Enhanced thermoelectric performance in the very low thermal conductivity
Ag2Se0.5Te0.5
Fivos Drymiotis, Tristan W. Day, David R. Brown, Nicholas A. Heinz, and G. Jeffrey Snyder
Citation: Applied Physics Letters
103
, 143906 (2013); doi: 10.1063/1.4824353
View online: http://dx.doi.org/10.1063/1.4824353
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Enhanced thermoelectric performance in the very low thermal conductivity
Ag
2
Se
0.5
Te
0.5
Fivos Drymiotis,
a)
Tristan W. Day, David R. Brown, Nicholas A. Heinz, and G. Jeffrey Snyder
Department of Materials Science, California Institute of Technology, Pasadena, California 91125, USA
(Received 24 July 2013; accepted 22 September 2013; published online 3 October 2013)
In this letter, we report the high-temperature thermoelectric properties of Ag
2
Se
0.5
Te
0.5
.Wefindthat
this particular composition displays very low ther
mal conductivity and competitive thermoelectric
performance. Specifically, in the temperature region 520 K
T
620 K, we observe non-hysteretic
behavior between the heating and cooling curves and
zT
values ranging from 1.2 to 0.8. Higher
zT
values are observed at lower temperatures on cooling. Our results suggest that this alloy is conducive
to high thermoelectric performance in the intermed
iate temperature range, and thus deserves further
investigation.
V
C
2013 AIP Publishing LLC
.[
http://dx.doi.org/10.1063/1.4824353
]
Devices based on thermoelectric (TE) materials convert
heat into electricity in a compact and robust package with
no moving parts. Development of higher efficiency thermo-
electric materials, as determined by the dimensionless fig-
ure-of-merit
zT
is crucial to grid-scale implementation of
thermoelectrics for waste heat conversion (e.g., from indus-
trial exhaust) and grid scale electrical generation (e.g., solar
thermal). The figure-of-merit is determined by the relative
values of heat and electrical transport properties:
zT
¼
a
2
T/
qj
(figure-of-merit), where
a
is the Seebeck coeffi-
cient or thermopower,
q
is the electrical resistivity,
j
is the
thermal conductivity, and
T
is the temperature.
1
Maximum
thermoelectric conversion efficiency can be achieved by
maximizing
a
,
while minimizing
q
and
j
. However, as these
properties are interrelated through the physics and chemistry
of the materials, it is not possible to engineer these proper-
ties separately. Certain classes of materials tend to display
good thermoelectric performance; for example, the binary
and ternary chalcogenides provide a low thermal conductiv-
ity platform combined with low electrical resistivity leading
to a high
zT
. An examination of the current state-of-the-art
thermoelectric materials reveals that the chalcogenides have
many representatives (PbTe,
2
Bi
2
Te
3
,
3
TAGS,
4
,
5
Sb
2
Te
3
,
6
and AgSbTe
2
.
7
,
8
) The binary silver chalcogenides (Ag
2
Se
and Ag
2
Te) have not gained as much attention even though
previous reports
9
–
13
indicate that they are very promising
materials. For example, the thermoelectric performance of
Ag
2
Se is rather high;
zT
¼
0.96 at
T
¼
300 K,
9
and recent
work showed that proper synthesis procedure leads to a sub-
stantial improvement of the thermoelectric performance of
Ag
2
Te.
14
Since, at room temperature, Ag
2
Te stabilizes in a
monoclinic structure, while Ag
2
Se stabilizes in an ortho-
rhombic structure,
15
it is worth exploring the stoichiometry
Ag
2
Se
0.5
Te
0.5
in order to assess whether phase competition
and subsequent complexity can improve thermoelectric per-
formance.
16
Because of the competing structures, we expect
that for specific
x
, phase separation will occur on solidifica-
tion, leading to the formation of a complex composite with
very low thermal conductivity possibly like those found in
Refs.
17
and
18
. Indeed, this is what can be inferred from
the Ag
2
Se-Ag
2
Te phase diagram (Figure
1
).
19
Ag, Te, and Se, all of purity 99.9999% were placed in
quartz tubes in the molar ratio 2:0.5:0.5. The quartz tubes
were then evacuated, sealed, and placed inside a box furnace.
The samples were subsequently heated to 1000
C, where
they were allowed to remain for 5 h, before finally being
allowed to cool down to 300
C at a rate of 10
C/h, at which
point the power to the furnace was turned off. The formed
ingots were removed from the quartz tubes and processed for
measurement. Disks of 8-mm diameter and approximately
2-mm thickness were cut from the ingots. The measured den-
sity of the disks was
d
¼
8.2 g/cm
3
6
5%. The structures
were confirmed using X-ray diffraction data obtained using a
commercial Rigaku MiniFlex
V
R
diffractometer. The thermal
diffusivity was obtained using the Netzsch LFA 457
V
R
laser
flash apparatus. The thermal conductivity values were calcu-
lated for each sample using the relation
j
¼
DdC
p
, with
D
being the measured diffusivity value,
d
the density, and
C
p
the heat capacity at constant pressure. The value of
d
used in
the calculations was the measured density at room tempera-
ture for the various samples. The value of
C
p
was taken to be
the value of the Dulong-Petit limit. The Seebeck coefficient
20
and the electrical resistivity and Hall effect
21
were measured
on equipment designed for this purpose at the California
Institute of Technology.
FIG. 1. The Ag
2
Se-Ag
2
Te phase diagram. The dark gray vertical line corre-
sponds to the 0.5/0.5 composition.
a)
Email: fivos@caltech.edu
0003-6951/2013/103(14)/143906/4/$30.00
V
C
2013 AIP Publishing LLC
103
, 143906-1
APPLIED PHYSICS LETTERS
103
, 143906 (2013)
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According to the X-ray diffraction data (Figure
2(a)
,
black line), the dominant structure is the orthorhombic Ag
2
Se.
The Rietveld refinement (Figure
2(a)
, red line) was performed
using the program Rietica and the structural model
P
2
1
2
1
2
1
(space group 19). The lattice parameters obtained from the fit
are
a
¼
4.4330 A
̊
,
b
¼
7.2345 A
̊
,and
c
¼
7.9676 A
̊
. The corre-
sponding lattice parameters for the stoichiometric Ag
2
Se
(Ref.
22
)are
a
¼
4.330 A
̊
,
b
¼
7.062 A
̊
,and
c
¼
7.764 A
̊
.The
2.5% increase in the lattice parameters is expected since Te is
larger than Se. Traces of a secondary phase might still be
present but not in a sufficient amount to be detected by X-ray
diffraction. The corresponding reduction in the thermal con-
ductivity between the stoichiometric and heavily doped phase
is also shown (Figure
2(b)
). The thermal conductivity of
Ag
2
Te is also shown for comparison. The X-ray data are con-
sistent with the Ag
2
Se-Ag
2
Te phase diagram (Figure
1
),
which shows that for this particular composition and tempera-
ture (16.67 at. % Te and room temperature), the alloy consists
of substituted orthorhombic Ag
2
Se and traces of doped mono-
clinic Ag
2
Te.
Both Ag
2
Se and Ag
2
Te undergo a structural phase transi-
tion in the intermediate temperature region;
15
,
19
the former
from orthorhombic to bcc at 124
C and the latter from mono-
clinic to fcc at 151
C), and both compounds display ionic
conductivity above the transition
23
(Ag
2
Te undergoes an addi-
tional transition from fcc to bcc at 794
C). According to the
phase diagram,
19
for the 0.5/0.5 composition (16.67 at. %,
dark gray vertical line in Figure
1
) and cooling from 1000
C,
the sample enters a solid-solution region at approximately
860
C; (the liquid-solid region above 860
C is neglected
since slowly cooling to 300
C will allow the mixture to settle
to a solid-solution). However, at approximately 380
C, the
sample reaches the solid-solution solvus line at which point
the Ag
2
Te (Se doped) fcc phase begins to precipitate. With
further cooling the mixture finally enters a single-phase ortho-
rhombic Te-doped Ag
2
Se region (
150
C).
Because of the super-ionic transition and the complex
structure, the electrical transport properties must be measured
carefully and consistently. A large hysteresis is observed in
both the electrical resistivity and Seebeck data during the first
heating and cooling cycle through the transition. This large
hysteresis may lead to high
zT
values that may not be repro-
ducible. However, cycling the sample through the transition
causes the hysteresis to be eliminated between 520 K and
620 K and to become consistent between 440 K and 520 K.
The hysteresis is presumably due to the multiple phases that
are represented in the Ag
2
Se-Ag
2
Te phase diagram.
19
Thus,
in order to assess the thermoelectric potential of this composi-
tion, we performed measurements on multiple samples, while
following a consistent protocol. The procedure was as fol-
lows: (1) we performed the Seebeck measurements first and
cycled the samples 2 to 3 times through the transition and up
to a maximum temperature of 350
C, (2) we performed the
thermal diffusivity measurements and cycled the samples
only once through the transition and up to a maximum tem-
perature of 350
C, and (3) we performed the resistivity and
Hall measurements, cycling the samples 2 to 3 times through
the transition and up to a maximum temperature of 350
C.
The samples were measured up to a maximum temperature of
350
C in order to avoid entering the solid solution region;
entering the solid-solution region results in a permanent
change in the transport properties. The dimensionless figur-
e-of-merit was calculated using the thermal diffusivity data
and the resistivity and Seebeck data obtained during the last
measurement cycle for each sample. All samples showed
similar behavior and comparable
zT
values. Presented is the
dimensionless figure-of-merit for all 3 samples measured. For
brevity, the electrical and thermal transport data are presented
from only sample 1.
The general features of the thermal and electrical trans-
port behavior of these samples are such that the thermal con-
ductivity decreases as the samples go through the structural
phase transition, while the magnitude of the thermopower
and the electrical resistivity (Figures
3(a)
and
3(c)
) increase.
Above the transition, the electrical resistivity values remain
rather low (
<
3m
X
-cm), the magnitude of the thermopower
increases and the thermal conductivity assumes values that
are much less than 1 W/mK. Hence, this particular composi-
tion is conducive to high thermoelectric performance.
The thermal conductivity of this alloy is extremely low
(Figure
2(b)
). The reduction in total thermal conductivity in
the case of Ag
2
Se
0.5
Te
0.5
, when compared to both Ag
2
Se and
FIG. 2. (a) X-ray diffraction data of an ingot sample of Ag
2
Se
0.5
Te
0.5
(black
spectrum). The Rietveld refinement is also displayed for comparison (red
spectrum). (b) Thermal conductivity of orthorhombic Ag
2
Se, monoclinic
Ag
2
Te and of Ag
2
Se
0.5
Te
0.5
(sample 1).
143906-2 Drymiotis
etal.
Appl. Phys. Lett.
103
, 143906 (2013)
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Ag
2
Te is rather dramatic. Since both Ag
2
Se and Ag
2
Se
0.5
Te
0.5
share the same structure and undergo a similar structure trans-
formation, it implies that the reduction in thermal conductivity
in the case of Ag
2
Se
0.5
Te
0.5
is due to point defect scattering.
24
The total thermal conductivity at room temperature remains
<
1 W/mK and it decreases as the sample goes through the
structural phase transition. It reaches a minimum value of
<
0.6 W/mK at
420 K before it starts increasing monotoni-
cally at high temperatures due to the presence of minority car-
riers. At approximately 575 K, the thermal conductivity value
of Ag
2
Se
0.5
Te
0.5
equals that of Ag
2
Te.
In the case of the thermopower (Figure
3(a)
), the abso-
lute value of the Seebeck coefficient decreases considerably
after the first temperature cycle. However, it assumes a rela-
tively constant value (
a
160
l
V/K) for a wide tempera-
ture range. During all cycles, the magnitude of the Seebeck
coefficient increases as we cross the structural phase transi-
tion and continues to increase with temperature until the
presence of a downturn due to minority carrier contribution.
The point at which the minority carrier contribution becomes
significant shifts to a lower temperature during cooling. This
feature remains regardless of the cycling and it presumably
relates to the changes in composition as the sample traverses
the phase diagram.
Finally, the resistivity values (Figure
3(c)
) also decrease
considerably after the first temperature cycle. During the
third cycle, the resistivity values below the structural phase
transition are
q
1m
X
-cm, and above the transition the re-
sistivity values on cooling remain
<
2m
X
-cm. Above the
structural phase transition, we also observe a continuous
increase in the carrier concentration (Figure
3(b)
) and a large
drop in mobility (Figure
3(d)
) that continues to decrease
monotonically with increasing temperature. The mobility
reduction explains the increase in the resistivity in the pres-
ence of increasing carrier concentration as the sample moves
through the structural phase transition, and it is most likely
due to the presence of mobile Ag ions. The carrier concentra-
tion at room temperature is
n
¼
4
10
18
cm
3
and at
T
¼
620 K it reaches a value of
n
¼
1
10
19
cm
3
. The mo-
bility of Ag
2
Se
0.5
Te
0.5
is very high; the mobility values
obtained are
l
>
2000 cm
2
/Vs at room temperature and
l
>
350 cm
2
/Vs at
T
¼
620 K. Thus, the mobility of this
highly disordered alloy is much greater than that of other
state-of-the-art n-type thermoelectric materials. For compari-
son, the mobility of Te-doped Bi
2
Te
3
is
l
¼
212 cm
2
/Vs,
25
and that of La
3
x
Te
4
is
l
¼
4cm
2
/Vs.
26
We only observe
very small hysteresis in the mobility data above the phase
transition, and the mobility values in that region do not vary
with cycling. Hysteresis is only observed below the phase
transition as the mobility in that region decreases with cy-
cling. The carrier concentration on the other hand increases
with cycling, in agreement with the reduction in resistivity,
and the crossover temperature (temperature for which
n
cooling
>
n
heating
on cooling) decreases. This crossover tem-
perature appears to correlate with the temperature at which
the bipolar contribution becomes significant.
The dimensionless figure-of-merit (
zT
) as a function of
temperature is shown in Figure
4
. The
zT
was calculated in
the temperature region extending from 420 K to 610 K since
this is the region of high thermoelectric efficiency (the
zT
values below the transition are of the order of
0.5 to 0.6).
The large hysteresis observed between the heating and cool-
ing curves is due to the hysteresis present in the Seebeck
coefficient; the hysteresis in the electrical resistivity is
reduced by cycling and the hysteresis in the thermal conduc-
tivity data remains small, but in the case of the Seebeck coef-
ficient the hysteresis remains pronounced and persistent. As
a result, significant hysteresis can be observed in the temper-
ature region
<
520 K. The highest
zT
values are observed on
cooling and in the temperature region
<
520 K. A consistent
maximum
zT
¼
1.2 is observed at
T
¼
440 K. The maximum
zT
on cooling is observed in the case of sample 2 for which
zT
¼
1.4 at 420 K, mainly due to a smaller value in the total
thermal conductivity versus sample 1 at 420 K (on cooling,
0.47 W/mK versus 0.51 W/mK). Nonetheless, the large hys-
teresis observed in that temperature region suggests that the
FIG. 3. (a) Seebeck coefficient, (b) carrier concentration, (c) resistivity, and
(d) mobility of Ag
2
Se
0.5
Te
0.5
(sample 1). The solid markers correspond to
the heating cycles, while the open markers correspond to the cooling cycles
(squares–cycle 1, circles–cycle 2, triangles–cycle 3).
FIG. 4.
zT
as a function of temperature for 3 samples of Ag
2
Se
0.5
Te
0.5
(sam-
ple 1, sample 2, and sample 3). The solid markers correspond to the heating
cycles, while the open markers correspond to the cooling cycles. The
zT
val-
ues were calculated using the data obtained in the last temperature cycle for
each sample.
143906-3 Drymiotis
etal.
Appl. Phys. Lett.
103
, 143906 (2013)
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high
zT
values might be due to the formation of a metastable
phase or kinetic effects resulting from the structural phase
transition. However,
zT
in the non-hysteretic temperature
region is very competitive (
zT
¼
1.0 at
T
¼
520 K and
zT
¼
0.8 at
T
¼
610 K) and the lack of hysteresis between the
heating and cooling curves suggests a stable alloy configura-
tion. More importantly, the slow decrease in
zT
versus tem-
perature (
d(zT)/dT
0.0015 K
1
) enables the potential for
substantial waste heat recovery through a wide temperature
region.
These results confirm that Ag
2
Se
1
x
Te
x
offers a very
appealing compositional space that is conducive to high ther-
moelectric performance in the intermediate temperature re-
gime. Specifically, the discussed composition (0.5/0.5)
outperforms many of the state-of-the-art thermoelectric
materials in the corresponding temperature range.
16
In addi-
tion, it provides an alternative system for the formation of
biphasic alloys and the study of the effects of structural com-
plexity and disorder on thermoelectric performance. Further
studies are required in order to establish a correlation
between the microstructure and the electrical and thermal
transport behavior of these alloys to ultimately optimize their
thermoelectric performance.
The authors would like to thank the U.S. Air Force
Office of Scientific Research for supporting this work.
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