Thermoelectric Properties and Scattering Factors of Finely Grained Bi 2 Te 3 -Related Materials Prepared by Mechanical Alloying

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1 Materials Transactions, Vol. 51, No. 5 (21) pp. 863 to 867 Special Issue on Growth of Ecomaterials as a Key to Eco-Society IV #21 The Japan Institute of Metals Thermoelectric Properties and Scattering Factors of Finely Grained Bi 2 Te 3 -Related Materials Prepared by Mechanical Alloying Kazuhiro Hasezaki, Takashi Hamachiyo*, Maki Ashida*, Takashi Ueda* and Yasutoshi Noda Department of Materials Science, Shimane University, Matsue , Japan Fine grained samples with a nominal composition of Bi :5 Sb 1:5 Te x (x ¼ 3: to 3.4) were prepared by mechanical alloying (MA). Average grain sizes were found to range from 1. to 2.1 mm. Tellurium precipitation at x ¼ 3:1 was observed by scanning electron microscopy (SEM), X- ray diffraction and differential thermal analysis (DTA). Electrical conductivity as well as Hall and Seebeck coefficients were measured from 3 to 47 K. Using the relationship between Hall mobility and temperature, carrier scattering factors of the Bi :5 Sb 1:5 Te x samples were estimated to range from r ¼ :9to 2:. The thermal conductivities of the samples were found to range from.94 to 1. Wm 1 K 1 at room temperature. Excess tellurium was recognized to be responsible for the decrease in thermal conductivity. The Lorenz number and the carrier component of thermal conductivity were calculated from the scattering factor and the Fermi integral. The phonon component of thermal conductivity was dominant in the Bi :5 Sb 1:5 Te x samples. The Seebeck coefficient of the Bi :5 Sb 1:5 Te x samples was higher than that from the available data which means that the absolute scattering factor of the Bi :5 Sb 1:5 Te x samples was large. A maximum figure of merit of 7:2 1 3 K 1 was obtained at 31 K for the Bi :5 Sb 1:5 Te 3:1 sample. This high figure of merit results from an enhanced Seebeck coefficient that is due to an increased absolute scattering factor. High thermoelectric performance can, therefore, be established by a reduction in the phonon component of the thermal conductivity and also by an enhanced Seebeck coefficient, which results from an increased absolute scattering factor for finely grained Bi :5 Sb 1:5 Te x samples that were prepared by MA. [doi:1.232/matertrans.mh291] (Received July 1, 29; Accepted July 17, 29; Published April 25, 21) Keywords: thermoelectric semiconductor, mechanical alloying, bismuth, tellurium, antimony, scattering factor 1. Introduction Bi 2 Te 3 related materials consist of solid solutions of Bi 2 Te 3 and Sb 2 Te 3 and are the best materials for use in thermoelectric power generation and thermoelectric cooling near room temperature. 1) These materials are eco-materials because they recover exhaust heat. These materials have a rhombohedral crystal structure with a R3m space group and have structures that are usually expressed as a hexagonal lattice with a sequence of atomic layer units: -Te(1)-Bi- Te(2)-Bi-Te(1)- along the hexagonal c-axis. The strong bonds between Bi and Te have iono-covalent character. Te- Te bonds are extremely weak because of their Van der Waals type interactions. 2) The presence of Van der Waals bonds results in the physical properties of Bi 2 Te 3 related materials being anisotropic 3) and thus their thermoelectric properties are excellent in the c-plane. 3,4) High thermoelectric performance was established by their improved electrical properties that results from the texture of the preferred orientation 3,4) and the reduced phonon component of the thermal conductivity that results from a fine grain size. 5) The thermoelectric material performance is usually estimated using the figure of merit (Z ¼ 2 =), where, and are the Seebeck coefficient, the electrical conductivity and the thermal conductivity, respectively. The thermal conductivity is obtained from the phonon and carrier components as shown in eq. (1), ¼ phonon þ carrier ¼ phonon þ LT; ð1þ where L and T are the Lorenz number and the temperature, respectively. To maintain a low phonon thermal conductivity, samples are usually prepared by a powder metallurgy process such as mechanical alloying (MA). 5,6) Sintered *Graduate Student, Shimane University compacts produced using MA powders have random crystal orientations that lead to decreased thermoelectric properties and reduced anisotropy for the electrical conductivity. Grain sizes could be varied by controlling the sintering temperature. However, the thermoelectric properties were affected due to evaporation of tellurium. 7) On the other hand, finely grained Bi 2 Te 3 -related materials that are prepared by MA effect the scattering factor r of the carrier. Using Ioffe s classical approximation, 8) the Seebeck coefficient is given by, ¼ k B r þ 2 þ ln 2ð2m k B TÞ 3=2 ; ð2þ e h 3 n where k B, e, m, h and n are the Boltzmann constant, the electric charge, the effective mass, Planck s constant and the carrier concentration, respectively. An increase in the absolute scattering factor r causes an increase in the Seebeck coefficient leading to an enhanced figure of merit, which has been experimentally observed for Bi :5 Sb 1:5 Te 3: elsewhere. 9) In this study, fine grain samples with a nominal composition of Bi :5 Sb 1:5 Te x (x ¼ 3: to 3.4) were prepared by MA. The composition x > 3: corresponds to a deviation from stoichiometry that contains excess Te. The excess Te was expected to be the scattering center of carrier without changing the carrier concentaration. 6) It was observed the metallurgical microstructures and measured the electrical conductivity as well as Hall and Seebeck coefficients from 3 to 47 K. The scattering factor was estimated from plots of mobility versus temperature. The Lorenz number and the carrier thermal conductivity were evaluated by calculating the Fermi integral using the observed scattering factor. The thermoelectric properties were also measured for the samples prepared by MA.

2 864 K. Hasezaki, T. Hamachiyo, M. Ashida, T. Ueda and Y. Noda Fig. 1 SEM micrograph of a cross section of p-type Bi:5 Sb1:5 Tex prepared by MA. (a) x ¼ 3:, (b) x ¼ 3:1, (c) x ¼ 3:2, (d) x ¼ 3:3, (e) x ¼ 3:4. 2. Experimental 2.1 Sample preparation MA samples of the Bi2 Te3 related material were prepared and had compositions of (Bi:5 Sb1:5 ) Tex (x ¼ 3:; 3:1; 3:3; 3:4). The raw materials Bi (5 N), Sb (6 N) and Te (5 N) were weighed according to the target composition. For the MA method, the raw materials were placed in a stainless steel vessel under argon and milled with silicon nitride balls. The milling was carried out using a planetary ball mill for 3 h. The resulting powder was sintered by hot pressing at 673 K and 39 MPa under argon. MA samples of the sintered compact had a relative density of more than 96% the theoretical density.6) 2.2 Sample evaluation Microstructures in cross-sections of the MA sample were observed by scanning electron microscopy (SEM). Grain size was measured by the linear intercept technique.1) The elemental dispersion of the Bi:5 Sb1:5 Te3:4 compact was observed by scanning transmission electron microscope (STEM)/energy dispersive X-ray spectrometer (EDS). A structural investigation of the MA samples was performed by X-ray diffraction (XRD) using CuK radiation in a Bragg angle range of 2 ¼ 2 8 deg. Differential thermal analysis (DTA) was performed at a heating rate of 2 K/min under nitrogen gas flow. The Hall coefficient RH and the electrical resistivity were measured by the van der Pauw method from 3 to 47 K under a magnetic field of.5 T and an electric current of 5 ma. The carrier concentration n and Hall mobility H were evaluated using eqs. (3) and (4), respectively: n ¼ 1=eRH ð3þ H ¼ RH : ð4þ and The thermo-electromotive force E was measured at a temperature difference T of up to 3 K and the Seebeck coefficient was estimated from the linear relationship between E and T using ¼ E= T. Thermal conductivity was measured using the static comparison method at room temperature.11) Thermoelectric performance was evaluated by the figure of merit Z using the values of and as observed in the temperature range from 3 to 473 K while that of was fixed at room temperature. 3. Results and Discussion All the MA samples of Bi:5 Sb1:5 Tex were p-type semiconductors. Figure 1 shows SEM micrographs of a cross section of the Bi:5 Sb1:5 Tex sample where fine grains are observed.12) Table 1 lists the average grain size of the samples and they were found to range from 1. to 2.1 mm.

3 Table 1 Grain size, scattering factor and Lorenz number of p-type Bi :5 Sb 1:5 Te x (x ¼ 3:; 3:1; 3:2; 3:3; 3:4) samples prepared by MA. Te content of Bi :5 Sb 1:5 Te x x Thermoelectric Properties and Scattering Factors of Finely Grained Bi 2 Te 3 -Related Materials Prepared by Mechanical Alloying 865 grain size d (mm) scattering factor r Lorenz number L (1 8 ) : : : : :9.51 Fig. 3 DTA curves of p-type Bi :5 Sb 1:5 Te x (x ¼ 3:; 3:1; 3:2; 3:3; 3:4) powder prepared by MA. Fig. 2 XRD patterns of p-type Bi :5 Sb 1:5 Te x (x ¼ 3:; 3:1; 3:2; 3:3; 3:4) prepared by MA. The Bi :5 Sb 1:5 Te 3:4 sample was observed using an area of 1.5 mm square of Te precipitation by STEM/EDS analysis. XRD patterns of the MA samples are shown in Fig. 2. The diffraction peaks were identified by the constituent phases of the (Bi,Sb) 2 Te 3 -related material as well as of tellurium. Weak peaks from the tellurium phase were observed at x values higher than x ¼ 3:1. Diffraction pattern intensities of MA samples corresponded to those of isotropic samples that were determined by calculated Rietvelt diffraction intensities 13) and they did not show l peaks, which indicates that the c-plane was preferentially oriented. Figure 3 shows DTA curves obtained by heating the MA samples. The first endothermic peaks at around 673 K were observed for x 3:1 with excess tellurium content. The peak height increased as the tellurium content increased. Results indicate that the first peak corresponds to the formation of a liquid phase because of a eutectic reaction between (Bi,Sb) 2 Te 3 and tellurium. The second endothermic peak of all samples at around 873 K corresponds to the melting point of (Bi :5 Sb 1:5 )Te 3. 3) The temperature of the second peak is slightly lower if the tellurium content is lower and this is consistent with the freezing point depression behavior of the tellurium solid solution. The DTA observation of tellurium precipitation at x > 3:1 supports the results from X-ray diffraction and SEM analysis. Carrier concentration, n / m Fig. 4 Carrier concentrations of p-type Bi :5 Sb 1:5 Te x (x ¼ 3:; 3:1; 3:2; Hall mobility, µ H / m 2 V -1 s T -3/2+r Fig. 5 Hall mobility of p-type Bi :5 Sb 1:5 Te x (x ¼ 3:; 3:1; 3:2; 3:3; 3:4) versus temperature. Figure 4 shows plots of carrier concentration versus temperature for the MA samples. The carrier concentration is almost independent of tellurium content indicating that excess tellurium has no effect on the carrier concentration as was reported elsewhere. 6,14) Plots of Hall mobility versus temperature for the MA samples are shown in Fig. 5. The relationship between H and T is generally given as follows,

4 866 K. Hasezaki, T. Hamachiyo, M. Ashida, T. Ueda and Y. Noda Electrical conductivity, σ / 1 4 Sm Fig. 6 Electrical conductivity of p-type Bi :5 Sb 1:5 Te x (x ¼ 3:; 3:1; 3:2; Seebeck coefficient, α / µvk Fig. 7 Seebeck coefficient of p-type Bi :5 Sb 1:5 Te x (x ¼ 3:; 3:1; 3:2; Thermal Conductivity κ / Wm -1 K : κ total, : κ carrier, : κ lattice Tellurium content, x Fig. 8 Thermal conductivity of p-type Bi :5 Sb 1:5 Te x (x ¼ 3:; 3:1; 3:2; 3:3; 3:4) prepared by MA as function of the tellurium content at room temperature. total : total thermal conductivity, carrier : carrier thermal conductivity, phonon : phonon thermal conductivity. Figure of merit, Z / 1-3 K Fig. 9 Figure of merit Z of p-type Bi :5 Sb 1:5 Te x (x ¼ 3:; 3:1; 3:2; 3:3; 3:4) versus temperature. H / T 3=2þr : The scattering factor r also appears in eq. (2), where r ¼ : and 1: represents scattering by acoustic phonons and the interaction between acoustic and optical phonon scattering, respectively ) Table 1 shows the r values determined for the MA samples from the slope of the H T curves in the temperature range of 3 to 4 K. The scattering mechanism is composed of the interaction between acoustical and optical phonons. 16,17) This type of high scattering factor has been reported for a crystal with a low carrier concentration (n ¼ 1 23 m 3 ) which was prepared by melt growth. 14) It is noteworthy that high r values were observed at n ¼ 1 25 m 3 as shown in Fig. 4. These high values are attributed to the metallography of the fine grain structure obtained by the MA process where the scattering is subject to an interaction between acoustical and optical phonons. Figure 6 shows plots of electrical conductivity versus temperature for the MA samples. The electrical conductivity is almost independent of tellurium content, indicating that excess tellurium does not affect the electrical conductivity of MA samples. Plots of the Seebeck coefficient versus temperature for the MA samples are shown in Fig. 7. The Seebeck coefficients were higher than those in available data 3) which means that the absolute scattering factor of the MA samples was large. ð5þ The carrier thermal conductivity is given by the Lorenz number L which is otherwise given by the following equation on the basis of a one-electron approximation. " L ¼ ðr þ 3ÞF rþ2ðþ ðr þ 2ÞF rþ1ðþ # 2 kb ðr þ 1ÞF r ðþ ðr þ 1ÞF r ðþ e Z 1 ; ð6þ x r F r ðþ ¼ expðx Þþ1 dx; ð7þ where and F r ðþ are the reduced Fermi energy and Fermi integral, respectively. 18,19) Table 1 lists the calculated L values for the MA samples which used r values at room temparature. 19) All the L values were found to be smaller than those of metals (L ¼ 2: V 2 K 2 ). Figure 8 shows plots of thermal conductivity for the MA samples versus the tellurium content at room temperature. The thermal conductivity of carrier and phonon components were estimated using eq. (1) and the L values of Table 1. The thermal conductivities were found to range from.94 to 1. Wm 1 K 1 and phonon thermal conductivity was dominant in the MA samples. Excess tellurium was found to decrease the thermal conductivity slightly. Figure 9 shows plots of the figure of merit Z versus temperature for the MA samples. The maximum figure of merit was found to be 7:2 1 3 K 1 at 31 K for Bi :5 Sb 1:5 Te 3:1. The reason for the high figure of merit was that the Seebeck coefficient was higher at a higher absolute scattering factor.

5 Thermoelectric Properties and Scattering Factors of Finely Grained Bi 2 Te 3 -Related Materials Prepared by Mechanical Alloying 867 These results indicate that an improvement in thermoelectric performance is achieved by a reduction in the phonon thermal conductivity and also by an increase in the Seebeck coefficient that results from an increased absolute scattering factor of the finely grained MA samples. 4. Conclusions In this study, Bi 2 Te 3 -related thermoelectric semiconductors that were prepared by MA were investigated for their thermoelectric properties and their scattering factor. The results are summarized as follows: (1) The MA Bi :5 Sb 1:5 Te X samples were isotropic. Average grain sizes ranged from 1. to 2.1 mm. Tellurium precipitation at x > 3:1 was confirmed by SEM observation, X-ray diffraction and DTA analysis. (2) By estimating the relationship between Hall mobility and temperature, carrier scattering factors of the Bi :5 Sb 1:5 Te X samples were estimated to range from :9 to 2:. (3) The Seebeck coefficient of the Bi :5 Sb 1:5 Te X samples were higher by comparison to the available data and this is attributed to the large absolute scattering factors for the Bi :5 Sb 1:5 Te X samples. (4) The thermal conductivities were found to range from.94 to 1. Wm 1 K 1 at room temperature. Excess tellurium was found to decrease the thermal conductivity slightly. (5) A maximum figure of merit of 7:2 1 3 K 1 was obtained at 31 K for Bi :5 Sb 1:5 Te 3:1. This high figure of merit is the result of its high Seebeck coefficient which leads to a higher scattering factor. These results indicate that the thermoelectric performance can be improved by reducing phonon thermal conductivity and also by increasing the Seebeck coefficient that results from increasing the absolute scattering factor of the finely grained Bi :5 Sb 1:5 Te X samples prepared by MA. REFERENCES 1) G. J. Snyder: Thermoelectric Handbook macro to nano, ed. by D. Rowe (CRC press, Taylor & Francis Group, 26) ch9. 2) S. Nakajima: J. Phys. Chem. Solids 24 (1963) ) H. Scherrer and S. Scherrer: Thermoelectric Handbook macro to nano, ed. by D. Rowe (CRC press, Taylor & Francis Group, 26) ch27. 4) H. Kaibe, Y. Tanaka, M. Sakata and I. Nishida: J. Phys. Chem. Solids 5 (1989) ) K. Hasezaki, M. Nishimura, M. Umata, H. Tsukuda and M. Araoka: Mater. Trans. JIM 35 (1994) ) K. Hasezaki: J. Jpn. Soc. Powder Metall. 54 (27) ) T. Hamachiyo, M. Ashida and K. Hasezaki: J. Electron. Mater. 38 (29) ) A. Ioffe: Semiconductor Thermo electrics and Thermoelectric Cooling, (Infosearch, London, 1957). 9) T. Hamachiyo, M. Ashida, K. Hasezaki, H. Matsunoshita, M. Kai and Z. Horita: Mater. Trans. 5 (29) ) J. C. Wurst and J. A. Nelson: J. Am. Ceram. Soc. 55 (1972) ) T. Hamachiyo, M. Ashida and K. Hasezaki: Mater. Trans. 5 (29) ) M. Ashida, T. Hamachiyo, K. Hasezaki, H. Matsunoshita, M. Kai and Z. Horita: J. Phys. Chem. Solids 7 (29) ) F. Izumi: The Rietveld Method, ed. by R. A. Young, (Oxford University Press, Oxford, 1995) Chap ) C. B. Sattethwaite and R. W. Ure, Jr.: Phys. Rev. 18 (1957) ) R. S. Allgair and W. W. Scanlon: Phys. Rev. 111 (1958) ) D. M. Brown and R. Bray: Phys. Rev. 127 (1962) ) G. S. Nolas, J. Sharp and H. J. Goldsmid: Thermoelectrics Basic Principles and New Materials Developments, (Springer-Verlag, Berlin, 21) pp ) I. J. Ohsugi, T. Kojima and I. Nishida: J. Appl. Phys. 63 (1988) ) M. Orihashi, Y. Noda, L. Chen and T. Hirai: Mater. Trans. JIM 41 (2)