In the system of PbTe and Sb_2Te_3, a metastable compound Pb_2Sb_6Te_(11) appears by solidification processing. It has been reported that this compound is decomposed into the two immiscible thermoelectric materials forming nanosized lamellar structure by heat treatments. The fraction transformed and the inter-lamellar spacing was systematically investigated. In this work, the thermal conductivities and the electrical resistivities have been measured as functions of annealing time through the transformation and the coarsening processes to clarify the effect of the fraction transformed and the inter-lamellar spacing. The thermal conductivity of Pb_2Sb_6Te_(11) is lower than that after the decomposition. The lattice part of the thermal conductivity of PbTe/Sb_2Te_3 lamellar samples decreases with decreasing inter-lamellar spacing. This is considered to be due to the coarsening of the microstructure

Haile, Sossina M.

Ikeda, Teruyuki

Ravi, Vilupanur A.

Snyder, G. Jeffrey

Toberer, Eric S.

English

Caltech Authors - Main

 
978-1-4244-2263-0/08/$25.00 ©2008 IEEE.                                                   2007 International Conference on Thermoelectrics 
1 
 
Lattice thermal conductivity of self-assembled PbTe-Sb2Te3 composites with nanometer lamellae 
 
Teruyuki Ikeda1, Eric S. Toberer1, Vilupanur A. Ravi2, Sossina M. Haile1, G. Jeffrey Snyder1 
1California Institute of Technology 
1200 E. California Blvd., Pasadena, CA 91106, USA 
2California State Polytechnic University 
3801 W. Temple Avenue, Pomona, CA 91768, USA 
 
Abstract 
In the system of PbTe and Sb2Te3, a metastable compound 
Pb2Sb6Te11 appears by solidification processing. It has been 
reported that heat treatments decomposes this compound into 
two immiscible thermoelectric materials forming nanosized 
lamellar structure. The fraction transformed and the inter-
lamellar spacing was systematically investigated. In this work, 
the thermal conductivities and the electrical resistivities have 
been measured as functions of annealing time through the 
transformation and the coarsening processes to clarify the 
effect of the fraction transformed and the inter-lamellar spac-
ing. The thermal conductivity of Pb2Sb6Te11 is lower than that 
after the decomposition. The lattice part of the thermal 
conductivity of PbTe/Sb2Te3 lamellar samples decreases with 
deccreasing inter-lamellar spacing. This is considered to be 
due to the coarsening of the microstructure. 
Introduction 
In order for thermoelectric devices to be more commonly 
used in large industrial fields for effective use of heat or elec-
trical energy, it is essential to discover materials with a high 
thermoelectric figure of merit, zT, defined as S2σT/κ, where S 
is the Seebeck coefficient, σ the electrical conductivity and κ 
the thermal conductivity. One way to improve a figure of 
merit zT is to introduce nano-sized structure into thermoelec-
tric materials [1-3]. This is achieved presumably by enhanced 
phonon scattering [4], which decreases thermal conductivity κ. 
Here, we examine a system of two immiscible thermoelectric 
materials: PbTe-Sb2Te3. In this system, it has been shown that 
the metastable compound Pb2Sb6Te11 appears at a compo-
sition close to that of the eutectic [5, 6] and decomposes into 
two thermoelectric compounds, PbTe and Sb2Te3, forming 
nano-sized lamellar structures [7, 8]. In the present work, 
eutectic PbTe-Sb2Te3 alloys were synthesized by quenching 
in a copper mold and then annealed at several temperatures to 
control the fraction transformed and inter-lamellar spacing. 
The electrical resistivity and the thermal conductivity of as-
quenched and annealed samples have been investigated as 
functions of the spacing.  
Experimental procedure 
Samples with overall composition matching the 
Pb2Sb6Te11 compound (Pb10.5Sb31.6Te57.9) were prepared by 
injection molding. Stoichiometric quantities of Pb, Sb, and Te 
granules were loaded into 12mm fused silica ampoules and 
then sealed under a vacuum of approximately 4 × 10-3 Pa to 
prevent oxidation at high temperatures. Samples were then 
melted in vertical furnace for 5 min and were subsequently 
water quenched. They were then cut into small pieces with a 
diamond saw. The small pieces, 15-20 g in total, were put into 
a fused silica tube with 12 mm outer diameter and with a hole 
of approximately 1 mm diameter and were melted by 
induction heating under vacuum of approximately 4 × 10-3 Pa. 
When the sample melted, the sample dropped through the 
hole into a copper mold of 20 × 30 × 　 mm3. For property 
measurements, samples with size of typically 10 × 10 mm2 
were cut out with a diamond saw and then the surfaces were 
ground to remove the surface layers until the final thickness 
was around 1.5 mm. 
Electrical resistivity and thermal conductivity measure-
ments were carried out before and after annealing the samples. 
For annealing, samples were sealed under vacuum in fused 
silica tubes. The annealing temperature was 673 K (78 h, 150 
h) or 773 K (1 h, 24 h, 126 h). 
 
 
 
 
Figure 1: Microstructure of Pb10.5Sb31.6Te57.9: (a) as quenched 
and (b) annealed at 673 K for 150 h. 
 
Figure 2: XRD profiles obtained from Pb10.5Sb31.6Te57.9 as 
quenched and annealed at 673 K for 150 h. Open squares ( ), 
open circles ( ) and solid triangles ( ) show the peaks from 
PbTe, Sb2Te3 and Pb2Sb6Te11 phases, respectively. 
 
The electrical resistivity (ρ) was measured up to 523 K, 
below which microstructure is not considered to practically 
change during measurements because of low atomic diffusiv-
ity [8], using the van der Pauw method with a current of 10 
mA as functions of temperature. The Hall coefficient (RH) 
was measured in the same apparatus with a forward and 
reverse magnetic field value of ~9500 G. The carrier density 
(n) was calculated from the Hall coefficient assuming a 
scattering factor of 1.0 in a single-carrier scheme, with n = 
1/RHe, where n is the densities of charge carriers (holes) and e 
the charge of the electron. 
The thermal diffusivities were measured up to 523 K 
using the same samples as the electrical resistivity measure-
ments by flash diffusivity technique (LFA457, NETSZCH). 
The thermal conductivity (κ) was calculated from the thermal 
diffusivity which was experimentally measured and the heat 
capacity which was estimated using Dulong-Petit law. 
The microstructures were observed using a field emission-
scanning electron microscope (Carl Zeiss LEO 1550 VP) 
equipped with a backscattered electron (BSE) detector for its 
high compositional contrast capabilities. The accelerating 
voltage was 20 kV. The microstructures were digitally ana-
lyzed using an image analysis program (Macscope, Mitani 
Corp.) to determine the inter-lamellar spacing (ILS) and the 
fraction transformed (Y). X-ray diffraction (XRD) 
experiments (Phillips X-Pert Pro diffractometer, Cu K-α 
radiation, 15˚ ≤ 2θ ≤  45˚) were performed directly on the as-
prepared ingots to identify phases.  
Results and discussion 
Microstructure 
Figure 1 (a) and (b) show the microstructure of the sam-
ples which are as-quenched and after annealing at 673 K for 
150 h, respectively. The sample in as-quenched state is almost 
entirely composed of the gray matrix phase, Pb2Sb6Te11. The 
thin dark acicular phase is Sb2Te3 and the bright dendrites are 
PbTe. The phases composing of as-quenched and annealed 
samples were also checked by XRD experiments as shown in 
Fig. 2. These features were consistent with the solidification 
microstructure of this system by water-quenching using fused 
silica tubes [6]. The inter-lamellar spacing in the solidification 
structure was 13 μm in the vicinity of the sample surface and 
16 μm in the middle, which were also consistent with that for 
water quenching using fused silica tube in the previous work. 
After annealing at 673 K for 78 h or at 773 K 126 h, 
Pb2Sb6Te11 is almost completely decomposed to Sb2Te3 and 
PbTe as reported in the previous work [7]. The backscattered 
electron images were digitally analyzed to determine the 
fraction transformed (Y) and the inter-lamellar spacing (ILS). 
The results of the image analysis is summarized in Table 1. In 
the sample annealed at 673 K for 78 or 150 h and the one 
annealed at 773 K for 126 h, the transformation to 
PbTe/Sb2Te3 lamellar structure is almost complete. It is also 
found that ILS is increased by annealing. 
 
Table 1. Fraction transformed (Y) and inter-lamellar spacing 
(ILS) of the samples annealed at 673 or 773 K. 
Annealing condition ILS (nm) Sample 
ID T / K t / h 
Y (%) 
Average Standard deviation
78 99.7 536 155 A 673 
150 100 575 153 
1 88.7 544 168 B 773 
126 100 1591 487 
 
Electrical resistivity 
Figure 3 shows the electrical resistivity and the carrier 
concentration measured as functions of temperature. The 
resistivity is found to decrease by the decomposition of 
Pb2Sb6Te11 to PbTe/Sb2Te3 lamellae. This is mainly due to the 
increase in carrier concentration. It is also found that the 
electrical resistivity is not significantly affected in the coars-
ening process. 
Thermal conductivity 
Figure 4 shows the temperature dependence of thermal 
conductivity of sample B, which was annealed at 773 K for 1 
h, 24 h and 126 h. The thermal conductivitivities (κtot) were 
calculated from the measured thermal diffusivity (α), the 
measured density (ρ), and the heat capacity (CP) evaluated by 
Dulong-Petit law using the relation, κtot = ρCPα. The electron 
part of the thermal conductivity, κel was evaluated by the 
Wiedemann-Franz law, κel = LT/ρ, where L is Lorenz number,  
 
 
Figure 3: Electrical resistivity and carrier concentration of 
Pb10.5Sb31.6Te57.9 in the as-quenched state and after annealings 
at 673 K or 773 K. 
 
Figure 4: Total, electronic part, and lattice part of the thermal 
conductivity of Pb10.5Sb31.6Te57.9 in the as-quenched state and 
after annealing at 773 K. 
 
2.45 × 10-8 Ω/K2. The lattice part of the thermal conductiv 
ity, κlat, was calculated using κtot = κel + κlat. The lattice part of 
the thermal conductivity in the as-quenched state, i.e. that of 
Pb2Sb6Te11, is significantly lower than those after the 
decomposition. While the electrical resistivity is almost 
constant after annealing for 1 h at 773 K, the thermal conduc-
tivity slightly increases. As seen in the figure, this is due to 
the increase of lattice component of the thermal conductivity. 
Table 1 shows that the microstructure is coarsened by 
annealing. This is qualitatively consistent with the previous 
work [8]. Thus, the increase in the lattice part of the thermal 
conductivity could be attributed to the lowering of phonon 
scattering at phase boundaries since the coarsening of micro-
structure is accompanied by the decrease in the total area of 
phase boundaries. Actually, as seen in Fig. 5, for samples 
annealed at 673 and 773 K, the lattice thermal conductivity 
decreases with decreasing inter-lamellar spacing.  
Measurements are underway to add more data points to this 
plot, e.g., data from samples annealed at 573K. 
It has previously been reported that adjacent Sb2Te3 and 
PbTe lamellae are oriented such that the close-packed planes, 
the <001> basal planes of Sb2Te3, and the <111> planes of 
PbTe are parallel and the lattice mismatch is only about 6% 
[7]. Therefore, the mass contrast due to the difference of 
phases or strain in the vicinity of phase boundaries could be 
the cause of the scattering of the phonon components which 
have the mean free path in similar orders of magnitude to the 
inter-lamellar spacing. On the other hand, electrical 
conductivity was not affected by the inter-lamellar spacing. 
This is possibly because the lattice mismatch at the interface 
is fairly small.  
It is interesting to note that the lattice thermal 
conductivity of Pb2Sb6Te11 is low (1.15 – 1.69 W/mK).  The 
period of similar atomic stacking within a unit cell of 
Pb2Sb6Te11 was taken to be 1.4 nm [9]. The Pb2Sb6Te11 phase 
is highly disordered in the cationic substructure; however, the 
Sb2Te3 and PbTe phases are significantly more ordered. The 
low thermal conductivity of Pb2Sb6Te11 may be due to one 
two possibilities: (a) disorder in the metallic sites [9] and (b) 
the small layer period and consequent increase in the total 
area of the “interfaces” of the crystalline layers. 
Conclusions 
Pb10.5Sb31.6Te57.9 (the composition corresponding to 
Pb2Sb6Te11) samples were prepared by solidification process-
ing using a copper mold. After the solidification, the samples 
were mainly composed of Pb2Sb6Te11. Pb2Sb6Te11 was 
decomposed to PbTe and Sb2Te3 by annealing at 673 or 773 
K. The fraction transformed and the inter-lamellar spacing 
(540-1600 nm) were controlled by annealing period. The 
electrical resistivity and the thermal conductivity were 
measured before and after annealing. The inter-lamellar 
spacing in the samples used in the property measurements 
was in the range between 540 and 1590 nm. It was found that 
the electrical resistivity is the highest for Pb2Sb6Te11 (without 
annealing). 
 
 
 
Figure 5: The dependence of lattice thermal conductivity of 
PbTe/Sb2Te3 lamellar composites and Pb2Sb6Te11 at 500 K on 
inter-lamellar spacing. Circles and Squares show the results 
from samples sample A and B, respectively. The point of 
sample B for smaller inter-lamellar spacing is in brackets 
since the decomposition is not complete (Y = 88.7 %).  
 
Then, the electrical resistivity decreases as the decomposition 
to PbTe/Sb2Te3 lamellae proceeds. The thermal conductivity 
increases as the decomposition proceeds and the resulting 
nanostructure is coarsened. The lattice thermal conductivity 
decreases with decreasing the inter-lamellar spacing. Further 
reduction in lattice thermal conductivity should be observed 
for even finer microstructure which we can achieve with 
lower temperature anneals. The self-assembled nanostructure 
is achieved even in bulk materials. This would greatly reduce 
interface problems of sublattice materials such as a relatively 
large electrical resistance and also simplify production proc-
esses.  
Acknowledgments 
This work was supported by the Office of Naval Research 
and Jet Propulsion Laboratory.  
References 
1 Caylor, J. C. et al., “Enhanced Thermoelectric 
Performance in PbTe-based Superlattice Structures from 
Reduction of Lattice Thermal Conductivity,” Appl. Phys. 
Lett. Vol. 87 (2005), p. 023105. 
2 Venkatasubramanian, R. et al., “Thin Film Thermoelectric 
Devices with High Room-Temperature Figures of Merit,” 
Nature 413 (2001), pp. 597-602. 
3 Harman, T. C. et al.,  “Quantum Dot Superlattice 
Thermoelectric Materials and Devices,” Science Vol. 297 
(2003), pp. 2229-2232. 
4 Chen, G., Proc Ninth Intersociety Conference on Thermal 
and Thermomechanical Phenomena In Electronic Systems 
2004 (IEEE Cat. No.04CH37543); p.8. 
5 Abrikosov, N. K. et al., “The System PbTe-Sb2Te3,” Inorg. 
Mater. Vol. 1 (1965), pp. 1944-1946. 
6 Ikeda, T. et al., “Solidification Processing of Alloys in the 
Pseudo-binary PbTe–Sb2Te3 System,” Acta Mater. Vol. 
55 (2007), pp. 1227-1239. 
7 Ikeda, T. et al., “Self-Assembled Nanometer Lamellae of 
Thermoelectric PbTe and Sb2Te3 with Epitaxy-like 
Interfaces,” Chem. Mater. Vol. 19 (2007), pp. 763-767. 
8  Ikeda, T. et al., “Development and Evolution of 
Nanostructure in Bulk Thermoelectric Pb-Te-Sb Alloys,” 
J. Electr. Mater., in press. 
9  Shelimova, L. E. et al., “Synthesis and structure of layered 
compounds in the PbTe-Bi2Te3 and PbTe-Sb2Te3 
systems,” Inorg Mater. Vol. 40 (2004), pp. 1264-1270.  
 


Lattice thermal conductivity of self-assembled PbTe-Sb_2Te_3 composites with nanometer lamellae

Lattice thermal conductivity of self-assembled PbTe-Sb2Te3 composites with nanometer lamellae 
 
Teruyuki Ikeda
1
, Eric S. Toberer
1
, Vilupaur A. Ravi
2
, Sossina M. Haile
1
, G. Jeffrey Snyder
1
 
1
California Institute of Technology 
1200 E. California Blvd., Pasadena, CA 91106, USA 
2
California State Polytechnic University 
3801 W. Temple Avenue, Pomona, CA 91768, USA 
 
Abstract 
In the system of PbTe and Sb2Te3, a metastable compound 
Pb2Sb6Te11 appears by solidification processing. It has been 
reported that this compound is decomposed into the two 
immiscible thermoelectric materials forming nanosized 
lamellar structure by heat treatments. The fraction 
transformed and the inter-lamellar spacing was systematically 
investigated. In this work, the thermal conductivities and the 
electrical resistivities have been measured as functions of 
annealing time through the transformation and the coarsening 
processes to clarify the effect of the fraction transformed and 
the inter-lamellar spacing. The thermal conductivity of  
Pb2Sb6Te11 is lower than that after the decomposition. The 
lattice part of the thermal conductivity of PbTe/Sb2Te3 
lamellar samples decreases with decreasing inter-lamellar 
spacing. This is considered to be due to the coarsening of the 
microstructure. 
Introduction 
In order for thermoelectric devices to be more commonly 
used in large industrial fields for effective use of heat or 
electrical energy, it is essential to discover materials with a 
high thermoelectric figure of merit, zT, defined as S
2?T/?, 
where S is the Seebeck coefficient, ? the electrical 
conductivity and ? the thermal conductivity. One way to 
improve a figure of merit zT is to introduce nano-sized 
structure into thermoelectric materials [Cay05, Ven01, 
Har03]. This is achieved presumably by enhanced phonon 
scattering [Che04], which decreases thermal conductivity ?. 
Here, we examine a system of two immiscible thermoelectric 
materials: PbTe-Sb2Te3. In this system, it has been shown that 
the metastable compound Pb2Sb6Te11 appears at a 
composition close to that of the eutectic [Abr65, Ike06] and 
decomposes into two thermoelectric compounds, PbTe and 
Sb2Te3, forming nano-sized lamellar structures [Ike07a, 
Ike07b]. In the present work, eutectic PbTe-Sb2Te3 alloys 
were synthesized by quenching in a copper mold and then 
annealed at several temperatures to control the fraction 
transformed and inter-lamellar spacing. The electrical 
resistivity and the thermal conductivity of as-quenched and 
annealed samples have been investigated as functions of the 
spacing.  
Experimental procedure 
Samples with overall composition matching the 
Pb2Sb6Te11 compound (Pb10.5Sb31.6Te57.9) were prepared by 
injection molding. Stoichiometric quantities of Pb, Sb, and Te 
granules were loaded into 12mm fused silica ampoules and 
then sealed under a vacuum of approximately 4 ? 10-3 Pa to 
prevent oxidation at high temperatures. Samples were then 
melted in vertical furnace for 5 min and were subsequently 
water quenched. They were then cut into small pieces with 
diamond saw. The small pieces of 15-20 g in total were put 
into a fused silica tube with 12 mm outer diameter and with a 
hole of approximately 1 mm diameter and were melted by 
induction heating under vacuum of approximately 4 ? 10-3 Pa. 
When the sample melted, the sample dropped through the hole 
into a copper mold of 20 ? 30 ?  mm3. For property 
measurements, samples with size of typically 10 ? 10 mm2 
were cut out with diamond saw and then the surfaces were 
ground to remove the surface layers until the final thickness 
was around 1.5 mm. 
Electrical resistivity and thermal conductivity 
measurements were carried out before and after annealing the 
samples. For annealing, samples were sealed under vacuum in 
fused silica tubes. Annealing temperature was 673 K (78 h, 
150 h) or 773 K (1 h, 24 h, 126 h). 
 
 
 
 
Figure 1: Microstructure of Pb10.5Sb31.6Te57.9: (a) as quenched 
and (b) annealed at 673 K for 150 h. 
 
Figure 2: XRD profiles obtained from Pb10.5Sb31.6Te57.9 as 
quenched and annealed at 773 K for 5 days. Open squares 
(?), open circles (?) and solid triangles (?) show the peaks 
from PbTe, Sb2Te3 and Pb2Sb6Te11 phases, respectively. 
 
The electrical resistivity (?) was measured up to 523 K, 
below which microstructure is not considered to practically 
change during measurements because of low atomic 
diffusivity [Ike07b], using the van der Pauw method with a 
current of 10 mA as functions of temperature. 
The thermal diffusivities were measured up to 523 K using 
the same samples as the electrical resistivity measurements by 
flash diffusivity technique (LFA457, NETSZCH). The 
thermal conductivity (?) was calculated from the thermal 
diffusivity which was experimentally measured and the heat 
capacity which was estimated using Dulong-Petit law. 
The microstructures were observed using field emission-
scanning electron microscope (Carl Zeiss LEO 1550 VP) 
equipped with a backscattered electron (BSE) detector for its 
high compositional contrast capabilities. The accelerating 
voltage was 20 kV. The microstructures were digitally 
analyzed using an image analysis program (Macscope, Mitani 
Corp.) to determine the inter-lamellar spacing (ILS) and the 
fraction transformed (Y). X-ray diffraction (XRD) 
experiments (Phillips X-Pert Pro diffractometer, Cu K-? 
radiation, 15˚ ? 2? ?  45˚) were performed directly on the as-
prepared ingots to identify phases.  
Results and discussion 
Microstructure 
Figure 1 (a) and (b) show the microstructure of the 
samples which are as-quenched and after annealing at 673 K 
for 150 h, respectively. The sample in as-quenched state is 
almost composed of the gray matrix phase, Pb2Sb6Te11. The 
thin dark acicular phase is Sb2Te3 and the bright dendrites are 
PbTe. The phases composing of as-quenched and annealed 
samples were also confirmed by XRD experiments as shown 
in Fig. 2. These features were consistent with the 
solidification microstructure of this system by water-
quenching using fused silica tubes [Ike06]. The inter-lamellar 
spacing in the solidification structure was 13 μm in the 
vicinity of the sample surface and 16 μm in the middle, which 
were also consistent with that for water quenching using fused 
silica tube in the previous work. After annealing at 673 K for 
78 h or at 773 K 126 h, Pb2Sb6Te11 is almost completely 
decomposed to Sb2Te3 and PbTe as reported in the previous 
work [Ike07a]. The backscattered electron images were 
digitally analyzed to determine the fraction transformed (Y) 
and the inter-lamellar spacing (ILS). The results of the image 
analysis is summarized in Table 1. In the sample annealed at 
673 K for 78 or 150 h and the one annealed at 773 K for 126 
h, the transformation to PbTe/Sb2Te3 lamellar structure is 
almost complete. It is also found that ILS is increased by 
annealing. 
 
Table 1. Fraction transformed (Y) and inter-lamellar spacing 
(ILS) of the samples annealed at 673 or 773 K. 
Annealing condition ILS (nm) 
Sample 
ID T / K t / h 
Y (%) 
Average 
Standard 
deviation 
78 99.7 536 155 
A 673 
150 100 575 153 
1 88.7 544 168 
B 773 
126 100 1591 487 
 
Electrical resistivity 
Figure 3 shows the electrical resistivity and the carrier 
concentration measured as functions of temperature. The 
resistivity is found to decrease by the decomposition of 
Pb2Sb6Te11 to PbTe/Sb2Te3 lamellae. This is mainly due to the 
increase in carrier concentration. It is also found that the 
electrical resistivity is not significantly affected in the 
coarsening process. 
Thermal conductivity 
Figure 4 shows the temperature dependence of thermal 
conductivity of sample B, which was annealed at 773 K for 1 
h, 24 h and 126 h. The thermal conductivitivities (?tot) were 
calculated from the measured thermal diffusivity (?), the 
measured density (?), and the heat capacity (CP) evaluated by 
Dulong-Petit law using the relation, ?tot = ?CP?. The electron 
part of the thermal conductivity, ?el was evaluated by 
Wiedemann-Franz law, ?el = LT/?, where L is Lorenz number. 
Moreover, the lattice part of the thermal conductivity, ?lat, was 
calculated using ?tot = ?el + ?lat. The lattice part of the thermal 
conductivity in the as-quenched state, i.e. that of Pb2Sb6Te11, 
is significantly lower than those after the decomposition. 
While the electrical resistivity is almost  
 
Figure 3: Electrical resistivity and carrier concentration of 
Pb10.5Sb31.6Te57.9 in the as-quenched state and after annealings 
at 673 K or 773 K. 
 
Figure 4: Total, electronic part, and lattice part of the thermal 
conductivity of Pb10.5Sb31.6Te57.9 in the as-quenched state and 
after annealing at 773 K. 
 
constant after annealing for 1 h at 773 K, the thermal 
conductivity slightly increases. As seen in the figure, this is 
due to the increase of lattice part of the thermal conductivity. 
As shown in Table 1, the microstructure is coarsened by 
annealing. That is qualitatively consistent with the previous 
work [Ike07b]. Thus, the increase in the lattice part of the 
thermal conductivity could be attributed to the lowering of 
phonon scattering at phase boundaries due to the coarsening 
of microstructure. The significantly low thermal conductivity 
of Pb2Sb6Te11 could be considered to be due to the strong 
effect of phonon scattering. 
Figure 5 shows the ILS dependence of the lattice thermal 
conductivity of Pb2Sb6Te11 and PbTe/Sb2Te3 lamellar 
composites. In the figure, the spacing of Pb2Sb6Te11 was taken 
to be 1.4 nm, which is the period of similar atomic stacking in 
the crystal structure [She04]. Lattice part of the thermal 
conductivity is lowered with decrease in ILS and the 
reduction the lattice thermal conductivity ultimately reaches 
that of Pb2Sb6Te11, which has a periodical layered crystal 
structure. Therefore, it is again considered that the reduction 
of the lattice thermal conductivity with the decrease of ILS is 
due to the enhancement of phonon scattering at phase 
boundaries. Thus, it is concluded that there is a significant 
effect of the nanosized lamellar structure on the reduction of 
lattice thermal conductivity. 
 
 
Figure 5: The dependence of lattice thermal conductivity of 
PbTe/Sb2Te3 lamellar composites and Pb2Sb6Te11 on inter-
lamellar spacing. Circles and Squares show the results from 
samples sample A and B, respectively. The spacing for 
Pb2Sb6Te11 was taken to be the period of similar atomic 
staking (1.4 nm) in the crystal structure [She04].  
 
Conclusions 
Pb10 .5Sb31.6Te57 .9  (the composition corresponding to 
Pb2Sb6Te11) samples were prepared by solidification 
processing using copper mold. After the solidification, the 
sample was mainly composed of Pb2Sb6Te11. Pb2Sb6Te11 was 
decomposed to PbTe and Sb2Te3 by annealing at 673 or 773 K. 
The fraction transformed and the inter-lamellar spacing (540-
1600 nm) were controlled by annealing period. The  
electrical resistivity and the thermal conductivity were 
measured before and after annealing. It was found that the 
electrical resistivity is the highest for Pb2Sb6Te11 (without 
annealing). Then, the electrical resistivity decreases as the 
decomposition to PbTe/Sb2Te3 lamellae proceeds. The 
thermal conductivity increases as the decomposition proceeds 
and the resulting nanostructure is coarsened.  
Acknowledgments 
This work was supported by the Office of Naval Research 
and Jet Propulsion Laboratory.  
References 
Abr65 Abrikosov, N. K. et al., “The System PbTe-Sb2Te3,” 
Inorg. Mater. Vol. 1 (1965), pp. 1944-1946. 
Ike06 Ikeda, T. et al., “Solidification Processing of Alloys 
in the Pseudo-binary PbTe–Sb2Te3 System,” Acta Mater. 
Vol. 55 (2007), pp. 1227-1239. 
Ike07a Ikeda, T. et al., “Self-Assembled Nanometer 
Lamellae of Thermoelectric PbTe and Sb2Te3 with 
Epitaxy-like Interfaces,” Chem. Mater. Vol. 19 (2007), pp. 
763-767. 
Ike07b  Ikeda, T. et al., “Development and Evolution of 
Nanostructure in Bulk Thermoelectric Pb-Te-Sb Alloys,” 
J. Electr. Mater., in press. 
Cay05 Caylor, J. C et al., “Enhanced Thermoelectric 
Performance in PbTe-based Superlattice Structures from 
Reduction of Lattice Thermal Conductivity,” Appl. Phys. 
Lett. Vol. 87 (2005), p. 023105. 
Ven01 Venkatasubramanian, R. et al., “Thin Film 
Thermoelectric Devices with High Room-Temperature 
Figures of Merit,” Nature 413 (2001), pp. 597-602. 
Har03 Harman, T. C. et al.,  “Quantum Dot Superlattice 
Thermoelectric Materials and Devices,” Science Vol. 297 
(2003), pp. 2229-2232. 
Che04 Chen, G., Proc Ninth Intersociety Conference on 
Thermal and Thermomechanical Phenomena In Electronic 
Systems 2004 (IEEE Cat. No.04CH37543); p.8. 
She04  Shelimova, L. E. et al., “Synthesis and structure of 
layered compounds in the PbTe-Bi2Te3 and PbTe-Sb2Te3 
systems,” Inorg Mater. Vol. 40 (2004), pp. 1264-1270.  
 


Lattice thermal conductivity of self-assembled PbTe-Sb_2Te_3 composites with nanometer lamellae

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