Thermoelectric transport properties of diamond-like Cu1−xFe1+xS2 tetrahedral
compounds
Yulong Li, Tiansong Zhang, Yuting Qin, Tristan Day, G. Jeffrey Snyder, Xun Shi, and Lidong Chen
Citation: Journal of Applied Physics 116, 203705 (2014); doi: 10.1063/1.4902849
View online: http://dx.doi.org/10.1063/1.4902849
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/20?ver=pdfcov
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Thermoelectric transport properties of diamond-like Cu
12x
Fe
11x
S
2
tetrahedral compounds
Yulong Li,
1,2,3
Tiansong Zhang,
1,2
Yuting Qin,
1,2,3
Tristan Day,
4
G. Jeffrey Snyder,
4
Xun Shi,
1,2,a)
and Lidong Chen
1,2,a)
1
State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute
of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China
2
CAS Key Laboratory of Materials for Energy Conversion, Shanghai Institute of Ceramics,
Chinese Academy of Sciences, Shanghai 200050, China
3
University of Chinese Academy of Sciences, Beijing 100049, China
4
Department of Materials Science, California Institute of Technology, Pasadena, California 91125, USA
(Received 4 September 2014; accepted 15 November 2014; published online 26 November 2014)
Polycrystalline samples with the composition of Cu
1x
Fe
1þx
S
2
(x ¼ 0, 0.01, 0.03, 0.05, 0.1) were
synthesized by a melting-annealing-sintering process. X-ray powder diffraction reveals all the sam-
ples are phase pure. The backscattered electron image and X-ray map indicate that all elements are
distributed homogeneously in the matrix. The measurements of Hall coefficient, electrical conduc-
tivity, and Seebeck coefficient show that Fe is an effective n-type dopant in CuFeS
2
. The electron
carrier concentration of Cu
1x
Fe
1þx
S
2
is tuned within a wide range leading to optimized power fac-
tors. The lattice phonons are also strongly scattered by the substitution of Fe for Cu, leading to
reduced thermal conductivity. We use Debye approximation to model the low temperature lattice
thermal conductivity. It is found that the large strain field fluctuation introduced by the disordered
Fe ions generates extra strong phonon scatterings for lowered lattice thermal conductivity.
V
C
2014
AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4902849]
I. INTRODUCTION
Thermoelectric materials have attracted extensive atten-
tion due to the potential applications in heat pumping and
power generation.
1,2
The performance of thermoelectric mate-
rials is determined by the dimensionless thermoelectric figure
of merit zT ¼ a
2
rT/j,wherea is the Seebeck coefficient, r is
the electrical conductivity, T is the absolute temperature, and
j is the thermal conductivity. The strategy of maximizing zT
is to obtain large power factor (a
2
r)aswellaslowthermal
conductivity.
3
Advanced thermoelectric materials including
Bi
2
Te
3
,
4
PbTe,
5,6
skutterudites,
7,8
clathrates,
9
Cu
2
X(X¼ S,
Se),
10,11
etc., have been continually discovered and investi-
gated to enhance the zTs. In particular, in order to meet
industry requirements, the high performance earth-abundant,
low-cost, nontoxic, and environmentally benign thermoelec-
tric materials have drawn lots of attention recently.
2,11,12
A family of compounds with diamond-like structure,
such as Cu
2
ZnSn
1x
In
x
Se
4
,Cu
2
Sn
1x
In
x
Se
3
, CuInTe
2
,and
CuGaTe
2
,
13–16
has emerged as promising thermoelectric
materials in the past few years. The diamond-like compounds
derive from binary cubic zinc-blende compounds by using
various elements substituted at Zn sites. Due to the different
physical and chemical properties of the substituted elements
at Zn sites, the crystal lattice is distorted from the perfectly
cubic diamond lattice to lower the lattice thermal conductiv-
ity. By combining the optimization of electrical properties, the
zTs up to 1.2–1.4 are reported in current diamond-like com-
pounds. These high zT values are mainly realized in the tetra-
hedral compounds such as CuInTe
2
and CuGaTe
2
.Byusing
first principle calculations, Zhang et al. did a systemic study
on the tetrahedral diamond-like compounds.
17
An effective
unity-g rule is proposed to explain the current high zTs in
CuInTe
2
,CuGaTe
2
,andCu
2
ZnSn
1x
In
x
Se
4
,whereg ¼ c/2a,
and c and a are lattice parameters. When g is around 1, the
crystal field splitting energy reaches the minimum state, lead-
ing to a cubic-like highly degenerate electronic band-edge
state for large power factors and high zT values. This unity-g
rule can also be used to predict and search for novel tetrahe-
dral non-cubic thermoelectric materials, in particular for those
diamond-like materials with similar crystal structures.
Chalcopyrite ore CuFeS
2
composed of earth-abundant,
non-toxic, and inexpensive elements Cu, Fe, and S, is also a
diamond-like compound with tetrahedral structure. The ex-
perimental lattice parameters are 10.42 A
˚
for c and 5.289 A
˚
for a. The calculated g value in CuFeS
2
is 0.985, which
shows a larger deviation than those in CuInTe
2
and
CuGaTe
2
, but still quite close to 1. This suggests that
CuFeS
2
might possess good electrical properties as well as
thermoelectric figure of merit since the lattice thermal con-
ductivity is usually low in these diamond-like compounds.
CuFeS
2
is a narrow band gap semicond uctor with a gap (E
g
)
of 0.53 eV by optical absorption measurement or 0.3 eV by
the calculation using spin-polarized self-consistent charge
discrete-variational Xa method.
18,19
A Seebeck coefficient
480 lV/K and a carrier concentration 10
19
cm
3
at room
temperature are reported.
20,21
These data confirmed that
CuFeS
2
is a good semiconductor within the range of heavily
doped materials, and these are particularly suitable for
advanced thermoelectric materials.
CuFeS
2
with stoichiometric chemical composition is an
intrinsic semiconductor with poor power factors. The carrier
a)
Electronic addresses: xshi@mail.sic.ac.cn and cld@mail.sic.ac.cn
0021-8979/2014/116(20)/203705/8/$30.00
V
C
2014 AIP Publishing LLC116, 203705-1
JOURNAL OF APPLIED PHYSICS 116, 203705 (2014)
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concentration must be tuned to the optimum value for ther-
moelectric performance. Li et al. used S deficiency to
increase carrier concentrations in CuFeS
2x
to approach the
optimum value, leading to enhanced power factors.
22
A
decreased thermal conductivity is also obtained by the
enhanced phonon-interface scattering. A maximum zT value
of 0.21 was obtaine d at 573 K for CuFeS
1.80
. Naohito Tsujii
and Takao Mori studied mainly the low temperature thermo-
electric properties of carrier-doped Cu
1x
Fe
1þx
S
2
. They
assumed that the strong magnetic moment can affect charge
carriers based on the early references, resulting in increased
electron effective mass and subsequently high power
factors.
23,24
However, the carrier-magnetic moment interac-
tions are expected to be weak or to disappear at high temper-
atures. Thus the electrical transpo rt at high temperatures in
the CuFeS
2
compound should be dominated by the material’s
band structure and carrier concentration. In addition, the lat-
tice defects by the arrangement of Cu and Fe atoms in the
material could also affect the heat conduction, in particular
for the material Cu
1x
Fe
1þx
S
2
with Cu and Fe contents sig-
nificantly shifted from the stoichiometric ratio. Both of these
two factors will obviously affect the thermoelectric proper-
ties and should be clarified to fully understand the chalcopy-
rite ore compound CuFeS
2
.
In this work, we present a systematic study of the ther-
moelectric properties of chalcopyrite Cu
1x
Fe
1þx
S
2
from
liquid helium temperature to 700 K. Significantly improved
electrical transport and lowered thermal conductivity are
observed to show enhanced zT values. The effect of the ex-
cessive Fe substituted at Cu sites in CuFeS
2
on the electrical
and thermal transport and their physical mechanisms are
discussed.
II. EXPERIMENT
Polycrystalline Cu
1x
Fe
1þx
S
2
(x ¼ 0, 0.01, 0.03, 0.05,
and 0.1) samples were synthesized by a melting-anneal ing-
sintering process. High purity elements Cu (shot, 99.999%),
Fe (pieces, 99.99%), and S (pieces, 99.999%) in stoichiomet-
ric proportions were sealed in evacuated quartz tubes. The
quartz tubes were heated slowly up to 1400 K and stayed at
this temperature for 36 h, and then naturally cooled to room
temperature. The obtained ingots were ground into fine pow-
ders and cold pressed into pellets. The pellets were resealed
in quartz tubes and annealed at 800–900 K for 7 days. The
resulted materials were reground into powders and then sin-
tered by spark plasma sintering at 800–820 K under a pres-
sure of 60 MPa to obtain densified bulk samples.
The phase, morphology, and chemical compositions of
the samples were characterized by powder X-ray diffraction
(XRD) analysis (Rigaku, Rint2000, Cu Ka), scanning elec-
tron microscope (SEM), and energy disp ersive spectrometer
(EDS), respectively.
The measurements of Hall coefficient R
H
, electrical con-
ductivity r, thermal conductivity j, and Seebeck coefficient
a at low temperature (2–300 K) were carried out in a
Quantum Design Physics Property Measurement System.
The high temperature measurements of electrical conductiv-
ity and Seebeck coefficient were performed in the ZEM-3
(ULVAC-RIKO) from 300 to 700 K. The high temperature
thermal diffusivity (k) was measured using the laser flash
method in flowing argon atmosphere (NETZSCH LFA 457).
The thermal conductivity was calculated from j ¼ kC
p
q,
where the Dulong-Petit value of 0.518 J/gK was used for the
specific heat capacity (C
p
) and the density (q) was measured
using Archimedes method. The velocity of sound was meas-
ured by using a Panametrics NDT 5800 pulser/receiver and
5 MHz and 25 MHz shear and longitudinal transducers from
Ultran.
III. RESULTS AND DISCUSSION
A. Structural and compositional characterizations
Figure 1 shows the powder X-ray diffraction patterns for
Cu
1x
Fe
1þx
S
2
samples. All diffraction peaks are consistent
with the standard pattern of tetragonal CuFeS
2
(JCPDS No.
65–1573) with the space group of I42d. Impurity phases are
not observed in the X-ray diffraction patterns even for the sam-
ple with the largest x value (x ¼ 0.1). In order to check the ele-
ment distribution of this sample in microscopic prospective,
the backscattered electron (BSE) image of the polished surface
andx-raymapbyEDSforsampleCu
0.9
Fe
1.1
S
2
are shown in
Figure 2. Element Cu, Fe, and S are all homogeneously distrib-
uted in the samples and no obvious large impurity phases are
detected. These data strongly suggest that the Fe atoms can
substitute at Cu sites with content up to at least 10%.
The atomic ratio of Fe/Cu by EDS measurements is
shown in Table I. Due to the measurement uncertainty or
errors, the atomic ratio of Fe/Cu is not idea lly equal to the
initial atomic ratios in all samples, even for samp le CuFeS
2
.
However, the atomic ratio of Fe/Cu increases monotonically
with increasing Fe content, which shows the same trend as
the designed staring compositions. Therefore, by combining
Figs. 1 and 2, and Table I, we conclude that the Fe/Cu
atomic ratios in CuFeS
2
can be tuned in a certain large com-
position range such as the composition of Cu
0.9
Fe
1.1
S
2
.
B. High-temperature thermoelectric properties
Figure 3 shows the temperature dependence of electrical
conductivity (r) and Seebeck coefficient (a) for all the sam-
ples. As Fe doping on the Cu site, the value of electrical
FIG. 1. XRD patterns for Cu
1x
Fe
1þx
S
2
.
203705-2 Li et al. J. Appl. Phys. 116, 203705 (2014)
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conductivity increases with increasing Fe doping content
while the absolute value of Seebeck coefficient decreases.
The detailed mechanisms will be discussed below. All sam-
ples exhibit negative Seebeck coefficients in the whole meas-
ured temperature range, indicating n-type materials with
electrons as the charge carriers. When temperature is
increasing, the absolute values of Seebeck coefficient
increase first and then decline due to thermal excitation of
carriers. This indicates these samples could be treated as
intrinsic semiconductors at high temperatures. For an intrin-
sic semiconductor, both electrons and holes contribute to the
electrical transport and they make opposite contributions to
the total Seebec k coefficient. Thus reduced Seebeck coeffi-
cients are expected, which can be described by
25
a ¼
a
e
r
e
þ a
h
r
h
r
e
þ r
h
; (1)
where the subscript symbols e and h represent electron and
hole, respectively.
For sample CuFeS
2
, the intrinsically thermal excitation
occurs at 400 K, which indicates a relatively small band gap
(E
g
). The E
g
can be estimated by
25
E
g
¼ 2ea
max
T
max
; (2)
where e is the electron charge, a
max
is the maximum value of
Seebeck coefficient, and T
max
is the temperature at which the
maximum thermopower occurs. The estimated E
g
for
CuFeS
2
is about 0.34 eV, in agr eement with the calculated
0.3 eV in Ref. 19, but smaller than the value by optical
absorption measurement.
18
With increasing Fe doping con-
tent, the T
max
moves towards high temperature gradually
except for the sample with x ¼ 0.1.
Like other high thermoelectric performance diamond-
like compounds, Cu
1x
Fe
1þx
S
2
also shows relatively low
thermal conductivity due to the highly distorted crystal struc-
tures, especially at high temperature, as shown in Figure 4.
The thermal conductivity is reduced dramatically with
increasing temperatures. This is similar to those in almost all
FIG. 2. (a) BSE image of the polished
surface and (b) x-ray map by EDS for
sample Cu
0.9
Fe
1.1
S
2
.
TABLE I. Nominal compositions, atom ratio of Fe/Cu based on the EDS measurement, volume of unit cell V, band gap E
g
, and room temperature lattice ther-
mal conductivity j
L
, electrical conductivity r, Seebeck coefficient a, Hall carrier concentration n, Hall mobility l
H
in Cu
1x
Fe
1þx
S
2
.
Nominal Fe/Cu V (a
2
c) j
L
ran l
H
E
g
Composition (atomic ratio) (A
˚
3
) (W/mK) (10
4
X
1
m
1
)(lV/K) (10
20
cm
3
) (cm
2
/Vs) (eV)
CuFeS
2
1.005 291.75 5.9 0.25 370 0.34 3.0 0.34
Cu
0.99
Fe
1.01
S
2
1.020 292.04 5.7 0.74 307 0.75 5.1 0.36
Cu
0.97
Fe
1.03
S
2
1.102 292.30 4.2 1.45 224 2.11 3.6 0.32
Cu
0.95
Fe
1.05
S
2
1.132 292.68 3.8 1.95 189 3.42 3.3 0.29
Cu
0.9
Fe
1.1
S
2
1.175 292.74 3.2 2.11 139 7.02 1.7 0.19
FIG. 3. Temperature dependence of
(a) electrical conductivity r and (b)
Seebeck coefficient a for Cu
1x
Fe
1þx
S
2
samples (300700 K).
203705-3 Li et al. J. Appl. Phys. 116, 203705 (2014)
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diamond-like compounds due to strong phonon Umklapp
scattering at high temperatures. In addition, the thermal con-
ductivity is decreases significantly with increasing Fe/Cu
atomic ratios in the entire temperature range. This could be
due to the extra lattice defects between the Fe and Cu atoms
and the details will be discussed in Sec. III D. The minimum
value of thermal conductivity for Cu
0.9
Fe
1.1
S
2
is about 1 W/
mK at 700 K, a quite low value in the diamond-like com-
pounds. Fig. 4 also lists the thermal conductivity of other
typical diamond-like compounds. CuFeS
2
-based materials
show lower thermal conductivity than those in other ternary
compounds such as CuInTe
2
and CuGaTe
2
. Even compared
with the thermal conductivity of quaternary compounds,
CuFeS
2
-based materials with large Fe/Cu atomic ratios still
show lower values at high temperatures.
13–16
Figure 5 shows the temperature dependence of the figure
of merit zT ( ¼ a
2
rT/j) from 300 to 700 K for Cu
1x
Fe
1þx
S
2
.
The zT values of the reported CuFeS
2
-based compounds from
reference 22 and 23 are also plotted in Figure 5 for a compari-
son. With the increase of temperature, the zT values increase
monotonically for all Cu
1x
Fe
1þx
S
2
samples and there is no
indication of reaching a maximum value at 700 K. As a result
of tuned electrical properties and suppressed thermal conduc-
tivity by enlarging the Fe/Cu atomic ratios, the zT value is
much improved, more than 50% enhancement in sample
Cu
0.97
Fe
1.03
S
2
and Cu
0.95
Fe
1.05
S
2
at 700 K compared with
CuFeS
2
. When the Fe content is 3% excess, chalcopyrite
Cu
1x
Fe
1þx
S
2
material exhibits a maximum zT value of about
0.33 at 700 K. Further optimization such as other doping with
other elements could further reduce the thermal conductivity
and enhance electrical properties for the realization of high
thermoelectric performance in such a Cu-Fe-S compound
with earth-abundant, non-toxic, and inexpensive elements.
C. Electrical transport properties
Hall carrier concentration (n) versus Fe doping content
(x) at room temperature for Cu
1x
Fe
1þx
S
2
is plotted in Figure
6. By excessive Fe substituted at Cu sites, the electron concen-
tration is significantly increased and a nice linear dependence
is observed in Fig. 6. The room temperature carrier concentra-
tion values are changed in a wide range from 3.410
19
cm
3
to 710
20
cm
3
, indicating that Fe is an effective dopant at
the Cu site. In CuFeS
2
, the charge state of S is usually treated
as 2
. The charge states of Cu and Fe are still open questions.
The measured and calculated results of the magnetic moment
show that the electron states of CuFeS
2
are a commixture of
Cu
þ
Fe
3þ
S
2
2
and Cu
2þ
Fe
2þ
S
2
2
.
19,26
The enhanced electron
concentration by extra Fe substituted at Cu sites indicates that
Fe donates more valence electrons than Cu. Therefore, the
charge states of Cu and Fe in CuFeS
2
could be þ1andþ3.
The temperature dependence of Hall mobility (l
H
) for
all the samples is shown in Figure 7. The room temperature
Hall mobility of doped samples decreases from 5 to 1.7 cm
2
/
Vs with increasing Fe content. These values are comparable
to the literature data.
23
For pure CuFeS
2
(x ¼ 0), the Hall mo-
bility follows a T
3/2
dependence indicative of ionized impur-
ities dominated carrier scattering. The ionized impurities in
CuFeS
2
lattice generate a long range Coulomb potential field
to scatter electrons strongly, leading to the very low mobility
FIG. 4. Temperature dependence of thermal conductivity (j) for
Cu
1x
Fe
1þx
S
2
. The data for other diamond-like compounds from literature
13–16 are also listed for data comparison.
13–16
FIG. 5. Temperature dependence of zT for Cu
1x
Fe
1þx
S
2
(300700 K). The
data for the reported CuFeS
2
-based compounds are listed for data
comparison.
22,23
FIG. 6. Hall carrier concentration (n) as a function of doping content (x)at
room temperature for Cu
1x
Fe
1þx
S
2
. The dashed line is a guide to the eyes.
203705-4 Li et al. J. Appl. Phys. 116, 203705 (2014)
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