Thermoelectric Properties of Fine-Grained PbTe Bulk Materials Fabricated by Cryomilling and Spark Plasma Sintering

Transcription

1 Materials Transactions, Vol. 52, No. 4 (2011) pp. 795 to 801 #2011 The Japan Institute of Metals EXPRESS REGULAR ARTICLE Thermoelectric Properties of Fine-Grained PbTe Bulk Materials Fabricated by Cryomilling and Spark Plasma Sintering Chia-Hung Kuo 1;2, Hsiu-Shan Chien 1, Chii-Shyang Hwang 1, Ya-Wen Chou 2, Ming-Shan Jeng 2 and Masahiro Yoshimura 1 1 Department of Materials Science and Engineering, National Cheng Kung University, Tainan 70101, Taiwan, R. O. China 2 Green Energy & Environment Research Laboratories, Industrial Technology Research Institute, Liujia Shiang, Tainan County 734, Taiwan, R. O. China Dense fine-grained PbTe bulk materials without oxide phases are fabricated using a process that combines cryomilling (mechanical milling at cryogenic temperature) and spark plasma sintering (SPS). In the process, micro-grained PbTe powder is cryomilled into nanocrystalline powders, which are then rapidly densified into dense bulk samples with fine grains by. The effect of cryomilling on the composition ratio, microstructure, and thermoelectric properties of sintered PbTe samples is investigated. Experimental results indicate that when the grain size decreases to the nano-scale, the Seebeck coefficient increases, the thermal conductivity decreases, and the electrical conductivity only slightly changes for all sintered samples. According to the results, the combination of cryomilling and spark plasma sintering can improve the thermoelectric transport properties of PbTe bulk materials. [doi: /matertrans.m ] (Received September 22, 2010; Accepted January 27, 2011; Published March 30, 2011) Keywords: lead telluride, cryomilling, spark plasma sintering, thermoelectric properties 1. Introduction Thermoelectric materials have been widely investigated for use in direct heat-to-electricity converters and electronic coolers. 1) Excellent thermoelectric materials exhibit a high Seebeck coefficient (commonly referred to as thermopower), high electrical conductivity, and low thermal conductivity. These attributes can be expressed as a dimensionless figure of merit, ZT ¼ S 2 T=, where S,, T, and are the Seebeck coefficient, electrical conductivity, absolute temperature, and thermal conductivity, respectively. Recent studies on thermoelectric materials have focused on modifying thermoelectric properties by incorporating nanostructures in order to increase the ZT value, which in turn increases the efficiency of energy conversion. 2,3) In PbTe-based alloy systems, excellent results were obtained for n-type PbSeTe/PbTe quantum-dot thin films 4) and in n-type AgPb m SbTe m+2 bulk alloys with nano-sized Ag-Sb-rich inclusions. 5) According to recent studies, powder metallurgy is a potential route for fabricating thermoelectric bulk materials. 6 9) Sintered bulk materials with fine grains generally have excellent mechanical strength, making them more suitable for large-scale energy applications than ingots with coarse grains. Notably, increasing the grain boundary area can increase the ZT value of PbTe-based alloys by increasing the Seebeck coefficient and reducing thermal conductivity ) Therefore, the nanoin-bulk (nanograins in bulk materials) concept probably facilitates the effects of grain boundary scattering to enhance the thermoelectric performance. Bulk samples with small grains are generally fabricated using a bottom-up strategy, which involves the hot pressing or spark plasma sintering of nano-sized powders or nanocrystalline powders. Nano-sized PbTe powders derived from chemical methods generally contain oxygen, which results in the formation of PbTeO 3 and influences the thermoelectric properties of sintered samples. 13) Nanocrystalline powders can be produced using a top-down method that involves mechanically milling ingots with coarse grains. Mechanical milling, especially cryomilling, is an effective means of manufacturing a large quantity of nanocrystalline metallic powders. Cryomilling is performed in a liquid nitrogen atmosphere, subsequently inducing nanocrystallites in metallic particles without recrystallization and avoiding oxidation of powders. The consolidation of cryomilled powders via spark plasma sintering is a rapid means of maintaining the nanostructure of sintered samples while suppressing grain growth. 14) In the present study, dense fine-grained PbTe bulk samples are prepared using a process that combines cryomilling and SPS. Material characteristics and thermoelectric transport properties of sintered PbTe samples are investigated with an emphasis on the effect of cryomilling. 2. Experimental Details PbTe powders with nanocrystallites were prepared by ball milling. In a typical process, 100 g of PbTe powder (Alfa Aesar, 99.99%) was cryomilled using a modified attritor (01- HD, Union Process) with a ball (stainless steel media with a diameter of 3 mm)-to-powder ratio of 10 : 1 for 6 h and 9 h under a liquid nitrogen environment at a rotor speed of 300 rpm. Unmilled and milled powders were then compacted by spark plasma sintering at a uniaxial pressure of 100 MPa in a vacuum. The sintering temperature and heating rate were 573 K and 100 K/min, respectively. The SPS-consolidated specimens were 20 mm in diameter and approximately 3.5 mm in thickness. The crystal structure of all samples was confirmed by X- ray diffraction (XRD, D5000, Siemens) at room temperature using Cu K radiation ( ¼ 0:15406 nm). The morphology and nanostructure of powders and sintered samples were identified using a field-emission scanning electron microscope (FE-SEM, JSM-7000F, JEOL) and a transmission electron microscope (TEM, JEM-2100, JEOL). The main compositions (Pb and Te) of all PbTe bulk samples were

2 796 C.-H. Kuo et al. Fig. 1 SEM image of (a) the unmilled PbTe powder and milled powders derived from cryomilling under (b) 300 rpm/6 h and (c) 300 rpm/ 9 h; TEM image and SAD pattern of milled PbTe powders derived from cryomilling under (d) 300 rpm/6 h and (e) 300 rpm/9 h. determined by inductively coupled plasma mass spectrometry (ICP-MS). The oxygen and nitrogen content in all bulk samples was determined via elemental inorganic analysis (TC-136, LECO). The bulk samples were cut into rectangular bars for verifying electrical conductivity and the Seebeck coefficient using commercially available equipment (ZEM-3, Ulvac Riko, Inc.) under a low-pressure inert-gas atmosphere at temperatures ranging from 300 to 500 K. The carrier concentration and mobility of bulk samples were then determined using four-probe Hall effect measurements. The thermal conductivity was estimated using ¼ CP, where is the bulk sample density determined using the Archimedes method of water displacement. The thermal diffusivity and specific heat CP were measured using a laser flash thermal constants analyzer (TC-9000, Ulvac Riko, Inc.) and a differential scanning calorimeter (DSC, Netzsch), respectively. 3. Results and Discussion Figure 1 shows the FE-SEM and TEM images of the unmilled PbTe powders and powders cryomilled for 6 h and 9 h. Figure 1(a) reveals that the unmilled powder has a

3 Thermoelectric Properties of Fine-Grained PbTe Bulk Materials Fabricated by Cryomilling and Spark Plasma Sintering 797 Fig. 2 XRD patterns of PbTe materials at different stages of preparation: (a) the unmilled powder; milled powders made by cryomilling under (b) 6 h and (c) 9 h; sintered samples prepared by SPS of the (d) unmilled, (e) 6 h-milled and (f) 9 h-milled powders at 573 K. broaden particle size distribution between 1 mm and 100 mm. According to Figs. 1(a), (b) and (c), the particle size of PbTe powders decreases after cryomilling. The PbTe powders obtained after cryomilling for 6 h and 9 h have a particle size distribution of 200 nm to 10 mm. The nanostructure of the milled powder was confirmed by a bright-field TEM image and a selected-area diffraction (SAD) pattern, as shown in Fig. 1(d) and (e), respectively. Nanocrystalline PbTe grains can be observed in the bright-field image. The SAD pattern reveals continuous rings, which are typical of polycrystalline materials. Figure 2 shows XRD patterns of the unmilled PbTe powder and cryomilled (for 6 h and 9 h) powders, as well as those of their bulk materials that were sintered by SPS. XRD analysis indicates that the powders derived from cryomilling and all bulk samples after are single-phase lead telluride. Pb, Te, and other crystalline phases, including oxides, were undetected, even in samples prepared by cryomilling and spark plasma sintering. The average crystallite sizes of 6 h- and 9 h-milled PbTe powders, as determined from the full-width at half-maximum (FWHM) of the XRD peak broadening, are 88 nm and 58 nm, respectively. As expected, the grain size of PbTe powder decreases with increasing cryomilling time. Based on Fig. 1 and the XRD peak broadening, the PbTe powders derived from cryomilling have a particle size ranging from 200 nm to 10 mm, but contain nanocrystallites with an average size of below 90 nm. Generally, it is difficult to mill alloy powders into separate nanoparticles due to their ductility. Cryomilling can induce localized deformation to become shear bands with a high dislocation density. Nano-sized sub-grains can form by the elimination and recombination of these dislocations. 14) This nanocrystalline microstructure expands throughout the PbTe powders during cryomilling. Figure 3 shows the FE-SEM images of fractured surfaces of bulk samples sintered from unmilled and milled powders. According to Fig. 3(a), the microstructure of unmilled PbTe bulk samples subjected to exhibits extremely coarse grains with a size exceeding 50 mm. Figures 3(b) and (c) show the microstructures of PbTe bulk samples prepared Fig. 3 SEM images of fracture surfaces of bulk samples prepared by SPS of the (a) unmilled, (b) 6 h-milled and (c) 9 h-milled powders at 573 K. using cryomilling (for 6 h and 9 h, respectively) and SPS at 573 K; the microstructures are considerably dense with nano and submicron grains. FE-SEM observations reveal a grain size distribution ranging from 80 to 800 nm in the PbTe samples fabricated using cryomilling and SPS. The relative

4 798 C.-H. Kuo et al. Table 1 Relative bulk densities and composition ratios of all sintered bulk samples. Without milling, Cryomilling for 6 h, Cryomilling for 9 h, Relative density, % Pb : Te : O : N, atomic ratio :000 : 0:998 : 0:053 : 0: :000 : 0:999 : 0:055 : 0: :000 : 0:998 : 0:051 : 0:010 densities of all sintered bulk samples exceed 98%, as listed in Table 1. Based on XRD, SEM, and TEM results, the PbTe cryomilled powders have a particle size on the submicro/ micro-scale (from 200 nm to 10 mm). These coarse particles consist of numerous nanocrystallites of nm. Subsequently, the PbTe bulk specimens prepared via the SPS of cryomilled powders have high relative densities (> 98%) and a broad grain size distribution (from 80 nm to 800 nm), as shown in Table 1 and Fig. 3. The PbTe samples prepared via cryomilling and SPS have nano and submicro grains. After SPS process, PbTe grains grow from nano (58 88 nm) to submicro-scale ( nm). During SPS consolidation, it is believed that most of the pulse current is distributed on the outer surface of the particle. The high current density within these inter-particle contact area results in an exceedingly high temperature due to Joule heat or spark plasma, which induces melting or drastic grain growth at these surface regions of particles. However, the current effect during the SPS process is insignificant in the inner region of an alloy particle. 14) Furthermore, densification takes place very rapidly, which further hinders grain growth of these inner parts during the final sintering stage. Therefore, the broad grain size distribution of the PbTe bulk samples made by the SPS of nanocrystalline powders is due to pulse current effects. Figure 4 shows TEM images of the bulk sample corresponding to Fig. 3(b) (PbTe sample prepared via cryomilling and SPS). The bright-field TEM image in Fig. 4(a) indicates the presence of nano and submicro grains, which is consistent with the SEM results. According to the high-resolution TEM image in Fig. 4(b), the grains in the sintered PbTe sample have good crystallinity and are densely packed. Boundaries between the randomly oriented grains are also apparent. The inverse Fourier-transformed image (see Fig. 4(c)) of one site in Fig. 4(b) shows dislocations (denoted by white circles) and indicates a high density of lattice defects caused by cryomilling and the SPS process. The SEM and TEM images reveal highly dense and randomly packed grains for the PbTe bulk samples prepared using cryomilling and SPS, suggesting a potential reduction of the thermal conductivity by defect and boundary scatterings. Table 1 shows the Pb, Te, O, and N element ratios of all sintered bulk samples. According to the table, all sintered samples have low oxygen content, which cannot be detected by XRD. This finding suggests that cryomilling can prevent the oxidation of nanocrystalline powders more efficiently than chemical methods, which lead to serious oxidation that can be detected by XRD. 13) Table 1 also shows that the nitrogen content of PbTe sintered samples increases with cryomilling time. Fig. 4 TEM images of the bulk sample fabricated by cryomilling for 6 h and : (a) bright-field TEM image; (b) high-resolution TEM image; (c) inverse Fourier-transformed image of one site in (b). Figure 5 shows the variation of room-temperature carrier concentration and mobility for various milling times. All samples prepared using cryomilling and SPS have carrier concentrations that are approximately 5: m 3 higher than that of the sintered sample prepared with the unmilled

5 Thermoelectric Properties of Fine-Grained PbTe Bulk Materials Fabricated by Cryomilling and Spark Plasma Sintering 799 Table 2 Experimental (S exp. ) and estimated (S carrier ) room temperature Seebeck coefficients, grain size (d), energy mean free path (l " ) and ratio of l " =d for all sintered PbTe samples. Without milling, Cryomilling for 6 h, Cryomilling for 9 h, S exp., S carrier, d, mvk 1 mvk 1 nm l ", nm (l " =d), % 364 >100; <0: Fig. 5 Carrier concentrations and carrier mobilities of all PbTe bulk samples sintered at 573 K with different cryomilling times. powder, which has a carrier concentration of 3: m 3. The Hall effect results indicate that p-type carriers can be induced after cryomilling and SPS. The carrier concentration of thermoelectric materials generally depends on the composition ratios and dopant levels. According to Table 1, the main composition of all samples in this study, with a Pb/Te ratio of close to 1.00, only slightly changed. Therefore, the increase in the carrier concentration may be attributed to more negatively charged ions (nitrogen ions or oxygen ions) becoming bonded to PbTe during cryomilling or spark plasma sintering, subsequently producing electronhole carriers. Figure 5 also indicates that the mobility of sintered bulk samples decreases from m 2 V 1 s 1 to m 2 V 1 s 1 in a milling time ranging from 0 h to 9 h. This decrease is mainly due to milling inducing more interfaces (grain boundaries) inside the bulk samples. Carrier concentration and grain size can influence the magnitude of the Seebeck coefficient. In this study, cryomilling affected the carrier concentration and grain size of samples. To understand how the carrier concentration and grain size affect the Seebeck coefficient, the variation of the Seebeck coefficient at room temperature was calculated as a function of carrier concentration and grain size of sintered samples; the results are shown in Table 2. For degenerate semiconductors, the Seebeck coefficient is expressed by: 15) S carrier ¼ 82 k 2 B T 3qh 2 m d 2=3 ð1þ 3n where n denotes the carrier concentration and m d is the effective mass, which can be obtained from the literature. 15) Equation (1) reveals that a decrease in carrier concentration decreases the Fermi energy, resulting in an increase in the Seebeck coefficient. From eq. (1), the Seebeck coefficient is proportional to ð1=nþ 2=3. Table 2 summarizes the calculation results of the Seebeck coefficient-s carrier of PbTe, whose carrier concentration corresponds to that of the samples prepared using cryomilling and SPS. In this study, S carrier of the samples prepared using cryomilling and SPS can be regarded as a variation of S exp. (experimental values) of the sample prepared using unmilled powder and SPS that is accompanied by an increasing carrier concentration. According to the calculations, the samples prepared using cryomilling (for 6 h and 9 h) and SPS should have lower Seebeck coefficients than those of the sample prepared using unmilled powder and SPS if only the carrier concentrations are considered. However, the experimental values (S exp. )of the PbTe samples prepared using cryomilling and SPS are higher than those of the sample prepared using unmilled powder and SPS; the effect of the grain size on the Seebeck coefficient thus needs to be considered. In this work, the main compositions of PbTe bulk samples are close to the stoichiometric ratio, allowing us to assume that the increase in the Seebeck coefficient of the samples prepared using cryomilling and SPS is attributed to the decrease in grain size. The contribution to the Seebeck coefficient by the grain size effect can be expressed by the ratio of ðs exp. S carrier Þ=S exp.. Based on S exp. and S carrier listed in Table 2, the contributions to the Seebeck coefficient induced by the grain boundary are 33.77% and 35.21% for 6 h-milled and 9 h-milled PbTe sintered samples, respectively. To further elucidate how grain size affects the Seebeck coefficient, the extent to which the grain boundary contributes to the Seebeck coefficient can be estimated using the potential barrier mechanism. Potential barrier scattering at grain boundaries can be described as follows. 16,17) The potential barriers induced by grain boundaries can result in a strong dependence of the mean free path for energy near the chemical potential if their height is close to that of the Fermi level. Carriers with energy lower than the barrier height are impeded, whereas most of those with energy higher than the barrier height can pass through it. The Seebeck coefficient can increase because the energy distribution of carriers deviates from that of those in thermal equilibrium. The energy distribution ultimately reaches that of thermal equilibrium, where the distance from the barrier refers to the energy mean free path. The extent to which the potential barrier effects (grain size effect) contribute to the enhancement of the Seebeck coefficient can be expressed by the ratio of the energy mean free path (l " ) to the grain size (d). The energy mean free path can be expressed by: 16) l " ¼ðkT " =eþ 1=2 ð2þ where " is the relaxation time, which can be obtained from the literature, 16,17) and is the carrier mobility. Based on the measured carrier mobility (), Table 2 shows the energy mean free path (l " ) of the unmilled, 6 h-milled, and 9 h-milled sintered samples. The table also lists the average grain size (d) of the 6 h-milled and 9 h-milled sintered PbTe, as estimated from the XRD peak broadening. According to the calculations for the value of (l " =d), the extents to which the potential barrier contributes to the Seebeck coefficient for

6 800 C.-H. Kuo et al. Fig. 6 Temperature-dependence of Seebeck coefficient for PbTe samples prepared by different cryomilling times and sintered at 573 K. Fig. 7 Temperature-dependence of electrical conductivity for PbTe samples prepared by different cryomilling times and sintered at 573 K. the unmilled, 6 h-milled, and 9 h-milled sintered samples are 0.03%, 32.15%, and 35.71%, respectively. The calculation results for the samples prepared using cryomilling and SPS are close to the above estimates of the contributions of grain size calculated using S exp. and S carrier. Figure 6 shows the temperature dependence of the Seebeck coefficient for all sintered samples. The Seebeck coefficients of all sintered specimens are positive within the measured temperature range of 300 to 450 K, which coincides with the Hall effect measurement results and corresponds to p-type conduction. Notably, the Seebeck coefficient of the sample prepared using unmilled powder and SPS is negative in the measured temperature range of 450 to 500 K, which can be attributed to the dramatic increase of the intrinsic electron carrier concentration at high temperature. In the temperature range of 300 to 500 K, the Seebeck coefficients of the samples prepared using cryomilling and SPS are larger than those of the sample prepared using unmilled powder and SPS, as shown in Fig. 6. In the temperature range of 300 K to 450 K, the Seebeck coefficient of the PbTe prepared using unmilled powder and SPS exhibits a nearly linear decrease. However, the Seebeck coefficients of the samples prepared using cryomilling and SPS are constant in the temperature range of 300 to 400 K and then decrease at temperatures over 400 K. The results demonstrate that bipolar conduction (two-band conduction) appears in all sintered samples without heavy doping. Based on the Hall effect measurements, carrier concentrations of the samples prepared using cryomilling and SPS are slightly larger than that of the sample prepared using unmilled powder and SPS. Therefore, the Seebeck coefficient of the samples prepared using cryomilling and SPS appears to be eliminated at higher measurement temperatures. Figure 7 shows the temperature dependence of the electrical conductivities of all sintered samples. The electrical conductivity changes slightly for all samples. The electrical conductivities of all bulk samples in this study are extremely low because no doping element (such as Na, I, Sn, or Se) was used. Electrical conductivity is a combination of the carrier concentration and mobility. Despite having higher carrier concentrations due to slight changes in composition, the samples prepared using cryomilling and SPS have low Fig. 8 Temperature-dependence of thermal conductivity for PbTe samples prepared by different cryomilling times and sintered at 573 K. electrical conductivities due to their lower carrier mobility. Moreover, the electrical conductivity of PbTe prepared using unmilled powder and SPS exhibits bipolar conduction, explaining why the conductivity increases slightly at high temperature, as shown in Fig. 7. In the temperature range of 300 K to 500 K, the electrical conductivities of samples prepared using cryomilling and SPS do not reveal a two-band conduction model due to their higher carrier concentrations. Figure 8 plots the temperature dependence of the thermal conductivity for all sintered PbTe samples. According to the figure, the samples prepared using cryomilling and SPS have lower thermal conductivities than that of the sample prepared using unmilled powder and SPS. A minimum value of 1.10 W m 1 K 1 was obtained at 500 K for the 9 h-milled PbTe sintered sample. The electrical conductivities of all sintered samples in this study are low, and therefore phonon transport should be the dominant mechanism of heat transfer. The decreases in the room-temperature thermal conductivities of 6 h-milled and 9 h-milled PbTe sintered samples as compared with that of the sample prepared using unmilled powder and SPS are 9% and 21%, respectively. Moreover, a longer cryomilling time can produce more interfaces and defects in PbTe sintered samples, which can cause more phonon scattering during heat transfer. The thermal con-

7 Thermoelectric Properties of Fine-Grained PbTe Bulk Materials Fabricated by Cryomilling and Spark Plasma Sintering 801 ductivity of the sample prepared using unmilled powder and SPS slightly increased above 450 K. The electron carriers of the sample prepared using unmilled powder and SPS can be induced by thermal activation at high measurement temperatures. Electron-hole pairs formed and accompanied with energy absorption from the hot side. These pairs can move the temperature gradient down and release the recombination energy. Therefore, the thermal conductivity of the sample prepared using unmilled powder and SPS can increase at high temperatures due to bipolar thermodiffusion. Because the samples prepared using cryomilling and SPS have higher carrier concentrations, the increase in thermal conductivity by bipolar thermodiffusion is not obvious. 4. Conclusions Polycrystalline PbTe bulks with fine grains were prepared via cryomilling and spark plasma sintering. The samples prepared using cryomilling and SPS had no oxide phases, high relative bulk densities of over 98%, and grain sizes in the range of 80 nm to 800 nm. The decrease of the grain size to the nano-scale increased the Seebeck coefficient and reduced thermal conductivity, with electrical conductivity remaining almost constant, in all sintered samples. The results of this study demonstrate that a cryomilling and spark plasma sintering can improve the thermoelectric performance of PbTe bulk samples due to an increased potential barrier and phonon scattering at grain boundaries. Acknowledgements This work is supported by Department of Industrial Technology, Ministry of Economic Affairs, Taiwan, R.O.C. REFERENCES 1) D. M. Rowe (ed.): CRC Handbook of Thermoelectrics, (CRC Press, New York, 1995). 2) R. Venkatasubramanian, E. Siivola, T. Colpitts and B. O Quinn: Nature 413 (2001) ) H. Ohta, S. Kim, Y. Mune, T. Mizoguchi, K. Nomura, S. Ohta, T. Nomura, Y. Nakanishi, Y. Ikuhara, M. Hirano, H. Hosono and K. Koumoto: Nat. Mater. 6 (2007) ) T. C. Harman, R. J. Taylor, M. P. Walsh and B. E. LaForge: Science 297 (2002) ) K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T. Hogan, E. K. Polychroniadis and M. G. Kanatzidis: Science 303 (2004) ) B. Poudel, Q. Hao, Y. Ma, Y. Lan, A. Minnich, B. Yu, X. Yan, D. Wang, A. Muto, D. Vashaee, X. Chen, J. Liu, M. S. Dresselhaus, G. Chen and Z. Ren: Science 320 (2008) ) L. D. Zhao, B. P. Zhang, W. S. Liu, H. L. Zhang and J. F. Li: J. Alloy. Compd. 467 (2008) ) W. Xie, X. Tang, Y. Yan, Q. Zhang and T. M. Tritt: Appl. Phys. Lett. 94 (2009) ) C. H. Kuo, C. S. Hwang, M. S. Jeng, W. S. Su, Y. W. Chou and J. R. Ku: J. Alloy. Compd. 496 (2010) ) J. P. Heremans, C. M. Thrush and D. T. Morelli: Phys. Rev. B 70 (2004) ) C. H. Kuo, M. S. Jeng, J. R. Ku, S. K. Wu, Y. W. Chou and C. S. Hwang: J. Electron. Mater. 38 (2009) ) J. Martin, L. Wang, L. Chen and G. S. Nolas: Phys. Rev. B 79 (2009) ) J. Martin, G. S. Nolas, W. Zhang and L. Chen: Appl. Phys. Lett. 90 (2007) ) J. Ye, L. Ajdelsztajn and J. M. Schoenung: Metall. Mater. Trans. A 37 (2006) ) J. P. Heremans, V. Jovovic, E. S. Toberer, A. Saramat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka and G. J. Snyder: Science 321 (2008) ) K. Kishimoto and T. Koyanagi: J. Appl. Phys. 92 (2002) ) K. Kishimoto, K. Yamamoto and T. Koyanagi: Jpn. J. Appl. Phys. 42 (2003)