se, which has the rocksalt structure with a = 5.84 A (upper right, Figure 4.1) [53],
while the bottom portion was composed of Cu1.78 Bi4.73 Se8 , which has a monoclinic structure
with a = 1.3759 nm, b = 0.41684 nm, c = 1.4683 nm, and β = 115.61◦ (lower right, Figure 4.1)
[52].
The separation of Cu2 Se and Cu1.78 Bi4.73 Se8 indicates that these phases are completely immiscible, which likely caused the crystallization in separate portions of the ampoule during slow
22

Relative Intensity (arb. Units)

Cu2Se
PDF#01-088-2044

10

30

50

70

Relative Intensity (arb. Units)

2θ (degrees)

10

Cu1.78Bi4.73Se8
PDF#01-075-3551

20

30

40

50

60

70

80

2θ (degrees)

Figure 4.1: Schematic representation of an as-synthesized CuBiSe2 sample after slow-cooling
and annealing at 400◦ C (left), XRD pattern of the top portion and powder diffraction file (PDF)
for Cu2 Se (upper right), and XRD pattern of the lower portion and PDF for Cu1.78 Bi4.73 Se8 .

23

cooling from 750◦ C. It is interesting to note that the lattice parameter of the Cu2 Se phase is similar
to that reported for CuBiSe2 by Zhuze et. al. [34]. Although they do not give specific synthesis
details, it is mentioned that their samples were synthesized in evacuated quartz ampules that were
drawn slowly out of a furnace to obtain large crystals. Based on the results above, the slow removal
of a CuBiSe2 sample from the furnace would more than likely result in formation of Cu2 Se and
Cu1.78 Bi4.73 Se8 crystals in different portions of the ampoule. If a Cu2 Se crystal was selected
by Zhuze for XRD analysis, it is possible that this binary compound was mistakenly identified as
CuBiSe2 .
In an attempt to avoid phase separation, several samples were prepared by quenching from
750◦ C into water. These samples solidified in one piece as expected, but XRD revealed them to
be multiphase (see Figure 4.2). Quenched samples were composed primarily of Cu1.78 Bi4.73 Se8 ,
along with a smaller portion of the high temperature phase of Cu2 Se (β-Cu2 Se, monoclinic, a = c
= 1.230 nm, b = 4.074 nm, β = 120◦ [53]). Annealing the quenched samples for periods of up to
2 weeks at moderate temperatures (250 - 400◦ C) had no effect on the multiphase microstructure.
From these results it is concluded that a CuBiSe2 rocksalt structure phase is not a thermodynamically stable compound.

24

Relative Intensity (Arb. units)

Cu1.78Bi4.73Se8
PDF#01-075-3551

10

20

30

40

50
2! (o)

60

70

80

90

Figure 4.2: XRD pattern of a quenched CuBiSe2 sample and PDF for
Cu1.78 Bi4.73 Se8 .

25

4.3.2

Cu3 BiSe3

Samples prepared with the starting composition Cu3 BiSe3 formed multiple phases regardless of
the synthesis method. Samples slow cooled from 750◦ C to 400◦ C at 0.1◦ C/min, annealed for 4
days, and cooled to room temperature at 0.1◦ C/min had a distinctly different XRD pattern than
those quenched in water from 750◦ C to room temperature, as shown in Figure 4.3(a) and (b).
Clearly neither of these samples have the single-phase rocksalt structure reported by Golovei (Figure 4.3(c) [47]), but in both patterns (a) and (b) the reported peaks all appear to be present. The
remaining peaks in both patterns could not be indexed using the computer software, therefore
these samples were examined using scanning electron microscopy (backscattered electron (BSE)
imaging) and energy dispersive X-ray sepctroscopy (EDS).
The EDS X-ray map of slow-cooled Cu3 BiSe3 sample shown in Figure 4.4 clearly indicates
the presence of two phases. The BSE image (upper left, Figure 4.4) shows light and dark regions,
indicating differences in average atomic mass. The X-ray maps indicate that the light regions are
Bi-rich whereas the dark regions are Bi-poor (white pixel indicates that the element was detected,
black pixel indicates that the element was absent). The average compositions of the light and
dark regions are given in Table 4.1, neither of which correspond to Cu3 BiSe3 . The compositions
indicate that Cu, Bi, and Se are present in both of the regions, but neither correlate to any known
ternary phase in the Cu-Bi-Se system. This could mean that this sample contains a finer distribution
of binary Cu-Se and Bi-Se phases than detected here, but since this multiphase microstructure is
stable even after extended annealing it was not investigated further.
The BSE image of a quenched Cu3 BiSe3 sample (Figure 4.5) appears to be nearly single phase,
with only a small amount of a light phase which is concentrated primarily at the grain boundaries.
EDS analysis of the grain boundary region (Figure 4.6) shows that the light region is slightly Birich and Cu-poor while the surrounding dark region appears to contain an even distribution of Cu,
Bi, and Se. The compositions of the light and dark regions given in Table 4.2 confirm that the grain
boundary region does contain a second phase with Cu, Bi, and Se present. The majority phase,
26

Relative Intensity (Arb. units)

(a)
slow cooled

(b)
quenched

(c)
reported

10

20

30

40

50

60

70

80

90

2! (degrees)

Figure 4.3: XRD patterns from Cu3 BiSe3 samples that were (a)
slow cooled from 750◦ C to 400◦ C and annealed for 4 days and (b)
quenched in water from 750◦ C, along with the reported pattern for
rocksalt Cu3 BiSe3 [47].

27

Cu3BiSe3 (slow cooled)

BSE

Cu K!1

Bi L!1

500µm

Se K!1

Figure 4.4: EDS X-ray mapping of a slow cooled Cu3 BiSe3 sample.
Upper left BSE image shows the mapped region, remaining images
show the distribution of Cu, Bi, and Se as indicated.

Table 4.1: Average compositions (determined by EDS) of the light
and dark phase regions in the slow cooled Cu3 BiSe3 sample shown
above.

Element
Cu
Bi
Se

Average Composition (at%)
Dark Region
Light Region
38.3%
28.0%
15.9%
35.8%
45.8%
36.2%

28

Table 4.2: Average compositions (determined by EDS) of the light
and dark phase regions in the quenched Cu3 BiSe3 sample shown
above.

Element
Cu
Bi
Se

Average Composition (at%)
Dark Region
Light Region
24.2%
41.4%
31.8%
15.6%
44.0%
43.0%

Table 4.3: Measured and reported room temperature thermoelectric
properties of Cu3 BiSe3
Property
Seebeck Coefficient (µV/K)

This Work
41.7

Pollak et. al. [50]
40.0

Electrical Resistivity (mΩ*cm)

5.2

3.0

Thermal Conductivity (W/m*K)

0.8

1.1

however, has a composition very near stoichiometric Cu3 BiSe3 . This indicates that, in contrast
to Karup-Moller [49], the ternary compound Cu3 BiSe3 does exist although based on the XRD
pattern in Figure 4.3(b) it likely has a more complex crystal structure than rocksalt. The room
temperature thermoelectric properties of the quenched Cu3 BiSe3 sample, given in Table 4.3, are
in reasonable agreement with those reported by Pollak et. al. [50]. The compound possesses a very
low thermal conductivity but poor electronic properties and thus ZT values not exceeding 0.013 at
room temperature. The microstructure remained the same after extended periods of annealing at
intermediate temperatures, and the thermoelectric properties were not improved. In particular, the
very low Seebeck coefficient in this compound could not be increased by extended annealing or
small compositional variations, which eliminates the possibility of optimizing the thermoelectric
properties through doping.

29

Cu3BiSe3 (quenched)

300µm
Figure 4.5: BSE image of a quenched Cu3 BiSe3 sample, showing
phase separation at the grain boundaries. Dashed line indicates region selected for X-ray mapping, shown in Figure 4.6 below.

30

Cu3BiSe3 (quenched)

BSE

Cu K!1

Bi L!1

60µm

Se K!1

Figure 4.6: EDS X-ray mapping of a quenched Cu3 BiSe3 sample.
Upper left BSE image shows the mapped region, remaining images
show the distribution of Cu, Bi, and Se as indicated.

31

4.3.3

Other Cu-Bi-Se Ternary Compounds

The exact composition and crystal structure of the CuBi3 Se5 phase has been the subject of some
debate in the literature. Garcia et. al. first identified the phase as Cu1.6 Bi4.8 Se8 (triclinic, P1,
˚
˚
˚
a = 4.168 A, b = 7.182 A, c = 13.39 A, α = 85.27◦ , β = 81.15◦ , γ = 73.16◦ [48]), Karup-Moller
reported Cu1.7 Bi4.7 Se8 without giving crystallographic data [49], and most recently Makovicky
˚
˚
et. al. found evidence of Cu1.78 Bi4.73 Se8 (monoclinic, C2/m, a = 13.759 A, b = 4.168 A, c =
˚
14.683 A, and γ = 115.61◦ [52]). Samples with each of the above compositions were synthesized
by cooling slowly from 750◦ C, and in all cases their crystal structure corresponded to that of
Cu1.78 Bi4.73 Se8 , as shown in Figure 4.7. This result suggests that the CuBi3 Se5 compound has a
relatively large phase region and thus can tolerate minor changes in composition.
The thermoelectric properties of these compounds are shown in Figure 4.8. All samples exhibited p-type conduction as evidenced by their positive Seebeck coefficients. The temperature
dependence of the resistivity is characteristic of a heavily doped semiconductor, in agreement with
the relatively modest room temperature Seebeck coefficients. More interestingly, the temperature
dependence of the lattice thermal conductivity (the electronic contribution is negligible as calculated from the Weidemann-Franz law) is characteristic of an amorphous material, and is well below
1 W/m*K for all samples over the entire temperature range. For a typical crystalline material, the
lattice thermal conductivity will increase rapidly with decreasing temperature as T-1 due to vanishing phonon-phonon scattering processes. For these compounds, there is clearly an inherent
anharmonicity in the lattice that strongly scatters phonons and limits their mean free path even at
low temperatures. Considering the nominal composition CuBi3 Se5 , a simple valence assessment
reveals that the Bi atoms should be in the 3+ valence state. Thus, as in the case of AgSbTe2 , it is
possible that the nonbonding lone-pair electrons around Bi contribute to increased anharmonicity
in the lattice, which will be revisited in Chapter 6.
Despite very low thermal conductivity, the CuBi3 Se5 compounds have low ZT values at room
temperature, mainly because of their large electrical resistivity. Rigorous doping studies were not
32

Relative Intensity (Arb. units)

Cu1.78Bi4.73Se8

Cu1.7Bi4.7Se8

Cu1.6Bi4.8Se8
Cu1.78Bi4.73Se8
PDF#01-075-3551

10

20

30

40

50
60
2! (degrees)

70

80

90

Figure 4.7: XRD patterns of CuBi3 Se5 compounds prepared with
different starting compositions as indicated. Lower plot shows
the powder diffraction file (PDF) for Cu1.78 Bi4.73 Se8 , reported by
Makovicky et al [52].

performed on these compounds since their Seebeck coefficients were already low (∼70 µV/K at
300K) without any doping.

33

60
40
#1
#2
#3

20
0

Total Thermal Conductivity
(W/m*K)

Seebeck Coefficient (µV/K)

80

0.016

0.025

0.012

0.02
ZT

Resistivity (!*cm)

0.03

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0.015
0.01

0.008
0.004

0.005
0

0
50

150

250

350

Temperature (K)

50

100

150

200

250

300

350

Temperature (K)

Figure 4.8: Low temperature thermoelectric properties of CuBi3 Se5 compounds. Compositions
of the samples are: #1 - Cu1.6 Bi4.8 Se8 , #2 - Cu1.7 Bi4.7 Se8 , #3 - Cu1.78 Bi4.73 Se8 .

4.4

Summary

From this portion of the work it is concluded that the previously reported ternary Cu-based rocksaltlike compounds do not exist. Following the procedure of AgSbTe2 , the Cu-V-VI2 family of compounds were investigated focusing on CuBiSe2 , which was reported as having the rocksalt-like
structure. Samples of CuBiSe2 prepared by slow cooling crystallized in two separate regions of
the ampoule, the upper portion corresponding to rocksalt α-Cu2 Se and the lower portion corresponding to monoclinic Cu1.78 Bi4.73 Se8 . The authors that reported rocksalt-like CuBiSe2 used a
slow-cooling synthesis procedure and likely selected an α-Cu2 Se crystal for XRD analysis, leading them to believe that their CuBiSe2 sample had the rocksalt structure. Quenched samples of
CuBiSe2 contained primarily Cu1.78 Bi4.73 Se8 along with smaller amounts of β-Cu2 Se. The presence of Cu1.78 Bi4.73 Se8 provides an explanation for the reported low thermal conductivity of
34

CuBiSe2 , since Cu1.78 Bi4.73 Se8 has a very low thermal conductivity.
The other ternary Cu-based rocksalt-like compound reported in the literature, Cu3 BiSe3 , was
investigated in a similar fashion. Samples prepared by slow cooling and quenching had distinctly
different XRD patterns, neither of which were readily indexed using the JCPDS database. SEM and
EDS analysis revealed that in both cases a multiphase microstructure was present. Large regions
of a Bi-rich phase were detected in slow cooled samples, while in quenched samples the Bi-rich
phase was concentrated at the grain boundaries. The majority phase in the quenched samples
corresponded to stoichiometric Cu3 BiSe3 , although a purely single phase microstructure could
not be obtained even after extended annealing treatments. The measured thermoelectric properties
of quenched Cu3 BiSe3 were in reasonable agreement with those previously reported. The thermal
conductivity is quite low, but the extremely low thermoelectric power factor resulted in low ZT
values. The thermoelectric properties were not improved after extended annealing treatments.
The ternary compound having nominal composition CuBi3 Se5 was studied for completeness.
Samples with starting compositions Cu1.6 Bi4.8 Se8 , Cu1.7 Bi4.7 Se8 , and Cu1.78 Bi4.73 Se8 were
prepared in accordance with three separate literature studies on the CuBi3 Se5 compound. All
samples consisted of a single phase corresponding to Cu1.78 Bi4.73 Se8 , which has a monoclinic
structure. This compound was found to have an extremely low thermal conductivity but poor
electronic properties, leading to modest ZT values. The temperature dependence of the thermal
conductivity resembles that of an amorphous material, which indicates a strong intrinsic phonon
scattering mechanism that limits the phonon mean free path to near its minimum value even at
low temperatures. Gaining a better understanding of this mechanism could help to identify other
materials with intrinsically minimal thermal conductivity, which is of significant interest for the
development of new thermoelectric materials as will be discussed in Chapter 6.

35

5

Diamond-Like Cu-Based Ternary Compounds

5.1

Background and Motivation

5.1.1

Why Study Diamond-Like Cu-Based Ternary Compounds?

The absence of rocksalt-like Cu-based ternary compounds eliminates the possibility of extending
the AgSbTe2 approach beyond the Ag-based systems. The methodology used to derive AgSbTe2 ,
however, can be applied to compounds with different crystal structures. Consider the well-known
group IV semiconductors Si and Ge with the diamond cubic crystal structure. It is known that
by replacing the Si or Ge atoms in equal proportions with group III and V or group II and VI
atoms, the valence electron to atom ratio is constant (4 valence electrons per atom, allowing for
sp3 hybridization of the valence electron orbitals and therefore tetrahedral coordination) and a
diamond-like structure is maintained, which is called the zincblende structure since two distinct
atomic species are present. Group III-V and II-VI semiconductors such as GaAs and CdTe are
well established technological materials with a wide array of applications. Now consider two unit
cells of a II-VI semiconductor (say Zn2 Se2 , for convenience) and replace the Zn atoms with Cu
and In atoms in equal proportions, thereby formulating the compound CuInSe2 . In the same way
as AgSbTe2 is derived from PbTe, CuInSe2 is derived from ZnSe and maintains a diamond-like
structure known as the chalcopyrite structure. Here the valence electron to atom ratio is still equal
to 4, allowing for tetrahedral coordination among the constituent atoms.
The I-III-VI2 family of compounds (sometimes referred to as chalcopyrite compounds) are well
characterized and have found various applications, most notably as photovoltaic materials due to
their favorable band gaps. Solid solutions of CuInSe2 and CuGaSe2 (dubbed CIGS compounds)
are some of the best known materials for thin film solar cells, with efficiencies approaching 20%
[54]. The chalcopyrite compounds are not well suited for thermoelectric applications due to their
relatively high thermal conductivities, in the range of 5 to 9 W/m*K at room temperature [55], and

36

large bandgaps in the range of 1 to 2 eV.
This approach can be expanded further by considering higher-order ternary derivatives of the IIVI semiconductors. Starting with three II-VI unit cells and replacing the group II atoms with group
I (Cu) and group IV (Ge, Sn) atoms in a 2:1 ratio, compounds of the form I2 -IV-VI3 are formulated.
In a similar fashion, compounds of the form I3 -V-VI4 have unit cells 4 times larger than those of
the II-VI compounds. The I2 -IV-VI3 and I3 -V-VI4 compounds have 4 valence electrons per atom
and both maintain diamond-like crystal structures.
Increasing the size of the unit cell while maintaining the diamond-like crystal structure presents
a distinct advantage for thermoelectric applications in that the lattice thermal conductivity of a
given crystalline material is known to decrease with increasing size of the unit cell. Slack [45],
and later Morelli and Slack [56], reviewed the thermal conductivity of nonmetallic crystals with 1
≤ n ≤ 4, where n is the number of atoms in the primitive crystallographic unit cell. Slack proposed
the following expression for the n-dependence of the lattice thermal conductivity:

κL =

¯
BMδ(θ0 )3
n2/3 T γ2

(5.1)

¯
where B is a constant, M is the average atomic mass, δ is the average volume per atom, θ0 is the
average Debye temperature estimated from elastic constants or specific heat, T is the absolute temperature in Kelvin, and γ is the dimensionless Gr¨ neisen constant [45]. It is clear from equation
u
5.1 that for a series of compounds with similar atomic mass and interatomic bonding, the lattice
thermal conductivity should follow a n−2/3 dependence at a fixed temperature T . Such a series is
constructed in Table 5.1 using select compositions from the diamond-like families of compounds
described above. Here κexp ∝ n−1.6 , representing a more drastic decrease in thermal conductivity with increasing n than predicted by equation 5.1. This offers a novel route towards compounds
with low intrinsic thermal conductivity, and thus increased thermoelectric figure of merit. The
n-dependence of the forbidden band gap (see Table 5.1) also shows a favorable trend. It has been

37

shown [57] that, for thermoelectric applications, to avoid minority carrier conduction while allowing for high mobility and doping level, a band gap of approximately 10 kB T is required, where
kB is Boltzmann’s constant and T is the operating temperature. For most applications, this means
that appropriate band gaps fall between 0.25 and 1 eV. From Table 5.1 it is clear that the I2 -IV-VI3
and I3 -V-VI4 families of compounds are promising candidates for thermoelectric applications, yet
they have seen little exploration to that extent.
Table 5.1: Reported thermal conductivities and band gaps for a series of
diamond-like semiconductors with increasing number of atoms per unit
cell.
Compound n (atoms) κexp (W/m*K)
ZnSe
2
19.0

Band Gap (eV)
2.7

Reference
[45]

CuInSe2

8.6

1.07

[58]

Cu2 SnSe3

6

3.3

0.66

[58]

Cu3 SbSe4

5.1.2

4
8

2.2

0.31

[58]

Third-Order Ternary Derivatives of II-VI: I2 -IV-VI3 Compounds

Hahn and his coworkers reported the Cu2 -IV-VI3 compounds as having the sphalerite crystal structure with lattice constants ranging from a = 0.53 - 0.604 nm [59]. Goryunova et. al. [60] previously
reported on the existence of Ag-based compounds in this series, but Scott [61] later found no evidence of ternary phases where I = Ag. The compounds Cu2 SnSe3 and Cu2 GeSe3 have been the
subjects of several crystallographic studies and sparse physical property characterization.
The crystal structure of Cu2 SnSe3 has been the subject of some debate in the literature. Palatnik et. al. [62] and Sharma et. al. [63] reported a cubic unit cell for Cu2 SnSe3 with a = 0.569 nm.
Marcano et. al. [64] and Delago et. al. [65] recently reevaluated the crystal structure of Cu2 SnSe3
using single crystal samples. They found additional low-angle peaks in the x-ray diffraction pattern corresponding to a lower symmetry unit cell, which they determined to be monoclinic (space
38

group Cc) with a = 0.6967 nm, b = 1.20493 nm, c = 0.69453 nm, and β = 109.19◦ [65]. The authors
seem to agree that Cu2 SnSe3 is a congruently melting compound which melts at 695◦ C.
Large discrepancies regarding the electronic properties of Cu2 SnSe3 exist in the literature.
While all authors agree that Cu2 SnSe3 exhibits p-type semiconducting behavior, the reported resistivity values range from 2.53×10−3 to 1.67×10−1 Ω*cm and the reported Seebeck coefficients
range from +51.1 µV/K to +250 µV/K [58], [67]. At the beginning of this work, no efforts to control the carrier concentration through doping had been completed on Cu2 SnSe3 .
The compound Cu2 GeSe3 was originally reported as cubic with a = 0.555 nm [67], but was
later found to have an orthorhombic unit cell with a = 1.1878 nm, b = 0.3941 nm, and c = 0.5485
nm [69]. Goryunova et. al. reported that Cu2 GeSe3 could incorporate up to 14% excess Ge,
and in the process transition from tetragonal to cubic symmetry [60]. Later Sharma and Singh
studied the crystal structure and microhardness of Ge-deficient and Ge-rich Cu2 GeSe3 [70]. They
found the composition Cu2 Ge0.85 Se3 to be monoclinic (a=0.5512 nm, b=0.5598 nm, c=0.5486
nm, β=89.7◦ ) and Cu Ge
Se to be cubic (a=0.5569 nm), and obtained single-phase samples
2

1.55

3

at all compositions bounded by these two compounds. In a subsequent paper they reported all
compositions above or below Cu2 Ge1.55 Se3 to be multiphase, with the cubic phase occurring
only at Cu2 Ge1.55 Se3 [71]. Spitzer reported a cubic compound having composition Cu2 Ge2 Se3
with a low room temperature thermal conductivity (0.84 W/m*K) [46]. Subsequent studies on the
crystal structure transformations and physical properties of these compounds are absent from the
literature.

5.1.3

Fourth-Order Ternary Derivatives of II-VI: I3 -V-VI4 Compounds

Wernick and Benson first mentioned compounds of the type Cu3 -V-VI4 where V = As or Sb
and VI = S or Se [33]. They reported Cu SbSe to be cubic with a melting point of 425◦ C,
3

4

and gave no further results. Pfitzner later conducted a thorough crystallographic study on the
¯
same compound and found the structure to be tetragonal (space group I 42m no. 121) with a =
39

0.56609 nm and c = 1.1280 nm [72]. Scott et. al. found that Cu3 SbSe4 forms by a peritectic
reaction at 390◦ C, indicating that the slow-cooled samples synthesized by Wernick and Benson
likely contained impurity phases [73]. The electronic properties of Cu3 SbSe4 have been reported
by several authors, who agree that it is a narrow band gap semiconductor (Eg between 0.13 and
0.42 eV at 300K) [73], [74], [75]. Controlling the carrier concentration in undoped samples is a
challenge due to large concentrations of intrinsic defects; the literature values span nearly an order
of magnitude from 2.4×1018 cm-3 to 2×1019 cm-3 .

5.1.4

Outline for the Present Work

Based on the approach outlined in Section 5.1.1 and the literature review, the objectives for this
portion of the work are as follows:
(1) Synthesize Cu2 SnSe3 , Cu2 GeSe3 , and Cu3 SbSe4 using the technique described in Seciton
3.1. Resolve the inconsistencies in the literature regarding the crystal structures of these compounds.
(2) Explore solid solutions with related compounds; determine the evolution of the crystal structure, lattice thermal conductivity, carrier mobility, and thermoelectric properties with composition.
(3) Identify dopant species and evaluate the effect of doping on the thermoelectric properties of
the compounds mentioned in (1).
(4) Determine the plausibility of these compounds as thermoelectric materials.
Since each of these compounds are unique in their crystal structure and physical properties, a
separate section will be devoted to each. The synthesis methods and experimental results for each
will be discussed individually.

40

5.2

Cu2 SnSe3

5.2.1

Experimental

Samples of Cu2 SnSe3 were reacted at 900◦ C for 12 hours in evacuated quartz ampoules. Samples
were slow cooled at 0.3◦ C/min to 400◦ C, annealed for 1-4 days, and cooled to room temperature.
To investigate high temperature phase modifications, some samples were quenched from 900◦ C
into room temperature water.

5.2.2

Results and Discussion

Both slow cooling and quenching resulted in single phase material, as determined by x-ray diffraction. Closer examination of the x-ray patterns revealed subtle differences that indicate differences
in the crystal structure. The x-ray pattern for the quenched sample (Figure 5.1) exactly matches
that of cubic Cu2 SnSe3 reported by Palatnik et. al. [62]. Additional low angle peaks are present
in the pattern for the slow cooled sample (see inset, Figure 5.2) which, as pointed out by Delago
et. al.[65], correspond to a monoclinic unit cell.
Figures 5.1 and 5.2 suggest that the structures proposed by Palatnik et. al. [62] and Delago [65]
are both correct, and differ only because of differences in their sample preparation. The primary
difference between the structures shown in Figures 5.1 and 5.2 is the ordering of Cu/Sn atoms on
the cation sublattice. A random arrangement of Cu and Sn atoms leads to a higher symmetry cubic
unit cell whereas an ordered arrangement of Cu and Sn atoms lowers the symmetry to monoclinic.
In agreement with these results, Rivet [76] reported an order/disorder transformation in Cu2 SnSe3
at 450◦ C.
Nominally undoped samples always displayed p-type conductivity, as confirmed by Seebeck
and Hall coefficient measurements, but controlling the hole concentration in these samples proved
to be a challenge. Separately made Cu2 SnSe3 samples had hole concentrations in the range of
4×1018 cm-3 to 1×1021 cm-3 at room temperature. Samples that were quenched in water from

41

Relative Intensity (Arb. Units)

Cu2SnSe3 (cubic)
PDF#01-089-2879

10

20

30

40

50

60

70

80

Cu/Sn
Se

90

2! (degrees)

Figure 5.1: X-ray diffraction pattern for Cu2 SnSe3 quenched in water from 900◦ C. All peaks
correspond to the cubic phase, shown at right, where the larger spheres represent the random
arrangement of Cu and Sn atoms on the cation sublattice.

900◦ C had hole concentrations greater than 1020 cm-3 at room temperature, presumably due to
a large concentration of defects introduced during the quenching process. The inner walls of the
ampoules became coated with a red/orange residue after quenching, likely caused by deposited Se
vapor, which would promote a large concentration of Se vacancies in the Cu2 SnSe3 lattice. A Se
vacancy in the lattice would likely act as an acceptor impurity, thereby leading to very large hole
concentrations.
For slow cooled samples, the hole concentrations were always less than 1020 cm-3 , but varied
significantly from sample to sample and even between different Hall specimens cut from the same

42

Relative Intensity (Arb. Units)

Cu2SnSe3 (monoclinic)
PDF#01-072-8034

10

20

30

40
50
60
2! (degrees)

70

80

Sn
Se
Cu

90

Figure 5.2: X-ray diffraction pattern for Cu2 SnSe3 slow cooled and annealed at 400◦ C. Inset
shows low angle peaks corresponding to the monoclinic structure, shown at right.

ingot. Annealing for up to 4 days at moderate temperatures (400◦ C) had no effect on the hole
concentration. One possible explanation is that these samples suffer from localized compositional
fluctuations that are not detectable using XRD. Cu2 SnSe3 is known to have a large phase region,
allowing for variations in composition while maintaining a single phase structure. In addition,
compounds with similar compositions exist, namely Cu2 Sn1-x Se3 and Cu2 SnSe4 . Sharma et. al.
reported that Sn-deficient Cu2 SnSe3 had a cubic crystal structure up to Cu2 Sn0.6 Se3 , but reported
no physical properties for these compounds [77]. Marcano et. al. found Cu2 SnSe4 to be a ptype semiconductor with the zincblende crystal structure, with lattice constant very similar to that
˚
of Cu2 SnSe3 (a = 5.6846(3) A) [78]. It is important to note that the XRD peaks for Cu2 SnSe4

43

nearly overlap those of Cu2 SnSe3 (cubic and monoclinic phase), and thus the two compounds
cannot be distinguished using XRD. They report a hole concentration of approximately 1.5×1021
cm-3 at room temperature for Cu2 SnSe4 , indicating that this compound could cause large hole
concentrations if present in Cu2 SnSe3 . Samples of Cu2 SnSe3 examined using EDS showed no
detectable compositional variations, although EDS cannot distinguish between phases with similar
average atomic mass.
Despite the challenges in controlling the hole concentration of Cu2 SnSe3 , doping studies were
conducted to determine if the hole concentration could be consistently altered by introducing impurities into the compound. Ga and In were chosen as dopant species for the Sn site since they
have one less valence electron and should act as acceptor impurities in the compound. The samples
were synthesized by slow cooling from 900◦ C to 400◦ C, annealing for 24 hours, and slow cooling
to room temperature. Taking the lowest measured hole concentration for Cu2 SnSe3 as the ”true”
concentration, the hole concentration increases with increasing Ga and In content (see Figure 5.3,
y = 0.01 and 0.025 not shown for clarity). When 5% Ga or In is added, the hole concentration
is ∼1.0×1021 -3 , causing some difficulty in the measurement due to a weak Hall signal. The
hole mobility (not shown) is ∼20 cm2 /V*s for Cu2 SnSe3 at 300K and decreases with increasing
doping, falling below 10 cm2 /V*s at 300K for all of the doped samples.
The low temperature thermoelectric properties of Ga-doped Cu2 SnSe3 are shown in Figure 5.4.
The electrical resistivity and Seebeck coefficient both decrease rapidly with increasing Ga content
due to the increasing hole concentration. The thermal conductivity follows a T-1 temperature
dependence as expected for these compounds in this temperature range due to phonon-phonon
scattering. At room temperature the thermal conductivity increases slightly with Ga content due
to an increased electronic contribution, which constitutes 13% of the total at room temperature for
the 5% Ga sample (estimated from the Wiedemann-Franz law using L0 = 2.45×10−8 W*Ω*K-2 )
. The 2.5% Ga sample has the largest ZT value, reaching 0.037 at room temperature. While this is
a modest value, it represents nearly a 3-fold increase as compared to the room temperature ZT of
44

Hole Concentration (!1019 cm-3)

1000
x=0

x=0.01

x=0.025

x=0.05

y=0.05

100

10

1

0.1
50

100

150

200

250

300

350

Temperature (K)

Figure 5.3: Temperature dependence of the hole concentration of
Cu2 Sn1-x Gax Se3 and Cu2 Sn1-y Iny Se3 compounds.

Cu2 SnSe3 .
The electronic properties of the 2.5% Ga doped sample were measured at higher temperatures,
shown in Figure 5.5. The resistivity and Seebeck coefficient both increase rapidly with temperature up to the highest measurement temperature of 600K. The power factor, defined as S2 σ (the
numerator of the ZT equation), reaches 6.2 µW/cm*K2 at this temperature. The estimated ZT
value (calculated by extrapolating the low temperature thermal conductivity data) approaches 0.28
for this sample at 600K.
Controlling the carrier concentration of the doped compounds again proved to be challenging.
In an attempt to reproduce the best composition, another 2.5% Ga sample was made in the same
way as the one shown in Figures 5.3 and 5.4. This sample clearly contained a hole concentration
gradient and had ZT values ranging from 0.008 to 0.017 at room temperature, never matching the
value measured for the first sample.
All Cu2 SnSe3 samples discussed above displayed p-type conduction. Attempts at producing
45

300
Cu2SnSe3
1% Ga
2.5% Ga
5% Ga

250
200
150
100
50

Total Thermal
Conductivity (W/m*K)

Seebeck Coefficient (µV/K)

14

350

0
1

12
10
8
6
4
2

0
0.04
0.03

0.1

0.025
ZT

Resistivity (!*cm)

0.035

0.02
0.015

0.01

0.01
0.005
0

0.001
50

150
250
Temperature (K)

350

50

150
250
Temperature (K)

350

Figure 5.4: Low temperature thermoelectric properties of the Cu2 Sn1-x Gax Se3 compounds.

n-type samples were unsuccessful due primarily to the already high hole concnetration in undoped
samples. Doping with Zn on the Cu site resulted in the formation of ZnSe as a secondary phase.
Doping with either Sb or Bi on the Sn site did not change the sign of the conduction, although no
secondary phases were detected using XRD. Adding excess Se did not systematically affect the
carrier concentration. No secondary phases were detected by XRD,which was expected due to the
wide phase region of Cu2 SnSe3 .
Shi et. al. recently reported that Cu2 SnSe3 can achieve ZT = 1.14 at 850K when doped with
10% In [79]. This result could not be reproduced for the purposes of this work, mainly because
Cu2 SnSe3 becomes unstable near 800K. Ga and In doped samples measured at high temperature
showed a dramatic increase in resistivity and Seebeck coefficient at this temperature, indicating
46

0.009

Resistivity (Ohm*cm)

0.008
0.007
0.006
0.005
0.004
0.003
0.002
2.5% Ga

0.001
0

Seebeck coefficient (µV/K)

250
200
150
100
50
0
0

200

400

600

800

Temperature (K)
Figure 5.5:
High temperature
Cu2 Sn0.975 Ga0.025 Se3 .

47

electronic

properties

of

softening of the sample (see Figure 5.14). In some cases, the samples were deformed during high
temperature measurement. Shi et. al. coated their samples with glass before high temperature
measurement, which could have provided some rigidity at high temperature. The same authors
have also reported solid solutions of Cu2 SnSe3 with ZnSe and CdSe as having ZT > 1 at high
temperature when appropriately doped [80], [81]. In light of these results, other solid solutions
based on Cu2 SnSe3 should be investigated for thermoelectric applications.
5.2.3

Summary

From this portion of the work it is concluded that the compound Cu2 SnSe3 holds potential as a
p-type thermoelectric material. Single phase samples can be synthesized by either quenching from
900◦ C into water or by slow cooling, annealing at 400◦ C, and slow cooling to room temperature.
Samples quenched from high temperature have a cubic sphalerite structure with a disordered arrangement of Cu and Sn atoms on the cation sublattice. Slow cooling and annealing allows for
ordering among the Cu and Sn atoms and results in a monoclinic crystal structure. No secondary
phases were detected in any of the samples. Quenched samples proved to be extremely brittle and
therefore their transport properties could not be reliably measured.
The hole concentration of undoped, slow-cooled samples shows large sample-to-sample variations, and is typically in the range of 1018 - 1020 cm-3 . The reason for the large variations is
not known, but is likely associated with intrinsic defects or compositional variations. The hole
concentration can be increased through either Ga or In doping on the Sn site, reaching 1021 cm-3
for 5% doping.
The thermoelectric properties vary systematically with doping level and are optimized for 2.5%
Ga doping, which gives ZT=0.037 at room temperature. High temperature measurements yielded
an estimated ZT value of 0.28 at 600K for this sample, with material stability concerns preventing
measurements at higher temperature.

48

5.3

The Cu2 SnSe3 -Cu2 GeSe3 Solid Solution

Averkieva et. al. reported that Cu2 SnSe3 and Cu2 GeSe3 formed a complete solid solution, yet
these compounds have not been studied for thermoelectric applications. For compounds of the
form Cu2 Sn1-x Gex Se3 , they reported a zincblende-type structure for x ≤ 0.67 and a tetragonal
structure for x > 0.67, with the smallest measured thermal conductivity of 2.97 W/m*K occurring
at x = 0.67 [82].

5.3.1

Experimental

Cu2 Sn1-x Gex Se3 samples with x ranging from 0 to 1 were prepared by reacting the pure elements
at 900◦ C as described in section 3.1. The melt was then brought to room temperature either by
quenching in water or by cooling at 0.3◦ C/min. Samples for transport property measurements
were cut directly from the solidified ingots using a diamond saw.

5.3.2

Results and Discussion

Water quenched samples were found to have a disordered zincblende-like structure (space group
¯
F 43m no. 216) for x ≤ 0.7 and an orthorhombic structure corresponding to that of Cu2 GeSe3 for
x > 0.7. The transistion from orthorhombic to cubic symmetry is gradual, and is manifested in the
gradual appearance of double peaks near 45◦ and 55◦ 2θ (see Figure 5.6). Slow cooled samples
had a monoclinic structure similar to that of Cu2 SnSe3 (space group Cc no. 9) for x ≤ 0.5 as
evidenced by the extra low angle peaks in the XRD pattern (see Figure 5.7). For 0.5 < x < 1.0 a
gradual transition from monoclinic to orthorhombic symmetry is evident from the gradual splitting
of the higher angle XRD peaks (see Figure 5.8). When x = 1.0, all peaks index to the orthorhombic
structure of Cu2 GeSe3 described by Parthe [69]. No secondary phases were detected using XRD
in any of the samples and the decreasing lattice spacing with increasing x, calculated from the
x-ray peak shift (see Figure 5.9), indicates that the smaller Ge atoms are substituting for Sn in the

49

Relative Intensity (arb. units)

x = 1.0
x = 0.9
x = 0.7
x = 0.5
x = 0.2
x = 0.1

x=0
10

20

30

40

50

60

70

80

90

2! (degrees)

Figure 5.6: X-ray diffraction patterns of quenched Cu2 Sn1-x Gex Se3 compounds, 0 ≤ x ≤ 1.0.

structure.
Transport property measurements were conducted only on the slow cooled samples since significant cracking in the quenched samples prevented reliable measurements. The electronic transport properties for the 0 ≤ x ≤ 0.5 samples (Figure 5.10) show no clear x dependence, which
is expected since Ge is isoelectronic to Sn. The Seebeck coefficient shows a maximum value of
+210 µV/K at 300 K for x = 0.1 and 0.2, and then decreases with increasing x. The x dependence of the electrical resistivity mirrors that of the Seebeck coefficient, indicating variations in
the hole concentration between samples. The measured hole concentrations were >1020 cm-3 for
all samples, indicating unintentional doping. Extended annealing at 400◦ C had no effect on the

50

Intensity (arb. unit)

x = 0.5
x = 0.3
x = 0.2
x = 0.1
x= 0
10

20

30

40

50

60

70

80

90

2! (degrees)

Intensity (arb. unit)

x = 0.5

14.5

x = 0.3
x = 0.2
x = 0.1
x= 0

19.5

24.5

29.5

2! (degrees)

Figure 5.7: X-ray diffraction patterns of slow cooled Cu2 Sn1-x Gex Se3 compounds, x ≤ 0.5.
Lower plot shows close-up view of low angle peaks indicating monoclinic structure, vertical lines
represent reported peak locations for monoclinic Cu2 SnSe3 [65].

51

Relative Intensity (arb. units)

x = 1.0

x = 0.9

x = 0.8

x = 0.7

x = 0.6
10

20

30

40

50

60

70

80

90

2! (degrees)
Figure 5.8: X-ray diffraction patterns of slow cooled Cu2 Sn1-x Gex Se3 compounds, x > 0.5.

hole concentration.
The lattice thermal conductivity of Cu2 SnSe3 decreases upon the addition of Ge as expected
due to phonon-impurity scattering. The measured thermal conductivities of the x = 0 and x =
0.5 compounds are shown in Figure 8; the values for 0 < x < 0.5 are bounded by these two
extremes. The decreasing thermal conductivity with increasing x can be understood using the
Debye approximation to the lattice thermal conductivity [84]:
4
kB
κL =
T3
2 h2 v
2π ¯

θ/T
0

r4 er
τ(r)dr
(er − 1)2

(5.2)

where kB is Boltzmann’s constant, v is the phonon velocity, θ is the Debye temperature, h is
¯
52

5.7

3.3

(a)

(b)

5.66

d-spacing (Å)

Lattice parameter (Å)

3.28

5.62

3.26
3.24
3.22

5.58

3.2
0

0.2

0.4

0.6

0.8

0

x (Ge content)

0.2

0.4

0.6

0.8

x (Ge content)

Figure 5.9: Lattice spacing of the Cu2 Sn1-x Gex Se3 compounds with Cu2 SnSe3 -type structure:
(a) lattice parameter of the cubic (quenched) samples, (b) interplanar spacing of the (200) planes
of the monoclinic (slow cooled) samples.

Plancks constant, and τ(r) is the phonon scattering time in terms of the dimensionless parameter r:

r=

hω
¯
kB T

(5.3)

where ω is the phonon frequency. Since optic phonon modes have low group velocity, the
majority of heat in a crystalline material is carried by the acoustic phonon modes. Thus, the values
for v, θ and τ(r) should correspond to the acoustic portion of the phonon spectrum only. Empirically determined values of v and θ for Cu2 SnSe3 have been reported, but represent averages over
all phonon modes in the crystal [85]. Slack showed that θa (acoustic mode Debye temperature)
can be estimated from θ0 (average Debye temperature, estimated from elastic constants or specific
heat) using [45]:

θa = θ0 n−1/3

(5.4)

where n is the number of atoms per primitive crystallographic unit cell. This yields θa = 86.4 K
53

250
x=0
x=0.3

Seebeck Coefficient (µV/K)

200

x=0.1

x=0.2

x=0.5

150

100

50

0

Resistivity (!!cm)

0.1

0.01

0.001
0

100

200
Temperature (K)

300

Figure 5.10: Temperature dependence of the Seebeck coefficient and electrical
resistivity of the Cu2 Sn1-x Gex Se3 compounds for x < 0.5

54

for Cu2 SnSe3 , which has n = 6. Similarly, the acoustic mode phonon velocity can be estimated by
taking the inverse cubic average of the reported longitudinal and transverse phonon velocities [86],
which gives va = 1664 m/s for Cu2 SnSe3 [85]. Assuming that the individual phonon scattering
rates are additive, the total τ−1 (r) can be expressed as the sum of the individual scattering rates
due to grain boundaries, point defects, and phonon-phonon Umklapp scattering:

−1
τ−1 (r) = τ−1 (r) + τ−1 (r) + τU (r).
P
G

(5.5)

Expressions for the individual scattering rates have been developed separately [87] - [89], and
were compiled and used by Morelli et. al. to predict the effect of isotope scattering on the thermal
conductivity of diamond-like semiconductors [90]. The same expression for the total scattering
rate is used to fit the present data:

τ−1 (r) =

va
+ A(r4 ) T 4 + B(r2 ) T 3 e−θa /T
L

(5.6)

where:
4
V kB Γ
A=
4π h4 v3
¯ a

(5.7)

h γ2
¯
Mv2 θa
a

(5.8)

and

B=

where L is the average grain size, V is the average volume per atom, γ is the Gr¨ neisen constant,
u
M is the average atomic mass, and Γ is the phonon-impurity scattering parameter. The original expression for Γ derived by Klemens required knowledge of the interatomic bonding forces in the
material and thus is not practical to use for new materials [88]. Abeles later developed an expression for Γ that accounts for differences in atomic mass and size between the host and impurity

55

atoms and only requires knowledge of the atomic masses and radii of the constituent atoms [91].
Recently Yang et. al. generalized this expression for compounds containing more than one sublattice [92]:

Γ = ΓM + ΓS

(5.9)

where ΓM and ΓS are the impurity scattering parameters for mass and strain field fluctuations
respectively. For the case of Cu2 Sn1-x Gex Se3 there are two distinct atoms on the Sn sublattice,
which are denoted below as A and B [92]:

cs
ΓM =

¯ 2
Ms
fA fB
¯
M

MA − MB
¯
Ms

2

rA − rB
r¯s

2

(5.10)

n
∑ ci
i=1

and

cs
ΓS =

¯ 2
Ms
f A f B εs
¯
M
n
∑ ci
i=1

(5.11)

¯
where cs , Ms , and r¯s are the total occupancy, average mass and average atomic radius of the
sublattice. f A,B , M A,B and rA,B are the fractional occupancies, atomic masses, and atomic radii
¯
of the A and B atoms respectively, M is the average mass of the compound, and ci is the total
occupancy of the ith sublattice. The phenomenological adjustable parameter εs depends on the
Gr´ neisen parameter and the elastic constants of the material and typically ranges from 10 to 100.
u
¯
Calculating ΓM for the Cu2 Sn1-x Gex Se3 compounds is straightforward using cs = 1, Ms =
¯
95.64, M Sn = 118.7, M Ge = 72.58, Σci = 6, and letting M vary with composition. The maximum
value of ΓM = 0.0151 is occurs at x = 0.5, corresponding to the maximum disorder in the lattice.

56

The only unknown parameter in the expression for ΓS (equation 5.11) is εs which, following the
procedure of Abeles [91], can be estimated using:

εs = 12.3 + 39.4γ + 31.5γ2

(5.12)

where γ is the Gr¨ neisen parameter. This yields εs = 116 for γ = 1.3, giving ΓS = 0.142 at x =
u
0.5. The lattice thermal conductivity of the Cu2 Sn1-x Gex Se3 compounds can now be calculated
using the following assumptions:
• The grain size does not vary substantially from sample to sample, a large grain size, L = 1
mm, is assumed for all samples such that grain size effects are essentially eliminated from
the model since phonon-impurity scattering is the primary interest.
• The compositional dependence of the Debye temperature follows Lindemann’s rule,
0.5
θ = a + bTm V −1 M −0.5 , where Tm , V , and M are the melting temperature, volume per
atom, and atomic mass of the compound, respectively [10].
• The phonon velocity does not vary significantly with composition, va = 1664 m/s is used for
all calculations.
• The Gr¨ neisen constant is treated as an adjustable parameter to fit the data of the x = 0
u
compound and is then held constant with composition. This procedure yields γ = 1.3, a very
reasonable estimate for zincblende-type compounds [45].
The calculated lattice thermal conductivities of the x = 0 and x = 0.5 compounds are plotted in
figure 5.11 along with the experimental data (the thermal conductivities of the x < 0.5 compounds
fall betweeen these two extremes). To obtain the fit for the x = 0.5 sample, only phonon-impurity
scattering due to mass fluctuations (ΓM ) was taken into account; the parameter εs in equation 5.11
was set to zero, resulting in ΓS = 0. This is in stark contrast to εs = 116 given by equation 5.12
57

Thermal Conductivity (W/m*K)

30

x=0

25

x=0.5
x=0 (fit)

20
15
10
5
0
0

100

200
Temperature (K)

300

Figure 5.11: Temperature dependence of the thermal conductivity of the Cu2 Sn1-x Gex Se3 compounds for x = 0 and
0.5. Dotted lines represent lattice thermal conductivity calculated from the Debye model (equation 5.2).

with γ = 1.3 but, as Abeles pointed out [91], the εs parameter should be treated as adjustable. The
fact that εs = 0 reveals that the substitution of Ge for Sn in Cu2 SnSe3 causes phonon scattering
primarily due to the atomic mass difference between Ge and Sn and results in little strain-field
fluctuation in the lattice. This is in agreement with the XRD patterns for these compounds (Figures
5.7 and 5.8) which show very little peak broadening for the intermediate compositions, indicating
little microstrain in the lattice [93].
The x = 0.2 sample showed the best thermoelectric properties, with ZT = 0.035 at room temperature. Doping the Cu2 Sn1-x Gex Se3 compounds with Ga or In on the Sn/Ge site were largely
unsuccessful due to the already large hole concentrations of the undoped compounds. The results (not shown) indicate that Ga and In can substitute on the Sn/Ge site, but do not improve the
thermoelectric properties.

58

5.3.3

Summary

The above results confirm the existence of a complete solid solution in the Cu2 SnSe3 -Cu2 GeSe3
system. Cu2 Sn1-x Gex Se3 samples cooled slowly from 900◦ C show a transition from the monoclinic Cu2 SnSe3 structure to the orthorhombic Cu2 GeSe3 structure at x = 0.5 as indicated by
XRD peak splitting for samples with x > 0.5. The high temperature cubic Cu2 SnSe3 phase was
prevalent in samples with x ≤ 0.7 that were quenched from 900◦ C, but these samples proved to be
too brittle for transport property measurements.
The lattice thermal conductivity of the slow-cooled Cu2 Sn1-x Gex Se3 compounds can be understood using the Debye model with the correct choice of phonon scattering rates. Allowing only
the point defect scattering rate to change with composition, an excellent fit to the experimental data
of the x = 0 and 0.5 samples was produced. An analysis of the phonon-impurity scattering parameter Γ revealed that phonons are scattered primarily due to the atomic mass difference between Ge
and Sn rather than lattice strain introduced from the difference in their atomic radii. The absence
of significant lattice strain is confirmed by the lack of peak broadening in the XRD patterns, and
may be an artifact of the gradual change from monoclinic to orthorhombic symmetry that occurs
in these compounds.
Optimization of the thermoelectric properties of the Cu2 Sn1-x Gex Se3 compounds was frustrated by large (>1020 cm-3 ) hole concentrations in the undoped material. Doping with Ga or
In on the Sn/Ge site failed to improve the modest ZT values achieved for the nominally undoped
compounds.

59

5.4

The Cu2 SnSe3 -Cu2 SnS3 Solid Solution

The compound Cu2 SnS3 exists in both high-temperature cubic (disordered) and low-temperature
monoclinic (ordered) variations, analogous to Cu2 SnSe3 . Irie reported a complete solid solution
for Cu2 SnSe3 -Cu2 SnS3 [68], with a 37% reduction in κL occurring near the 50% composition.
The thermoelectric properties of this system have not been reported and are evaluated here as a
means of improving upon those of Cu2 SnSe3 and potentially stabilizing the compound at high
temperatures.

5.4.1

Experimental

Samples of Cu2 SnSe3-x Sx (0 ≤ x ≤ 1.5) were prepared by slow cooling the melt (24◦ C/hour)
from 900◦ C to 500◦ C, annealing for 4 days, and slow cooling to room temperature. The resulting
ingots were vibratory ball milled for 30 minutes and hot pressed at 500◦ C for 30 minutes at a
pressure of 70 MPa, giving pellets with >94% of the theoretical density. Samples for transport
property measurements were cut directly from the hot pressed pellets.

5.4.2

Results and Discussion

The X-ray diffraction patterns of selected Cu2 SnSe3-x Sx compounds are shown in Figure 5.12.
The low-temperature monoclinic structure is maintained at all compositions studied, as indicated
by the extra low angle peaks in the X-ray patterns. The X-ray peaks shift to lower 2θ values with
increasing x indicating a contraction of the lattice, which is expected due to the smaller size of S
relative to Se. No secondary phases were detected in any of the compounds using X-ray diffraction
or EDS (not shown).
The temperature dependence of κL of the samples shown in Figure 5.12 is plotted in Figure
5.13 (electronic contribution is negligible in the undoped compounds). The magnitude of κL decreases dramatically with increasing S content, and is reduced by as much as 70% at 80K and 40%

60

Relative Intensity (Arb. Units)

x=1.5

x=0.9

x=0
10

20

30

40

50

60

70

80

90

2! (degrees)
Figure 5.12: X-ray diffraction patterns of the Cu2 SnSe3-x Sx compounds.

at 300K. It is counterintuitive that the x=0.9 sample has a lower κL than the x=1.5 sample since the
maximum disorder should be achieved at x=1.5, but the minimum in κL is not always achieved at
the 50% composition for a given solid solution. The difference in κL between the end compounds
(Cu2 SnSe3 and Cu2 SnS3 in this case) can cause the compositional dependence of κL to become
skewed, causing the minimum in κL to occur outside of the 50% composition.
The x=0.9 composition was chosen for doping studies since it has the lowest κL . Both Ga and
In were found to be effective p-type dopant species when substituted for Sn. The problem of sample to sample variations in hole concentration again plagued repeatability in these samples, with
lengthy annealing and minor changes in composition unable to produce consistent results. The high
temperature thermoelectric properties of the best-performing sample, Cu2 Sn0.925 In0.075 Se2.1 S0.9 ,
61

20
x=0

16

x=0.9

14
!L (W/m*K)

18

x=1.5

12
10
8
6
4
2
0
0

50

100

150

200

250

300

350

Temperature (K)

Figure 5.13: Lattice thermal conductivity of the Cu2 SnSe3-x Sx
compounds.

are shown in Figure 5.14. The ZT reaches 0.62 at 760K, at which point the sample softened, causing an abrupt increase in the resistivity. There is no evidence in the available phase diagrams for
Cu2 SnSe3 of a decomposition near 800K.

62

Resistivity (Ohm*cm)

300
250
200
150
100
50

0.025
0.02
0.015
0.01
0.005

0
2.5

0
0.7

2

0.6
0.5

1.5
ZT

Seebeck Coefficient (uV/K)
Thermal Conductivity (W/mK)

0.03

350

1

0.4
0.3
0.2

0.5

0.1

0

0
200

400

600

800

1000

Temperature (K)

200

400

600

800

1000

Temperature (K)

Figure 5.14: High temperature thermoelectric properties of Cu2 Sn0.925 In0.075 Se2.1 S0.9

5.4.3

Summary

From this portion of the work it is concluded that S for Se substitution is a viable way to improve
the thermoelectric performance of Cu2 SnSe3 . The lattice thermal conductivity is decreased by
70% at 80K and 40% at 300K when 30% S is added. Both Ga and In are effective p-type dopants
in the Cu2 SnSe3-x Sx compounds, although reproducibly controlling the hole concentration is still
an issue. Sample-to-sample variations in the hole concentration were always present independent
of the synthesis procedure or doping level, which indicates that intrinsic defects play a major role
in determining the hole concentration.
The optimum thermoelectric performance was obtained for the Cu2 Sn0.925 In0.075 Se2.1 S0.9
compound, which reaches ZT=0.62 at 760K. Above this temperature the material undergoes soft63

ening which limits the viable operating temperature range for these compounds. Despite the reproducibility and softening problems, the relatively large ZT value obtained for these compounds
warrants further exploration. Electronic band structure and defect thermodynamics calculations
could provide insight as to an appropriate method of controlling the hole concentration. An investigation of the mechanical properties of these compounds would allow for a better understanding
of the softening that occurs near 800K.

64

5.5

Off-Stoichiometric Cu2 GeSe3 Compounds

The stoiciometric compound Cu2 GeSe3 has been studied to some extent for thermoelectric applications, but there is a wide range of compounds with similar compositions that have remain
unexplored. It has been reported that Cu2 GeSe3 can accommodate both a deficiency and an excess
of Ge, and the evolution of the physical properties with composition has not been reported.

5.5.1

Experimental

Samples with composition Cu2 Ge1+x Se3 (x ranging from -0.15 to 2) were prepared according to
the procedure outlined in Section 3.1. Samples were cooled either by quenching the melt from
900◦ C into water or by slow-cooling from 900◦ C to room temperature at 0.4◦ C/min. SEM analysis was performed at the MSU center for advanced microscopy. Samples for transport property
measurements were cut directly from the solidified ingots.

5.5.2

Results and Discussion

The orthorhombic crystal structure of Cu2 GeSe3 reported by Parthe [69] was prevalent for both
slow cooled and quenched x = 0 samples, as shown in Figures 5.6 and 5.8, indicating that ordering
among the Cu and Ge atoms is preferred over a disordered structure which would have a higher
symmetry unit cell (likely cubic as for quenched Cu2 SnSe3 ). Early reports of cubic Cu2 GeSe3
may have been erroneous due to inaccuracy of the older XRD techniques employed, or a cubic
Cu2 GeSe3 phase may be possible if very fast cooling rates are achieved. All Cu2 GeSe3 samples
were p-type with degenerate hole concentrations on the order of 1020 cm-3 over the temperature range studied. Initial results indicated that doping with Ga or In on the Ge site successfully
increased the hole concentration, however the largest room temperature ZT value of 0.016 was
obtained for the undoped compound.
The primary interest here is the Cu2 GeSe3 compounds of off stoichiometric composition, some

65

Relative Intensity (arb. units)

x = !0.15

x = !0.1

x = !0.05

x = !0.01

x=0
10

20

30

40

50

60

70

80

90

2! (degrees)

Figure 5.15: XRD patterns for slow cooled Cu2 Ge1+x Se3 compounds with negative values of x.

of which have reportedly low thermal conductivity [46]. Compounds deficient in Ge (negative
values of x) were reported by Sharma [70] as having a monoclinic crystal structure associated with
the terminal compound Cu2 Ge0.85 Se3 . The XRD patterns for samples with negative values of
x (Figure 5.15) show a gradual transition from orthorhombic (x = 0) to monoclinic (x = -0.15)
symmetry, as evidenced by the gradual change in the peaks near 45◦ and 55◦ 2θ. All of the peak
locations for the x = -0.15 sample matched with those reported by Sharma and no impurity phases
were detected in any of the samples [70].
The thermoelectric properties of the Ge deficient compounds are shown in Figure 5.16. The
electrical resistivity and Seebeck coefficient decrease rapidly with decreasing x, indicating that
the Ge deficiency has a strong doping effect on Cu2 GeSe3 . The change in x did not change the

66

sign of the carriers and all samples displayed p-type conduction. The x = -0.1 and -0.15 samples
show essentially metallic character, indicated by their low and temperature independent Seebeck
coefficients. There is a substantial electronic contribution to the thermal conductivity for the x <
0 compounds, which comprises 29% of the total at room temperature for the x = -0.15 sample as
calculated from the Wiedemann-Franz law using L0 = 2.45×10−8 WΩK-2 . The lattice thermal
conductivity (lower right, Figure 5.16) decreases with decreasing x at low temperature, which
could be due to phonon scattering at vacancies created from the decreasing Ge content. The x =

200

12

x=0
x=-0.01
x=-0.05
x=-0.1
x=-0.15

120

10
!T (W/m*K)

160

8
6

80

4

40

2

0

0
12

0.1

10
!L (W/m*K)

Resistivity (Ohm*cm)

Seebeck Coefficient (uV/K)

-0.01 sample has the largest ZT value, but it reaches only 0.011 at room temperature.

0.001

8
6
4
2

0.00001

0
50

100

150
200
250
Temperature (K)

300

350

50

100

150
200
250
300
Temperature (K)

350

Figure 5.16: Temperature dependence of the electrical resistivity, Seebeck coefficient, and thermal
conductivity for slow cooled Cu2 Ge1+x Se3 compounds with negative values of x.

The change in crystal symmetry for positive values of x was found to be considerably more
complex than the gradual distortion observed for negative x values. Due to the wide range of
compositions studied the results are split into two groups, x≤ 0.55 and x≥ 0.55, based on previ-

67

ous results that indicate the solubility limit of Ge in Cu2 GeSe3 is x=0.55 [70]. The x-ray pattern
changes significantly when excess Ge is initially added (Figure 5.17), and the double peaks indicative of the Cu2 GeSe3 structure are nearly gone at x = 0.4. When x = 0.55, only peaks corresponding
to the cubic Cu2 Ge1.55 Se3 structure remain. The evolution of the x-ray patterns suggest that the
intermediate compositions, 0 < x < 0.55, are mixtures of the two end compounds Cu2 GeSe3 and
Cu2 Ge1.55 Se3 . The x-dependence of the thermal conductivity (Figure 5.18) highlights the transition between these two compounds, which occurs between x = 0.4 and x = 0.5, resulting in a
50% reduction in thermal conductivity at 80K. The electronic transport properties show no clear x

Relative Intensity (arb. units)

dependence, indicating that the addition of excess Ge has no doping effect on Cu2 GeSe3 .

x = 0.55

x = 0.5

x = 0.4

x = 0.2

x=0
10

20

30

40

50

60

70

80

90

2! (degrees)

Figure 5.17: XRD patterns for the Cu2 Ge1+x Se3 compounds with 0 ≤ x ≤ 0.55.

The x-ray diffraction patterns for the x ≥ 0.55 samples (Figure 5.19) suggest that a single phase
68

120
80
40

Resistivity (Ohm*cm)

x=0
x=0.2
x=0.4
x=0.5
x=0.55

160

1

0.1

0
12

0.01
0.02

10

0.016

8

0.012

ZT

Thermal Cond. (W/m*K)

Seebeck coeff. (uV/K)

200

6

0.008

4
2

0.004

0

0
50

100

150 200 250 300
Temperature (K)

350

50

100

150 200 250 300
Temperature (K)

350

Figure 5.18: Temperature dependence of the thermoelectric properties of the Cu2 Ge1+x Se3 compounds with 0 ≤ x ≤ 0.55.

cubic (zincblende) structure is maintained for 0.55 ≤ x ≤ 1.0. For all samples with x > 1.0 (not
shown), elemental Ge was present as a secondary phase. The Seebeck coefficient increases with
increasing x but the resistivity shows no obvious x dependence, indicating that excess Ge does
not have a doping effect in Cu2 Ge1.55 Se3 (Figure 5.20). The thermal conductivity again shows a
transition, in this case a 40% reduction is realized at 80K between the x=0.6 and 0.8 samples (lower
left, Figure 5.20). The results from a water quenched x=1.0 sample (denoted x = 1.0Q) are also
shown in Figures 5.19 and 5.20. The peaks shift to lower 2θ values, indicating an increase in the
lattice constant, and the thermal conductivity is the lowest observed for any of the Cu2 Ge1+x Se3
compounds. It is likely that more Ge is incorporated into the lattice of the quenched sample (similar
to the case of the Cu2 SnSe3 -Cu2 GeSe3 solid solution).
˚
˚
Since Cu2 Ge1.55 Se3 (a = 5.569 A) and elemental Ge (a = 5.66 A) have the same crystal struc69

Relative Intensity (arb. units)

x = 1.0 Q

x = 1.0 SC

x = 0.8

x = 0.6

x = 0.55
10

20

30

40

50

60

70

80

90

2! (degrees)

Figure 5.19: XRD patterns for the Cu2 Ge1+x Se3 compounds with 0.55 ≤ x ≤ 1.0, ”SC” and ”Q”
labels indicate slow cooled and quenched samples respectively.

ture and similar lattice constants, the possibility of a solid solution between these two materials
should be considered. Assuming that excess Ge will occupy the Cu, Ge, and Se sites with equal
probability, the solid solution takes the form (Cu2 Ge1.55 Se3 )1-y Gey , or Cu2-2y Ge1.55-0.55y Se3-3y .
Using this notation, the y = 0.5 composition would correspond to the compound Cu2 Ge2.55 Se3 ,
which according to the present results does not exist, and the y = 0.3 composition corresponds to
the compound Cu2 Ge2 Se3 (data shown in Figures 5.19 and 5.20). The data extracted from Figures
5.19 and 5.20 for the Cu2 Ge1+x Se3 compounds are in excellent agreement with what one would
expect for the Cu2 Ge1.55 Se3 -Ge solid solution. Figure 5.21 shows the calculated lattice constants
and measured thermal conductivities (at 80K) versus Ge content (in terms of y) for the compounds
studied here. The lattice constants show a nearly linear relationship with Ge content (as predicted
70

x=0.55
x=0.6
x=0.8
x=1.0 SC
x=1.0Q

200
160
120

Resistivity (Ohm*cm)

Seebeck coeff. (uV/K)

240

80

0.05
0.04
0.03
0.02
0.01

0
6

0
0.02

5

0.016

4
ZT

Thermal cond. (W/m*K)

40

0.06

3
2

0.012
0.008

1

0.004

0

0
50

100

150 200 250 300
Temperature (K)

350

50

100

150 200 250 300
Temperature (K)

350

Figure 5.20: Temperature dependence of the thermoelectric properties of the Cu2 Ge1+x Se3 compounds with 0.55 ≤ x ≤ 1.0, ”SC” and ”Q” labels indicate slow cooled and quenched samples
respectively.

by Vegard’s law) and the thermal conductivity decreases with increasing Ge content, as we would
expect for compositions below 50%. These results are the first experimental evidence that the
Cu2 Ge1+x Se3 (x ≥ 0.55) compounds are a solid solution between Cu2 Ge1.55 Se3 and elemental
Ge, as originally proposed by Sharma and Singh [70].
SEM and EDS were completed on the excess Ge samples (positive x values) to determine the
effect of Ge on the microstructure of Cu2 Ge1+x Se3 and evaluate the possibility of a Cu2 GeSe3 Ge solid solution. It was found that all samples with x>0 contained small inclusions of a Ge-rich
phase (essentially pure Ge as determined by EDS) as shown in Figure 5.22. The Ge inclusions are
discontinuous, typically measuring tens of microns in diameter, and comprise only a small fraction
(<10%) of the microstructure. The remaining phase (light region in Figure 5.22 BSE) contains Cu,
71

Thermal conductivity (W/m*K)

1000
(a)

100

10

1

Calculated lattice parameter (Å)

5.68
(b)
5.64

5.6

5.56

5.52
0

0.2

0.4

0.6

0.8

1

Ge content (y)

Figure 5.21:
Measured thermal conductivity at 80K (a)
and calculated lattice constant (b) versus Ge content for the
(Cu2 Ge1.55 Se3 )1-y Gey solid solution. The dashed line in (b) represents the linear relation predicted by Vegard’s law. The data for
pure Ge are taken from [45] and [94].

72

Ge, and Se. The results of EDS analysis on the majority phase in the Cu2 Ge1+x Se3 samples given
in Table 5.2 indicate that the composition of the majority phase region is changing with increasing
x. The increasing measured Ge content with increasing x (see Figure 5.23) confirms the hypothesis
that the Cu2 GeSe3 lattice is able to incorporate excess Ge, and refutes the claim by Sharma et. al.
that the only off-stoichiometric ternary compound occurs at x = 1.55 [71].

BSE

Cu K!1

Ge K!1

10µm

Se K!1

Figure 5.22: EDS X-ray mapping of a typical region of a
Cu2 Ge1+x Se3 sample. Upper left BSE image shows the mapped
region, remaining images show the distribution of Cu, Ge, and Se as
indicated

Figure 5.23 shows that the measured composition is always slightly greater than the ideal composition until x=1.2 where the Ge content begins to saturate. The Cu2 Ge2.2 Se3 sample was found
to have very large Ge-rich regions (see Figure 5.24), likely because the solubility limit of Ge in
Cu2 GeSe3 was reached and the excess Ge was rejected. Based on these results it is concluded
that Ge is soluble in Cu2 GeSe3 although this system does not form a complete solid solution. The
73

Table 5.2: EDS compositions of the majority phase for selected Cu2 Ge1+x Se3
compounds.
Ideal Composition
Cu2 GeSe3
Cu2 Ge1.2 Se3
Cu2 Ge1.4 Se3
Cu2 Ge1.55 Se3
Cu2 Ge1.6 Se3
Cu2 Ge1.8 Se3
Cu2 Ge2 Se3
Cu2 Ge2.2 Se3

ideal
measured
ideal
measured
ideal
measured
ideal
measured
ideal
measured
ideal
measured
ideal
measured
ideal
measured

at% Cu
33.3
33.43
32.26
28.47
31.25
26.28
30.53
28.64
30.30
29.18
29.41
27.64
28.57
27.73
27.78
30.63

at% Ge
16.67
16.44
19.35
27.54
21.88
25.32
23.66
27.64
24.24
29.00
26.47
30.24
28.57
29.74
30.55
30.35

at% Se
50.00
50.13
48.39
43.99
46.88
48.41
45.80
43.72
45.45
41.82
44.12
42.13
42.86
42.52
41.67
39.03

EDS Composition
Cu2.01 Ge0.99 Se3.01
Cu1.77 Ge1.71 Se2.73
Cu1.68 Ge1.62 Se3.10
Cu1.87 Ge1.81 Se2.86
Cu1.93 Ge1.91 Se2.76
Cu1.87 Ge2.06 Se2.86
Cu1.94 Ge2.08 Se2.98
Cu2.21 Ge2.19 Se2.81

results from EDS analysis and lattice thermal conductivity measurements indicate that the solubility limit of Ge in Cu2 GeSe3 is approximately 16.67%, in reasonable agreement with the original
finding of 14% by Goryunova [60].
The microstructure of the quenched Cu2 Ge2 Se3 sample was also investigated using SEM and
EDS, and no secondary phases were found. Quenching the Cu2 Ge1+x Se3 may be a viable route to
forming single phase compounds, but the brittle nature of the resulting ingots makes transport property measurements difficult. This could potentially be avoided using ball milling and hot pressing,
but a separate investigation on the effect of hot pressing on the microstructure of these compounds
would be required which is beyond the scope of this work. In addition, the isolated secondary
phase regions found in the slow cooled samples will likely have little impact on the thermal con74

ductivity values reported here since they comprise only a small portion of the microstructure and
are on the order of tens of microns, much larger than would be required to produce a substantial

Atomic percent Ge (at%)

phonon scattering effect.

40
35
30
25
20
15
10
5
0

Measured
Ideal
0

0.5
1
Ge content (x)

1.5

Figure 5.23: EDS composition (at% Ge) versus starting Ge content
(x) for Cu2 Ge1+x Se3 compounds. Error bars indicate ±10% error
associated with EDS measurement.

75

Cu2Ge2.2Se3

BSE

Cu K!1

Ge K!1

1mm

Se K!1

Figure 5.24: EDS X-ray mapping of a typical region of a
Cu2 Ge2.2 Se3 sample. Upper left BSE image shows the mapped region, remaining images show the distribution of Cu, Ge, and Se as
indicated

76

5.5.3

Summary

The structural and thermoelectric properties of Cu2 Ge1+x Se3 compounds with x ranging from
−0.15 to 1.2 have been evaluated. The stoichiometric Cu2 GeSe3 compound was found to have
an orthorhombic structure with a =1.1878 nm, b = 0.3941 nm, and c = 5.485 nm in agreement
with Parthe [69]. The orthorhombic structure formed independent of cooling rate indicating that a
disordered cubic phase is unlikely for this compound, in contrast to Cu2 SnSe3 . Off-stoichiometric
Cu2 GeSe3 was investigated as a means of reducing the lattice thermal conductivity and improving
the thermoelectric properties.
For compounds with x<0 the crystal structure gradually changed from orthorhombic to monoclinic as x decreased. The compound Cu2 Ge0.85 Se3 had a purely monoclinic structure with a =
0.5512 nm, b = 0.5598 nm, c = 0.5486 nm, and β = 89.7◦ , in agreement with Sharma et. al.
[70]. The lattice thermal conductivity did not decrease substantially as a result of the change in
composition, indicating that vacancies are not being created in the lattice. The Ge deficiency did
have a large effect on the electronic properties; the hole concentration increased rapidly with decreasing x and at x = −0.15 the compound is essentially metallic, as evidenced by its low electrical
resistivity and small temperature independent Seebeck coefficient. The thermoelectric properties
of Cu2 GeSe3 were improved only slightly for the x = −0.01 sample, and thus the x<0 compounds
were not pursued further.
For compounds with x>0 the crystal structure gradually changed from orthorhombic to cubic
for small x values, and at x = 0.55 the structure was purely cubic (zincblende) with a = 0.5561
nm, in agreement with Sharma et. al. [70]. When x>0.55 the structure remained cubic and the
X-ray diffraction peaks shifted to lower 2θ values with increasing x, indicating an expansion of
the lattice from excess Ge substitution. The lattice thermal conductivity decreased substantially
with increasing x and was approximately 32% lower at room temperature for the x = 1 sample
relative to the x = 0 sample. The shifted X-ray peaks and lowered lattice thermal conductivity
indicated a solid solution between the cubic Cu2 Ge1.55 Se3 and Ge which, based on calculated
77

lattice constants, seemed likely. SEM and EDS were used to evaluate the microstructure and phase
purity of the x>0 samples. For all samples with excess Ge small (tens of microns) inclusions of a
Ge rich phase (nearly pure Ge) were always present in a matrix of a Cu, Ge, and Se ternary phase.
The composition of the majority phase changed with increasing x as expected, indicating that the
excess Ge is incorporated in to the Cu2 GeSe3 lattice. The Ge content saturates at approximately
x = 1, and for x = 1.2 very large (millimeter size) Ge rich phase regions were present. The Gerich inclusions can be eliminated by quenching the sample in water from high temperature, but
the resulting ingots are extremely brittle which makes reliable transport property measurements
challenging. The thermoelectric properties were optimized for the x = 1.0 sample, which showed
ZT = 0.016 at room temperature. Controlling the carrier concentration proved to be a problem
in these compounds and sample to sample variations in the electronic properties were prevalent,
similar to the situation encountered for Cu2 SnSe3 .

78

5.6

Cu3 SbSe4

The compound Cu3 SbSe4 , a fourth-order ternary derivative of ZnSe, was identified by Hirono et.
al. [67] and Nakanishi et. al. [74] as a potential thermoelectric material, yet it has since been
explored very little for thermoelectric applications. At the beginning of this work no systematic
doping studies had been completed, and thus the original intent of this work was to identify dopant
species and optimize the carrier concentration for thermoelectric applications.

5.6.1

Experimental

Samples of Cu3 Sb1-x Ax Se4 (A = Ge or Sn) were prepared according to the procedure outlined in
Section 3.1. The reaction temperature was 900◦ C and samples were cooled to room temperature
either by water quenching or slow cooling in the furnace.
Water quenched samples were found to have significant red/orange deposits on the inside of the
ampoule after quenching and were subsequently annealed for 48 hours at 300◦ C. After annealing
all of the deposited material was reincorporated into the ingot, and samples were prepared for
transport measurements.
The as-solidified ingots were very brittle and preparing a sample for reliable transport measurements proved to be a challenge. Thus, powder processing was used to form high-quality samples
for all of the measurements reported here. The annealed Cu3 Sb1-x Ax Se4 ingots were ball milled
in an argon environment for 30 minutes using a SPEX 8000M vibratory mixer equipped with a
stainless steel vial and grinding media. The milled powders were then sieved using a 100 mesh
screen to remove any remaining large pieces. Finally, the powders were hot pressed in a graphite
die under argon using 70 MPa of pressure at 400◦ C for 30 minutes. The hot pressed samples had
measured densities >93% of the theoretical density (measured using the Archimedes method), and
samples for transport property measurements were cut directly from the hot pressed pellets. SEM
analysis for this portion of the work was completed at Oak Ridge National Laboratory.

79

5.6.2

Results and Discussion

Slow cooled samples of Cu3 SbSe4 were found to contain Sb2 Se3 as an impurity phase (see Figure 5.25), in agreement with the results of Scott and Kench [73]. Since Cu3 SbSe4 forms via a
peritectic reaction, only quenched samples had a single phase microstructure. Originally, samples
were quenched from 900◦ C, but it was later determined that quenching from 500◦ C produced the
same single phase microstructure without vigorous splashing of the melt. Thus, all of the samples reported here were quenched from 500◦ C into water. Figure 5.26 shows the XRD pattern of
a Cu3 SbSe4 sample quenched from 500◦ C and hot pressed at 400◦ C, illustrating that the single
phase microstructure is maintained after hot pressing. All of the peak positions match with those
¯
˚
˚
reported by Pfitzner for tetragonal Cu3 SbSe4 (space group I 42m, a = 5.6609 A, c = 11.28 A). The
single phase microstructure was confirmed using scanning electron microscopy; Figure 5.27 shows
EDS X-ray mapping of a typical region of Cu3 SbSe4 , indicating a homogeneous distribution of
Cu, Sb, and Se. No high temperature cubic phase was found for Cu3 SbSe4 , indicating that the Cu
and Sb atoms prefer an ordered arrangement.
Similar to the Cu2 -(Ge, Sn)-Se3 compounds, controlling the carrier concentration in Cu3 SbSe4
proved to be a challenge. Samples that were prepared without the post-quench annealing step had
hole concentrations >1019 cm-3 , with large variations in the hole concentration from sample to
sample. As mentioned above, after annealing at 300◦ C for 48 hours all of the deposited red/orange
material was reincorporated into the Cu3 SbSe4 ingot. The deposited material was likely amorphous Se since Se has the highest vapor pressure among the constituent elements. With deposited
Se on the ampoule wall after quenching the stoichiometry of the Cu3 SbSe4 ingot is deviated from
••
ideal, causing Se vacancies in the structure. A Se vacancy (VSe ) acts as an acceptor impurity in
Cu3 SbSe4 , causing the hole concentration to increase. This self doping causes a hole concentration
of ∼1019 cm-3 that is degenerate over the entire temperature range studied (Figure 5.29). After
annealing, the stoichiometry is returned to the ideal 3:1:4 and the hole concentration is decreased
to ∼ 4×1017 (see Figure 5.29). The temperature dependence of the hole mobility follows a T-3/2
80

Relative Intensity (Arb. Units)

Sb2Se3 PDF#01-075-3742

Cu3SbSe4 PDF#01-085-0003

10

20

30

40

50
60
2! (degrees)

70

80

90

Figure 5.25: XRD pattern of a Cu3 SbSe4 sample slow cooled from 900◦ C to
room temperature, along with the PDF data for Sb2 Se3 and Cu3 SbSe4 .

81

Relative Intensity (Arb. Units)

Cu3SbSe4 PDF#01-085-0003

10

20

30

40

50

60

70

80

90

2! (degrees)

Figure 5.26: XRD pattern of a Cu3 SbSe4 sample quenched
from 500◦ C to room temperature, along with the PDF data for
Cu3 SbSe4 .

trend, indicating that holes are scattered predominantly by acoustic phonons. The lowered hole
concentration is easily reproduced for samples that are prepared by quenching, annealing, and hot
pressing as described above.
Subsequent to establishing the synthesis procedure for Cu3 SbSe4 , the focus was shifted to systematically controlling the carrier concentration. Ge and Sn were chosen as p-type dopant species
because they have one less valence electron than Sb, and they will act as acceptor impurities on
the Sb site. Samples with up to 4% Ge or Sn on the Sb site were synthesized with no detectable

82

Cu3SbSe4

BSE

Cu Kα1

Sb Kα1

300µm

Se Kα1

Figure 5.27: EDS X-ray mapping of a typical region of Cu3 SbSe4
(work completed at ORNL). Upper left image shows a backscattered
electron image of a 600µm x 600µm region, and the distributions of
Cu, Sb, and Se in the same region are shown as indicated (white pixel
indicates presence of element).

impurity phases. The hole concentration and mobility of the Ge and Sn doped samples are shown
in Figure 5.29. The hole concentration increases with increasing doping and is degenerate for all
doped samples, and the mobility decreases with increasing doping due to ionized impurity scattering. The mobilities of the Ge-doped samples are slightly larger than those of the Sn-doped samples
likely due to the smaller electronegativity difference between Sn and Sb which, as discussed by
Slack, causes increased carrier scattering [99].
The electronic properties (80 - 630K) of the doped compounds are shown in Figure 5.30. The
onset of intrinsic conduction occurs just above room temperature for the undoped (x = 0) com-

83

Hole Concentration
(!1019 cm-3)

10

Annealed
Unannealed

1

0.1

Hole Mobility (cm2/V*s)

0.01
500
400
T-3/2

300
200
100
0
50

100

150

200

250

300

350

Temperature (K)

Figure 5.28: Temperature dependence of the hole concentration and
mobility for Cu3 SbSe4 , with and without the post-quench 300◦ C/48
hrs annealing step. Dashed line indicates the T-3/2 temperature dependence characteristic of carrier scattering by acoustic phonons.

pound, as evidenced by the simultaneous decrease in Seebeck coefficient (S) and electrical resistivity (ρ). Intrinsic conduction is suppressed with doping, and S and ρ both increase with temperature for all of the doped samples. S and ρ decrease with increasing doping as is expected due to
the increasing carrier concentration. The power factor (S2 /ρ) is optimized at the 3% doping level
for both Ge and Sn, although it is higher for the 3% Ge doped sample due to the slightly higher
mobility. The power factor reaches nearly 16 µW/cm*K2 for the 3% Ge doped sample at 630K,
rivaling that of state of the art thermoelectric materials such as PbTe in this temperature range [95].
The thermal conductivity (Figure 5.31) follows a T-1 temperature dependence over the entire

84

Hole concentration
(!1019 cm-3)

10
x=0
x=0.01 Ge
x=0.02 Ge
x=0.03 Ge

1
0.1

x=0
x=0.01 Sn
x=0.02 Sn
x=0.03 Sn

0.01
Hole Mobility (cm2/V*s)

1000
100
10
1
0

100
200
Temperature (K)

0

300

50

100 150 200 250
Temperature (K)

300

350

Figure 5.29: Temperature dependence of the hole concentration and mobility of Cu3 Sb1-x Ax Se4
compounds (A = Ge or Sn).

temperature range, indicative of phonon-phonon Umklapp scattering, and is still decreasing at
630K. The high temperature thermal conductivity was calculated as follows:

κ = D ρ cp

(5.13)

where D, ρ, and c p are the measured values for thermal diffusivity, density, and specific heat capacity respectively (for measurement techniques refer to Section 3.3). The total thermal conductivity
approaches 1 W/m*K at 630K and increases slightly with increasing doping level due to the electronic contribution, which constitutes approximately 15% of the total at high temperature for the
3% doped samples (calculated from the Wiedemann-Franz law using L0 = 2.44×10−8 WΩK-2 ).
The 2% doped samples have the highest ZT values (lower plot, Figure 5.31), in the neighborhood

85

Seebeck Coeff. (µV/K)

x=0
x=0.01 Ge
x=0.02 Ge
x=0.03 Ge

100

x=0
x=0.01 Sn
x=0.02 Sn
x=0.03 Sn

10
1
0.1
0.01

0.001
0.0001

Power Factor (W/cm*K2)

Resistivity (Ohm*cm)

1000

16
12
8
4
0
0

8000

200
400
600
Temperature (K)

200

400
600
Temperature (K)

800

Figure 5.30: Temperature dependence of the electronic properties of the Cu3 Sb1-x Ax Se4 compounds (A = Ge, Sn).

86

0.8

ZT

0.6
0.4

Thermal Cond. (W/m*K)

0.2
0
16
x=0.02 Ge

x=0.02 Sn

x=0.03 Ge

12

x=0.03 Sn

8
4
0
0

200
400
600
Temperature (K)

800 0

200
400
600
Temperature (K)

800

Figure 5.31: Temperature dependence of the thermal conductivity and dimensionless thermoelectric figure of merit of the Cu3 Sb1-x Ax Se4 compounds (A = Ge, Sn).

of 0.7 at 630K. These ZT values rival some of the best p-type thermoelectric materials in this
temperature range including PbTe, Ce-filled skutterudites, and TAGS compounds. They have the
added advantage of being free of toxic Pb, costly Ag, and rare earth elements that are in uncertain
supply. Unfortunately, the low melting temperature of these compounds (∼460◦ C) prevents the
extension of the measurements to higher temperatures.
Many attempts were made to produce n-type Cu3 SbSe4 , but all were unsuccessful. Zn doping
on the Cu site was tried first in an effort to reproduce the results of Scott et. al. [73], but n-type
conductivity was never achieved. The problem with Zn doping in Cu3 SbSe4 is that its crystal
structure is very similar to ZnSe, and a ZnSe impurity in Cu3 SbSe4 cannot be detected by XRD.
This similarity in crystal structure was exploited in an attempt to formulate compounds of the form
(Cu3 SbSe4 )1-x (ZnSe)x and in particular the quaternary compound Cu3 ZnSbSe5 (in the spirit of
87

the Cu2 SnSe3 - ZnSe solid solution which is known to contain Cu2 ZnSnSe4 , a thermoelectric
material with ZTmax = 0.95 [18]), but it was found that Cu3 SbSe4 and ZnSe are immiscible.
Subsequent n-type doping attempts included Ga and In on the Cu site, Br and I on the Se site, and
Se on the Sb site (varying the Sb/Se ratio), but none were able to produce n-type material. The
strong preference of Cu3 SbSe4 towards p-type conductivity is attributed to intrinsic defects which
create impurity levels in the band structure and dominate the conduction even after optimizing the
synthesis procedure and adding n-type dopants.

5.6.3

Summary

This work has revealed Cu3 SbSe4 to be a promising new p-type thermoelectric material. Singlephase material can be easily produced by quenching the melt from 500◦ C into water, suppressing
the formation of secondary phases that are present in slow-cooled samples. The crystal structure of
Cu3 SbSe4 is tetragonal wtih the Cu and Sb atoms assuming an ordered arrangement on the cation
sublattice. The hole concentration of as-quenched, undoped material is always >1019 cm-3 and
varies from sample to sample. A post-quench 300◦ C annealing step reincorporates lost Se into
the material, presumably decreasing the number of intrinsic defects which cause self-doping, and
produces samples with hole concentrations reproducibly near 1018 cm-3 .
P-type doping can be accomplished using Ge or Sn as dopant species on the Sb site. The hole
concentration increases with increasing Ge or Sn content, and all doped samples studied here were
found to be degenerate. The hole mobility remains above 25 cm2 /V*s at room temperature for
all doping levels. The Seebeck coefficient and electrical resistivity both decrease with increasing
doping, and the optimized thermoelectric power factor reaches 16 µW/cm*K2 for the 3% Ge doped
compound. The thermal conductivity follows a T-1 temperature dependence and approaches 1
W/m*K at high temperature. The highest ZT value is obtained for the 2% Sn doped sample, which
has ZT=0.72 at 630K, approaching that of some of the best p-type thermoelectric materials in this
temperature range.
88

The Cu3 SbSe4 -based compounds offer several advantages over traditional thermoelectric materials in that they contain no toxic or expensive elements and require no nanostructure to achieve
good thermoelectric performance. Their operating temperature is limited by the melting temperature of the compound, but could be used in applications with 300-400◦ C operating temperatures.

89

5.7

The Cu3 SbSe4 -Cu3 SbS4 Solid Soluiton

The above results on Cu3 SbSe4 are promising, but there is much room for improvement. The lattice thermal conductivity of the Cu3 Sb1-x Ax Se4 compounds is in the range of 0.9 - 1.0 W/m*K at
the highest measurement temperature, approximately twice that of the calculated minimum lattice
thermal conductivity of 0.46 W/m*K (refer to Section 6 for a discussion of ”minimum thermal
conductivity”). Thus, in an effort to reduce the lattice thermal conductivity and improve the thermoelectric properties of Cu3 SbSe4 , solid solutions with similar compounds were investigated. The
only reported solid solution in the I3 -V-VI4 family of compounds has been Cu3 AsS4 -Cu3 SbS4 ,
which forms a complete solid solution with a structural transformation at 80% Cu3 AsS4 [96]. The
options for isoelectronic substitutions in Cu3 SbSe4 are limited since As is highly toxic and Agbased compounds do not exist in this series. Bi substitution on the Sb site and Te substitution on
the Se site were attempted, but neither element was able to be incorporated into the Cu3 SbSe4 lattice. This leaves Cu3 SbS4 , which has the same tetragonal crystal structure as the selenide (space
¯
˚
˚
group I 42m no. 121) with smaller lattice constants a = 5.391 A and c = 10.764 A [97]. Cu3 SbS4
has seen mainly structural investigations, although it is known to be a semiconductor with Eg =
0.46 eV [98]. No investigations of the Cu3 SbSe4 -Cu3 SbS4 system appear in the literature.
5.7.1

Experimental

Samples of Cu3 SbSe4-x Sx (x ranging from 0 to 4) were prepared in the same way as the Cu3 SbSe4
compounds (see Section 5.6.1). The only difference was that compounds with x > 0 were quenched
from 600◦ C and then annealed at 350◦ C to account for the increase in melting temperature with S
content. Additional XRD data were collected at Oak Ridge National Laboratory from 15 to 140◦
2θ on a Panalytical MPD with Cu Kα radiation, parafocusing geometry, and a position-sensitive
detector. The lattice parameters were then refined using the Rietveld method, with the HighScore
Plus computer program. All hot pressed samples were > 94% dense, and all samples for transport

90

property measurements were cut directly from the hot pressed pellets.

5.7.2

Results and Discussion

Cu3 SbSe4 and Cu3 SbS4 form a complete solid solution, as evidenced by the gradual shift of the
XRD peaks to higher 2θ values with increasing S content (Figure 5.32), indicating a gradual contraction of the lattice. The refined lattice parameters (Figure 5.33 and Table 5.3) decrease linearly
with S content, in agreement with Vegard’s law (indicated by dashed lines). The refined lattice constants of the end compounds (x = 0 and 4.0) given in Table 5.3 are in reasonable agreement with
previously reported values [72], [97]. The XRD peaks for the intermediate compositions broaden
considerably due to increased microstrain in the lattice, which arises due to the smaller S atoms
substituting on the Se sites.
Table 5.3: Refined lattice constants for the
Cu3 SbSe4-x Sx compounds, estimated standard
deviation of the last digit is given in parentheses.
˚
Cu3 SbS4 content (x)
a (A)
0
5.65813(9)

˚
c (A)
11.2584(3)

0.4

5.62992(5)

11.2052(1)

1.2

5.5773(1)

11.1070(4)

2.0

5.5235(1)

11.0090(5)

2.8

5.4698(3)

10.854(1)

3.6

5.4177(3)

10.765(1)

4.0

5.3937(3)

10.724(1)

Hall data for the Cu3 SbSe4-x Sx compounds (x ≤ 2.0) are shown in Figure 5.34. The optimized
synthesis procedure again produced samples with low hole concentrations on the order of 1017 1018 cm-3 . The hole concentration tends to increase with increasing S content, presumably due
to defects that were not eliminated during annealing. The hole mobility decreases with increasing
91

Relative Intensity (Arb. units)

x = 4.0
x = 3.6
x = 2.8
x = 2.0
x = 1.2
x = 0.4
x=0
10

20

30

40

50

60

70

80

90

2! (degrees)
Figure 5.32: XRD patterns of Cu3 SbSe4-x Sx samples.

S content due to neutral impurity scattering, but remains above 10 cm2 /V*s for all samples (x ≤
2.0).
The primary interest here is the effect of S substitution on the lattice thermal conductivity (κL )
of Cu3 SbSe4 . The temperature dependence of κL for selected samples is shown in Figure 5.35.
For the x = 0 sample, the temperature dependence is the typical T-1 indicative of phonon-phonon
scattering only, but the addition of just 10% S causes the temperature dependence to weaken substantially due to phonon-impurity scattering. When 50% S is added, κL scales as just T-0.5 , and
is reduced by nearly 75% at 80K. The temperature and compositional dependencies of κL can be
understood using the Debye model, following the same procedure as the Cu2 Sn1-x Gex Se3 solid
92

a/a0

1.00

c /c0

0.95
1.00

0.95
0.0

0.2 0.4 0.6 0.8 1.0
Fractional Occupation S

Figure 5.33:
Refined lattice constants of the
Cu3 SbSe4-x Sx samples (from Figure 5.32) versus
fractional occupation S (equal to x/4). Dashed lines
indicate linear relationship predicted by Vegard’s law.

93

100
Hole Concentration
(!1017 cm-3)

0% S
10% S
20% S
30% S

10

Mobility (cm2/V*s)

1
1000
100
10
1
0

100
200
300
Temperature (K)

400

Figure 5.34: Hole concentration and mobility of the Cu3 SbSe4-x Sx
compounds.

94

16
0% (data)

Thermal Conductivity (W/mK)

14

0% (model)
10% (data)

12

10% (model)
10

50% (data)
50% (model)

8
6
4
2
0
50

100

150

200

250

300

350

Temperature (K)
Figure 5.35: Temperature dependence of the thermal conductivity of selected Cu3 SbSe4-x Sx compounds. Dashed lines are the calculated lattice thermal conductivities obtained from the Debye
model. Error bars indicate ±5% experimental error.

solution.
Following the procedure in Section 5.3.2, phonon scattering rates corresponding to grain boundaries, point defects, and phonon-phonon interactions (equation 5.6) are chosen for the calculation
of κL from the Debye model (equation 5.2). Once again normal phonon-phonon processes are
−1
neglected due to the imperfect nature of the hot-pressed specimens studied, and thus τU corresponds to phonon-phonon Umklapp scattering only. Based on SEM analysis, a grain size (L) of
20µm is used for the boundary scattering rate expression for all samples. The Gr¨ neisen parameter
u
95

(γ) is again treated as adjustable to fit the data of the x = 0 sample and then held constant with
composition. This procedure yields γ = 1.05, which is a reasonable estimate for zincblende-like
compounds based on previous results [45]. Since no information is available regarding the Debye
temperature (θ) or phonon velocity (v) of Cu3 SbS4 , estimates of the compositional dependence of
these parameters must be made. The phonon velocity is held constant at 1991.2 m/s, corresponding
to the estimated acoustic mode phonon velocity of Cu3 SbSe4 [85]. The compositional dependence
of θ is estimated from the expression:

β = θ M 1/2 V 3/2

(5.14)

where M and V are the average mass and volume per atom, and β is a constant for a given crystal
system [91]. Using the procedure of Slack [45] and the reported Debye temperature of Cu3 SbSe4
(θ0 = 131K), the acoustic mode Debye temperature is estimated as θa = 65.5K. Now the compositional dependence of the Debye temperature can be estimated, and θa for Cu3 SbS4 is found to be
84.4K.
The only remaining parameter to be calculated is ΓT , the phonon-impurity scattering parameter. The best fit to the experimental data is obtained using ε = 190 in the calculation for ΓS , in
reasonable agreement with ε = 136 calculated from equation 5.12 using γ = 1.05 [91]. From equations 5.10 and 5.11, the phonon-impurity scattering parameters due to atomic mass differences
(ΓM ) and strain field fluctuations (ΓS ) are calculated and given in Table 5.4. In stark contrast
to the Cu2 Sn1-x Gex Se3 solid solution, the strain-field fluctuation term is dominant for x ≤ 0.5
and still contributes significantly for x > 0.5, indicating that the size mismatch between S and Se
contributes strongly to the reduced lattice thermal conductivity.
The calculated lattice thermal conductivity at 80 and 300K as a function of composition is
shown in Table 5.4 and Figure 5.36. At room temperature the model fits the experimental data
to within ± 16%, which is quite remarkable considering that no adjustable parameters were used

96

28

data (80K)
model (80K)

!L (W/mK)

24
20
16
12
8
4
0
5

data (300K)
model (300K)

!L (W/mK)

4
3
2
1
0
0

0.5

1

1.5
2
2.5
Cu3SbS4 Content (x)

3

3.5

4

Figure 5.36: Compositional dependence of the lattice thermal conductivity
(κL ) of the Cu3 SbSe4-x Sx compounds at 80K and 300K. Dashed lines are the
calculated lattice thermal conductivities obtained from the Debye model. Error
bars indicate ±5% experimental error.

97

Table 5.4: Phonon-impurity scattering parameters along with calculated (κcalc ) and measured (κexp ) thermal conductivities (in W/m*K) for the Cu3 SbSe4-x Sx compounds.
Cu3 SbS4
content (x)
0

ΓM

ΓS

ΓT

0

0

0.4

0.01704

1.2

0

κcalc
(80K)
12.42

κexp
(80K)
13.43

κcalc
(300K)
2.96

κexp
(300K)
2.91

0.04120

0.05824

6.14

6.55

2.31

2.42

0.04516

0.08576

0.13091

4.45

4.17

1.94

1.80

2.0

0.06157

0.08810

0.14967

4.26

3.54

1.91

1.75

2.8

0.05982

0.06089

0.12071

4.85

3.27

2.08

1.79

3.6

0.03000

0.01997

0.04996

7.28

9.62

2.66

2.90

4.0

0

0

0

15.92

23.30

3.57

3.96

to produce the fit. There is considerably more deviation between the calculated and measured κL
at 80K for x > 0.5, presumably because va and γ are not really constant with composition. In
addition, extrinsic factors such as grain size and porosity will have a much larger effect on the
magnitude of κL at low temperature, causing larger deviations from the model. The Deybe model
fit to the temperature dependence of κL is also quite accurate (black lines, Figure 5.35). Regardless
of the accuracy of the model, the data in Figure 5.36 show that the lattice thermal conductivity of
Cu3 SbSe4 can be reduced by as much as 40% at room temperature by introducing S impurities
into the lattice. With the low initial hole concentrations still maintained for the Cu3 SbSe4-x Sx
compounds, the hole concentration can be adjusted and optimized through doping.
The Cu3 SbSe4 -Cu3 SbS4 solid solution is particularly attractive for thermoelectric applications
due to the nature of the Se/S substitution. Slack [99] reviewed the characteristics of established
thermoelectric semiconductor solid solutions and developed a set of criteria that should be met in
order for a given solid solution to show high ZT. First, he identified an important parameter for all
thermoelectric compounds, the weighted mobility, defined as:

98

U = µ[m∗ /m0 ]3/2

(5.15)

where µ is the carrier mobility, m∗ is the carrier effective mass, and m0 is the free electron mass
(9.11×10−31 kg). In general, U can be used as a guideline to judge the potential of a new material
for thermoelectric applications. The expression for ZT can be rewritten using the WiedemannFranz law (κe = L0 σT ):

ZT =

L0 )2
κL
1 + L σT
0
(S/

(5.16)

which, when combined with the expressions for weighted mobility (equation 5.15) and electrical
conductivity of a p-type semiconductor (σ = peµ where p is the hole concentration), gives:
L0 )2
ZT =
κL [m∗ /m0 ]1.5
1+ L 1
p
0 eT U
(S/

.

(5.17)

The material-dependent parameters governing ZT are then U/κL , which is intrinsic to the
chosen material, and [m∗ /m0 ]1.5 /p which depends on doping level. Slack determined that in
order to conserve U while reducing κL in a solid solution, the electronegativity difference (∆X)
between the host and impurity atoms should be as small as possible, ideally less than 0.05. The
Se/S pair satisfies this criterion (X(S) − X(Se) = 0.03) whereas the Se/Te pair, more commonly
used for thermoelectric materials, does not (X(Se) − X(Te) = 0.15). In addition, the Se/S pair
should provide comparable phonon scattering to Se/Te since the mass difference is similar (M Se −
M S = 46.9 versus M Te − M Se = 48.64) and the Se/S pair also has a large strain-field effect in
Cu3 SbSe4-x Sx as discussed above.
To determine the most suitable compositions for thermoelectric applications, U/κL values
99

U/kL (cm3*K/W*V*S

2500
2000
1500
1000
500
0
0

0.5

1

1.5

2

S (x)
Figure 5.37: Ratio of the weighted mobility (U) to lattice thermal conductivity (κL ) versus composition in the
Cu3 SbSe4-x Sx system for x≤2.

were calculated for samples with x≤2. Values of m∗ /m0 were extracted from Hall and Seebeck
coefficient measurements using the following expressions [100]:
4
p= √
π

2πm∗ kT 3/2
F1/2 (η)
h2

(5.18)

and

S=±

F (η)
k
2 1
−η
e
F0 (η)

(5.19)

where p is the hole concentration, S is the Seebeck coefficient, and Fn (η) are Fermi integrals of
order n evaluated at the reduced Fermi energy η. The resulting values of U/κL are shown in Figure
5.37. While none of the x>0 compounds match the U/κL value of Cu3 SbSe4 , it is clear that the
x = 0.8 and 1.2 compositions are the most promising from the Cu3 SbSe4-x Sx system; their room
temperature properties are listed in Table 5.5 .
Both Ge and Sn doping on the Sb site were again evaluated for the Cu3 SbSe4-x Sx compounds,

100

although in this case the addition of Sn caused a more drastic decrease in hole mobility and was not
explored further. Doping studies with Ge on the Sb site were completed for compounds with x =
0.8 and x = 1.2, producing compounds of the form Cu3 Sb1-y Gey Se1-x Sx . The room temperature
properties of the compounds studied are given in Table 5.5

Table 5.5: Room temperature properties of the Cu3 Sb1-y Gey Se4-x Sx compounds.
Hole
Seebeck
Mobility
Coefficient
(µV/K)
(cm2 /V*s)

Electrical
Resistivity
(mΩ*cm)

Thermal
Conductivity
(W/m*K)

Effective
Mass
(m∗ /m0 )

Composition

Hole
Concentration
(×1019 cm-3 )

x=0.8, y=0

0.0765

36.0

449

230

2.2

0.83

x=0.8, y=0.02

14.02

15.4

146

2.89

1.7

2.19

x=0.8, y=0.03

19.39

17.1

124

1.89

1.94

2.22

x=1.2, y=0

0.0711

26.0

445

340

1.8

0.77

x=1.2, y=0.02

12.78

17.8

142

2.75

1.88

2.00

x=1.2, y=0.03

20.32

14.8

127

2.08

1.88

2.33

Doping with 2% and 3% Ge increased the hole concentration to approximately 1.3×1020 cm-3
and 2.0×1020 cm-3 respectively, independent of S content, resulting in similar Seebeck coefficients for the y=0.02 and 0.03 samples (Figure 5.38). The doped samples have slightly lower
mobility than the undoped samples due to ionized impurity scattering, but the mobility remains
relatively constant with x, as evidenced by the similar electrical resistivity for the y=0.02 and
0.03 samples (Figure 5.38). The total thermal conductivity (Figure 5.39) follows a T n temperature dependence, where n ∼ -0.5 at low temperature (T ≤300K) and n ∼ -1 at high temperature
(T >300K). The change in temperature dependence arises because at low temperature phononimpurity scattering dominates and weakens the temperature dependence whereas at high temperature phonon-phonon scattering dominates and phonon-impurity scattering is essentially constant,
resulting in the characteristic T −1 temperature dependence.
101

Seebeck Coefficient
(µV/K)

300
250
200
x=0.8, y=0.02
x=0.8, y=0.03
x=1.2, y=0.02
x=1.2, y=0.03

150
100
50

Resistivity (Ohm*cm)

0
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
0

200

400
600
Temperature (K)

800

Figure 5.38: Temperature dependence of the Seebeck coefficient and
Electrical resistivity of the Cu3 Sb1-y Gey Se4-x Sx compounds

The electronic contribution to the thermal conductivity (κe ) was again calculated from the
Weidemann-Franz law, but with Lorentz numbers (L0 ) estimated for each sample according to
[100]:
2
k 2 3F0 (η)F2 (η) − 4F1 (η)
L0 =
2
e
f0 (η)

(5.20)

where the reduced Fermi energy η is estimated from the Seebeck coefficient data given in Table 5.5
using equation 5.19. The calculated high temperature lattice thermal conductivity (κL = κT − κe )

102

Thermal Conductivity (W/m*K)

7
x=0.8, y=0.02

6

x=0.8, y=0.03

5

x=1.2, y=0.02
x=1.2, y=0.03

4
3
2
1
0
1

0.8

ZT

0.6
0.4
0.2
0
0

100

200

300
400
500
Temperature (K)

600

700

800

Figure 5.39: Temperature dependence of the thermal conductivity and dimensionless thermoelectric figure of merit of the
Cu3 SbSe4-x Sx compounds

103

is shown in Figure 5.40. κL is approximately equal for all samples and independent of x, and agrees
quite well with the estimate obtained from the Debye model, calculated following the procedure
described above for the x=1.2 composition using γ=1.3 (dashed line, Figure 5.40). The κL for
the x>0 compounds is approximately 40% lower than that of the x=0, y=0 compound over the
entire temperature range due to constant phonon-impurity scattering, and approaches 0.6 W/m*K
at 650K for all samples. Using the average measured specific heat (C = 1.85 J/cm3 K) and the
reported longitudinal sound velocity for Cu3 SbSe4 (v = 3.0 km/sec [85]), it is possible to estimate
the phonon mean free path ( ) at 650K using the expression [44]:
1
κL = Cv .
3

(5.21)

The estimated phonon mean free path at 650K is ∼ 0.3 nm, only slightly larger than the average
interatomic spacing in Cu3 SbSe4 and Cu3 SbS4 (0.246 nm and 0.234 nm respectively), which
represent the minimum possible value of in these compounds.
The relatively large power factor and low thermal conductivity in these compounds leads to
very respectable ZT values at high temperature, approaching 0.9 at 650K (Figure 5.39). All of
the compounds studied here have ZT > 0.8 at 650K, and the maximum value is ZT = 0.89 for the
x=1.2, y=0.03 sample. These values are comparable with the best performing p-type thermoelectric materials at this temeprature, including PbTe [101], double-filled skutterudites [102], and the
AgSbTe2 -GeTe (TAGS) compounds [103].
5.7.3

Summary

The Cu3 SbSe4 -Cu3 SbS4 system has been studied for the first time. These two compounds form
a complete solid solution, maintaining the tetragonal crystal structure of the end compounds at all
compositions. Samples prepared by quenching from 600◦ C and annealing at 350◦ C are singlephase with hole concentrations on the order of 1018 cm-3 at room temperature. The hole concen-

104

3.5

x=0.8, y=0.02
x=0.8, y=0.03
x=1.2, y=0.02
x=1.2, y=0.03
x=0.0, y=0.0
Debye Model

3
!L (W/m*K)

2.5
2

1.5
1

0.5
0
250

350

450
550
Temperature (K)

650

750

Figure 5.40: High temperature lattice thermal conductivity of the
Cu3 SbSe4-x Sx compounds. Dashed line indicates κL calculated
from the Debye model for x=1.2 using γ=1.3.

tration increases slightly with increasing S content, presumably due to an increase in the number of
intrinsic defects in the material resulting from S loss during synthesis. The hole mobility also decreases with increasing S content due to neutral impurity scattering, but remains above 10 cm2 /V*s
at all compositions.
Substitution of S for Se in Cu3 SbSe4 is ideal for improving its thermoelectric performance
because it produces a substantial reduction in κL without significantly degrading the electronic
properties of the material. The κL of Cu3 SbSe4 is reduced by as much as 70% at low temperature and 40% at room temperature and above by introducing S impurities into the lattice. Using
the Debye model to fit the experimental κL data revealed that both the atomic mass and size
difference between Se and S contribute to increased phonon scattering in the material. The small
electronegativity difference between Se and S helps to conserve the carrier mobility at intermediate
compositions in the Cu3 SbSe4-x Sx system, such that the electronic properties are not significantly

105

degraded. Both Ge and Sn are effective p-type dopants, although Sn doping tends to give lower
hole mobility and was not extensively explored. Doping with 3% Ge on the Sb site gives rise
to a thermoelectric power factor of 12 µW/cm*K2 at 650K. The thermoelectric performance of
Cu3 SbSe4 is optimized with 3% Ge on the Sb site and 30% S on the Se site, which gives ZT = 0.9
at 650K.
The Cu3 Sb1-y Gey Se4-x Sx compounds offer the same advantages as Cu3 SbSe4 in that they do
not contain toxic or expensive elements or complex nanostructures. The melting temperature is
increased slightly with S content, which allows for higher operating temperatures. With further
optimization of the doping level and S content, ZT values greater that unity are likely, making
these compounds attractive for thermoelectric power generation at intermediate temperatures.

106

5.8

Cu-Based Diamond-Like Ternary Compounds: Conclusions and Future
Work

From this portion of the work it is concluded that ternary variations on the elemental diamond structure semiconductors are viable candidates for thermoelectric power generation applications. The
diamond-like Cu-based ternary compounds are derived schematically from the group IV elemental
semiconductors through successive atomic substitutions, which increase the size and complexity
of the unit cell and lead to little-known narrow band gap ternary semiconductors with low lattice
thermal conductivities. The two-fold ternary derivatives having compositions of the form I-III-VI2
are not well suited for thermoelectric applications due to their relatively wide band gaps and high
thermal conductivity, and thus were not studied here. The three and four-fold ternary derivatives,
having compositions of the form I2 -IV-VI3 and I3 -V-VI4 , were the focus of this work. From these
systems, compounds with I = Cu and VI = Se were found to exist as single phase compounds with
reported band gaps in the range appropriate for thermoelectric applications.
Cu2 SnSe3 exists in both low and high temperature modifications, with the high temperature cubic phase corresponding to a disordered arrangement of Cu and Sn atoms and the low temperature
monoclinic phase corresponding to an ordered arrangement. The quenching procedure required to
form the cubic phase of Cu2 SnSe3 results in extreme brittleness in the material and thus transport
property measurements were conducted exclusively on slow-cooled samples. Undoped samples
were always p-type and exhibited a wide range of hole concentrations, 1018 to 1020 cm-3 at room
temperature, likely due to self-doping via intrinsic defects. Both Ga and In are effective p-type
dopants in Cu2 SnSe3 , although large fluctuations in the hole concentration were still present in
doped samples. Lengthy annealing treatments and minor changes in composition did not improve
the reproducibility of the samples.
Cu2 SnSe3 forms a complete solid solution with Cu2 GeSe3 , maintaining a single phase at all
compositions. For compounds of the form Cu2 Sn1-x Gex Se3 , a structural transformation occurred

107

at either x=0.5 or x=0.7 depending on the synthesis procedure. For quenched samples, the cubic structure of Cu2 SnSe3 was maintained until x=0.7 before a transition to the orthorhombic
Cu2 GeSe3 lattice occurred. For slow-cooled samples the transition from monoclinic to orthorhombic symmetry occurred at x=0.5. The lattice thermal conductivity decreases slightly with increasing
x and can be approximated quite accurately using the Debye model. An analysis of the phonon impurity scattering parameter (Γ) revealed that the decrease in lattice thermal conductivity is almost
exclusively due to the atomic mass difference between Sn and Ge with no contribution from lattice
strain arising from the atomic radius mismatch. The thermoelectric properties of Cu2 SnSe3 were
not improved by adding Cu2 GeSe3 .
The Cu2 SnSe3 -Cu2 SnS3 system also forms a complete solid solution, in agreement with previous results [68]. The monoclinic structure of Cu2 SnSe3 was maintained at all compositions
(only slow-cooled samples were investigated). The lattice thermal conductivity is reduced by approximately 40% at room temperature upon the addition of Cu2 SnS3 due to mass and strain field
fluctuations in the lattice. Both Ga and In are effective p-type dopants, and the thermoelectric
performance was optimized for 7.5% In doping on the Sn site. Large sample-to-sample hole concentration variations still plague these compounds, along with a mechanical instability near 800K
that causes softening of the sample.
Cu2 GeSe3 maintains an orthorhombic structure when quenched or slow-cooled, indicating a
strong preference for ordering among the Cu and Ge atoms. The ability of this compound to accommodate a wide range of Ge concentration was investigated, with an emphasis on the structural
transformations and the effect on the transport properties. Cu2 Ge1+x Se3 compounds with negative
values of x (Ge deficiency) showed a gradual transition from orthorhombic (x=0) to monoclinic
(x=-0.15) symmetry accompanied by a transition from semiconducting to metallic transport behavior. This indicates that a Ge deficiency in Cu2 GeSe3 has a strong doping effect, but it was
found that it does not improve the thermoelectric performance. The addition of excess Ge (positive x values) induced a transition from orthorhombic to cubic symmetry at x=0.55, with a cubic
108

lattice being maintained for 0.55≤x≤1.0. The lattice thermal conductivity decreased strongly
with increasing Ge content, which suggests that these compounds are actually a solid solution.
Cu2 Ge1.55 Se3 and elemental Ge have the same crystal structure and similar lattice constants, and
an analysis of the lattice constant change, lattice thermal conductivity reduction, and average composition (determined by EDS) strongly indicates a solid solution. The solubility limit of Ge in
Cu2 GeSe3 occurs at x=1.2, at which point large Ge-rich regions precipitate out. Doping studies
on the excess Ge compounds were largely unsucessful and mainly frustrated by the already large
hole concentrations in the undoped compounds.
Cu3 SbSe4 was found to exist only with an ordered tetragonal structure, with no high temperature disordered phase possible. Single phase samples were obtained by quenching, although large
hole concentration gradients were found in quenched samples. Annealing the quenched samples
at 300-350◦ C in the same ampoules produced samples with hole concentrations on the order of
1018 cm-3 with good reproducibility, presumably due to homogenization during the annealing
procedure. Doping with Ge or Sn on the Sb site systematically varied the hole concentration and
optimized the thermoelectric power factor near 16 µW/cm*K2 at 630K. The lattice thermal conductivity approached 1 W/m*K at 630K, resulting in ZT values near 0.7, competitive with some of
the best p-type thermoelectric materials.
The Cu3 SbSe4 -Cu3 SbS4 system forms a complete solid solution with the tetragonal structure of Cu3 SbSe4 maintained at all compositions. The lattice thermal conductivity is decreased
by as much as 40% at room temperature due to atomic mass and strain field fluctuations. The
hole mobility remains relatively large (above 20 cm2 /V*s) at all compositions due to the small
electronegativity difference between Se and S. The reduction in lattice thermal conductivity is realized even at high temperatures, and the minimum possible value is reached at approximately
650K. Ge-doped samples achieved ZT=0.89 at 650K, in the range of many state of the art p-type
thermoelectric materials.
There are numerous opportunities for future work on these compounds. The two-fold ternary
109

derivates Cu2 SnSe3 and Cu2 GeSe3 would benefit from electronic band structure and defect calculations, which could provide a means of understanding the unexplained variability of the hole
concentration in these compounds. If the hole concentration can be controlled, the Cu2 SnSe1-x Sx
are promising as p-type thermoelectric materials. Band structure, defect, and phonon dispersion
calculations are currently underway for Cu3 SbSe4 . Equally important to understanding electrical and thermal transport in these compounds is evaluating their mechanical properties. Many
of the compounds studied in this work are quite brittle, and poor mechanical properties would
likely prevent them from being widely used in thermoelectric applications despite their impressive
performance and environmental benefits.

110

6

The Effect of Lone Electron Pairs on the Lattice Thermal
Conductivity of Group VA Chalcogenides

In the preceding chapters, the discussion has focused primarily on the synthesis, characterization,
and optimization of Cu-based diamond-like semiconductors for thermoelectric applications. These
compounds all possess low κL at room temperature which then increases rapidly with decreasing
temperature due to vanishing phonon-phonon interactions, as is typical for a crystalline material.
More interesting for thermoelectric applications is the case of glass-like thermal conductivity in
a crystalline material, where the phonon mean free path is limited to its minimum possible value
even at low temperature. This phenomenon occurs in AgSbTe2 , one of the motivating factors for
this work, and has been reported in relatively few other compounds.
In characterizing the Cu-based ternary systems for this work, namely the Cu-Sb-Se and CuBi-Se systems, several compounds that exhibited glass-like thermal conductivity were found. The
common thread among these compounds is that they all contain a group V element which is nominally in the trivalent (+3) state, meaning two fewer electrons per atom are lost than one would
naively expect considering only the group number, leaving two valence electrons that do not participate in bonding. Morelli et. al. indicated that the ”non-bonding” or ”lone-pair” electrons
around Sb in AgSbTe2 could have an effect on the lattice thermal conductivity [44], but concrete
evidence of a relation between the two is absent from the literature. The present chapter delves
deeper into the effect of lone electron pairs (LEPs) on the physical properties of semiconductors, in
particular κL , and how this could be used as a part of the selection criteria for new thermoelectric
materials.

6.1

Background and Motivation

The transport of heat in crystalline solids has long been a topic of interest in solid-state physics.
Thermal energy is conducted primarily by electrons and phonons in most materials, with the rel111

ative contributions of each determined by the physical properties of the crystal. The electronic
contribution to the thermal conductivity of a given material, for instance, is directly proportional to
its electrical conductivity as defined by the Wiedemann-Franz law. The electronic contribution is
negligible in insulators and many semiconductors, but the phononic contribution is always present
in any solid, exhibiting a surprisingly large range of values. Debye studied heat transport by lattice
phonons in 1912 [104] and to this day the lattice thermal conductivity of a vast array of crystalline
materials can be estimated, to a first approximation, using some form of the Debye model.
An interesting problem arises when one encounters a material whose lattice thermal conductivity cannot be explained using conventional phonon transport theory. Such is the case for ordered
crystals that exhibit minimum thermal conductivity behavior at ordinary temperatures. In developing his famous PGEC (phonon glass electron crystal) concept for thermoelectric materials, Slack
[99] showed that κL must approach the minimum possible value in a given material in order to
obtain very large (>1.5) ZT values. The concept of ”minimum thermal conductivity” was first
described by Slack many years earlier [45], which he defined as the case where all phonons are
scattered so frequently that the average mean free path is on the order of one phonon wavelength.
The minimum phonon mean free path, as pointed out by Roufosse and Klemens [105], is on the
order of one interatomic spacing. Cahill et. al. later experimentally confirmed the ”minimum
thermal conductivity” concept by studying a wide range of materials with glass-like thermal conductivity, none of which exhibited κL much lower than the κmin estimated using a modified Einstein model. It is not uncommon for κL of an ordered crystalline material to approach κmin near
its melting temperature due to phonon-phonon interactions alone, however similar behavior near
room temperature is quite rare. The underlying mechanism behind glass-like thermal conductivity in ordered crystals at low temperatures is not well understood; based on the results of Slack
and Cahill there must be an intrinsic phonon scattering process that limits the mean free path over
the entire phonon spectrum. Extrinsic modifications such as introducing substitutional impurities
cannot produce glass-like phonon scattering. Obviously, a better understanding of such intrinsi112

cally limited κL is of paramount importance for the design of high performance thermoelectric
materials.
The existence of glass-like thermal conductivity in the rocksalt structure I-V-VI2 compounds
where I = Ag, V = Sb or Bi and VI = Se or Te was first reported many years ago by Hockings
[36]. Zhuze [34] reported linear thermal expansion coefficients in excess of 20 ppm for these
compounds, indicating a high degree of anharmonicity in the crystal lattice. Petrov and Shtrum
[37] noted the large difference in thermal conductivity and thermal expansion between the chalcopyrite I-III-VI2 compounds and the I-V-VI2 compounds, which they attributed to differences in
interatomic bonding. In particular, they hypothesized that the interaction of nonbonding electrons
around the nominally trivalent group V atoms contribute to a large anharmonicity in the I-V-VI2
lattice which is not present in the sp3 hybridized I-III-VI2 compounds where all valence electrons
participate in bonding. Recently Morelli et. al. came to a similar conclusion for the case of
AgSbTe2 versus AgInSe2 , and showed that the phonon mean free path in AgSbTe2 is limited to
the minimum possible value even at cryogenic temperatures [44]. Based on specific heat measurements and the reported thermal expansion they estimated the Gr¨ neisen parameter of AgSbTe2 to
u
be 2.05, which is a large value compared to most crystalline materials with simple crystal structures. This reaffirms that AgSbTe2 has a high degree of lattice anharmonicity since the Gr¨ neisen
u
parameter is a direct measure of anharmonicity. Although the κL difference between AgSbTe2 and
AgInTe2 is intuitively explained using the nonbonding electron argument of Petrov and Shtrum, no
concrete evidence in favor of a relation between LEPs and lattice anharmonicity has been provided.
The valence electron configuration of Sb in both naturally occurring and synthetic compounds
has long been a topic of interest in the field of solid-state chemistry. There is a large body of work
devoted to the stereochemistry of Sb compounds, in particular relating the valence state of Sb to
its local atomic environment [106]. Several recent studies have focused on the effect of Sb valence
on atomic coordination and electronic properties in Sb chalcogenides [107] - [109], and provide
experimental evidence relating the ”activity” of the Sb lone pair (the delocalization of the lone pair
113

from the Sb nucleus) to the Sb coordination environment. This relation, as will be discussed in the
following sections, will be used to relate Sb valence state to κL .
The characterization of the Cu-Sb-Se system for the preceding chapters of this manuscript
revealed a unique opportunity to establish a link between Sb valence and κL . In this system there
exist three ternary compounds, CuSbSe2 , Cu3 SbSe3 , and Cu3 SbSe4 , which contain Sb nominally
in the +3, +3, and +5 valence state respectively, as determined by a simple charge-balance analysis.
Initial analysis of Cu3 SbSe3 versus Cu3 SbSe4 revealed a glass-like thermal conductivity for the
former compound and a crystalline-like thermal conductivity for the latter, as shown in Figure 6.1
[110]. The glass-like thermal conductivity in Cu3 SbSe3 was again attributed to increased lattice
anharmonicity arising from the interaction between the LEPs around Sb3+ and neighboring atoms.
Using the relation between Sb valence and local atomic environment, the available structural data
on the Cu-Sb-Se ternary compounds [111], [72], [112], and the lattice thermal conductivity data
for Cu3 SbSe3 and Cu3 SbSe4 [110] as well as new data for CuSbSe2 , a relationship between Sb
valence and lattice thermal conductivity can now be established.

6.2

Experimental

The synthesis procedure for Cu3 SbSe4 has already been described in section 5.5.1. Synthesis of
Cu3 SbSe3 and CuSbSe2 followed a similar procedure, although obtaining single phase samples
of these compounds proved challenging. Samples of CuSbSe2 were prepared by quenching from
900◦ C in room temperature water and also by slow cooling the melt from 900◦ C to room temperature. Samples of Cu3 SbSe3 were prepared by quenching from 900◦ C into an ice water bath.
After quenching the Cu3 SbSe3 samples were annealed in the same ampoules at 400◦ C for 5 days.
All of the Cu-Sb-Se samples reported here were vibratory ball milled under argon for 30 minutes,
sieved (-100 mesh), and hot pressed at 400◦ C for 30 minutes using 70 MPa of pressure.

114

Total Thermal Conductivity (mW/cmK)

200
160
120
80
40
0
50

100

150

200

250

300

350

Temperature (K)

Figure 6.1: Temperature dependence of the thermal conductivity of Cu3 SbSe3 (open symbols) and Cu3 SbSe4 (closed symbols). The electronic contribution is negligible for all samples.

6.3

Results and Discussion

6.3.1

Phase Purity of CuSbSe2 and Cu3 SbSe3

The phase purity of CuSbSe2 and Cu3 SbSe3 were investigated using XRD and SEM (ORNL).
Slow cooled samples of CuSbSe2 contained a single phase with an orthorhombic structure (space
group Pnma, a = 0.6014 nm, b = 0.37882 nm, c = 1.4472 nm), in agreement with single crystal
studies [112]. Slow cooled samples of Cu3 SbSe3 always contained multiple phases, and thus
quenching was used exclusively for this compound.
SEM backscattered electron images of separate samples of Cu3 SbSe3 quenched from 500◦ C
and 900◦ C are shown in Figure 6.2. It is clear that these samples are multiphase, but the relative
amounts of the secondary phases are quite different (see Table 6.1. X-ray mapping (Figure 6.3)
revealed the dark regions to be Cu-rich, the light regions to be Sb-rich, and the distribution of
selenium to be relatively uniform. The sample quenched from 900◦ C contains considerably less of
115

Table 6.1: Relative amounts of phases present in Cu3 SbSe3
samples quenched from 500◦ C and 900◦ C in room temperature
water.
Phases present
Synthesis method
Cu2-x Se
Cu3 SbSe3
CuSbSe2
Quenched from 500◦ C
30%
47%
24%
Quenched from 900◦ C
11%
22%
68%

the unwanted Cu2-x Se and CuSbSe2 phases compared to the sample quenched from 500◦ C, likely
due to the faster cooling rate achieved upon quenching from higher temperature.

(a)

50µm

(b)

50µm

Figure 6.2: Backscattered electron images of Cu3 SbSe3 quenched from (a) 900◦ C and (b) 500◦ C
into room temperature water with three phases labeled: A = Cu2-x Se, B = Cu3 SbSe3 , C =
CuSbSe2 .

Based on the above results, subsequent Cu3 SbSe3 samples were prepared by quenching from
900◦ C into an icewater bath in order to achieve a faster cooling rate. The icewater quenched
samples were found to have a fine dendritic microstructure composed of primarily Cu3 SbSe3 and
CuSbSe2 . Annealing at 400◦ C for 5 days resulted in nearly single phase Cu3 SbSe3 with only small
inclusions of CuSbSe2 , and these samples were used for thermal conductivity measurements. The
116

Cu3SbSe3 (quenched from 500oC)

BSE

Cu Kα1

Sb Kα1

50µm

Se Kα1

Figure 6.3: X-ray mapping on a similar region of the sample shown in Figure
6.2(b).

117

X-ray diffraction pattern of a Cu3 SbSe3 sample that was quenched from 900◦ C into icewater and
annealed at 400◦ C for 5 days is shown in Figure 6.4. All of the peaks match with the references

Relative Intensity (arb. units)

lines from the JCPDS database, indicating that the sample is composed primarily of Cu3 SbSe3 .

Cu3SbSe3 PDF 01-086-1751

10

20

30

40

50
60
2! (degrees)

70

80

90

Figure 6.4: X-ray diffraction pattern of a Cu3 SbSe3 sample quenched from
900◦ C into icewater and annealed at 400◦ C for 5 days.

118

6.4

The Lattice Thermal Conductivity of CuSbSe2 , Cu3 SbSe3 , and Cu3 SbSe4

The initial interest in CuSbSe2 and Cu3 SbSe3 stemmed from the promising thermoelectric properties of Cu3 SbSe4 , but it was found that the former compounds are not well suited for thermoelectric applications and the results will not be discussed here. In the process of characterizing these
compounds, however, it was noticed that the thermal conductivity behavior of each was very different despite their similar compositions. Figure 6.5 shows the temperature dependence of κL (the
electronic contribution is less than 1% in these undoped samples) of the Cu-Sb-Se compounds.
Intuitively one would expect these three compounds to have very similar thermal conductivity
since their average atomic masses are nearly the same and none of them possesses a complex crystal structure. The only reasonable explanation for this difference is that there must be a phonon
scattering mechanism inherent in these materials that is acting with increasing strength as the composition changes from Cu3 SbSe4 to CuSbSe2 to Cu3 SbSe3 . These results are consistent with
the hypothesis that the LEP around Sb contributes to anharmonicity in the lattice, but since Sb is
nominally trivalent (+3) in both CuSbSe2 and Cu3 SbSe3 the difference in κL between these two
compounds is not immediately clear.
To better understand the thermal conductivity behavior of these compounds, the subtle differences in their crystal structures will be examined. Of particular interest is the coordination
environment of Sb, which has been studied extensively in relation to LEPs.

6.5

The Effect of Lone-Pair Electrons on the Coordination Environment of
Sb

Trivalent Sb can adopt coordination numbers ranging from 3 to 6 depending on the bonding nature
between Sb and the other atomic species present [106]. The coordination environment of Sb in
CuSbSe2 , Cu3 SbSe3 , and Cu3 SbSe4 is illustrated schematically in Figure 6.6. For Cu3 SbSe4 , Sb
is coordinated by 4 selenium atoms with ideal tetrahedral Se−Sb−Se bond angles of 109.5◦ , indi-

119

Thermal conductivity (W/mK)

16

Cu3SbSe4 4
Cu3SbSe
CuSbSe
CuSbSe2 2
Cu3SbSe
Cu3SbSe3 3

14
12
10
8
6
4
2
0
50

100

150

200

250

300

350

Temperature (K)
Figure 6.5: Temperature dependence of the lattice thermal conductivity of
CuSbSe2 , Cu3 SbSe3 , and Cu3 SbSe4 .

cating sp3 hybridization of the Sb valence electron orbitals. In this case, all of the valence electrons
of Sb form bonds with neighboring Se atoms as indicated in Figure 6.6. For the case of CuSbSe2 ,
Sb is coordinated by 3 Se atoms in a pyramidal configuration with an average Se−Sb−Se bond
angle of 95.24◦ . In this arrangement only the Sb 5p electrons participate in bonding with Se,
leaving the Sb 5s electrons ”free” to orient themselves along the missing vertex of the tetrahedra 1 .
1 The term ”free” as used here does not imply that these electrons are free in the sense of

conduction electrons in a semiconductor or metal; rather it is only meant to signify that they are
capable of assuming a specific orientation about the Sb nucleus to which they belong

120

The configuration is similar for Cu3 SbSe3 only the average Se−Sb−Se bond angle is 99.42◦ , intermediate to that of the other two compounds. Once again the Sb 5s lone pair electrons form a
tetrahedron with the Sb 5p bonding electrons.

Cu3SbSe3

CuSbSe2

Se

Sb

Cu3SbSe4

e-

Figure 6.6: Local coordination environment of Sb in CuSbSe2 , Cu3 SbSe3 and Cu3 SbSe4 . Shaded
lines represent bonds, dotted ovals represent the approximate morphology of the LEP orbital.

The coordination environment of Sb in Cu3 SbSe4 requires little interpretation as it is analogous
to the well known group IV, III-V, and II-VI compounds. In CuSbSe2 and Cu3 SbSe3 on the
other hand, Sb has the same coordination yet the Se−Sb−Se angle is quite different. This effect
was studied by Wang and Liebau, who noted that the change in X−Sb−X bond angle (where
X is a chalcogen atom) is related to the delocalization of the Sb 5s lone pair away from the Sb
nucleus [109]. This phenomenon stems from the fact that the actual valence of Sb in a given
compound is not necessarily purely trivalent or pentavalent, but rather a combination between
these two extremes. For a purely pentavalent Sb compound, as in the case of Cu3 SbSe4 , all of the
Sb valence electrons are completely delocalized from the Sb nucleus and form bonds that assume
the ideal tetrahedral angle of 109.5◦ . For a purely trivalent compound, the Sb 5s electrons remain
concentrated around the Sb nucleus thereby inducing a Coulombic repulsion with the bonding Sb
121

5p electrons, causing the X−Sb−X bond angle to approach 90◦ . As the actual Sb valence varies
from +3 to +5 the 5s lone pair progressively retracts from the nucleus which weakens the repulsion
and causes the bonding angle to increase. Wang and Liebau compiled X−Sb−X bond angles from
the literature and derived an expression for the effective valence of Sb3+ in SbXn polyhedra [109]:

ef fV
(α ) = 3[1 + 0.0128(αi − 90)]
Sb3+ i

(6.1)

where αi is the average X−Sb−X bond angle.
The difference in Se−Sb−Se bond angle between CuSbSe2 and Cu3 SbSe3 can now be interpreted as a difference in effective Sb valence state. e f f V 3+ = 3.2 for CuSbSe2 while for
Sb
ef fV
= 3.36, indicating that the lone pair electrons are retracted farther from the
Cu3 SbSe3
Sb3+
Sb nucleus in Cu3 SbSe3 than in CuSbSe2 , as illustrated in Figure 6.6. The main idea behind
the relationship between lone pair electrons and low κL is that as atoms approach one another
during thermal agitation, the wave functions of lone pair electrons will interact with those of electrons from nearby atoms causing increased anharmonicity in the lattice. The closer the lone pair
electrons are to the Sb nucleus, the less chance they will have of interacting with electrons from
adjacent atoms and the less they will influence the lattice thermal conductivity. The highest degree
of anharmonicity should thus be achieved when the lone pair electrons are far removed from the
Sb nucleus yet not participating in bonding, intermediate to the case of Sb3+ (αi = 90◦ ) and Sb5+
(αi = 109.5◦ ). This explains the thermal conductivity difference between the three Cu-Sb-Se compounds shown in Figure 6.5 and provides concrete evidence in favor of a relationship between Sb
valence state and κL .

6.6

Generalization to Group VA Chalcogenides

The ternary compounds in the Cu-Sb-Se system provide a basis for the argument that lone-pair
electrons can affect κL , but it remains to be seen whether or not this holds true for similar com-

122

pounds. If there exists a universal relationship between Sb valence state and lattice anharmonicity,
then it should be possible to generalize the results of the Cu-Sb-Se compounds to other group VA
chalcogenides. With this in mind, a comprehensive literature review of the crystal structures (in
particular the group VA coordination environment) and room temperature κL values of binary and
ternary group VA chalcogenides was conducted. Literature data are given in Table 6.2 for compounds of the form M2 -X3 and Ai -Mj -Xk where M = As, Sb, or Bi, X = S, Se, or Te, and A =
Cu, Ag, Tl, or an alkali metal. The average X−M−X bond angles were calculated from the bond
angles of the nearest neighbor M−X atoms, which comprise the MXn coordination polyhedra of
interest. For compounds in which M is coordinated by more than 4 chalcogen atoms, bond angles
>109.5◦ (corresponding to chalcogen atoms on opposite sides of the M atom) were not included in
the calculation.
The room temperature κL versus average X−M−X bond angle of 33 group VA chalcogenides
are plotted in Figure 6.7 (for raw data see Table 6.2). The shaded region represents the range of
minimum κL for these compounds, calculated from κL = 1/3Cv using the Dulong-Petit value for
the specific heat (C), 3000 m/s for the phonon velocity (v) and the average interatomic distance for
the phonon mean free path ( ). The minimum in κL between the smallest and largest X−M−X
bond angle corroborates the trend observed in the Cu-Sb-Se system, but clearly there is not a
singular value of αi that produces minimum κL . The broad minimum in κL values suggests there
is more than one factor affecting κL with increasing αi .
The data from Figure 6.7 (not including the compounds with ideal tetrahedral coordination and
αi = 109.5◦ ) are shown in Figure 6.8 separated according to the coordination number (CN) of the
M atom. In each case, κL decreases nearly linearly with increasing αi , and the rate of decrease
(indicated by the dashed lines in Figure 6.8) increases with increasing CN. Figure 6.8 shows that
the magnitude of κL depends not only on the retraction of the LEP from the nucleus of the M
atom, but also the coordination environment of the M atom. When the M atom is surrounded
by 6 or more chalcogen atoms (octahedral or greater coordination), the LEP assumes a spherical
123

3.5
Sb compounds
As compounds

3

Bi compounds

!L (W/mK)

2.5

2

1.5

1

0.5

0
85

90

95

100

105

110

" (o)
Figure 6.7: Lattice thermal conductivity versus average X-M-X bond angle of
the group VA chalcogenides.

!

124

CN " 6

3.5

CN 3

CN 4 - 5

!L (W/mK)

3
2.5
2
1.5
1
0.5
0
85

87

89

91 90

" (degrees)

92

94

96

" (degrees)

98 95

97

"

99
(degrees)

101

Figure 6.8: Lattice thermal conductivity versus average X-M-X bond angle of the group VA
chalcogenides, separated according to the coordination number (CN) of the group V atom.

!

!

!

distribution around the M nucleus and even a small retraction of the LEP away from the M nucleus
will result in an interaction with a neighboring chalcogen atom. Thus with increasing αi , κL
decreases rapidly (slope = -0.64) up to αi = 90◦ , which is the largest possible bond angle before
the CN≥6 coordination environment becomes unstable. The crowded local environment of the
M atom in the CN ≥ 6 configuration also explains why the sulfides in this group generally have
lower κL than the tellurides despite their lower average atomic mass (see, for example, Sb2 S3
versus Sb2 Te3 and AgSbS2 versus AgSbTe2 ). The smaller S atoms lie closer to the central M
atom (the average Sb X bond lengths for Sb2 S3 and Sb2 Te3 are 2.506 and 3.074 respectively)
thus increasing the likelihood of an interaction with the LEP. This effect is also manifested in the
κL difference between the monoclinic and NaCl-type phases of AgSbS2 ; the latter has a lower κL
(0.4 W/m*K) due to the crowded atomic environment of Sb (CN = 6) while the latter has κL =
0.49 W/m*K and CN = 5.
For CN = 4 - 5 there is more ”open space” around the M atom due to the loss of 1 - 2 coordinating chalcogen atoms, and thus a larger retraction of the LEP is required before interaction with
neighboring atoms occurs. Certain compounds in this series such as AgSbS2 and CuBiS2 have,

125

strictly speaking, CN = 3 but an assessment of the M X bond lengths reveals three short bonds,
two intermediate bonds, and one long bond, and are thus considered here to have CN = 5. In this
arrangement, the LEP is stereochemically active and retracted from the M nucleus in the direction
of the missing chalcogen atom(s). The absence of a complete octahedron around the M atom results in a more gradual decrease of κL with αi (slope = -0.37) due to less interaction between the
LEP and surrounding chalcogen atoms.
For CN = 3 the LEP occupies the missing vertex of the tetrahedron and can move far away
from the M nucleus without encountering a neighboring atom. The absence of nearby chalcogen
atoms in this direction means that strong lattice anharmonicity will not be achieved until the LEP
is far removed from the M nucleus, and indeed very low κL values are not observed in these
compounds until αi ≥ 98◦ . Clearly from the gap in αi values in Figure 6.7, the CN = 3 environment
becomes unstable around αi = 100◦ . Compounds that have CN = 3 with αi ≥ 100◦ will likely have
extremely low κL , as in the case of Tl3 AsSe3 , which has αi = 118.7◦ and κL = 0.35 W/m*K at
room temperature [130], [131].

6.7

Summary

It has been demonstrated that lone-pair electrons can produce minimum thermal conductivity behavior in group VA chalcogenides. Both the morphology of the lone-pair electron orbital and the
coordination environment of the group VA atom affect the intensity of the anharmonic forces that
are produced in the crystal lattice. Based on these results, the propensity of a given group VA
chalcogenide compound to exhibit minimum thermal conductivity can be evaluated based solely
on crystallographic data. For compounds with CN ≥ 6, an X−M−X bond angle close to αi =90◦ is
preferred, whereas for CN = 4-5 and 3 αi should be in the range of 95-96◦ and ≥ 99◦ respectively
to achieve anomalously low κL . These guidelines could prove useful in identifying potential new
compounds for thermoelectric applications as well as thermal barrier coatings.

126

Table 6.2: Properties of group VA chalcogenides taken from the literature (continues on next page)
κL at 300K
(W/m*K)
1.30

References

6

αi
(◦ )
89.22

Orthorhombic (Pbnm)
¯
Rhombohedral (R3m)

6

90.00

1.00

[109], [46]

6

88.00

2.40

[114], [46]

Orthorhombic (Pbnm)
¯
Rhombohedral (R3m)

6

88.30

2.06

[115], [46]

6

86.50

2.40

[114], [46]

¯
Rhombohedral (R3m)
¯
Triclinic (P1)

6

88.65

1.70

[114], [46]

4

92.00

2.22

[109], [116]

4

92.80

1.58

[109], [117]

KSbSe2

Monoclinic (C2/c)
¯
Triclinic (P1)

4

93.05

1.30

[109], [116]

RbSbS2

¯
Triclinic (P1)

4

91.83

1.60

[118], [116]

CsSbS2

3

95.02

1.20

[119], [116]

CuAsSe2

Monoclinic (C2/c)
¯
Rhombohedral (R3m)

4

107.82

3.2

[120], [46]

CuSbS2

Orthorhombic (Pnma)

3

95.84

1.50

[112], [46]

CuSbSe2

Orthorhombic (Pnma)

3

95.24

1.49

[112], [121]

CuBiS2

Orthorhombic (Pnma)

5

96.13

0.50

[122], [46]

AgSbS2

Monoclinic (C121)

5

94.85

0.49

[123], [46]

AgSbS2

Cubic (Fm3m)

6

90.00

0.40

[124], [121]

AgSbSe2

Cubic (Fm3m)

6

90.00

0.77

[34], [46]

AgSbTe2

Cubic (Fm3m)

6

90.00

0.68

[34], [44]

AgBiSe2

Cubic (Fm3m)

6

90.00

0.62

[34], [44]

TlAsS2

Monoclinic (P21/a)

3

98.7

0.95

[125], [117]

TlSbS2

Triclinic (P1)

4

93.50

1.20

[109], [117]

TlBiS2

¯
Rhombohedral (R3m)

6

90.00

0.875

[126], [117]

Cu3 AsS3

Orthorhombic (Pnma)

3

98.37

1.10

[123], [46]

Cu3 SbSe3

Orthorhombic (Pnma)

3

99.42

0.49

[72], [121]

Tl3 SbS3

Rhombohedral (R3m)

3

99.20

0.42

[127], [46]

Compound
Sb2 S3
Sb2 Se3
Sb2 Te3
Bi2 S3
Bi2 Se3
Bi2 Te3
NaSbS2
KSbS2

Crystal Structure
(Space Group)
Orthorhombic (Pnma)

CN

127

[113], [46]

Table 6.3: (continued)

4

αi
(◦ )
86.83

κL at 300K
(W/m*K)
3.10

[119], [128]

K2 Bi8 Se13

Crystal Structure
(Space Group)
Triclinic (P1)

β-K2 Bi8 Se13

Monoclinic (P21/m)

6

89.05

1.28

[128]

AgBi3 S5

Monoclinic (C2/m)

6

89.08

1.2

[129]

Cu3 AsS4

Orthorhombic (Pmn21)
¯
Tetragonal (I42m)

4

109.5

3.02

[96],

4

109.5

2.70

[96], [121]

Cubic (Pm3m)
¯
Tetragonal (I42m)

4

109.5

2.70

[58]

4

109.5

2.90

[72], [121]

Compound

Cu3 SbS4
Cu3 AsSe4
Cu3 SbSe4

7

CN

References

Conclusions and Future Work

The aim of this work was to identify materials with inherently low lattice thermal conductivity,
favorable electronic properties, and inexpensive elemental constituents for use in thermoelectric
power generation applications. Materials that met these unique criteria were selected using a novel
approach in which complex ternary semiconductors were derived from simple binary semiconductors through successive isoelectronic atomic substitutions. The resulting ternary compounds
had a larger number of atoms per primitive unit cell, resulting in low lattice thermal conductivity, yet maintain crystal structures closely related to those of their parent binary compounds and
are still semiconductors. Using this approach, several different ternary semiconductors composed
primarily of Cu and Se were identified and investigated as potential thermoelectric materials.
The first portion of this work was devoted to finding low-cost alternatives to ternary Ag-based
rocksalt-like semiconductors. Compounds such as AgSbTe2 are ternary derivatives of PbTe and
have excellent thermoelectric properties, but are too costly for large-scale use. Two Cu-based
compounds, CuBiSe2 and Cu3 BiSe3 , were previously reported as having the rocksalt-like structure
and were investigated as potential replacements for AgSbTe2 . It was found that CuBiSe2 is not a

128

thermodynamically stable phase and Cu3 BiSe3 exists but not in the rocksalt-like crystal structure.
As such, neither of these compounds was investigated further.
The majority of this work focused on Cu-based ternary compounds derived from the zincblende
structure II-VI semiconductors. Three and four-fold ternary derivatives of the II-VI semiconductors were chosen as the most promising families of compounds due to their low lattice thermal
conductivities and appropriate band gaps for thermoelectric power generation. Compounds of the
form I2 -IV-VI3 and I3 -V-VI4 where I = Cu, IV = Ge or Sn, V = Sb, and VI = Se or S were synthesized, characterized, and optimized for thermoelectric applications. From the I2 -IV-VI3 family of
compounds, Cu2 SnSe3 and Cu2 GeSe3 were prepared as single-phase samples with crystal structures closely related to that of zincblende. Ga and In were found to be effective p-type dopant
species in Cu2 SnSe3 when substituted for Sn and improved the thermoelectric properties of the
compound, but sample-to-sample variations in hole concentration prevented further optimization.
Cu2 SnSe3 forms a complete solid solution with both Cu2 GeSe3 and Cu2 SnS3 ; the lattice thermal
conductivity is reduced to a much larger extent in the Cu2 SnSe3 - Cu2 SnS3 solid solution due to
the significant atomic mass and size differences between Se and S. The optimum thermoelectric
performance was achieved using 30% S substitution on the Se site and 7.5% In doping on the Sn
site, resulting in ZT=0.62 at 760K. Above this temperature the sample softened and was physically
deformed in the measurement apparatus. It was found that Cu2 GeSe3 can accommodate excess
Ge up to Cu2 Ge2 Se3 , which induces a structural transition from orthorhombic to cubic symmetry
near Cu2 Ge1.55 Se3 . The lattice thermal conductivity decreases appreciably with increasing Ge
content, presumably due to phonon-impurity scattering, although controlling the hole concentration in these compounds proved to be problematic and doping studies were largely unsuccessful.
From these results it is concluded that the I2 -IV-VI3 compounds are promising potential thermoelectric materials but a better understanding of how to reproducibly control the hole concentration
is needed. Future work in this area should include electronic band structure and defect calculations
in order to identify possible self-doping mechanisms in these compounds.
129

From the I3 -V-VI4 family of compounds Cu3 SbSe4 was prepared as a single phase with a
crystal structure similar to that of zincblende. A quenching and annealing procedure was developed that produced homogeneous samples with reproducible hole concentration. It was found that
both Ge and Sn are effective p-type dopant species when substituted on the Sb site, and optimally
doped Cu3 SbSe4 achieved ZT = 0.72 at 630K. The previously unexplored Cu3 SbSe4 - Cu3 SbS4
system was investigated over the entire compositional range and found to form a complete solid
solution. The lattice thermal conductivity was reduced by 40% at high temperature and reached
the estimated minimum value for these compounds, 0.5 W/m*K, at 650K. When optimally doped,
the Cu3 SbSe4-x Sx compounds can achieve ZT = 0.89 at 650K, rivaling the thermoelectric performance of state of the art p-type materials. These compounds present a distinct advantage over
many high performance p-type materials in that they contain no toxic or overly expensive elements. Future work in this area should include an investigation of the mechanical properties of
these compounds as well as fine-tuning the doping level and S concentration to increase ZT.
A detailed analysis of the Cu-Sb-Se system revealed three possible ternary compounds: Cu3 SbSe4 ,
Cu3 SbSe3 , and CuSbSe2 . It was found that these compounds have vastly different lattice thermal conductivities despite their similar compositions and crystal structures. A simple valence
assessment revealed Sb to be pentavalent (5+) in Cu3 SbSe4 and trivalent (3+) in Cu3 SbSe3 , and
CuSbSe2 , meaning that Sb does not donate its 5s valence electrons to the bonding network in the
latter two compounds. The displacement of these lone-pair electrons from the Sb nucleus can be
evaluated based on the Se-Sb-Se bond angle, which is known from crystallographic analyses. It
was found that when the lone-pair is far removed from the Sb nucleus, which correlates to a large
Se-Sb-Se bond angle, the lattice thermal conductivity is lower than when the lone-pair is located
near to the Sb nucleus, corresponding to a small Se-Sb-Se bond angle, due to repulsive interactions
between the lone-pair and neighboring negatively charged Se ions. This effect is illustrated by the
three Cu-Sb-Se compounds, and was generalized to all group VA chalcogenides using literature
data. The trend of decreasing lattice thermal conductivity with increasing bond angle holds true
130

for the group VA chalcogenides, and it was established that the coordination number of the group
VA atom plays a role in the rate of decrease. This is the first direct evidence in favor of a relationship between lattice thermal conductivity and lone-pair electrons, and could prove useful in
the search for new high performance thermoelectric materials. Numerous opportunities for new
research exist in this area, including high energy X-ray studies (such as Mossbauer spectroscopy)
of these materials to probe the electron density around the group VA nucleus, experimental investigations of candidate materials that meet bond angle criteria for low thermal conductivity, and
calculations of the Gruneisen parameters of these materials, which would provide more insight as
to the effect of lone-pair electrons on lattice anharmonicity.

131

REFERENCES

132

REFERENCES

[1] G.S. Nolas, J. Sharp, H.J. Goldsmid, Thermoelectrics Basic Principles and New Materials
Developments, Springer-Verlag Berlin Heidelberg New York (2001), pg. 4.
[2] G.L. Bennett, J.L. Lombardo, R.J. Hemler, G. Silverman, C.W. Whitmore, W.R. Amos, E.W.
Johnson, A. Schock, R.W. Zocher, T. K. Keenan, J.C. Hagan, R.W. Englehart, ”Mission of
daring: the general-purpose heat source radioisotope thermoelectric generator”, AIAA 20064096, 4th International Energy Conversion Engineering Conference and Exhibit (IECEC),
26-29 June 2006.
[3] ”Estimated U.S. Energy Use in 2009: 94.6 Quads” Source: LLNL 2010. Data is based on
DOE/EIA-0384(2009). Web address: https://flowcharts.llnl.gov/.
[4] F. Stabler, ”Automotive Thermoelectric Generator Design Issues” DOE Thermoelectric Applications Workshop.
[5] D. Kraemer, B. Poudel, H.P. Feng, J. C. Caylor, B. Yu, X. Yan, Y. Ma, X. Wang, D. Wang,
A. Muto, K. McEnaney, M. Chiesa, Z. Ren, and G. Chen, ”High-performance flat-panel
solar thermoelectric generators with high thermal concentration”, Nature Materials, 10, 532
(2011).
[6] C.B. Vining, ”An inconvenient truth about thermoelectrics”, Nature Materials 8, 83 (2009).
[7] E.S. Toberer, A.F. May, G.J. Snyder, ”Zintl chemistry for designing high efficiency thermoelectric materials”, Chemistry of Materials 22, 624 (2010).
[8] A.F. Ioffe, ”Heat transfer in semiconductors”, Canadian Journal of Physics 34, 1342 (1956).
[9] A.V. Ioffe, A.F. Ioffe, ”Thermal conductivity of semiconductor solid Solutions”, Soviet
Physics Solid State 2, 719 (1960).
[10] B. Abeles, D.S. Beers, G.D. Cody, J.P. Dismukes, ”Thermal conductivity of Ge-Si alloys at
high temperatures” Physical Review 125, 44 (1962).
[11] I. Kudman, ”Lattice thermal conductivities of semiconductor alloys” Thermal Conductivity
Spec. Publ. No. 302, National Bureau of Standards, Washington, D. C. 20234, 97 (1968).
[12] I.V. Gasenkova, T.E. Svechnikova, ”Structural and transport properties of Sn-doped
Bi2 Te3-x Sex single crystals” Inorganic Materials 40, 570 (2004).
[13] M.A. Afromowitz, ”Thermal conductivity of Ga1-x Alx As alloys” Journal of Applied Physics
44, 1292 (1973).
[14] G.A. Slack, V.G. Tsoukala, ”Some properties of semiconducting IrSb3 ”, Journal of Applied
Physics 76, 1665 (1994).
133

[15] D.J. Braun, V. Jeitschko, ”Preparation and structural investigations of antimonides with the
LaFe4 P12 structure” Journal of the Less Common Metals 72, 147 (1980).
[16] D.T. Morelli, G.P. Meisner, ”Low temperature properties of the filled skutterudite
CeFe4 Sb12 ”, Journal of Applied Physics 77, 3777 (1995).
[17] B.C. Sales, D. Mandrus, R.K. Williams, ”Filled skutterudite antimonides: a new class of
thermoelectric materials”, Science 31, 5266, 1325 (1996).
[18] X. Shi, J.R. Salvador, J. Yang, H. Wang, ”Thermoelectric properties of n-type multiple-filled
skutterudites” Journal of Electronic Materials 38, 930 (2009).
[19] G.S. Nolas, J.L. Cohn, G.A. Slack, S.B. Schujman, ”Semiconducting Ge clathrates: Promising candidates for thermoelectric applications” Applied Physics Letters 73, 178 (1998).
[20] Y. Saiga, K. Suekuni, S.K. Deng, T. Yamamoto, Y. Kono, N. Ohya, T. Takabatake, ”Optimization of thermoelectric properties of type-VIII clathrate Ba8 Ga1 6Sn3 0 by carrier tuning”,
Journal of Alloys and Compounds 507, 1 (2010).
[21] J.H. Roudebush, E.S. Toberer, H. Hope, G.J. Snyder, S.M. Kauziarich, ”Crystal structure,
characterization and thermoelectric properties of the Type-I clathrate Ba8-y Sry Al14 Si32
(0.6≤y≤1.3), prepared by aluminum flux”, Journal of Solid State Chemistry, 184, 1176
(2011).
[22] H.J. Goldsmid, A.W. Penn, ”Boundary scattering of phonons in solid solutions”, Physics
Letters 27A, 523 (1968).
[23] D.M. Rowe, V.S. Shukla, ”The effect of phonon-grain boundary scattering on the lattice
thermal conductivity and thermoelectric conversion efficiency of heavily doped, fine-grained,
hot-pressed silicon germanium alloy”, Journal of Applied Physics 52, 7421 (1981).
[24] D.H. Kim, T. Mitani, ”Thermoelectric properties of fine-grained Bi2 Te3 alloys” Journal of
Alloys and Compounds 399 14 (2005).
[25] W. Xie, X. Tang, Y. Yan, Q. Zhang, T.M. Tritt, ”Unique nanostructures and enhanced thermoelectric performance of melt-spun BiSbTe alloys”, Applied Physics Letters 94, 102111
(2009).
[26] L.D. Hicks, M.S. Dresselhaus, ”Effect of quantum-well structures on the thermoelectric figure of merit” Physical Review B 47, 12727 (1993).
[27] M.S. Dresselhaus, G. Chen, M.Y. Tang, R. Yang, H. Lee, D. Wang, Z. Ren, J.P. Fleurial, P.
Gogna, ”New directions for low-dimensional thermoelectric materials”, Advanced Materials
19, 1043 (2007).
[28] T.C. Harmon, M.P. Walsh, B.E. Laforge, G.W. Turner, ”Nanostructured thermoelectric materials”, Journal of Electronic Materials 34, L19 (2005).
134

[29] C. Zhou, J. Sakamoto, D. Morelli, ”Thermoelectric properties of Co0.9 Fe0.1 Sb3 -based
skutterudite nanocomposites with FeSb2 nanoinclusions”, Journal of Applied Physics 109,
063722 (2011).
[30] E.J. Skoug, C. Zhou, Y. Pei, D.T. Morelli, ”High thermoelectric power factor in alloys based
on CoSi”, Applied Physics Letters 94, 022115 (2009).
[31] E.J. Skoug, C. Zhou, Y. Pei, D.T. Morelli, ”High thermoelectric power factor near room
temperature in full-heusler alloys”, Journal of Electronic Materials 38, 1221 (2009).
[32] C.H.L Goodman, R.W. Douglas, ”New semiconducting compounds of diamond type structure”, Physica 20, 1107 (1954).
[33] J.H. Wernick, K.E. Benson, ”New semiconducting ternary compounds”, Journal of Physics
and Chemistry of Solids 3, 157 (1957).
[34] V.P. Zhuze, V.M. Sergeeva, E.L. Shtrum, ”Semiconducting compounds with the general formula ABX2 ” Soviet Physics - Technical Physics 3, 1925 (1958).
[35] T. Hirai, K. Kurata, Y. Takeda ”Derivation of new semiconducting compounds by cross substitution for group IV semiconductors, and their semiconducting and thermal properties”,
Solid-State Electronics 10, 975 (1967).
[36] E.F. Hockings, ”The thermal conductivity of silver antimony telluride”, Journal of Physics
and Chemistry of Solids 10, 341 (1959).
[37] A.V. Petrov, E.L. Shtrum, ”Heat conductivity and the chemical bond in ABX2 -type compounds”, Soviet Physics - Solid State 4, 1061 (1962).
[38] F.D. Rosi, E.F. Hockings, N.E. Lindenblad ”Semiconducting materials for thermoelectric
power generation”, RCA Review 22, 82 (1961).
[39] R.W. Armstrong, J.W. Faust, W.A. Tillier, ”Structural study of the compound AgSbTe2 ”,
Journal of Applied Physics 31, 1954 (1960).
[40] V. Jovovic, J.P. Heremans, ”Measrements of the energy band gap and valence band structure
of AgSbTe2 ”, Physical Review B 77, 245204 (2008).
[41] V. Jovovic, J.P. Heremans, ”Doping effects on the thermoelectric properties of AgSbTe2 ”
Journal of Electronic Materials 38, 1504 (2009).
[42] K.F. Hsu, S. Loo, F. Guo, W. Chen, J.S. Dyck, C. Uher, T. Hogan, E.K. Polychroniadis,
M.G. Kanatzidis, ”Cubic AgPbm SbTe2+m : Bulk thermoelectric materials with high figure of
merit”, Science 303, 818 (2004).

135

[43] E. Quarez, K.F. Hsu, R. Pcionek, N. Frangis, E.K. Polychroniadis, M.G. Kanatzidis, ”Nanostructuring, compositional fluctuations, and atomic ordering in the thermoelectric materials
AgPbm SbTe2+m . The myth of solid solutions.”, Journal of the American Chemical Society
127, 9177 (2005).
[44] D.T. Morelli, V. Jovovic, J.P. Heremans, ”Intrinsically minimal thermal conductivity in cubic
I-V-VI2 semiconductors”, Physical Review Letters 101, 035901 (2008).
[45] G.A. Slack, ”The thermal conductivity of nonmetallic crystals”, Solid State Physics 34, 1
(1979).
[46] D.P. Spitzer ”Lattice thermal conductivity of semiconductors: a chemical bond approach”
Journal of Physics and Chemistry of Solids 31 19 (1970).
[47] M. Golovei, ”Investigation of Cu(Ag, Tl)-BV -Se systems” (in Russian), Izvestiya Vysshikh
Uchebnykh Zavedenii Khimiya I Khimicheskaya 28, 7 (1985).
[48] J.C. Garcia, G. Brun, B. Liautard, J.C. Tedenac, M. Maurin, ”Etude des equilibres de phases
dans le systeme Cu2 Se - Bi2 Se3 . Caracterisation des composes intermediaires” (in French),
Materials Research Bulletin 25 241 (1990).
[49] S. Karup-Moller, ”The Cu-Bi-Se phase system at temperatures between 300 degrees and 750
degrees C”, Neues Jahrbuch fur Mineralogie Monatshefte 12 556 (2003).
[50] P.I. Pollak, J.B. Conn, E.J. Sheehan, C.J. Barolay, ”Structural investigations in thermoelectric
materials”, Quarterly Report No. 1, Merck Sharp & Dohme Research Laboratories (1962).
[51] Bi-Cu-Se Phase Diagram (1990 Garcia J.C.), ASM Alloy Phase Diagrams Center, P. Villars,
editor-in-cheif; H. Okamoto and K. Cenzual, section editors; ASM International, Materials
Park, OH (2007). Phase diagram reproduced from [48].
[52] E. Makovicky, I. Sotofte, S. Karup-Moller, ”The crystal structure of Cu1.78 Bi4.73 Se8 , an N
= 3 pavonite homologue with a Cu-for-Bi substitution”, Zeitschrift fur Kristallographie 221,
122 (2006).
[53] N. Frangis, C. Manolikas, and S. Amelinckx, ”Vacancy-ordered superstructures in Cu2 Se”,
Physica Status Solidi (a) 126, 9 (1991).
[54] T. Wada, Y. Hashimoto, S. Nishiwaki, T. Satoh, S. Hayashi, T. Negami, H. Miyake, ”Highefficiency CIGS solar cells with modified CIGS surface”, Solar Energy Materials and Solar
Cells 67, 305 (2001).
[55] S.M. Wasim, ”Thermal conductivity of ternary compounds”, Physica Status Solidi (a) 51,
K35 (1979).
[56] D.T. Morelli and G.A. Slack, in High Thermal Conductivity Materials, edited by S. Shinde
and J. Goela (Springer, New York, 2005), p. 42-47.
136

[57] J.O. Sofo, G.D. Mahan, ”Optimum band gap of a thermoelectric material”, Physical Review
B 49, 7 (1994).
[58] L.I. Berger, V.D. Prochukhan, Ternary Diamond-Like Semiconductors, Translated from Russian by Albin Tybulewicz, Consultants Bureau, New York (1969).
[59] H. Hahn, W. Klingen, P. Ness, H. Schulze, ”Ternary Chalcogenides. XVII. Ternary Chalcogenides of silicon, germanium, and tin”, Naturwissenschaften 53, 18 (1966).
[60] N.A. Goryunova, G.K. Averkieva, Y.V. Alekseev, ”Quaternary Homogeneous Phases with
Zinc Blend Structure based on Cu2GeSe3” Izv. Moldavsk. Filiala Adad. Nauk SSSR, 3, 99
(1960).
[61] W. Scott, ”Some properties of Cu2SnSe3, Cu2GeSe3, and other A2BC3 compounds”, Journal of Electronic Materials 3, 1 (1974).
[62] L.S. Palatnik Y.F. Komnik, E.K. Belova, L.V. Atroshchenko, ”Investigation of the Ternary
Semiconductor Compounds Containing Copper and Elements of Groups IV and VI” Kristallografiya 6, 960 (1961).
[63] B.B. Sharma, F.R. Chavada, ”Variation of lattice parameter with temperature and thermal
expansion of the compound Cu2 SnSe3 ”, Physica Status Solidi (a) 14, 639 (1972).
[64] G. Marcano, C. Ricon, L.M. de Chalbaud, D.B. Bracho, G. Sanchez Perez, ”Crystal growth
and structure, electrical and optical properties of the semiconductor Cu2 SnSe3 ”, Journal of
Applied Physics 90, 1847 (2001).
[65] G.E. Delgado, A.J. Mora, G. Marcano, C. Rincon, ”Crystal structure refinement of the semiconducting compound Cu2 SnSe3 from x-ray powder diffraction data”, Materials Research
Bulletin 38, 1949 (2003).
[66] Materials Science International Team MSIT R , and Lebrun, Nathalie, Perrot, Pierre,
Tomashik, Vasyl: Cu-Se-Sn (Copper-Selenium-Tin). Effenberg, G., Ilyenko, S. (ed.).
SpringerMaterials - The Landolt-B¨ rnstein Database. DOI: 10.1007/10915981 26.
o
[67] K. Hirono, M. Kono, ”On the electrical and thermal properties of the ternary chalcogenides
A2 BX3 , ABX2 , A3 BX4 (A=Cu, B=Ge,Sn, X=S, Se, Te) I. Thermoelectric Properties at
Room Temperature”, Japanese Journal of Applied Physics 7, 1 (1968).
[68] T. Irie, ”Lattice thermal conductivity of disordered alloys of ternary compound semiconductors Cu2 (Sn, Ge)(Se, S)3 (Ag, Pb, Sb)Te2 , and (Ag, Sn, Sb)Te2 ” Japanese Journal of Applied
Physics 5, 854 (1966).
[69] E. Parthe, J. Garin, ”Zinkblende- und Wurtzit¨ berstrukturen bei tern¨ ren Chalkogeniden der
u
a
Zusammensetzung 12463” Monatshefte f¨ r Chemie 102 1197 (1971).
u

137

[70] B.B. Sharma, H. Singh, ”Stability of the tetrahedral phase in the Cu-Ge-Se system”, Journal
of Solid State Chemistry 11 285 (1974).
[71] B.B. Sharma, R. Ayyar, H. Singh, ”The cubic phase in the Cu2GeSe3-Ge system”, Physica
Status Solidi (a) 29 K17 (1975).
[72] A. Pfitzner, ”Crystal Structure of tricopper tetraselenoantimonate (V) Cu3 SbSe4 ”, Zeitschrift
f¨ r Kristallographie 209, 685 (1995).
u
[73] W. Scott, J.R. Kench, ”Phase diagram and properties of Cu3 SbSe4 and other A3 BC4 compounds”, Materials Research Bulletin 8, 1257 (1973).
[74] H. Nakanishi, S. Endo, T. Irie, ”On the electrical and thermal properties of the ternary chalcogenides A2 BX3 , ABX2 , A3 BX4 (A=Cu, B=Ge,Sn, X=S, Se, Te) II. Electrical and Thermal
properties of Cu3 SbSe4 ”, Japanese Journal of Applied Physcis 8, 4 (1969).
[75] S.N. Aliev, G.G. Gadzhiev, Y.B. Magomedov, ”Electrical and thermal conductivity of
Cu3 AsSe4 and Cu3 SbSe4 ”, Soviet Physics-Semiconductors 3, 11 (1970).
[76] J. Rivet, Investigation of some ternary sulphides, selenides and tellurides of copper with
elements of IVb groupe (in French), Ann. Chim. (Paris), 10, 243 (1965).
[77] B.B Sharma, R. Ayyar, H. Singh, ”Stability of the tetrahedral phase in the AI 2 BIV CVI 3 group
of compounds”, Physica Status Solidi (a) 40, 691 (1977).
[78] G. Marcano, C. Rincon, G. Marin, R. Tovar, G. Delgado, ”Crystal growth and characterization of the cubic semiconductor Cu2 SnSe4 ” Journal of Applied Physics 92, 1811 (2002).
[79] X. Shi, L. Xi, J. Fan, W. Zhang, L. Chen, ”Cu-Se bond network and thermoelectric compounds with complex diamondlike structure” Chemistry of Materials 22, 6029 (2010).
[80] X. Y. Shi, F. Q. Huang, M. L. Liu, L. D. Chen, ”Thermoelectric properties of tetrahedrally bonded wide-gap stannite compounds Cu2 ZnSn1-x Inx Se4 ” Applied Physics Letters
94, 122103 (2009).
[81] M. L. Liu, I. W. Chen, F. Q. Huang, L.D. Chen, ”Improved thermoelectric properties of Cudoped quaternary chalcogenides of Cu2 CdSnSe4 ”, Advanced Materials 21, 3808 (2009).
[82] G.K. Averkieva, A.A. Vaipolin, N.A. Goryunova, ”Some ternary compounds of the A2 BC3
type and solid solutions based on them”, Soviet Research in New Semiconducting Materials,
26 (1965).
[83] E.J. Skoug, J.D. Cain, D.T. Morelli, ”Thermoelectric properties of the Cu2 SnSe3 -Cu2 GeSe3
solid solution” Journal of Alloys and Compounds 506, 18 (2010).
[84] R. Berman, Thermal Conduction in Solids Oxford University Press, 1976, pg. 23.
[85] L.I. Berger, Semiconductor Materials, CRC Press, Boca Raton, FL, 1997, pg. 260.
138

[86] N.W. Ashcroft, N.D. Mermin, Solid State Physics, Thomson Learning, Inc. 1976, pg. 457.
[87] G.A. Slack, S. Galginaitis, ”Thermal conductivity and phonon scattering by magnetic impurities in CdTe” Physical Review 133, A253 (1964).
[88] P.G. Klemens, ”The scattering of low-frequency lattice waves by static imperfections” Proc.
R. Soc. London, Ser. A 68, 1113 (1955).
[89] J. Callaway, H.C. von Baeyer, ”Effect of point imperfections on lattice thermal conductivity”
Physical Review 120, 1149 (1960).
[90] D.T. Morelli, J.P. Heremans, G.A. Slack, ”Estimation of the isotope effect on the lattice
thermal conductivity of group IV and group III-V semiconductors”, Physical Review B 66,
195304 (2002).
[91] B. Abeles, ”Lattice thermal conductivity of disordered semiconductor alloys at high temperatures” Physical Review 131, 1906 (1963).
[92] J. Yang, G.P. Meisner, L. Chen, ”Strain field fluctuation effects on lattice thermal conductivity
of ZrNiSn-based thermoelectric compounds” Applied Physics Letters 85, 1140 (2004).
[93] B.D. Cullity and S.R. Stock, Elements of X-ray Diffraction, Third Edition, Prentice-Hall, Inc.,
NJ, 2001, pp. 390-395.
[94] A. Smakula, J. Kalnajs, ”Precision determination of lattice constants with a Geiger counter
x-ray diffractometer” Physical Review 99 1737 (1955).
[95] Y. Gelbstein, Z. Dashevsky, M.P. Dariel ”High performance n-type PbTe-based materials for
thermoelectric applications”, Physica B: Condensed Matter 363, 196 (2005).
[96] A. Pfitzner, T. Bernert, ”The system Cu3 AsS4 -Cu3 SbS4 and investigations on normal tetrahedral structures”, Zeitschrift f¨ r Kristallographie 219, 20 (2004).
u
[97] A. Pfitzner, S. Reiser, ”Refinement of the crystal structures of Cu3 PS4 and Cu3 SbS4 and a
comment on normal tetrahedral structures”, Zeitschrift f¨ r Kristallographie 217, 51 (2002).
u
[98] Kh. I. Amirkhanov, G.G. Gadzhiev, Ya. B. Magomedov, Teplofiz. Vys. Temp. 16, 1232 (1978).
[99] G.A. Slack, ”New materials and performance limits for thermoelectric cooling”, CRC Handbook of Thermoelectrics, edited by D.M. Rowe, CRC Press, Boca Raton, FL (1995).
[100] V.I. Fistul’, Heavily Doped Semiconductors, Plenum Press, New York, 1969, p. 155.
[101] Y. Pei, A. LaLonde, S. Iwanaga, and G.J. Snyder, ”High thermoelectric figure of merit in
heavy hole dominated PbTe” Energy & Environmental Science 4, 2085 (2011).
[102] X. Tang, H. Li, Q. Zhang, M. Niino, and T. Goto, ”Synthesis and thermoelectric properties
of double-atom-filled skutterudite compounds Cam Cen Fex Co4-x Sb12 ” Journal of Applied
Physics 100, 123702 (2006).
139

[103] S.H. Yang, T.J. Zhu, T. Sun, J. He, S.N. Zhang, X.B. Zhao, ”Nanostructures in high performance thermoelectric materials (GeTe)x (AgSbTe2 )100-x ” Nanotechnology 19, 245707
(2008).
[104] ’Zur Theorie der spezifischen Waerme’, Annalen der Physik (Leipzig) 39(4), 789 (1912)
[105] M.C. Roufosse, P.G. Klemens, ”Lattice thermal conductivity of minerals at high temperatures”, Journal of Geophysical Research 79, 703 (1974).
[106] T.N. Polynova, M.A. Porai-Koshits, ”Stereochemistry of trivalent antimony compounds”
Translated from Zhurnal Strukturnoi Khimii 7, 146 (1966).
[107] I. Lefebvre, M. Lannoo, G. Allan, A. Ibanez, J. Fourcade, J.C. Jumas, ”Electronic properties
of antimony chalcogenides”, Physical Review Letters 59, 2471 (1987).
[108] J. Oliver-Fourcade, A. Ibanez, J.C. Jumas, M. Maurin, I. Lefebvre, P. Lippens, M. Lannoo,
G. Allan, ”Chemical bonding and electronic properties in antimony chalcogenides”, Journal
of Solid State Chemistry 87, 366 (1990).
[109] X. Wang and F. Liebau, ”Studies on bond and atomic valences. I. Correlation between bond
valence and bond angles in SbIII chalcogen compounds: the influence of lone-electron pairs”,
Acta Crystallographica 52, 7 (1996).
[110] E.J. Skoug, J.D. Cain, D.T. Morelli, ”Structural effects on the lattice thermal conductivity
of ternary antimony and bismuth-containing chalcogenide semiconductors”, Applied Physics
Letters 96, 181905 (2010).
[111] A. Pfitzner, ”Cu3 SbSe3 : synthese und kristallstruktur”, Zeitschrift f¨ r Anorganische und
u
Allegemeine Chemie 621 685 (1995).
[112] J. Zhou, G.Q. Bian, Q.Y. Zhu, Y. Zhang, C.Y. Li, J. Dai, ”Solvothermal crystal growth of
CuSbQ2 (Q = Se, Se) and the correlation between macroscopic morphology and microscopic
structure”, Journal of Solid State Chemistry 182, 259 (2009).
[113] A. Kyono, M. Kimata, M. Matsuhisa, Y. Miyashita, K. Okamoto, ”Low-temperature crystal structures of stibnite implying orbital overlap of Sb 5s2 inert pair electrons”, Physical
Chemistry of Minerals 29, 254 (2002).
[114] Collaboration: Authors and editors of the volumes III/17E-17F-41C: Antimony telluride
(Sb2Te3) crystal structure, chemical bond, lattice parameters (including data for Bi2Se3,
Bi2Te3). O. Madelung, U. R¨ ssler, M. Schulz (ed.). SpringerMaterials - The Landolto
B¨ rnstein Database.
o
[115] Y. Takeuchi, T. Ozawa, ”The structure of Cu4 Bi4 S9 and its relation to the structures of
covellite, CuS and bismuthinite, Bi2 S3 ”, Zeitschrift f¨ r Kristallographie 141, 217 (1975).
u

140

[116] V.A. Bazakutsa, M.P. Vasileva, ”Thermal conductivity of triple semiconductors of A1 SbC2 6
type as a function of chemical composition and structure”, Journal of Engineering Physics
and Thermophysics 34, 137 (1978).
[117] V.A. Bazakutsa, M.P. Vasileva, V.N. Ustimenko, L.M. Mokhir, ”Lattice thermal conductivity
and chemical bond in the hypovalent two-cation semiconductors A1 BC2 6 and TlB5 C2 6 ”,
Journal of Engineering Physics and Thermophysics 37 1191 (1979).
[118] A.S. Kanishcheva, V.G. Kuznetsov, V.B. Lazarev, T.G. Tarasova, ”Crystal Structure of
RbSbS2 ”, Journal of Structural Chemistry 18, 849 (1978).
[119] T.J. McCarthy, S.P. Ngeyi, J.H. Liao, D.C. DeGroot, T. Hogan, C.R. Kannewurf, M.G.
Kanatzidis, ”Molten salt synthesis and properties of three new solid state ternary bismuth
chalcogenides, β-CsBiS2 , γ-CsBiS2 , and K2 Bi8 Se13 ”, Chemistry of Materials 5, 331 (1993).
[120] K.S. Liang, A. Bienenstock, C.W. Bates, ”Structural studies of glassy CuAsSe2 and CuAs2 Se3 alloys”, Physical Review B 10, 1528 (1974).
[121] Compounds synthesized and measured for the present work.
[122] J.C. Portheine, W. Nowacki, ”Refinement of the crystal structure of emplectite, CuBiS2 ”,
Zeitschrift f¨ r Kristallographie 141, 387 (1975).
u
[123] Y. Takeuchi, R. Sadanaga ”Structural principles and classification of sulfosalts”, Zeitschrift
f¨ r Kristallographie 130 346 (1969).
u
[124] A. Orliukas, V. Valiukenas, A. Kybartas Kezionis, V. Vilnius, ”Peculiarities of phase transitions in α and β-AgSbS2 single crystals” Ferroelectrics 38 897 (1981).
[125] Z.M. Yang, F. Pertlik, ”The thallium sulfarsenites Tl3 AsS3 and TlAsS2 [thallium(I)thioarsenates(III)]: structural characterization and syntheses”, Journal of Alloys and Compounds 216, 155 (1994).
[126] C.L. Teske, W. Bensch, ”TlBiS2 ”, Acta Crystallographica E62, i163 (2006).
[127] A. Olsen, P. Goodman, H.J. Whitfield, ”The structure Tl3 SbS3 , Tl3 SbSe3 , Tl3 SbS3-x Sex ,
and Tl3 Sby As1-y Se3 ” Journal of Solid State Chemistry 60, 305 (1985).
[128] D.Y. Chung, K.S. Choi, L. Iordanidis, J.L. Schindler, P.W. Brazis, C.R. Kannewurf, B.
Chen, S. Hu, C. Uher, M.G. Kanatzidis, ”High thermopower and low thermal conductivity in
semiconducting ternary K-Bi-Se compounds. Synthesis and properties of β-K2 Bi8 Se13 and
K2.5 Bi8.5 Se14 and their Sb analogues”, Chemistry of Materials 9, 3060 (1997).
[129] J.H. Kim, D.Y. Chung, D. Bilc, S. Loo, J. Short, S.D. Mahanti, T. Hogan, M.G.
Kanatzidis, ”Crystal growth, thermoelectric properties, and electronic structure of AgBi3 S5
and AgSbx Bi3-x S5 (x=0.3)”, Chemistry of Materials 17, 3606 (2005).

141

[130] H. Y-P. Hong, J.C. Mikkelsen Jr., ”Crystal structure of Tl3 AsSe3 ”, Materials Research Bulletin 9, 365 (1974).
[131] M.D. Ewbank, P.R. Newman, H. Kuwamoto, ”Thermal conductivity and specific heat of the
chalcogenide salt: Tl3 AsSe3 ”, Journal of Applied Physics 53, 6450 (1982).

142