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Thermoelectric properties of CoSb3
Journal of Alloys and Compounds 315 (2001) 193–197
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Thermoelectric properties of CoSb 3 Yoshiyuki Kawaharada*, Ken Kurosaki, Masayoshi Uno, Shinsuke Yamanaka Department of Nuclear Engineering, Graduate School of Engineering, Osaka University, Yamadaoka 2 -1, Suita, Osaka 565 -0871, Japan Received 18 September 2000; accepted 6 October 2000
Abstract The typical skutterudite structure compound CoSb 3 was prepared by arc melting followed by sintering. The samples were characterized by powder X-ray diffraction method, electron probe microanalysis (EPMA), and the thermoelectric properties such as the thermal diffusivity, electrical resistivity, and Seebeck coefficient were measured in the temperature range from room temperature to about 750 K. The thermal conductivity of CoSb 3 was estimated from the heat capacity, the experimental density, and the thermal diffusivity measured by the laser flash method. The calculated dimensionless figure of merit, ZT of CoSb 3 was lower than that of state of the art thermoelectric materials. In order to enhance the ZT, it was attempted to reduce the lattice thermal conductivity of CoSb 3 . The electronic contribution to the thermal conductivity was estimated by Wiedemann–Franz law, and the lattice thermal conductivity was determined. It was found that the lattice thermal conductivity of CoSb 3 can be decreased, and ZT of CoSb 3 can potentially be enhanced. 2001 Elsevier Science B.V. All rights reserved. Keywords: Thermoelectric; Transition metal compounds; Electrical transport; Heat conduction
1. Introduction Thermoelectric materials can directly change heat to electric power by the Seebeck effect. This process involves only the materials. In other words, the power-generating module of these materials has no movements. The power generation using these materials also has high reliability and produces no noise, requires no frequency maintenance, and exhausts no waste. Therefore, the materials are attracting worldwide attention now, for reuse of the exhaust heat from power plant or automobile. Using these modules in a power plant would lead to reuse of the exhaust heat, and increase the efficiency of the whole power generation system. The efficiency of power generation of these materials is indexed by the dimensionless figure of merit, ZT(5TS 2 s / k ), where T is the temperature, S is the Seebeck coefficient, s is the electrical conductivity, and k is the thermal conductivity. A large magnitude of ZT indicates a high efficiency. The value ZT51 has been thought to be the maximum limit, experimentally. But in recent years, some compounds with ZT .1 have been discovered. Among these materials are skutterudite compounds [1,2]. The skutterudite compounds have a cubic structure, and *Corresponding author. E-mail address: [email protected] (Y. Kawaharada).
the space group is Im-3. Fig. 1a shows the structure of the binary skutterudites of the type MX 3 where M is Co, Rh or Ir and X is P, As or Sb. There are two cages per unit cell in the structure. The skutterudites form covalent structures with low coordination numbers for the constituent atoms and so it is possible to incorporate atoms into the cages [3]. The formula of the compounds turns out to be RM 4 X 12 . The structure is called filled-skutterudite structure, where R is most often a rare-earth element. The R atom is bonded weakly with the other atoms and rattles. Therefore, the introduction of R atoms into the cages of the skutterudites is an effective method of reducing the lattice thermal conductivity. It results in a raise the magnitude of ZT. In this study, as a first step to evaluate the thermoelectric properties of the skutterudite compounds, the thermoelectric properties of CoSb 3 are determined, and the possibilities for ZT enhancement are discussed.
2. Experimental Polycrystalline CoSb 3 samples were prepared as follows. First, cobalt (99.99% pure) powder and antimony (99.9999% pure) shots in stoichiometric ratio were loaded into an arc furnace and melted. The resulting ingots were ground into powder particles of some millimeters or less. Then the products were loaded into quartz ampoules.
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 00 )01275-5
Y. Kawaharada et al. / Journal of Alloys and Compounds 315 (2001) 193 – 197
194
Fig. 1. (a) The structure of binary skutterudite compounds. (b) The structure of filled skutterudite compounds.
These ampoules were sealed under vacuum. They were heated in a furnace to 1473 K at 5 K / min, left at 1473 K for 1 h, cooled to 1073 K at 5 K / min, and finally annealed at 1073 K for 50 h. For the electrical transport measurements, columns (9.8 mm in diameter, 8.2 mm in height) or rectangular blocks (e.g. 3.833.8317 mm 3 ) were cut from the annealed products. For the thermal conductivity measurements, disks (e.g. 1 mm in diameter, 1.2 mm in thickness) were cut from the bottom of the annealed products. The structural analysis of the products was carried out by powder X-ray diffraction. The densities of the samples were calculated from the size and the mass. To estimate the Sb / Co atomic ratio, inductively coupled plasma spectrometry (ICP) and electron probe microanalysis (EPMA) was employed using the instruments SHIMADZU ICPS7500 and JSM-5800LV, respectively. EPMA was carried out at three points of the rectangular sample. The electrical resistivity and the Seebeck coefficient were measured simultaneously on rectangular solids by a standard four probe dc method using ULVAC ZEM-1 between room temperature and 723 K in a He atmosphere. The thermal diffusivity was measured on the disks in the same temperature range in vacuum by the laser flash method using ULVAC TC-7000. The specific heat capacity of CoSb 3 was obtained from the thermodynamic database of MALT2 (Japan’s Thermal Measurement Society Thermodynamics data base for personal computer MALT2). The thermal conductivity was calculated from the following relationship k 5 DCp d,
where D is the thermal diffusivity; Cp is the specific heat capacity; and d is the density. The shear and longitudinal sound velocities were also measured by an ultrasonic pulse-echo method using a frequency of 5 MHz at room temperature.
3. Results and discussions The powder X-ray diffraction pattern of the samples showed that single phase CoSb 3 of the cubic skutterudite type structure was obtained in the present study. The lattice parameter and X-ray density of CoSb 3 were obtained from the X-ray diffraction analysis. The bulk densities of the samples were 84–95% of the theoretical density. The Sb / Co ratio of the sample was measured by ICP–Auger electron spectroscopy (AES) or EPMA. The longitudinal and shear sound velocity of CoSb 3 were measured by an ultrasonic pulse-echo method at room temperature. The sample characterizations of CoSb 3 are shown in Table 1. The temperature dependence of the electrical resistivity of CoSb 3 is shown in Fig. 2 together with the data of Bi 2 Te 3 -based alloys. The Bi 2 Te 3 -based alloys [4] are used currently as the state-of-the-art thermoelectric materials at around room temperature. At high temperatures the value of the electrical resistivity of CoSb 3 decreases with increasing temperature, indicating that the samples has semiconductor behavior. The electrical resistivity of CoSb 3 is higher than that of Bi 2 Te 3 -based alloy in the whole temperature region investigated. From the slope of the 1000 /T2 r curve, in the high temperature region, the
Table 1 Physical parameters of CoSb 3 Property
Units
Column sample
Rectangular sample
Disc sample
Lattice parameter X-ray density Shear sound velocity Transversal sound velocity Sb / Co ratio Debye temperature
˚ A %T.D. m/s m/s – K
9.038 91.6 4089 2674 2.65 306.5
9.026 83.3 – – 3.02 –
9.038 89.0 – – 2.65 –
Y. Kawaharada et al. / Journal of Alloys and Compounds 315 (2001) 193 – 197
195
Fig. 2. Temperature dependence of the electrical resistivity for CoSb 3 . Fig. 4. Temperature dependence of the thermal conductivity for CoSb 3. .
energy gap of CoSb 3 was estimated to be about 0.4 eV using the following equation,
S D
Eg r 5 A exp ] , 2kT where r is the electrical resistivity; A is a constant; Eg is the energy gap; and k is the Boltzmann constant. This value is in good agreement with an estimated value of 0.5 eV obtained at high temperature [5], and with a calculated value of 0.57 eV [6]. The temperature dependence of the Seebeck coefficient, S, is shown in Fig. 3. The absolute value of the Seebeck coefficient of CoSb 3 is much larger than that of the Bi 2 Te 3 -based alloys. From Fig. 3, it was found that CoSb 3 has negative values at low temperatures, while the sign of the Seebeck coefficient turns to positive with increasing temperature. This indicates that the major carrier has changed in nature with increasing temperature. The reason
Fig. 3. Temperature dependence of the Seebeck coefficient for CoSb 3 .
of this phenomenon may be caused by the Sb / Co ratio, but details are now being investigated. Fig. 4 shows the temperature dependence of the thermal conductivity of CoSb 3 , together with the data of UO 2 [7] and an Bi 2 Te 3 -based alloy [4] (100%T.D.). The thermal conductivity was calculated from the heat capacity, the experimental density, and the thermal diffusivity measured by the leaser flash method. The thermal conductivity of CoSb 3 decreases with increasing temperature up to about 600 K. This indicates that the thermal conductivity of CoSb 3 is mainly due to phonon conduction at low temperatures. The thermal conductivity of CoSb 3 is about seven times larger than that of Bi 2 Te 3 -based alloys at room temperature. The dimensionless figure of merit, ZT, was calculated for CoSb 3 . The temperature dependence of the dimensionless figure of merit ZT for CoSb 3 is shown in Fig. 5. The maximum of ZT was obtained at 723 K and reached 0.051.
Fig. 5. Temperature dependence of the dimensionless figure of merit ZT for CoSb 3 .
196
Y. Kawaharada et al. / Journal of Alloys and Compounds 315 (2001) 193 – 197
The value is too low for actual use as thermoelectric module. This may be due to the high electrical resistivity and high thermal conductivity of our sample. A lower thermal conductivity should lead to a large ZT. Therefore the possibility of enhancement of the ZT value as a result of a decreasing thermal conductivity is discussed. By inserting third elements R into a binary skutterudite compound MX 3 , a ternary compound RM 4 X 12 called filled skutterudite is obtained (Fig. 1). It seems that the R atoms can undergo large local anharmonic vibrations, and hence will dramatically reduce the lattice thermal conductivity of the filled skutterudite. Supposing that the binary skutterudite of our CoSb 3 can be transformed into a filled skutterudite by inserting the third elements, the lattice thermal conductivity was evaluated. When a single sign of charge carrier is predominant, the total thermal conductivity of the material ktotal can be written as
Fig. 6. Temperature dependence of the lattice thermal conductivity for CoSb 3 .
ktotal 5 kel 1 klat , where kel is the electronic contribution; and klat is the lattice contribution. In order to separate klat from kel , the electronic contribution to the thermal conductivity was calculated using the Wiedemann–Franz law,
kel 5 Ls T, where L is the Lorentz number; s is the electrical conductivity; and T is the absolute temperature. The temperature dependence of klat follows a 1 /T law, which indicates that klat is composed of phonon contribution. A simple estimate of the minimum lattice thermal conductivity kmin of our material is obtained with the following relationship, 1 klat 5 ]Cv vl h , 3 where Cv is the heat capacity per unit volume; v is the average sound velocity; and l h is the mean free path of heat carrier. The average sound velocity v is calculated from the longitudinal sound velocity and shear sound velocity, vl and vs using the following relationship,
1 l h 5 ]], A 1 BT where A and B are constants. In this form, the constants A and B are the reciprocal numbers of l i , and l u , respectively; l i is the mean free path of impurity scattering and l u is the mean free path associated with Umklapp processes. Adopting these assumptions for the column shaped sample, l i was estimated to be about 10 nm. This value is about ten times larger than the lattice parameter of CoSb 3 . Assuming that the R atoms reduce l h to the interatomic spacing of the R elements (0.782 nm), the minimum lattice thermal conductivity, kmin was estimated. The temperature dependence of the minimum lattice thermal conductivity is shown in Fig. 6. The minimum lattice thermal conductivity is about one sixth smaller than the experimental results obtained at around room temperature, which indicates that the values of ZT can be enhanced by a factor of six or more. From the present study, it was found that the skutterudite CoSb 3 has possibilities to obtain large values of ZT and to be good thermoelectric material.
vl 1 2vs v 5 ]]]. 3
4. Conclusion
In the present study, the longitudinal and shear sound velocity of CoSb 3 were measured by an ultrasonic pulseecho method at room temperature. The Debye temperature was estimated from the sound velocity, and Cv was calculated using the Debye temperature. The results are shown in Table 1. Supposing that Cv and v are constant and the mean free path, l h , decreases as 1 /T as the number of phonons increase in the present temperature range, l h is written as,
Polycrystalline CoSb 3 samples were prepared. The electrical resistivity, the Seebeck coefficient, and the thermal diffusivity were measured, and the dimensionless figure of merit, ZT, was calculated for CoSb 3 . The value is too low for actual use as thermoelectric module. But it was found that the skutterudite CoSb 3 has the potential to reach large values of ZT and to be a promising thermoelectric material. Efforts should now focus on producing filled skutterudite materials for the dispersion of phonons aiming
Y. Kawaharada et al. / Journal of Alloys and Compounds 315 (2001) 193 – 197
at exceptionally low thermal conductivities, and on studying the thermoelectric properties of it.
References [1] J.P. Flurial, A. Borshchevsky, T. Caillat, D.T. Morelli, G.P. Meisner, Proceedings of the XV International Conference on Thermoelectrics, Pasadena, California, USA, 1996, p. 91.
197
[2] B.C. Sales, D. Mandrus, R.K. Williams, Science 272 (1996) 1352. [3] G.S. Nolas, G.A. Slack, D.T. Morelli, T.M. Tritt, A.C. Ehrlich, J. Appl. Phys. 79 (8) (1996) 4002. [4] K. Matsubara, H. Anno, T. Koyanagi, Materia 35 (9) (1996) 948. [5] L.D. Dudkin, N.K. Abrikosov, Russ. J. Inorganic Chem. 1 (1956) 169. [6] D.J. Singh, W.E. Pickett, Phys. Rev. B 50 (15) (1994) 11235. [7] D.G. Martin, J. Nuclear Mater. 110 (1982) 73.
L
www.elsevier.com / locate / jallcom
Thermoelectric properties of CoSb 3 Yoshiyuki Kawaharada*, Ken Kurosaki, Masayoshi Uno, Shinsuke Yamanaka Department of Nuclear Engineering, Graduate School of Engineering, Osaka University, Yamadaoka 2 -1, Suita, Osaka 565 -0871, Japan Received 18 September 2000; accepted 6 October 2000
Abstract The typical skutterudite structure compound CoSb 3 was prepared by arc melting followed by sintering. The samples were characterized by powder X-ray diffraction method, electron probe microanalysis (EPMA), and the thermoelectric properties such as the thermal diffusivity, electrical resistivity, and Seebeck coefficient were measured in the temperature range from room temperature to about 750 K. The thermal conductivity of CoSb 3 was estimated from the heat capacity, the experimental density, and the thermal diffusivity measured by the laser flash method. The calculated dimensionless figure of merit, ZT of CoSb 3 was lower than that of state of the art thermoelectric materials. In order to enhance the ZT, it was attempted to reduce the lattice thermal conductivity of CoSb 3 . The electronic contribution to the thermal conductivity was estimated by Wiedemann–Franz law, and the lattice thermal conductivity was determined. It was found that the lattice thermal conductivity of CoSb 3 can be decreased, and ZT of CoSb 3 can potentially be enhanced. 2001 Elsevier Science B.V. All rights reserved. Keywords: Thermoelectric; Transition metal compounds; Electrical transport; Heat conduction
1. Introduction Thermoelectric materials can directly change heat to electric power by the Seebeck effect. This process involves only the materials. In other words, the power-generating module of these materials has no movements. The power generation using these materials also has high reliability and produces no noise, requires no frequency maintenance, and exhausts no waste. Therefore, the materials are attracting worldwide attention now, for reuse of the exhaust heat from power plant or automobile. Using these modules in a power plant would lead to reuse of the exhaust heat, and increase the efficiency of the whole power generation system. The efficiency of power generation of these materials is indexed by the dimensionless figure of merit, ZT(5TS 2 s / k ), where T is the temperature, S is the Seebeck coefficient, s is the electrical conductivity, and k is the thermal conductivity. A large magnitude of ZT indicates a high efficiency. The value ZT51 has been thought to be the maximum limit, experimentally. But in recent years, some compounds with ZT .1 have been discovered. Among these materials are skutterudite compounds [1,2]. The skutterudite compounds have a cubic structure, and *Corresponding author. E-mail address: [email protected] (Y. Kawaharada).
the space group is Im-3. Fig. 1a shows the structure of the binary skutterudites of the type MX 3 where M is Co, Rh or Ir and X is P, As or Sb. There are two cages per unit cell in the structure. The skutterudites form covalent structures with low coordination numbers for the constituent atoms and so it is possible to incorporate atoms into the cages [3]. The formula of the compounds turns out to be RM 4 X 12 . The structure is called filled-skutterudite structure, where R is most often a rare-earth element. The R atom is bonded weakly with the other atoms and rattles. Therefore, the introduction of R atoms into the cages of the skutterudites is an effective method of reducing the lattice thermal conductivity. It results in a raise the magnitude of ZT. In this study, as a first step to evaluate the thermoelectric properties of the skutterudite compounds, the thermoelectric properties of CoSb 3 are determined, and the possibilities for ZT enhancement are discussed.
2. Experimental Polycrystalline CoSb 3 samples were prepared as follows. First, cobalt (99.99% pure) powder and antimony (99.9999% pure) shots in stoichiometric ratio were loaded into an arc furnace and melted. The resulting ingots were ground into powder particles of some millimeters or less. Then the products were loaded into quartz ampoules.
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 00 )01275-5
Y. Kawaharada et al. / Journal of Alloys and Compounds 315 (2001) 193 – 197
194
Fig. 1. (a) The structure of binary skutterudite compounds. (b) The structure of filled skutterudite compounds.
These ampoules were sealed under vacuum. They were heated in a furnace to 1473 K at 5 K / min, left at 1473 K for 1 h, cooled to 1073 K at 5 K / min, and finally annealed at 1073 K for 50 h. For the electrical transport measurements, columns (9.8 mm in diameter, 8.2 mm in height) or rectangular blocks (e.g. 3.833.8317 mm 3 ) were cut from the annealed products. For the thermal conductivity measurements, disks (e.g. 1 mm in diameter, 1.2 mm in thickness) were cut from the bottom of the annealed products. The structural analysis of the products was carried out by powder X-ray diffraction. The densities of the samples were calculated from the size and the mass. To estimate the Sb / Co atomic ratio, inductively coupled plasma spectrometry (ICP) and electron probe microanalysis (EPMA) was employed using the instruments SHIMADZU ICPS7500 and JSM-5800LV, respectively. EPMA was carried out at three points of the rectangular sample. The electrical resistivity and the Seebeck coefficient were measured simultaneously on rectangular solids by a standard four probe dc method using ULVAC ZEM-1 between room temperature and 723 K in a He atmosphere. The thermal diffusivity was measured on the disks in the same temperature range in vacuum by the laser flash method using ULVAC TC-7000. The specific heat capacity of CoSb 3 was obtained from the thermodynamic database of MALT2 (Japan’s Thermal Measurement Society Thermodynamics data base for personal computer MALT2). The thermal conductivity was calculated from the following relationship k 5 DCp d,
where D is the thermal diffusivity; Cp is the specific heat capacity; and d is the density. The shear and longitudinal sound velocities were also measured by an ultrasonic pulse-echo method using a frequency of 5 MHz at room temperature.
3. Results and discussions The powder X-ray diffraction pattern of the samples showed that single phase CoSb 3 of the cubic skutterudite type structure was obtained in the present study. The lattice parameter and X-ray density of CoSb 3 were obtained from the X-ray diffraction analysis. The bulk densities of the samples were 84–95% of the theoretical density. The Sb / Co ratio of the sample was measured by ICP–Auger electron spectroscopy (AES) or EPMA. The longitudinal and shear sound velocity of CoSb 3 were measured by an ultrasonic pulse-echo method at room temperature. The sample characterizations of CoSb 3 are shown in Table 1. The temperature dependence of the electrical resistivity of CoSb 3 is shown in Fig. 2 together with the data of Bi 2 Te 3 -based alloys. The Bi 2 Te 3 -based alloys [4] are used currently as the state-of-the-art thermoelectric materials at around room temperature. At high temperatures the value of the electrical resistivity of CoSb 3 decreases with increasing temperature, indicating that the samples has semiconductor behavior. The electrical resistivity of CoSb 3 is higher than that of Bi 2 Te 3 -based alloy in the whole temperature region investigated. From the slope of the 1000 /T2 r curve, in the high temperature region, the
Table 1 Physical parameters of CoSb 3 Property
Units
Column sample
Rectangular sample
Disc sample
Lattice parameter X-ray density Shear sound velocity Transversal sound velocity Sb / Co ratio Debye temperature
˚ A %T.D. m/s m/s – K
9.038 91.6 4089 2674 2.65 306.5
9.026 83.3 – – 3.02 –
9.038 89.0 – – 2.65 –
Y. Kawaharada et al. / Journal of Alloys and Compounds 315 (2001) 193 – 197
195
Fig. 2. Temperature dependence of the electrical resistivity for CoSb 3 . Fig. 4. Temperature dependence of the thermal conductivity for CoSb 3. .
energy gap of CoSb 3 was estimated to be about 0.4 eV using the following equation,
S D
Eg r 5 A exp ] , 2kT where r is the electrical resistivity; A is a constant; Eg is the energy gap; and k is the Boltzmann constant. This value is in good agreement with an estimated value of 0.5 eV obtained at high temperature [5], and with a calculated value of 0.57 eV [6]. The temperature dependence of the Seebeck coefficient, S, is shown in Fig. 3. The absolute value of the Seebeck coefficient of CoSb 3 is much larger than that of the Bi 2 Te 3 -based alloys. From Fig. 3, it was found that CoSb 3 has negative values at low temperatures, while the sign of the Seebeck coefficient turns to positive with increasing temperature. This indicates that the major carrier has changed in nature with increasing temperature. The reason
Fig. 3. Temperature dependence of the Seebeck coefficient for CoSb 3 .
of this phenomenon may be caused by the Sb / Co ratio, but details are now being investigated. Fig. 4 shows the temperature dependence of the thermal conductivity of CoSb 3 , together with the data of UO 2 [7] and an Bi 2 Te 3 -based alloy [4] (100%T.D.). The thermal conductivity was calculated from the heat capacity, the experimental density, and the thermal diffusivity measured by the leaser flash method. The thermal conductivity of CoSb 3 decreases with increasing temperature up to about 600 K. This indicates that the thermal conductivity of CoSb 3 is mainly due to phonon conduction at low temperatures. The thermal conductivity of CoSb 3 is about seven times larger than that of Bi 2 Te 3 -based alloys at room temperature. The dimensionless figure of merit, ZT, was calculated for CoSb 3 . The temperature dependence of the dimensionless figure of merit ZT for CoSb 3 is shown in Fig. 5. The maximum of ZT was obtained at 723 K and reached 0.051.
Fig. 5. Temperature dependence of the dimensionless figure of merit ZT for CoSb 3 .
196
Y. Kawaharada et al. / Journal of Alloys and Compounds 315 (2001) 193 – 197
The value is too low for actual use as thermoelectric module. This may be due to the high electrical resistivity and high thermal conductivity of our sample. A lower thermal conductivity should lead to a large ZT. Therefore the possibility of enhancement of the ZT value as a result of a decreasing thermal conductivity is discussed. By inserting third elements R into a binary skutterudite compound MX 3 , a ternary compound RM 4 X 12 called filled skutterudite is obtained (Fig. 1). It seems that the R atoms can undergo large local anharmonic vibrations, and hence will dramatically reduce the lattice thermal conductivity of the filled skutterudite. Supposing that the binary skutterudite of our CoSb 3 can be transformed into a filled skutterudite by inserting the third elements, the lattice thermal conductivity was evaluated. When a single sign of charge carrier is predominant, the total thermal conductivity of the material ktotal can be written as
Fig. 6. Temperature dependence of the lattice thermal conductivity for CoSb 3 .
ktotal 5 kel 1 klat , where kel is the electronic contribution; and klat is the lattice contribution. In order to separate klat from kel , the electronic contribution to the thermal conductivity was calculated using the Wiedemann–Franz law,
kel 5 Ls T, where L is the Lorentz number; s is the electrical conductivity; and T is the absolute temperature. The temperature dependence of klat follows a 1 /T law, which indicates that klat is composed of phonon contribution. A simple estimate of the minimum lattice thermal conductivity kmin of our material is obtained with the following relationship, 1 klat 5 ]Cv vl h , 3 where Cv is the heat capacity per unit volume; v is the average sound velocity; and l h is the mean free path of heat carrier. The average sound velocity v is calculated from the longitudinal sound velocity and shear sound velocity, vl and vs using the following relationship,
1 l h 5 ]], A 1 BT where A and B are constants. In this form, the constants A and B are the reciprocal numbers of l i , and l u , respectively; l i is the mean free path of impurity scattering and l u is the mean free path associated with Umklapp processes. Adopting these assumptions for the column shaped sample, l i was estimated to be about 10 nm. This value is about ten times larger than the lattice parameter of CoSb 3 . Assuming that the R atoms reduce l h to the interatomic spacing of the R elements (0.782 nm), the minimum lattice thermal conductivity, kmin was estimated. The temperature dependence of the minimum lattice thermal conductivity is shown in Fig. 6. The minimum lattice thermal conductivity is about one sixth smaller than the experimental results obtained at around room temperature, which indicates that the values of ZT can be enhanced by a factor of six or more. From the present study, it was found that the skutterudite CoSb 3 has possibilities to obtain large values of ZT and to be good thermoelectric material.
vl 1 2vs v 5 ]]]. 3
4. Conclusion
In the present study, the longitudinal and shear sound velocity of CoSb 3 were measured by an ultrasonic pulseecho method at room temperature. The Debye temperature was estimated from the sound velocity, and Cv was calculated using the Debye temperature. The results are shown in Table 1. Supposing that Cv and v are constant and the mean free path, l h , decreases as 1 /T as the number of phonons increase in the present temperature range, l h is written as,
Polycrystalline CoSb 3 samples were prepared. The electrical resistivity, the Seebeck coefficient, and the thermal diffusivity were measured, and the dimensionless figure of merit, ZT, was calculated for CoSb 3 . The value is too low for actual use as thermoelectric module. But it was found that the skutterudite CoSb 3 has the potential to reach large values of ZT and to be a promising thermoelectric material. Efforts should now focus on producing filled skutterudite materials for the dispersion of phonons aiming
Y. Kawaharada et al. / Journal of Alloys and Compounds 315 (2001) 193 – 197
at exceptionally low thermal conductivities, and on studying the thermoelectric properties of it.
References [1] J.P. Flurial, A. Borshchevsky, T. Caillat, D.T. Morelli, G.P. Meisner, Proceedings of the XV International Conference on Thermoelectrics, Pasadena, California, USA, 1996, p. 91.
197
[2] B.C. Sales, D. Mandrus, R.K. Williams, Science 272 (1996) 1352. [3] G.S. Nolas, G.A. Slack, D.T. Morelli, T.M. Tritt, A.C. Ehrlich, J. Appl. Phys. 79 (8) (1996) 4002. [4] K. Matsubara, H. Anno, T. Koyanagi, Materia 35 (9) (1996) 948. [5] L.D. Dudkin, N.K. Abrikosov, Russ. J. Inorganic Chem. 1 (1956) 169. [6] D.J. Singh, W.E. Pickett, Phys. Rev. B 50 (15) (1994) 11235. [7] D.G. Martin, J. Nuclear Mater. 110 (1982) 73.