Large thermoelectric figure of merit at high temperature
in Czochralski-grown clathrate Ba
8
Ga
16
Ge
30
A. Saramat,
a兲,b兲
G. Svensson, and A. E. C. Palmqvist
a兲,c兲
Department of Chemical and Biological Engineering, Chalmers University of Technology,
SE-412 96 Göteborg, Sweden
C. Stiewe, E. Mueller, and D. Platzek
German Aerospace Centre (DLR), Institute of Materials Research, Linder Hoehe 51147 Cologne, Germany
S. G. K. Williams and D. M. Rowe
NEDO Centre for Thermoelectric Engineering, University of Cardiff, Newport Road Cardiff CF24 3TF,
United Kingdom
J. D. Bryan and G. D. Stucky
Department of Chemistry and Biochemistry 9510, University of California, Santa Barbara,
California 93106-9510
共Received 15 July 2005; accepted 2 December 2005; published online 25 January 2006兲
The Czochralski method was used to grow a 46-mm-long crystal of the Ba
8
Ga
16
Ge
30
clathrate,
which was cut into disks that were evaluated for thermoelectric performance. The Seebeck
coefficient and electrical and thermal conductivities all showed evidence of a transition from
extrinsic to intrinsic behavior in the range of 600–900 K. The corresponding figure of merit 共ZT兲
was found to be a record high of 1.35 at 900 K and with an extrapolated maximum of 1.63 at
1100 K. This makes the Ba
8
Ga
16
Ge
30
clathrate an exceptionally strong candidate for medium and
high-temperature thermoelectric applications. © 2006 American Institute of Physics.
关DOI: 10.1063/1.2163979兴
I. INTRODUCTION
Efficient thermoelectric 共TE兲 materials are characterized
by a high Seebeck coefficient 共S兲 and a comparably high
electrical conductivity 共
兲 combined with a low thermal con-
ductivity 共兲, which results in a high TE figure of merit
共ZT=TS
2
/, where T is the absolute temperature兲. Re-
cently there has been significant progress in the area of TE
materials development. Promising classes of TE materials
are skutterudites such as CeFe
4
Sb
12
共Ref. 1兲 and
Yb
0.2
Co
4
Sb
12
,
2
antimonides such as Zn
4
Sb
3
共Ref. 3兲 and
half-Heusler alloys,
4
and tellurides such as Tl
2
SnTe
5
,
5
Tl
9
BiTe
6
,
6
pentatellurides,
7
and La
3−x
Te
4
, with 0 ⬍ x⬍ 1/3.
8
Recently Hsu et al. showed that AgPb
18
SbTe
20
hasaZTof
2.2 at 800 K.
9
In addition, artificial superlattice thin-film
structures of Bi
2
Te
3
/Sb
2
Te
3
grown using metal-organic
chemical-vapor deposition
10
共MOCVD兲 have shown excep-
tionally high ZT of ⬃2.4 at 300 K, while
molecular-beam-epitaxy
11
共MBE兲-grown superlattices of
PbSb
0.98
Te
0.02
/PbTe have shown a ZT of 2.0 at 550 K .
Clathrates have received much attention as potential
high-performance TE materials
12–26
and are discussed within
the framework of the “phonon-glass, electron-crystal”
共PGEC兲 concept.
27
The search for high-performance TE
materials in the high-temperature region 共above 800 K兲 has
lead to promising results for the germanium-based
clathrates.
14,16,26
The majority of work on clathrates has focused on group
IV based compounds with the type I structure 共isostructural
with the gas-hydrate clathrates兲, and their importance has
increased since the discovery of their potential use in TE
devices.
25
For alkaline-earth metal guests, the composition of
these clathrates can be represented by X
8
Y
16
Z
30
共X= Ca, Sr,
and Ba, Y =Al, Ga, and In, and Z = Si, Ge, and Sn兲, where the
Ba
8
Ga
16
Ge
30
clathrate has shown especially high ZT values
at temperatures above 800 K.
14,16,26
An important issue of
clathrates to address is the reproducibility of their TE
properties,
15
which is a key factor in the development of TE
devices. The wide distribution of TE properties of
germanium-based clathrates reported is likely due to differ-
ences incurred by the various synthetic procedures used to
prepare them.
15,17,24,26
Recent theoretical and experimental
studies
12,13,17–23,28,29
have recognized the Ga/Ge molar ratio
of the Ba
8
Ga
16
Ge
30
compound to be a key parameter for
explaining the large variability in TE properties found in the
literature for this compound.
13,16,29
The Czochralski method is a well-known technique for
controlling crystallization rates, phase purity, and composi-
tion during growth of congruently melting solids,
30,31
and is
used to deliver consistently homogenous and reproducible
silicon for the semiconductor industry. Establishing repro-
ducible synthesis parameters for the growth of the
Ba
8
Ga
16
Ge
30
compound using the Czochralski technique
would pave the way for possible large-scale production and
use of this class of promising TE materials. For this method
to work the compound must melt congruently, meaning that
if it is heated above its melting point and cooled down below
the melting point, it reforms. According to the literature,
there exists a very narrow phase width or nonstoichiometry
a兲
Authors to whom correspondence should be addressed.
b兲
Electronic mail: saramat@chalmers.se
c兲
Electronic mail: adde@chalmers.se
JOURNAL OF APPLIED PHYSICS 99, 023708 共2006兲
0021-8979/2006/99共2兲/023708/5/$23.00 © 2006 American Institute of Physics99, 023708-1
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region for M
8
Ga
16
Ge
30
共M =Ba and Sr兲 clathrates.
15,32
Here
we have used the Czochralski technique for the growth of a
large crystal of the Ba
8
Ga
16
Ge
30
clathrate. The crystal was
cut into disks along its length and the TE performance of
these disks was evaluated up to 1000 K showing a record
high ZT at temperature above 800 K.
II. MATERIALS AND METHODS
A. Sample preparation and processing
A batch of 70 g Ba
8
Ga
16
Ge
30
powder was prepared ac-
cording to a previously described method
15,29
and placed in a
20 ml EK90 graphite crucible manufactured by Ringsdorff-
Werke GmbH. The crucible was placed in a materials prepa-
ration and crystal growth system 关共MPCGS兲-Crystalox Ltd.兴
at the Department of Chemical and Biological Engineering at
Chalmers University of Technology. The atmosphere of the
MPCGS chamber was flushed with high-purity argon four
times before the temperature was raised to the melting point
of Ba
8
Ga
16
Ge
30
. A 7 –13 mm in diameter and 46-mm-long
Ba
8
Ga
16
Ge
30
crystal, shown in Fig. 1, was pulled from the
melt using the Czochralski method. After cooling to room
temperature, the crystal was embedded in an epoxy polymer
resin 共Struers兲, and cut into 18 disks with a thickness of
approximately 1.5 mm using a diamond saw 共South Bay
Technology Inc, Model 660兲. In the following, disk 18 refers
to the disk closest to the pulling rod, while disk 1 is furthest
away from the rod.
B. Thermoelectric evaluations
The TE properties of the disks were evaluated as a func-
tion of temperature both at the German Aerospace Center,
Cologne, Germany 共DLR兲, and at the Centre for Thermoelec-
tric Engineering, Cardiff, UK 共NEDO兲. A round-robin
test program to standardize the measurements between these
two laboratories has previously established excellent
reproducibility.
33
At DLR, an in-house built apparatus
34
was
used for measuring S 共on bar-shaped samples cut out of disks
5, 15, and 16兲 and
on disk 15 within a temperature range of
300–1066 K. The specific-heat capacity 共c
p
兲 was measured
at DLR using a differential scanning calorimeter 共NETZSCH
DSC 404兲. At NEDO, measurements of S on disks 1, 4, 6, 7,
9, and 18 and
on disk 18 were performed over a tempera-
ture range of 300– 900 K. The NEDO apparatus utilizes an
alpha-sigma 共
␣
-
兲 probe, previously described in detail
elsewhere.
35
Thermal diffusivity 共D
th
兲 was measured at
NEDO between front and back surfaces of the disk sample
using the laser flash technique,
35
at nine equidistant tempera-
tures within the temperature range of 400– 1200 K. The total
was calculated using the relationship between D
th
, c
p
, and
the density 共
兲 of the material, given in Eq. 共1兲.
=
c
p
D
th
共1兲
The value of the density used in Eq. 共1兲 was calculated from
measurements, at room temperature, of volume and weight
of a small cube cut out from the disk sample. The volume of
the cube was measured using a micrometer.
The elemental composition of the selected sample disks
was analyzed by electron probe micro analyzer 共EPMA兲 us-
ing a JEOL JXA-8600 apparatus. To relate the measured in-
tensity ratio to the concentration of the elements x-ray ab-
sorption, secondary fluorescence, electron backscattering,
and the electron stopping power need to be taken into ac-
count. This was done using the conventional 共ZAF兲 method,
which uses fundamental factors to correct for the effects of
atomic number 共Z兲, absorption 共A兲, and fluorescence 共F兲.
The data obtained from the measurements were correlated to
the standard references 关BaTiO
3
, elemental Ge 共⬎99%兲, and
GaAs 共⬎99%兲兴 using a ZAF-based correction method called
共PRZ兲.
36
III. RESULTS AND DISCUSSION
A. Sample preparation and characterization
Figure 1 shows the Ba
8
Ga
16
Ge
30
crystal grown using the
Czochralski method and analyzed for TE performance. The
crystal was rod shaped 共slightly faceted兲 with a varying di-
ameter of 7–13 mm, a length of 46 mm, and a weight of
11.49 g. The sample density at room temperature was more
than 99% of the theoretical density indicating a low degree
of voids and grain boundaries in the crystal. The crystal
structure of the powder collected from the cuttings agreed
well with that of the Ba
8
Ga
16
Ge
30
structure previously
reported.
32
The normalized elemental composition of se-
lected disk samples, cut from the large crystal, is summa-
rized in Table I. The samples contained a lower Ga/ Ge ratio
FIG. 1. Photograph of a Ba
8
Ga
16
Ge
30
crystal grown using the Czochralski
method and subsequently analyzed for thermoelectric performance.
TABLE I. Elemental composition of n-type Ba
8
Ga
16
Ge
30
disks. The quan-
titative relative error using the 共EPMA兲 can in this case be estimated to be
approximately 2%. The estimation is based upon knowledge of the instru-
mental conditions and quantifications made on material with known compo-
sitions. When comparing the result from the different samples the signifi-
cance should be considered based upon the standard deviation 共given in
parenthesis below the values兲 of the ten analytical points from each sample.
Disk No. Ba Ga Ge 共Ba/Ga兲
at
共Ba/ Ge兲
at
共Ga/ Ge兲
at
3
a
8.00 15.16 30.20 0.5277 0.2649 0.5020
共0.044兲共0.082兲共0.100兲
10
a
8.00 15.29 30.20 0.5232 0.2649 0.5063
共0.039兲共0.083兲共0.072兲
15
a
8.00 15.31 30.48 0.5225 0.2625 0.5023
共0.045兲共0.047兲共0.056兲
16
b
7.99 15.37 30.63 0.5198 0.2609 0.5018
共0.048兲共0.065兲共0.055兲
18
b
7.94 15.33 30.67 0.5179 0.2589 0.4998
共0.052兲共0.045兲共0.069兲
a
Normalized so that Ba= 8.00.
b
Normalized so that Ga+ Ge = 46.00.
023708-2 Saramat et al. J. Appl. Phys. 99, 023708 共2006兲
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and a higher Ba/ Ga ratio than suggested from the idealized
8:16:30 composition in agreement with previous reports for
n-type samples of this material.
16,29
The composition of the
crystal varied only slightly along the pulling axis possibly
being somewhat richer in Ga in the middle of the crystal, and
with a small, but continuous increase in 共Ba/ Ga兲
at
ratio
along the growth direction of the crystal.
B. Electrical transport measurements
The results from the temperature-dependent S measure-
ments are shown between 300 and 1050 K in Fig. 2共a兲 for a
number of disks originating from different parts throughout
the entire length of the grown crystal. All measured disk
samples showed to be n -type with values of S ranging from
−42 to −50
V/ K, at room temperature. The absolute val-
ues of S increased with temperature and there was a notice-
able variation in the slope of the curves between the different
disks with increasing temperature resulting in a larger spread
of S, from −150 to − 300
V/ K at 900 K for the samples
measured. The S curves of disks originating close to the two
ends of the crystal appeared to be quite similar, whereas
those from disks originating from the middle of the crystal
were larger in magnitude.
For Ba
8
Ga
16
Ge
30
Sales et al. reported a S value of
−50
V/ K at 300 K for a single-crystal sample,
17
while
Bryan et al. reported S between −20 and −40
V/K at
300 K, and −35 and −60
V/ K at 400 K for zone-refined
samples.
29
Only a few TE characterization measurements
have been made at temperatures above 400 K.
14,16,26
Kuz-
netsov et al. reported a S of −66
V/K 共300 K兲 for a poly-
crystalline sample and with a maximum magnitude of
−194
V/ K at 740 K.
26
Anno et al. found S to be highly
dependent on x in Ba
8
Ga
x
Ge
46−x
with negative values for x
=12– 16 and positive values for x= 17– 20.
16
The
Czochralski-grown samples reported here exhibit x values
between 15 and 16 共Table I兲, and the temperature-dependent
S values obtained 关Fig. 2共a兲兴 fall within the range of those
previously reported for n-type samples. In particular, disks 1,
15, 16, and 18 showed temperature-dependent S values be-
tween those with x = 14 and 15 reported by Anno et al.
16
while disks 4, 5, and 6 had S values between those with x
=15 and 16. This agrees with the observed increase in
共Ga/ Ge兲
at
ratio in the middle of the grown crystal.
Temperature-dependent
measurements could only be per-
formed on two disks 共15 and 18兲 due to size limitations of
the equipment and were done in the temperature range from
300 to 1070 K, as shown in Fig. 2共b兲. The observed values
of
were in agreement with earlier reports.
16,17,26,29
The two
disks had very similar conductivity values across the whole
temperature range, though disk 15 exhibited a smaller scatter
of the data than disk 18. For disk 15 the data were measured
up to 1066 K and above this temperature the curve is ex-
trapolated using a second-order polynom up to 1200 K. The
values obtained for disks 15 and 18 were between those of
the samples having x =14 and 15, presented by Anno et al.
16
At first sight of Fig. 2共a兲 an extrapolation of S using a
straight line for disks 15 and 18 may seem most suitable, but
there are several hints towards a maximum absolute value of
S between 1100 and 1200 K for these samples. For instance,
a plateau was observed for
at the highest measured tem-
perature 关Fig. 2共b兲兴 interpreted as the beginning of a transi-
tion from extrinsic to intrinsic semiconducting behavior. For
this reason the extrapolation in Fig. 2共b兲 was done to larger
values of
at higher temperatures. In Fig. 2共a兲, the curvature
of S itself was small but pointed towards a maximum in 兩S兩 at
higher temperatures. Near 700 K in Fig. 2共a兲, d
2
S/ dT
2
changes sign due to an increasing contribution from minority
charge carriers 共holes兲. This change in sign of d
2
S/ dT
2
strongly supports the existence of a maximum in the absolute
value of S at higher temperatures. The data shown in Fig.
2共a兲 for disks 15 and 18 were extrapolated to higher tempera-
tures using a third-order polynom. The maximum in 兩S兩 cor-
relates with a minimum in
appearing around 1000 K. The
reason for this minimum to appear at a lower temperature
than the maximum in 兩S兩 is because the second derivative of
was positive already in the extrinsic low-temperature re-
gion; while for S it had to change sign to reach a maximum.
Measurements with varying temperature 共from low tem-
perature to high temperature and vice versa兲 have been re-
FIG. 2. 共a兲 Seebeck coefficient 共S兲 as a function of temperature for disks
1共〫兲,4共䊐兲,5共⽧兲,6共䉮兲,7共⫻兲,9共⫹兲,15共䊊兲,16共*兲, and disk 18共쎲兲 cut
from the large Ba
8
Ga
16
Ge
30
clathrate crystal. The lines are fits and extrapo-
lations to experimental values for disks 15共—兲 and 18共---兲. 共b兲 Electrical
conductivity 共
兲 as a function of temperature for disk 15共䊊兲, its fit and
extrapolation up to 1200 K 共---兲, and disk 18共쎲兲. 共c兲 Total thermal conduc-
tivity 共兲 as a function of temperature for disk 18 and its extrapolation up to
1200 K 共---兲. 共d兲 Figure of merit 共ZT兲 as a function of temperature for disk
15共䊊兲 and disk 18共쎲兲, and their extrapolation up to 1200 K 共---兲.
023708-3 Saramat et al. J. Appl. Phys. 99, 023708 共2006兲
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peated several times, leading to the same results, thus show-
ing an impressive chemical and physical stability of the
Ba
8
Ga
16
Ge
30
clathrate.
C. Thermal conductivity
By measuring c
p
,
, and D
th
of the samples and using
Eq. 共1兲, was calculated. Since none of the disks satisfied
the size restrictions for c
p
measurements, disks 10, 15, and
16 were ground and pressed to one single disk, which was
used for the c
p
measurement. For D
th
a linear extrapolation
was used for the calculation of 共and c
p
was assumed to be
constant above 1000 K兲. The resulting is given in Fig. 2共c兲,
showing that was approximately 1.8 W / m K at room tem-
perature and 1.25 W / m K at 900 K. Above 900 K, in-
creased up to 1200 K where it was estimated to be
2.10 W / m K. The room-temperature value agrees well with
previous reports on low for n-type Ba
8
Ga
16
Ge
30
,
16,17,29,37
as does the small temperature dependence between 300 and
900 K.
16
Several recent papers have been devoted to eluci-
dating the underlying mechanisms for the low of the
Ba
8
Ga
16
Ge
30
clathrates.
16,17,19,22,29,37
However, the increase
in above 900 K has not previously been reported or dis-
cussed. These temperature-dependent data reveal the stron-
gest evidence for the extrinsic to intrinsic transition. Below
900 K, decreased with increasing temperature due to in-
creasing phonon-phonon scattering 共Umklapp processes兲.
The electrical contribution to was not affected in this ex-
trinsic region since the charge-carrier density remained
nearly constant here. At the temperature around the mini-
mum in there is strong evidence for bipolar heat
conduction.
8
This means that the minority charge carriers
began to affect the transport by carrying heat in the same
direction as the majority charge carriers resulting in an in-
crease of above 900 K. In the case of
, however, the
contribution of the minority charge carriers is cancelled by
the contribution of the majority charge carriers, and hence
the electrical conductivity shown in Fig. 2共b兲 is not changed
significantly at temperatures above 900 K.
D. Figure of merit
The dimensionless ZT of disks 15 and 18 was calculated
assuming that was the same for both samples, and the
obtained values are shown in Fig. 2共d兲. Furthermore, all fits
共for S,
, and 兲 were done in the range of existing measure-
ment data. Disk 15 had a maximum measured ZT of 1.24 at
1000 K, while disk 18 showed a record high ZT of 1.35 at
900 K. Using the extrapolated values for S,
, and the
value for ZT reaches a maximum around 1100 K for both
disks and becomes 1.25 and 1.63, respectively. The observed
differences in ZT between these disks originate from the dif-
ference in S rather than
, which seems to be less affected
than S by small variations in the elemental composition
共Table I兲.
These values indicate that the optimum value of x in
Ba
8
Ga
x
Ge
46−x
for the n type is somewhere between 15 and
16, and that the large crystal grown using the Czochralski
method has improved TE performance compared with previ-
ous reports on powders. Taking into account recent theoreti-
cal calculations
12
and experiments
16
suggesting that p-type
Ba
8
Ga
16
Ge
30
clathrates give even higher ZT values than
n-type, continued research on controlled crystal growth of
clathrates is strongly encouraged.
IV. CONCLUSIONS
A 46 mm long and 7 – 13 mm in diameter crystal of the
clathrate Ba
8
Ga
16
Ge
30
could successfully be grown as an
n-type specimen using the Czochralski method. The atomic
ratio of 共Ga / Ge兲
at
was lower than the idealized 16:30 and
found to be only slightly changing throughout the length of
the crystal with a somewhat higher value in the middle of the
crystal. Disk samples cut from the crystal were found to have
an S ranging from approximately −45
V/ K at 300 K to
between −150 and −300
V/ K at 900 K. With increasing
temperature
decreased gradually from 1500 to
600 共⍀ cm兲
−1
at 300 and 1066 K, respectively. Whereas,
was found to be close to 1.8 W / m K at room temperature
and slightly decreasing with increasing temperature to 1.25
at 900 K, above which it was found to increase rapidly.
Combining these results, the dimensionless ZT for one disk
was found to increase from ZT= 0.08 at room temperature to
ZT= 1.35 at 900 K without passing through a maximum.
Furthermore, temperature-dependent measurements of S,
,
and all showed evidence of a transition from extrinsic to
intrinsic semiconductor behavior with increasing temperature
suggesting an extrapolated maximum in ZT= 1.63 around
1100 K. Achievement of these high ZT values with a crystal
that was grown using an industrial growth method is of great
importance for high-temperature TE applications such as
power generation.
ACKNOWLEDGMENTS
This work was supported by the European Community
under Contract No. G5RD-CT2000-00292, NanoThermel
project. We direct our gratitude to the other partners in this
project: M. Muhammed, M. Toprak, Y. Zang, and K.
Billqvist, Royal Institute of Technology, Stockholm, Sweden,
B.B. Iversen and M. Christiansen, University of Aarhus,
Denmark, C. Gatti and L. Bertini, Istituto di Scienze e Tec-
nologie Molecolari, Milano, Italy, L. Holmgren, Termo-Gen
AB, Lärbro, Sweden, and G. Noriega, Cidete Ingenieros S.
L., Barcelona, Spain.
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