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Thermoelectric properties and structural instability of type-I clathrate Ba8Ga16Sn30 at high temperatures
Solid State Communications 152 (2012) 1902–1905
Contents lists available at SciVerse ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Thermoelectric properties and structural instability of type-I clathrate Ba8Ga16Sn30 at high temperatures Y. Saiga a, K. Suekuni a, B. Du a,b, T. Takabatake a,c,n a
Department of Quantum Matter, ADSM, Hiroshima University, Kagamiyama 1-3-1, Hihashi-Hiroshima 739-8530, Japan School of Physics and Chemistry, Henan Polytechnic University, Jiaozuo 454000, China c Institute for Advanced Materials Research, Hiroshima University, Higashi-Hiroshima 739-8530, Japan b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 June 2012 Accepted 26 June 2012 Available online 27 July 2012
Type-I clathrate Ba8Ga16Sn30 is known as a typical example showing glass-like behavior in the thermal conductivity at low temperatures. We report on thermoelectric properties above room temperature for the p- and n-type single crystals which were grown from Ga–Sn double flux and Sn single flux, respectively. The measurements of electrical resistivity showed hysteretic behaviors when the sample was heated to 600 K. Powder X-ray diffraction analysis indicated that the type-I structure changed to the type-VIII after the sample was heated to 600 K. By using the data of Seebeck coefficient, electrical resistivity, and thermal conductivity, we estimated the dimensionless figure of merit ZT for the type-I Ba8Ga16Sn30. For the p- and n-type samples, the values of ZT reach 0.58 and 0.50 at around 450 K, respectively, which values are approximately half of those for the type-VIII counterparts. & 2012 Elsevier Ltd. All rights reserved.
Keywords: A. Energy material A. Thermoelectric material A. Ba8Ga16Sn30 C. Clathrate
1. Introduction Thermoelectric power generation has attracted much attention in times of energy shortage. Direct conversion from waste heat to electrical energy is feasible by using a thermoelectric module made of p- and n-type materials [1]. The thermoelectric efficiency of a given material is evaluated by the dimensionless figure of merit ZT, defined as ZT¼ a2T/rk, where a is the Seebeck coefficient, r is the electrical resistivity and k is the thermal conductivity. For searching materials with low r and low k, which do not reconcile each other usually, the concept of ‘‘phonon-glass electron-crystal’’ (PGEC) was proposed by Slack in 1995 [2]. According to this guiding principle, caged compounds such as filled skutterudites and clathrates have been synthesized and their physical and structural properties have been investigated extensively [3–10]. Most intermetallic clathrates are Zintle compounds in which the charge balance is well maintained between the guest ions and cage network. Therefore, stoichiometric clathrates show semiconducting behavior while small deviation from the ideal stoichiometry induces charge carriers in real samples. If the carrier density is controlled to be in the range of 1020/cm3, then rather high a can coexist with rather low r [11]. Another requisite for enhancing ZT is low k which is also achieved often in type-I n Corresponding author at: Hiroshima University, Department of Quantum Matter, ADSM, Kagamiyama 1-3-1, Hihashi-Hiroshima 739-8530, Japan. Tel.: þ81 82 424 7025; fax: þ 81 82 424 7029. E-mail address: [email protected] (T. Takabatake).
0038-1098/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ssc.2012.06.027
clathrates with a large mismatch between the guest ion size and the cage size. Thereby, large-amplitude anharmonic vibrations of the guest ion are thought to scatter acoustic phonons carrying the heat [12,13]. Furthermore, the anti-crossing of the acoustic mode with the guest vibration mode gives rise to the decrease of the group velocity of the acoustic mode, and thus suppresses the lattice thermal conductivity kL(T) [14]. The unit cell of type-I structure consists of six tetrakaidecahedra and two dodecahedra both of which are composed of group 13 and 14 elements. The cage encloses the group 1 and 2 elements as the guest atoms which vibrate with much larger amplitude than that of cage atoms. Among type-I intermetallic clathrates, Ba8Ga16Sn30 (BGS) shows a typical glass-like behavior in kL(T) with a plateau at 3–10 K [13,15]. In fact, the magnitude of kL in the plateau is lower than that of the amorphous SiO2. In type-I BGS, the Ba guest moves among off-centered 24k sites in the tetrakaidecahedron. The off-center rattling with the characteristic energy of approximately 20 K is thought to be responsible for the plateau in kL(T). Although thermoelectric and dynamic properties of type-I BGS have been extensively studied at low temperatures, physical properties above room temperature are less known. So far, preliminary measurements of a and r above 300 K have been performed [16], but not published yet. The BGS is dimorphic and adopts type-I and type-VIII structures. The single crystals of both types have been selectively grown by an empirical method due to the lack of knowledge of the phase diagram [13,15–18]. The unit cell of type-VIII clathrate consists of eight distorted dodecahedra. The Ba guest occupies the centered site in the dodecahedron. The guest vibrations are well
Y. Saiga et al. / Solid State Communications 152 (2012) 1902–1905
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described by an Einstein oscillator model with the characteristic energy of 50 K. The kL(T) shows a typical crystalline peak at around 10 K [13,16], which is in contrast to the glass-like plateau in the type-I BGS. The electronic band structure calculation showed that type-I BGS and type-VIII BGS are narrow-gap semiconductors with indirect gaps of 0.51 and 0.32 eV, respectively [19]. Our measurements of a and r at temperatures above 300 K suggested that type-VIII samples are more stable than type-I samples. We therefore concentrated on the assessment of thermoelectric potential of type-VIII BGS at high temperatures [18]. Single crystals grown from Ga and Sn flux, respectively, exhibit the p- and n-type conduction. Optimization of carrier density in type-VIII BGS has enhanced the ZT values for p- and n-type samples up to 1.0 and 0.9 at 480 K, respectively [18]. In view of the low kL(T), the type-I BGS might have higher ZT than type-VIII BGS at high temperatures. Keeping this in mind, we have studied the thermoelectric properties and structural stability of type-I BGS from 300 to 600 K. Fig. 1. (Color online) Temperature dependences of electrical resistivity for p- and n-type samples of type-I Ba8Ga16Sn30 in the virgin cycle between 300 and 600 K.
2. Experimental Single crystals of type-I BGS were grown by the flux method as reported previously [13]. The Ga–Sn double flux and single Sn flux, respectively, were used to tune the charge carrier to p-type and n-type. The starting compositions of Ba:Ga:Sn were 8:32:60 for the p-type samples and 8:16:50 for the n-type samples. High purity elements of Ba (99.9%), Ga (99.9999%) and Sn (99.999%) in proper atomic ratios were loaded in a quartz ampoule which was evacuated and shielded. The ampoule was heated to 1173 K in a box furnace and kept at this temperature for 4 h. The ampoule was cooled to 873 K for 1 h, and then slowly cooled to 623 K at a rate of 2 K/h. At 623 K, the ampoule was removed from the furnace and single crystals were separated from the molten flux by centrifuging. Single crystals obtained by the Ga–Sn double flux and the Sn flux were 5 mm and 10 mm in the maximum diameter, respectively. The powder X-ray diffraction (XRD) experiment was performed on the crushed samples by using a Rigaku D/teX ultradetector with Cu Ka radiation in the 2y range from 101 to 1201. All diffraction peaks were well indexed as the type-I clathrate structure. The lattice parameters were estimated to be 11.707 and 11.686 A˚ for p- and n-type samples, respectively, which values agree with the reported values [13]. The electrical resistivity r was measured in a homemade system by a standard dc four-probe method. The Seebeck coefficient a was measured by the differential method with a commercial system (MMR technologies, Inc). The thermal diffusivity D and specific heat Cp were simultaneously measured by the laserflash method (LFA-502, Kyoto Electronics). Because the measurements require the sample larger than 5 5 mm2, we could obtain the reliable data only for the n-type sample. All measurements were performed in a vacuum to avoid oxidation.
3. Results and discussion 3.1. Structural instability First, we show the data of r(T) measured on heating and cooling between 300 and 600 K in Fig. 1. In the virgin heating process, r(T)s for the p- and n-type samples show a maximum at 550 K which is followed by a decrease on further heating to 600 K. After the sample was kept at 600 K for 30 min, the cooling process started. On cooling, r(T)s monotonically increase without showing a maximum. The values at 300 K are several times larger than those in the initial state. To understand this hysteretic behavior in r(T), we examined
Fig. 2. (Color online) Powder X-ray diffraction patterns for the n-type sample of Ba8Ga16Sn30 (a) before and (b) after the electrical resistivity measurement up to 600 K. The initial structure is type-I while the final structure is type-VIII.
the crystal structure of the samples used for the r(T) measurement by the powder XRD. As an example, the XRD pattern for the n-type sample after heated to 600 K is compared with that for the initial state in Fig. 2. We find that the type-I clathrate structure has completely modified to the type-VIII one. This structural transformation was observed also in the p-type sample. These observations suggest that the type-I and type-VIII are the low- and hightemperature phases of the dimorphic clathrate BGS, respectively. However, the transformation is not reversible because no phase transition from type-VIII to type-I occurred in the cooling process from 600 to 300 K. The phase transition on heating was not observed by the differential thermal analysis, which showed the identical melting point at 793 K for both type-I and type-VIII phases [13]. It is necessary to examine this structural transformation by in-situ X-ray diffraction on both heating and cooling. In the temperature range below 520 K, we have found that r(T) of type-I BGS shows a reversible behavior. Powder XRD measurements for the sample used for r(T) measurement up to 520 K confirmed the stability of type-I structure. To avoid the phase transformation from type-I to type-VIII, the highest temperature was set at 520 K for the measurements of r, a, and thermal diffusivity. 3.2. Thermoelectric properties Fig. 3(a) and (b) show, respectively, the absolute values of a and r for type-I BGS samples with p- and n-type carriers as a
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Y. Saiga et al. / Solid State Communications 152 (2012) 1902–1905
Fig. 3. (Color online) Temperature dependences of (a) Seebeck coefficient and (b) electrical resistivity for the p- and n-type samples of type-I Ba8Ga16Sn30 in the range from 300 to 520 K.
Fig. 4. (Color online) Temperature dependence of thermal conductivity k for the n-type samples of type-I Ba8Ga16Sn30 in the range from 300 to 520 K. The data of k for the n-type sample of type-VIII Ba8Ga16Sn30 are taken from Ref. [18].
function of temperature for 300 K oTo520 K. The values of a (300 K) are 345 and 370 mV/K for the p- and n-type samples, respectively, which agree with the reported values [13]. With increasing temperature, the values of 9a9 for p- and n-type samples increase and approach a saturated value 450 mV/K. The value of r (300 K) for the n-type samples is 30 mO cm, which is slightly higher than that for the p-type one. The two curves of r(T) linearly increase in parallel on heating and are saturated at around 500 K. The thermal conductivity k was calculated by inserting the data of the thermal diffusivity D and specific heat Cp in the formula k ¼DCpd, where d is the sample density. We note that, on heating from 300 to 520 K, Cp(T) slightly increased from 0.23 to 0.27 J/gK, which coincides with the Dulong–Petit value 0.23 J/gK. Fig. 4 displays the temperature variation of k(T) for the type-I BGS single crystal with n-type carriers, together with the result for
Fig. 5. (Color online) Temperature dependences of (a) power factor PF and (b) dimensionless figure of merit ZT for the p- and n-type samples of type-I and type-VIII Ba8Ga16Sn30. The data for the type-VIII are taken from Ref. [18].
type-VIII BGS with n-type carriers [18]. The obtained value of k(300 K) for type-I is 0.39 W/Km which is half of 0.72 W/Km for type-VIII. It is worth noting that the carrier thermal conductivity ke is smaller in type-I than in type-VIII. The ke can be calculated using the Wiedemann–Franz law ke ¼LT/r, where the Lorenz number L of 2.45 10 8 V2/K2 is used for a degenerated semiconductor [20]. By using r (300 K)¼30 mO cm, the value of ke at 300 K is estimated to be 0.03 W/Km, which is only 7.7% of the measured value of k. The temperature gradient of k(T) becomes steeper above 450 K. This upswing in k(T) is attributed to the carrier excitations from the top of the valence band to the conduction bands, which is called as the bipolar effect [21]. Fig. 5(a) and (b) show, respectively, the power factor PF ¼ a2/r and the dimensionless figure of merit ZT¼ a2T/rk for both type-I and type-VIII single crystals. For this calculation, we used the data of k(T) for the n-type sample for the lack of the data for p-type samples. It was due to the fact that the size of the p-type crystals was not large enough for the thermal diffusivity measurement. For both p- and n-type samples of type-I BGS, the values of PF are in the range between 4 and 6 mW/cm K2, which are smaller than half the values for the type-VIII. As a result, in spite of the low k(T) of 0.4–0.5 W/Km, the ZT values of type-I BGS are much lower than the type-VIII in the whole temperature range from 300 to 520 K. The ZT of type-VIII has a broad maximum at around 450 K, whose values are 0.58 and 0.50 for p- and n-types, respectively. In order to improve the thermoelectric potential of type-I BGS, chemical substitutions would be effective as has been satisfactory performed for type-VIII BGS [22].
4. Conclusion We studied the thermoelectric properties and structural stability for single crystals of the type-I clathrate BGS above room temperature. The measurements of r and powder XRD indicated that the type-I structure transforms into the type-VIII one on heating above 520 K while the opposite transition does not occur on the cooling process. In-situ X-ray diffraction measurements on
Y. Saiga et al. / Solid State Communications 152 (2012) 1902–1905
heating and cooling would provide more information on this phase transformation. The thermoelectric figure of merit of type-I BGS was assessed by the measurement of a, r and k up to 520 K. k is as low as 0.39 W/Km at 300 K and stays at 70% of those for type-VIII in the temperature range up to 520 K. Despite of the lower k than in the type-VIII, the maximum ZT values for p- and n-type samples of type-I BGS are 0.58 and 0.50 at around 450 K, respectively, which are approximately half of those for type-VIII BGS.
Acknowledgments We thank Y. Kono for the measurements of thermal diffusivity and specific heat for type-I Ba8Ga16Sn30. This work was supported by NEDO Grant no. 09002139-0 and Grant-in-Aid for Scientific Research from MEXT of Japan, Grant nos. 19051011 and 20102004. References [1] D.M. Rowe (Ed.), Handbook of Thermoelectrics: Macro to Nano, CRC Press, Taylor & Francis Group, Bocs Raton, FL, 2006. (and references therein). [2] G.A. Slack, in: D.M. Rowe (Ed.), CRC Handbook of Thermoelectrics, CRC, Boca Raton, FL, 1995, p. 407. [3] B.C. Sales, D. Mandrus, R.K. Williams, Science 272 (1996) 1325. [4] G.S. Nolas, G.A. Slack, S.B. Schujman, in: T.M. Tritt (Ed.), Semiconductors and Semimetals, Vol. 69, Academic Press, San Diego, 2001, p. 255. (and references therein).
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[5] W.Y. Zhao, C.L. Dong, P. Wei, W. Guan, L.S. Liu, P.C. Zhai, X.F. Tang, Q.J. Zhang, J. Appl. Phys. 102 (2007) 113708. [6] X. Shi, H. Kong, C.P. Li, C. Uher, J. Yang, J.R. Salvador, H. Wang, L. Chen, W. Zhang, Appl. Phys. Lett. 92 (2008) 182101. [7] V.L. Kuznetsov, L.A. Kuznetsova, A.E. Kaliazin, D.M. Rowe, J. Appl. Phys. 87 (2000) 7871. [8] A. Saramat, G. Svensson, A.E.C. Palmqvist, C. Stiewe, E. Mueller, D. Platzek, S.G.K. Williams, D.M. Rowe, J.D. Bryan, G.D. Stucky, J. Appl. Phys. 99 (2006) 023708. [9] I. Fujita, K. Kishimoto, M. Sato, H. Anno, T. Koyanagi, J. Appl. Phys. 99 (2006) 093707. [10] J.H. Kim, L. Norihiko, K.K. Okamoto, T. Katsushi, I. Haruyuki, Acta. Mater. 54 (2006) 2057. [11] G.J. Snyder, E.S. Toberer, Nat. Mater. 7 (2008) 105. [12] B.C. Sales, B.C. Chakoumakos, R. Jin, J.R. Thompson, D. Mandrus, Phys. Rev. B 63 (2001) 245113. [13] K. Suekuni, M.A. Avila, K. Umeo, H. Fukuoka, S. Yamanaka, T. Nakagawa, T. Takabatake, Phys. Rev. B 77 (2008) 235119. [14] M. Christensen, A.B. Abrahamsen, N.B. Christensen, F. Juranyi, N.H. Andersen, K. Lefmann, J. Andreasson, C.R.H. Bahl, B.B. Iversen, Nat. Mater. 7 (2008) 811. [15] M.A. Avila, K. Suekuni, K. Umeo, H. Fukuoka, S. Yamanaka, T. Takabatake, Appl. Phys. Lett. 92 (2008) 041901. [16] K. Suekuni, Thermoelectric and Phononic Properties of Type-I Clathrates Sr8Ga16Si30 xGex and Ba8Ga16Sn30, Ph.D. Thesis, Hiroshima University, 2010. [17] D. Huo, T. Sakata, M.A. Avila, M. Tsubota, F. Iga, H. Fukuoka, S. Yamanaka, S. Aoyagi, T. Takabatake, Phys. Rev. B 71 (2005) 075113. [18] Y. Saiga, K. Suekuni, S.K. Deng, T. Yamamoto, Y. Kono, N. Ohya, T. Takabatake, J. Alloys Compd. 507 (2010) 1. [19] Y. Kono, N. Ohya, T. Taguchi, M.A. Avila, K. Suekuni, T. Takabatake, S. Yamamoto, K. Akai, J. Appl. Phys. 107 (2010) 123720. [20] G. Chester, A. Thellung, Proc. Phys. Soc., London 77 (1961) 1005. [21] H.J. Goldsmid, Introduction to Thermoelectricity, Springer, Heidelberg, 2010. [22] S. Deng, Y. Saiga, K. Kajisa, T. Takabatake, J. Appl. Phys. 109 (2011) 103704.
Contents lists available at SciVerse ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Thermoelectric properties and structural instability of type-I clathrate Ba8Ga16Sn30 at high temperatures Y. Saiga a, K. Suekuni a, B. Du a,b, T. Takabatake a,c,n a
Department of Quantum Matter, ADSM, Hiroshima University, Kagamiyama 1-3-1, Hihashi-Hiroshima 739-8530, Japan School of Physics and Chemistry, Henan Polytechnic University, Jiaozuo 454000, China c Institute for Advanced Materials Research, Hiroshima University, Higashi-Hiroshima 739-8530, Japan b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 June 2012 Accepted 26 June 2012 Available online 27 July 2012
Type-I clathrate Ba8Ga16Sn30 is known as a typical example showing glass-like behavior in the thermal conductivity at low temperatures. We report on thermoelectric properties above room temperature for the p- and n-type single crystals which were grown from Ga–Sn double flux and Sn single flux, respectively. The measurements of electrical resistivity showed hysteretic behaviors when the sample was heated to 600 K. Powder X-ray diffraction analysis indicated that the type-I structure changed to the type-VIII after the sample was heated to 600 K. By using the data of Seebeck coefficient, electrical resistivity, and thermal conductivity, we estimated the dimensionless figure of merit ZT for the type-I Ba8Ga16Sn30. For the p- and n-type samples, the values of ZT reach 0.58 and 0.50 at around 450 K, respectively, which values are approximately half of those for the type-VIII counterparts. & 2012 Elsevier Ltd. All rights reserved.
Keywords: A. Energy material A. Thermoelectric material A. Ba8Ga16Sn30 C. Clathrate
1. Introduction Thermoelectric power generation has attracted much attention in times of energy shortage. Direct conversion from waste heat to electrical energy is feasible by using a thermoelectric module made of p- and n-type materials [1]. The thermoelectric efficiency of a given material is evaluated by the dimensionless figure of merit ZT, defined as ZT¼ a2T/rk, where a is the Seebeck coefficient, r is the electrical resistivity and k is the thermal conductivity. For searching materials with low r and low k, which do not reconcile each other usually, the concept of ‘‘phonon-glass electron-crystal’’ (PGEC) was proposed by Slack in 1995 [2]. According to this guiding principle, caged compounds such as filled skutterudites and clathrates have been synthesized and their physical and structural properties have been investigated extensively [3–10]. Most intermetallic clathrates are Zintle compounds in which the charge balance is well maintained between the guest ions and cage network. Therefore, stoichiometric clathrates show semiconducting behavior while small deviation from the ideal stoichiometry induces charge carriers in real samples. If the carrier density is controlled to be in the range of 1020/cm3, then rather high a can coexist with rather low r [11]. Another requisite for enhancing ZT is low k which is also achieved often in type-I n Corresponding author at: Hiroshima University, Department of Quantum Matter, ADSM, Kagamiyama 1-3-1, Hihashi-Hiroshima 739-8530, Japan. Tel.: þ81 82 424 7025; fax: þ 81 82 424 7029. E-mail address: [email protected] (T. Takabatake).
0038-1098/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ssc.2012.06.027
clathrates with a large mismatch between the guest ion size and the cage size. Thereby, large-amplitude anharmonic vibrations of the guest ion are thought to scatter acoustic phonons carrying the heat [12,13]. Furthermore, the anti-crossing of the acoustic mode with the guest vibration mode gives rise to the decrease of the group velocity of the acoustic mode, and thus suppresses the lattice thermal conductivity kL(T) [14]. The unit cell of type-I structure consists of six tetrakaidecahedra and two dodecahedra both of which are composed of group 13 and 14 elements. The cage encloses the group 1 and 2 elements as the guest atoms which vibrate with much larger amplitude than that of cage atoms. Among type-I intermetallic clathrates, Ba8Ga16Sn30 (BGS) shows a typical glass-like behavior in kL(T) with a plateau at 3–10 K [13,15]. In fact, the magnitude of kL in the plateau is lower than that of the amorphous SiO2. In type-I BGS, the Ba guest moves among off-centered 24k sites in the tetrakaidecahedron. The off-center rattling with the characteristic energy of approximately 20 K is thought to be responsible for the plateau in kL(T). Although thermoelectric and dynamic properties of type-I BGS have been extensively studied at low temperatures, physical properties above room temperature are less known. So far, preliminary measurements of a and r above 300 K have been performed [16], but not published yet. The BGS is dimorphic and adopts type-I and type-VIII structures. The single crystals of both types have been selectively grown by an empirical method due to the lack of knowledge of the phase diagram [13,15–18]. The unit cell of type-VIII clathrate consists of eight distorted dodecahedra. The Ba guest occupies the centered site in the dodecahedron. The guest vibrations are well
Y. Saiga et al. / Solid State Communications 152 (2012) 1902–1905
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described by an Einstein oscillator model with the characteristic energy of 50 K. The kL(T) shows a typical crystalline peak at around 10 K [13,16], which is in contrast to the glass-like plateau in the type-I BGS. The electronic band structure calculation showed that type-I BGS and type-VIII BGS are narrow-gap semiconductors with indirect gaps of 0.51 and 0.32 eV, respectively [19]. Our measurements of a and r at temperatures above 300 K suggested that type-VIII samples are more stable than type-I samples. We therefore concentrated on the assessment of thermoelectric potential of type-VIII BGS at high temperatures [18]. Single crystals grown from Ga and Sn flux, respectively, exhibit the p- and n-type conduction. Optimization of carrier density in type-VIII BGS has enhanced the ZT values for p- and n-type samples up to 1.0 and 0.9 at 480 K, respectively [18]. In view of the low kL(T), the type-I BGS might have higher ZT than type-VIII BGS at high temperatures. Keeping this in mind, we have studied the thermoelectric properties and structural stability of type-I BGS from 300 to 600 K. Fig. 1. (Color online) Temperature dependences of electrical resistivity for p- and n-type samples of type-I Ba8Ga16Sn30 in the virgin cycle between 300 and 600 K.
2. Experimental Single crystals of type-I BGS were grown by the flux method as reported previously [13]. The Ga–Sn double flux and single Sn flux, respectively, were used to tune the charge carrier to p-type and n-type. The starting compositions of Ba:Ga:Sn were 8:32:60 for the p-type samples and 8:16:50 for the n-type samples. High purity elements of Ba (99.9%), Ga (99.9999%) and Sn (99.999%) in proper atomic ratios were loaded in a quartz ampoule which was evacuated and shielded. The ampoule was heated to 1173 K in a box furnace and kept at this temperature for 4 h. The ampoule was cooled to 873 K for 1 h, and then slowly cooled to 623 K at a rate of 2 K/h. At 623 K, the ampoule was removed from the furnace and single crystals were separated from the molten flux by centrifuging. Single crystals obtained by the Ga–Sn double flux and the Sn flux were 5 mm and 10 mm in the maximum diameter, respectively. The powder X-ray diffraction (XRD) experiment was performed on the crushed samples by using a Rigaku D/teX ultradetector with Cu Ka radiation in the 2y range from 101 to 1201. All diffraction peaks were well indexed as the type-I clathrate structure. The lattice parameters were estimated to be 11.707 and 11.686 A˚ for p- and n-type samples, respectively, which values agree with the reported values [13]. The electrical resistivity r was measured in a homemade system by a standard dc four-probe method. The Seebeck coefficient a was measured by the differential method with a commercial system (MMR technologies, Inc). The thermal diffusivity D and specific heat Cp were simultaneously measured by the laserflash method (LFA-502, Kyoto Electronics). Because the measurements require the sample larger than 5 5 mm2, we could obtain the reliable data only for the n-type sample. All measurements were performed in a vacuum to avoid oxidation.
3. Results and discussion 3.1. Structural instability First, we show the data of r(T) measured on heating and cooling between 300 and 600 K in Fig. 1. In the virgin heating process, r(T)s for the p- and n-type samples show a maximum at 550 K which is followed by a decrease on further heating to 600 K. After the sample was kept at 600 K for 30 min, the cooling process started. On cooling, r(T)s monotonically increase without showing a maximum. The values at 300 K are several times larger than those in the initial state. To understand this hysteretic behavior in r(T), we examined
Fig. 2. (Color online) Powder X-ray diffraction patterns for the n-type sample of Ba8Ga16Sn30 (a) before and (b) after the electrical resistivity measurement up to 600 K. The initial structure is type-I while the final structure is type-VIII.
the crystal structure of the samples used for the r(T) measurement by the powder XRD. As an example, the XRD pattern for the n-type sample after heated to 600 K is compared with that for the initial state in Fig. 2. We find that the type-I clathrate structure has completely modified to the type-VIII one. This structural transformation was observed also in the p-type sample. These observations suggest that the type-I and type-VIII are the low- and hightemperature phases of the dimorphic clathrate BGS, respectively. However, the transformation is not reversible because no phase transition from type-VIII to type-I occurred in the cooling process from 600 to 300 K. The phase transition on heating was not observed by the differential thermal analysis, which showed the identical melting point at 793 K for both type-I and type-VIII phases [13]. It is necessary to examine this structural transformation by in-situ X-ray diffraction on both heating and cooling. In the temperature range below 520 K, we have found that r(T) of type-I BGS shows a reversible behavior. Powder XRD measurements for the sample used for r(T) measurement up to 520 K confirmed the stability of type-I structure. To avoid the phase transformation from type-I to type-VIII, the highest temperature was set at 520 K for the measurements of r, a, and thermal diffusivity. 3.2. Thermoelectric properties Fig. 3(a) and (b) show, respectively, the absolute values of a and r for type-I BGS samples with p- and n-type carriers as a
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Fig. 3. (Color online) Temperature dependences of (a) Seebeck coefficient and (b) electrical resistivity for the p- and n-type samples of type-I Ba8Ga16Sn30 in the range from 300 to 520 K.
Fig. 4. (Color online) Temperature dependence of thermal conductivity k for the n-type samples of type-I Ba8Ga16Sn30 in the range from 300 to 520 K. The data of k for the n-type sample of type-VIII Ba8Ga16Sn30 are taken from Ref. [18].
function of temperature for 300 K oTo520 K. The values of a (300 K) are 345 and 370 mV/K for the p- and n-type samples, respectively, which agree with the reported values [13]. With increasing temperature, the values of 9a9 for p- and n-type samples increase and approach a saturated value 450 mV/K. The value of r (300 K) for the n-type samples is 30 mO cm, which is slightly higher than that for the p-type one. The two curves of r(T) linearly increase in parallel on heating and are saturated at around 500 K. The thermal conductivity k was calculated by inserting the data of the thermal diffusivity D and specific heat Cp in the formula k ¼DCpd, where d is the sample density. We note that, on heating from 300 to 520 K, Cp(T) slightly increased from 0.23 to 0.27 J/gK, which coincides with the Dulong–Petit value 0.23 J/gK. Fig. 4 displays the temperature variation of k(T) for the type-I BGS single crystal with n-type carriers, together with the result for
Fig. 5. (Color online) Temperature dependences of (a) power factor PF and (b) dimensionless figure of merit ZT for the p- and n-type samples of type-I and type-VIII Ba8Ga16Sn30. The data for the type-VIII are taken from Ref. [18].
type-VIII BGS with n-type carriers [18]. The obtained value of k(300 K) for type-I is 0.39 W/Km which is half of 0.72 W/Km for type-VIII. It is worth noting that the carrier thermal conductivity ke is smaller in type-I than in type-VIII. The ke can be calculated using the Wiedemann–Franz law ke ¼LT/r, where the Lorenz number L of 2.45 10 8 V2/K2 is used for a degenerated semiconductor [20]. By using r (300 K)¼30 mO cm, the value of ke at 300 K is estimated to be 0.03 W/Km, which is only 7.7% of the measured value of k. The temperature gradient of k(T) becomes steeper above 450 K. This upswing in k(T) is attributed to the carrier excitations from the top of the valence band to the conduction bands, which is called as the bipolar effect [21]. Fig. 5(a) and (b) show, respectively, the power factor PF ¼ a2/r and the dimensionless figure of merit ZT¼ a2T/rk for both type-I and type-VIII single crystals. For this calculation, we used the data of k(T) for the n-type sample for the lack of the data for p-type samples. It was due to the fact that the size of the p-type crystals was not large enough for the thermal diffusivity measurement. For both p- and n-type samples of type-I BGS, the values of PF are in the range between 4 and 6 mW/cm K2, which are smaller than half the values for the type-VIII. As a result, in spite of the low k(T) of 0.4–0.5 W/Km, the ZT values of type-I BGS are much lower than the type-VIII in the whole temperature range from 300 to 520 K. The ZT of type-VIII has a broad maximum at around 450 K, whose values are 0.58 and 0.50 for p- and n-types, respectively. In order to improve the thermoelectric potential of type-I BGS, chemical substitutions would be effective as has been satisfactory performed for type-VIII BGS [22].
4. Conclusion We studied the thermoelectric properties and structural stability for single crystals of the type-I clathrate BGS above room temperature. The measurements of r and powder XRD indicated that the type-I structure transforms into the type-VIII one on heating above 520 K while the opposite transition does not occur on the cooling process. In-situ X-ray diffraction measurements on
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heating and cooling would provide more information on this phase transformation. The thermoelectric figure of merit of type-I BGS was assessed by the measurement of a, r and k up to 520 K. k is as low as 0.39 W/Km at 300 K and stays at 70% of those for type-VIII in the temperature range up to 520 K. Despite of the lower k than in the type-VIII, the maximum ZT values for p- and n-type samples of type-I BGS are 0.58 and 0.50 at around 450 K, respectively, which are approximately half of those for type-VIII BGS.
Acknowledgments We thank Y. Kono for the measurements of thermal diffusivity and specific heat for type-I Ba8Ga16Sn30. This work was supported by NEDO Grant no. 09002139-0 and Grant-in-Aid for Scientific Research from MEXT of Japan, Grant nos. 19051011 and 20102004. References [1] D.M. Rowe (Ed.), Handbook of Thermoelectrics: Macro to Nano, CRC Press, Taylor & Francis Group, Bocs Raton, FL, 2006. (and references therein). [2] G.A. Slack, in: D.M. Rowe (Ed.), CRC Handbook of Thermoelectrics, CRC, Boca Raton, FL, 1995, p. 407. [3] B.C. Sales, D. Mandrus, R.K. Williams, Science 272 (1996) 1325. [4] G.S. Nolas, G.A. Slack, S.B. Schujman, in: T.M. Tritt (Ed.), Semiconductors and Semimetals, Vol. 69, Academic Press, San Diego, 2001, p. 255. (and references therein).
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