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Growth and thermoelectric properties of Ba8Ga16Ge30 clathrate crystals
Journal of Alloys and Compounds 482 (2009) 544–547
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Growth and thermoelectric properties of Ba8 Ga16 Ge30 clathrate crystals Xiaowei Hou 1 , Yanfei Zhou, Li Wang, Wenbin Zhang, Wenqing Zhang, Lidong Chen ∗ State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China
a r t i c l e
i n f o
Article history: Received 28 January 2009 Received in revised form 13 April 2009 Accepted 16 April 2009 Available online 23 April 2009 Keywords: Clathrate Crystal Structural refinement Thermoelectric property
a b s t r a c t Ba8 Ga16 Ge30 clathrate crystals were grown by Czochralski method. The influence of growth condition on the composition and thermoelectric property of the obtained crystals was investigated. The lower pulling rate and higher pressure resulted in a larger Ga/Ge ratio in the grown crystals, and the elemental composition was homogeneous. The sample with a higher Ga/Ge ratio showed the larger electrical conductivity than the sample with a lower Ga/Ge ratio, but the Seebeck coefficient was not sensitive to the Ga/Ge ratio, which led to a larger power factor. The higher Ga/Ge ratio also resulted in a lower lattice thermal conductivity and as a result led to a higher ZT value, which was measured to be 0.93 at 850 K and could reach 1.3 as extrapolated to 1000 K. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Thermoelectric materials have been receiving great interests in recent decades because of their ability to convert waste heat into usable electricity. However, the relatively low energy conversion efficiency limits their applications. The performance of thermoelectric materials is usually evaluated by the dimensionless figure-of-merit (ZT) defined as ZT = S2 T/, where S, , and T are the Seebeck coefficient, electrical conductivity, thermal conductivity and absolute temperature, respectively. Recently, in virtue of the concept of phonon glass electron crystals (PGEC), open-structured compounds such as filled skutterudites and clathrates have been extensively investigated due to their relatively low , which leads to a enhanced ZT. The extremely low thermal conductivity in cagestructured compound is usually attributed to the ability of the metal atoms encapsulated in the cages to scatter low-frequency heat-carrying phonons, while electronic conduction mainly takes place through the cage framework, keeping electrical conductivity remain relatively high [1]. Clathrate compounds which form in a variety of structure types belong to the typical cage-structured compounds and have been extensively investigated in recent years. One of these is the type I with the chemical formula of M8 E46 (M = Ba, Sr; E represent cage atoms, usually group IV elements Si, Ge, and Sn), the cubic unit cell of which consists of two pentagonal dodecahedra (E20 cage) and six tetrakaidecahedra (E24 cage) encapsulating guest atoms.
∗ Corresponding author. E-mail address: [email protected] (L. Chen). 1 Also at Graduate School of the Chinese Academy of Sciences, Beijing, China. 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.04.072
Nolas et al. first demonstrated that Sr8 Ga16 Ge30 is a potential thermoelectric material whose ZT value was estimated to exceed 1.0 above 700 K [2]. Since then an increasing number of papers treating the thermoelectric properties of type I clathrates have been published, such as Sr8 GaX Ge46−X , Ba8 Ga16 Ge30 and Eu8 Ga16 Ge30 [3–6]. It has been reported that the thermoelectric properties of type I clathrate vary in a wide range with the stoichiometric composition and homogeneity. For example, the maximum ZT value of Ba8 Ga16 Ge30 synthesized by Martin et al. was reported as 0.8 at 850 K [7], while a similar material prepared by Fujita et al. only owned maximum ZT of 0.62 at 800 K [3]. Synthesizing homogeneous and reproducible clathrate material with high ZT values is still a challenge. Especially, the wide distribution of thermoelectric properties of germanium-based clathrates has aroused the enthusiasm of growing crystals of Ba8 Ga16 Ge30 . Using Czochralski method, Saramat et al. grew a 46-mm-long crystal of Ba8 GaX Ge46−X which had a peak ZT of 1.35 at 900 K [8]. However, the Seebeck coefficients of the samples varied drastically along the pulling direction because of the great inhomogeneity of chemical composition. On the other hand, Toberer et al. also prepared a Ba8 Ga16 Ge30 crystal and reported the highest ZT value of 0.8 at 1050 K, which was similar to that of polycrystalline [9]. The experimental variables in singlecrystal growth process, such as the pulling rate, rotation speed and atmosphere pressure should greatly influence the stoichiometric composition (such as Ga/Ge and Ba/(Ga + Ge) ratios) and the composition homogeneity as well as the quality of the crystal, and thus greatly affect the thermoelectric performance. In the present work, Ba8 Ga16 Ge30 clathrate crystals were grown by Czochralski (CZ) method with two different growth conditions. The comparison of the chemical composition and their thermoelectric properties of the two crystals were also carried out. The
X. Hou et al. / Journal of Alloys and Compounds 482 (2009) 544–547
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Fig. 1. Ba8 Ga16 Ge30 crystals grown with Czochralski method.
crystal grown with the lower pulling rate and higher pressure has higher Ga/Ge ratio and shows better thermoelectric performance. The measured maximum ZT value reaches 0.93 at 850 K and is could reach 1.3 when extrapolated to 1000 K. This consistently homogeneous crystal showed a bright future of broad applications.
2. Experimental procedures The melt used to pull the crystal was formed from the polycrystalline Ba8 Ga16 Ge30 compounds. The polycrystalline Ba8 Ga16 Ge30 compounds were prepared by melting the mixture of Ge (purity 99.9999%), Ga (purity 99.9999%) and Ba (purity 99.9%) by using a carbon crucible. Because of the loss of Ba during reaction, excess Ba was usually needed in the starting materials. Before determining the optimal proportion of Ba:Ga:Ge in the mixture, a series of synthesis experiments with different Ba amounts were carried out, and it was found that when Ba:Ga:Ge = 10:16:30, no impurity was detected in the product. During the synthesis, the crucible was placed in a vacuum sealed quartz ampoule. After being melted at 1355 K for 8 h, the samples in quartz ampoule were annealed at 920 K for 120 h followed by HCl acid washing for 3 times to remove impurities. Flux growth method was employed to grow the seeds. Stoichiometric amounts of Ba and Ge, together with much excessive Ga, were mixed and reacted at 1355 K in a pyrolitic boron nitride (BN) crucible for 1 day and then slowly cooled to 1180 K at the rate of 3 K/h before cooling to room temperature. After being washed in hot water to remove the excess Ga, faceted crystals with sizes ranging up to 3–5 mm in diameter were obtained. The crystals of Ba8 Ga16 Ge30 were grown by a conventional induction-heating CZ furnace with a corundum crucible (30 mm in diameter and 25 mm in height). The growth chamber was filled with high-purity argon after being evacuated. Before crystal growth, the melt of polycrystalline material described above were maintained at 1370 K for several hours in order to obtain homogenized composition distribution. The argon pressure was kept at 0.8 and 1.1 atm and the pulling rate was 8 and 5 mm/h for samples A and B, respectively. After growth, the crystals were cooled to room temperature at a rate of 60 K/h. Fig. 1 shows the pictures of crystals A and B. The growth conditions are summarized in Table 1. After pulling, the crystals were annealed under vacuum at 900 K for 7 days to eliminate the stress. A wire saw was used to cut one disk from crystal A and three disks from crystal B. The three disks from crystal B were labeled as B1, B2 and B3, respectively, where disk B1 was furthest away from the pulling rod. The crystal structures of the samples were studied by X-ray diffraction (XRD). The elemental compositions of the samples were analyzed by electron probe micro analyzer (EPMA). Sample density was determined by the Archimedes method. Measurements of electrical conductivity and Seebeck coefficient were made with ULVAC ZEM-3 apparatus under He atmosphere in the temperature range from 300 to 850 K. Thermal conductivity () was obtained using the relation = CP after the thermal diffusivity () was measured by laser flash method in an argon-filled box in the temperature range from 300 to 1000 K, where is sample density and CP is specific heat. The uncertainties in the measurements of electrical conductivity, Seebeck coefficient and thermal diffusivity are 7%, 5% and 5%, respectively.
Fig. 2. XRD spectra of powdered Ba8 Ga16 Ge30 crystal (a) and polycrystalline Ba8 Ga16 Ge30 sample (b), together with a calculated pattern of Ba8 Ga16 Ge30 (c).
3. Results and discussion XRD scans of polycrystalline Ba8 Ga16 Ge30 sample before melting and powdered Ba8 Ga16 Ge30 crystal as well as the calculated intensities of the type I clathrate are shown in Fig. 2. All the diffraction peaks observed in both samples could be identified as type I clathrate, without any Ge peak being found. Very small crystal has been isolated from crystal B and investigated by employing a singlecrystal X-ray diffraction with Mo K␣ (=0.7107 Å) radiation. The structure is solved and refined using the Rigaku Crystal-structure crystallographic software package. The structural refinement con¯ The lattice parameter firms the assignment of space group Pm3n. is 10.833(2) Å, which is in close agreement with reported values [10,11]. The “agreement” factors are Rwp = 0.0463, Rp = 0.0196, and the “goodness of fit” GOF = 1.28. Such low values of Rwp , Rp and GOF for a complex and disordered system evidence the good crystallization of the sample. Refined atomic coordinates, occupancies and isotropic displacement parameters of the sample are summarized in Table 2. Table 3 shows the actual elemental composition of samples measured by EPMA. The average Ga content of crystal B is about 15.8, which is higher than that in crystal A, and much closer to the
Table 1 Growth conditions, electrical conductivities , Seebeck coefficients S and thermal conductivities at 300 K of crystals A and B. Sample
Argon pressure (atm)
Pulling rate (mm/h)
Rotation speed (rpm)
Electrical conductivity, (×105 −1 m−1 )
Seebeck coefficient, S (V/K)
Thermal conductivity, (W/(m K))
A B1 B2 B3
0.8
8
20
1.1
5
20
1.21 1.75 1.74 1.77
−45 −42 −43 −40
2.03 2.19 2.18 2.21
546
X. Hou et al. / Journal of Alloys and Compounds 482 (2009) 544–547
Table 2 Atomic coordinates, isotropic displacement parameters Ueq and occupational parameters for Ba8 Ga16 Ge30 crystal at 300 K. Atom
Site
x
y
z
Ueq (Å2 )
Occupational parameters
Ba(1) Ba(2) Ga(1)/Ge(1) Ga(2)/Ge(2) Ga(3)/Ge(3)
2a 6d 6c 16i 24k
0 −1/4 0 −0.18452(4) 0
0 −1/2 −1/2 −0.18452(4) −0.30847(6)
0 0 −1/4 −0.18452(4) −0.11817(6)
0.0046(3) 0.0338(3) 0.0036(3) 0.0027(2) 0.0032(2)
1 1 0.348/0.652 0.348/0.652 0.348/0.652
Table 3 Measured elemental compositions of samples at room temperature. Sample
Ba
Ga
Ge
Ga/Ge
A B1 B2 B3
8 8 8 8
15.27 15.72 15.79 15.84
30.57 30.15 30.12 30.11
0.500 0.521 0.524 0.526
stoichiometric value. Crystal B shows nearly identical Ga/Ge ratio at different positions, which slightly decreases along the growth direction. The temperature dependence of the electrical conductivity (), Seebeck coefficient (S) and power factor (PF, PF = S2 ) for the obtained crystals are plotted in Fig. 3(a)–(c). In virtue of the constant chemical content, the thermoelectric properties of the three disks from crystal B are very close, so we just show one curve (sample B1) in the figures. The values for the obtained crystals over the entire temperature range are much higher than polycrys-
Fig. 3. Temperature dependence of electrical conductivity (), Seebeck coefficient (S) and power factor (S2 ) for samples A () and B (), and their extrapolations up to 1000 K.
talline sample, and even larger than those of the crystals previously reported [8,9,12]. Crystal B possesses a larger , whose value is 1.75 × 105 −1 m−1 at room temperature, as compared with crystal A. Such difference can be associated with the different Ga/Ge ratios. As suggested by Blake et al., in a caged-structure compound, the electron overlap between guest atom and the cage framework would affect the transfer of the valence electrons from the guest atoms to the cage framework and therefore affect the electrical transport property of the crystal [13]. It is believed that larger atomic size of the atoms in the cage framework would lead to a more efficient transfer of valence electrons from the guest atoms. In the present work, the values in crystal B are larger than that in crystal A because crystal B contains higher content of Ga which has a larger covalent radius (0.126 nm) than Ge (0.122 nm). Besides, some other factors, such as the quality of crystals, could also affect the values. The Seebeck coefficient S versus the temperature is shown in Fig. 3(b). As can be seen from Fig. 3(a), there exists about 44% difference between the electrical conductivity of crystals A and B at 300 K. However, the S values and their temperature dependence of the two crystals are almost the same, different from what is expected that a trend similar to electrical conductivity should be observed. Such phenomenon is similar to what Toberer et al. have reported [9]. All Seebeck coefficients are negative and the absolute values increase with increasing temperature. The S value for the crystal A is −45 V/K at room temperature, similar to Saramat’s result [8]. The Seebeck coefficients of the samples do not reach their maximum values in the measured temperature range. The observed S value for crystal B is −151 V/K at 850 K, slightly lower than that of earlier report [8]. The calculated power factor (S2 ) is shown in Fig. 3(c). The power factor for crystal B is 15.8 W/(cm K2 ) at 850 K, much larger than that of crystal A, which is 11.3 W/(cm K2 ) at the same temperature. Comparing the trend of and S with earlier reports, [8,9] it is reasonable to extrapolate these values to 1000 K. The thermal conductivity is measured from 300 to 1000 K and shown in Fig. 4. The value of crystal A is lower, due to the lower electrical conductivity than that of crystal B. The value of thermal conductivity decreases with the increase of temperature before 900 K. The value for crystal B is 2.19 W/(m K) at room temperature and reaches its minimum of 1.43 W/(m K) at 900 K. The rise of around 900 K is considered to be caused by bipolar heat conduction that the minority charge carriers began to affect the transport by carrying heat in the same direction as the majority carriers [8]. However, the effect of the minority charge carriers on electrical conductivity could be ignored, so the temperature dependence of electrical conductivity keeps the same trend at high temperature as shown in Fig. 3(a). With the Wiedemann–Franz approximation, = l + LT, the lattice component of thermal conductivity l is estimated by taking Lorenz number L as 2.0 × 10−8 J2 /K2 C2 . At 300 K, the l is 1.30 W/(m K) for crystal A and 1.14 W/(m K) for crystal B. Such phenomenon should be associated with the different Ga/Ge ratios of the obtained crystals. For the type I clathrate compounds in the Ba–Ga–Ge system, it was reported that the value of atomic displacement parameters (ADP) at the Ba site in the tetrakaidecahedral cage was extraordinary large and could be enhanced with the increase in
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tion. It is expected to further improve the thermoelectric property of Ba8 Ga16 Ge30 crystal by optimizing the chemical composition through controlling the growth conditions. 4. Conclusions
Fig. 4. Temperature dependence of thermal conductivity (). The inset shows the temperature dependence of lattice thermal conductivity (l ).
Two Ba8 Ga16 Ge30 clathrate crystals were fabricated with Czochralski method. The elemental composition and thermoelectric properties were proved to be related to the growth conditions. The lower pulling rate and higher pressure lead to a higher Ga/Ge ratio in the grown crystals. The obtained Ba8 Ga16 Ge30 clathrate crystals show relatively good homogeneity in chemical composition. The higher Ga/Ge ratio leads to the larger electrical conductivity and similar Seebeck coefficient S, resulting in a larger power factor PF. The different lattice component of thermal conductivity l should also arouse from the shifted Ga/Ge ratio which results in the different ADP values of Ba atoms in the tetrakaidecahedral cage. All the disks cut from crystal B exhibit higher ZT values. The measured ZT is 0.93 at 850 K for crystal B. Using the extrapolated values, the maximum ZT value is expected to be able to reach 1.30 at 1000 K. Acknowledgements This work was partially supported by the National Basic Research Program of China (2007CB607503), the National High Technology Research and Development Program of China (2007AA03Z233) and the National Natural Science Foundation of China (50821004). References
Fig. 5. Temperature dependence of calculated dimensionless figure-of-merit ZT for sample A (), sample B () and their extrapolations up to 1000 K.
the Ga content because Ga had larger covalent radius than Ge [14]. A larger ADP of the guest atom was considered to lead to a more glasslike lattice thermal conductivity for clathrate [15]. So the l for crystal B is lower because B has a relatively higher Ga/Ge ratio than that of crystal A. Fig. 5 shows the temperature dependence of ZT for the crystals. The value for crystal A is smaller, which is 0.70 at 850 K, while crystal B exhibits higher ZT value. The calculated ZT for crystal B is 0.93 at 850 K and it could reach 1.30 around 1000 K with extrapola-
[1] V.L. Kuznetsov, L.A. Kuznetsova, A.E. Kaliazin, D.M. Rowe, J. Appl. Phys. 87 (2000) 7871. [2] G.S. Nolas, J.L. Cohn, G.A. Slack, S.B. Schujman, Appl. Phys. Lett. 73 (1998) 178. [3] I. Fujita, K. Kishimoto, M. Sato, H. Anno, T. Koyanagi, J. Appl. Phys. 99 (2006) 093707. [4] J.D. Bryan, N.P. Blake, H. Metiu, B.B. Iversen, R.D. Poulsen, A. Bentien, J. Appl. Phys. 92 (2002) 7281. [5] J. Martin, S. Erickson, G.S. Nolas, P. Alboni, T.M. Tritt, J. Yang, J. Appl. Phys. 99 (2006) 044903. [6] B.C. Sales, B.C. Chakoumakos, R. Jin, J.R. Thompson, D. Mandrus, Phys. Rev. B 63 (2001) 245113. [7] J. Martin, H. Wang, G.S. Nolas, Appl. Phys. Lett. 92 (2008) 222110. [8] A. Saramat, G. Svensson, A.E.C. Palmqvist, C. Stiewe, E. Mueller, D. Platzek, S.G.K. Williams, D.M. Rowe, J. Appl. Phys. 99 (2006) 023708. [9] E.S. Toberer, M. Christensen, B.B. Iversen, G.J. Snyder1, Phys. Rev. B 77 (2008) 075203. [10] B. Einsenmann, H. Schafer, R. Zagler, J. Less-Common Met. 118 (1986) 43. [11] J.D. Bryan, V.I. Srdanov, G.D. Stucky, D. Schmidt, Phys. Rev. B 60 (1999) 3064. [12] J.D. Bryan, N.P. Blake, H. Metiu, G.D. Stucky, B.B. Iversen, R.D. Poulsen, A. Bentien, J. Appl. Phys. 92 (2002) 7281. [13] N.P. Blake, S. Latturner, J.D. Bryan, G.D. Stucky, H. Metiu, J. Chem. Phys. 115 (2001) 8060. [14] N.L. Okamoto, K. Kishida, K. Tanaka, H. Inui, J. Appl. Phys. 100 (2006) 073504. [15] I. Zerec, V. Keppens, M.A. McGuire, D. Mandrus, B.C. Sales, P. Thalmeier, Phys. Rev. Lett. 92 (2004) 185502.
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Growth and thermoelectric properties of Ba8 Ga16 Ge30 clathrate crystals Xiaowei Hou 1 , Yanfei Zhou, Li Wang, Wenbin Zhang, Wenqing Zhang, Lidong Chen ∗ State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China
a r t i c l e
i n f o
Article history: Received 28 January 2009 Received in revised form 13 April 2009 Accepted 16 April 2009 Available online 23 April 2009 Keywords: Clathrate Crystal Structural refinement Thermoelectric property
a b s t r a c t Ba8 Ga16 Ge30 clathrate crystals were grown by Czochralski method. The influence of growth condition on the composition and thermoelectric property of the obtained crystals was investigated. The lower pulling rate and higher pressure resulted in a larger Ga/Ge ratio in the grown crystals, and the elemental composition was homogeneous. The sample with a higher Ga/Ge ratio showed the larger electrical conductivity than the sample with a lower Ga/Ge ratio, but the Seebeck coefficient was not sensitive to the Ga/Ge ratio, which led to a larger power factor. The higher Ga/Ge ratio also resulted in a lower lattice thermal conductivity and as a result led to a higher ZT value, which was measured to be 0.93 at 850 K and could reach 1.3 as extrapolated to 1000 K. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Thermoelectric materials have been receiving great interests in recent decades because of their ability to convert waste heat into usable electricity. However, the relatively low energy conversion efficiency limits their applications. The performance of thermoelectric materials is usually evaluated by the dimensionless figure-of-merit (ZT) defined as ZT = S2 T/, where S, , and T are the Seebeck coefficient, electrical conductivity, thermal conductivity and absolute temperature, respectively. Recently, in virtue of the concept of phonon glass electron crystals (PGEC), open-structured compounds such as filled skutterudites and clathrates have been extensively investigated due to their relatively low , which leads to a enhanced ZT. The extremely low thermal conductivity in cagestructured compound is usually attributed to the ability of the metal atoms encapsulated in the cages to scatter low-frequency heat-carrying phonons, while electronic conduction mainly takes place through the cage framework, keeping electrical conductivity remain relatively high [1]. Clathrate compounds which form in a variety of structure types belong to the typical cage-structured compounds and have been extensively investigated in recent years. One of these is the type I with the chemical formula of M8 E46 (M = Ba, Sr; E represent cage atoms, usually group IV elements Si, Ge, and Sn), the cubic unit cell of which consists of two pentagonal dodecahedra (E20 cage) and six tetrakaidecahedra (E24 cage) encapsulating guest atoms.
∗ Corresponding author. E-mail address: [email protected] (L. Chen). 1 Also at Graduate School of the Chinese Academy of Sciences, Beijing, China. 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.04.072
Nolas et al. first demonstrated that Sr8 Ga16 Ge30 is a potential thermoelectric material whose ZT value was estimated to exceed 1.0 above 700 K [2]. Since then an increasing number of papers treating the thermoelectric properties of type I clathrates have been published, such as Sr8 GaX Ge46−X , Ba8 Ga16 Ge30 and Eu8 Ga16 Ge30 [3–6]. It has been reported that the thermoelectric properties of type I clathrate vary in a wide range with the stoichiometric composition and homogeneity. For example, the maximum ZT value of Ba8 Ga16 Ge30 synthesized by Martin et al. was reported as 0.8 at 850 K [7], while a similar material prepared by Fujita et al. only owned maximum ZT of 0.62 at 800 K [3]. Synthesizing homogeneous and reproducible clathrate material with high ZT values is still a challenge. Especially, the wide distribution of thermoelectric properties of germanium-based clathrates has aroused the enthusiasm of growing crystals of Ba8 Ga16 Ge30 . Using Czochralski method, Saramat et al. grew a 46-mm-long crystal of Ba8 GaX Ge46−X which had a peak ZT of 1.35 at 900 K [8]. However, the Seebeck coefficients of the samples varied drastically along the pulling direction because of the great inhomogeneity of chemical composition. On the other hand, Toberer et al. also prepared a Ba8 Ga16 Ge30 crystal and reported the highest ZT value of 0.8 at 1050 K, which was similar to that of polycrystalline [9]. The experimental variables in singlecrystal growth process, such as the pulling rate, rotation speed and atmosphere pressure should greatly influence the stoichiometric composition (such as Ga/Ge and Ba/(Ga + Ge) ratios) and the composition homogeneity as well as the quality of the crystal, and thus greatly affect the thermoelectric performance. In the present work, Ba8 Ga16 Ge30 clathrate crystals were grown by Czochralski (CZ) method with two different growth conditions. The comparison of the chemical composition and their thermoelectric properties of the two crystals were also carried out. The
X. Hou et al. / Journal of Alloys and Compounds 482 (2009) 544–547
545
Fig. 1. Ba8 Ga16 Ge30 crystals grown with Czochralski method.
crystal grown with the lower pulling rate and higher pressure has higher Ga/Ge ratio and shows better thermoelectric performance. The measured maximum ZT value reaches 0.93 at 850 K and is could reach 1.3 when extrapolated to 1000 K. This consistently homogeneous crystal showed a bright future of broad applications.
2. Experimental procedures The melt used to pull the crystal was formed from the polycrystalline Ba8 Ga16 Ge30 compounds. The polycrystalline Ba8 Ga16 Ge30 compounds were prepared by melting the mixture of Ge (purity 99.9999%), Ga (purity 99.9999%) and Ba (purity 99.9%) by using a carbon crucible. Because of the loss of Ba during reaction, excess Ba was usually needed in the starting materials. Before determining the optimal proportion of Ba:Ga:Ge in the mixture, a series of synthesis experiments with different Ba amounts were carried out, and it was found that when Ba:Ga:Ge = 10:16:30, no impurity was detected in the product. During the synthesis, the crucible was placed in a vacuum sealed quartz ampoule. After being melted at 1355 K for 8 h, the samples in quartz ampoule were annealed at 920 K for 120 h followed by HCl acid washing for 3 times to remove impurities. Flux growth method was employed to grow the seeds. Stoichiometric amounts of Ba and Ge, together with much excessive Ga, were mixed and reacted at 1355 K in a pyrolitic boron nitride (BN) crucible for 1 day and then slowly cooled to 1180 K at the rate of 3 K/h before cooling to room temperature. After being washed in hot water to remove the excess Ga, faceted crystals with sizes ranging up to 3–5 mm in diameter were obtained. The crystals of Ba8 Ga16 Ge30 were grown by a conventional induction-heating CZ furnace with a corundum crucible (30 mm in diameter and 25 mm in height). The growth chamber was filled with high-purity argon after being evacuated. Before crystal growth, the melt of polycrystalline material described above were maintained at 1370 K for several hours in order to obtain homogenized composition distribution. The argon pressure was kept at 0.8 and 1.1 atm and the pulling rate was 8 and 5 mm/h for samples A and B, respectively. After growth, the crystals were cooled to room temperature at a rate of 60 K/h. Fig. 1 shows the pictures of crystals A and B. The growth conditions are summarized in Table 1. After pulling, the crystals were annealed under vacuum at 900 K for 7 days to eliminate the stress. A wire saw was used to cut one disk from crystal A and three disks from crystal B. The three disks from crystal B were labeled as B1, B2 and B3, respectively, where disk B1 was furthest away from the pulling rod. The crystal structures of the samples were studied by X-ray diffraction (XRD). The elemental compositions of the samples were analyzed by electron probe micro analyzer (EPMA). Sample density was determined by the Archimedes method. Measurements of electrical conductivity and Seebeck coefficient were made with ULVAC ZEM-3 apparatus under He atmosphere in the temperature range from 300 to 850 K. Thermal conductivity () was obtained using the relation = CP after the thermal diffusivity () was measured by laser flash method in an argon-filled box in the temperature range from 300 to 1000 K, where is sample density and CP is specific heat. The uncertainties in the measurements of electrical conductivity, Seebeck coefficient and thermal diffusivity are 7%, 5% and 5%, respectively.
Fig. 2. XRD spectra of powdered Ba8 Ga16 Ge30 crystal (a) and polycrystalline Ba8 Ga16 Ge30 sample (b), together with a calculated pattern of Ba8 Ga16 Ge30 (c).
3. Results and discussion XRD scans of polycrystalline Ba8 Ga16 Ge30 sample before melting and powdered Ba8 Ga16 Ge30 crystal as well as the calculated intensities of the type I clathrate are shown in Fig. 2. All the diffraction peaks observed in both samples could be identified as type I clathrate, without any Ge peak being found. Very small crystal has been isolated from crystal B and investigated by employing a singlecrystal X-ray diffraction with Mo K␣ (=0.7107 Å) radiation. The structure is solved and refined using the Rigaku Crystal-structure crystallographic software package. The structural refinement con¯ The lattice parameter firms the assignment of space group Pm3n. is 10.833(2) Å, which is in close agreement with reported values [10,11]. The “agreement” factors are Rwp = 0.0463, Rp = 0.0196, and the “goodness of fit” GOF = 1.28. Such low values of Rwp , Rp and GOF for a complex and disordered system evidence the good crystallization of the sample. Refined atomic coordinates, occupancies and isotropic displacement parameters of the sample are summarized in Table 2. Table 3 shows the actual elemental composition of samples measured by EPMA. The average Ga content of crystal B is about 15.8, which is higher than that in crystal A, and much closer to the
Table 1 Growth conditions, electrical conductivities , Seebeck coefficients S and thermal conductivities at 300 K of crystals A and B. Sample
Argon pressure (atm)
Pulling rate (mm/h)
Rotation speed (rpm)
Electrical conductivity, (×105 −1 m−1 )
Seebeck coefficient, S (V/K)
Thermal conductivity, (W/(m K))
A B1 B2 B3
0.8
8
20
1.1
5
20
1.21 1.75 1.74 1.77
−45 −42 −43 −40
2.03 2.19 2.18 2.21
546
X. Hou et al. / Journal of Alloys and Compounds 482 (2009) 544–547
Table 2 Atomic coordinates, isotropic displacement parameters Ueq and occupational parameters for Ba8 Ga16 Ge30 crystal at 300 K. Atom
Site
x
y
z
Ueq (Å2 )
Occupational parameters
Ba(1) Ba(2) Ga(1)/Ge(1) Ga(2)/Ge(2) Ga(3)/Ge(3)
2a 6d 6c 16i 24k
0 −1/4 0 −0.18452(4) 0
0 −1/2 −1/2 −0.18452(4) −0.30847(6)
0 0 −1/4 −0.18452(4) −0.11817(6)
0.0046(3) 0.0338(3) 0.0036(3) 0.0027(2) 0.0032(2)
1 1 0.348/0.652 0.348/0.652 0.348/0.652
Table 3 Measured elemental compositions of samples at room temperature. Sample
Ba
Ga
Ge
Ga/Ge
A B1 B2 B3
8 8 8 8
15.27 15.72 15.79 15.84
30.57 30.15 30.12 30.11
0.500 0.521 0.524 0.526
stoichiometric value. Crystal B shows nearly identical Ga/Ge ratio at different positions, which slightly decreases along the growth direction. The temperature dependence of the electrical conductivity (), Seebeck coefficient (S) and power factor (PF, PF = S2 ) for the obtained crystals are plotted in Fig. 3(a)–(c). In virtue of the constant chemical content, the thermoelectric properties of the three disks from crystal B are very close, so we just show one curve (sample B1) in the figures. The values for the obtained crystals over the entire temperature range are much higher than polycrys-
Fig. 3. Temperature dependence of electrical conductivity (), Seebeck coefficient (S) and power factor (S2 ) for samples A () and B (), and their extrapolations up to 1000 K.
talline sample, and even larger than those of the crystals previously reported [8,9,12]. Crystal B possesses a larger , whose value is 1.75 × 105 −1 m−1 at room temperature, as compared with crystal A. Such difference can be associated with the different Ga/Ge ratios. As suggested by Blake et al., in a caged-structure compound, the electron overlap between guest atom and the cage framework would affect the transfer of the valence electrons from the guest atoms to the cage framework and therefore affect the electrical transport property of the crystal [13]. It is believed that larger atomic size of the atoms in the cage framework would lead to a more efficient transfer of valence electrons from the guest atoms. In the present work, the values in crystal B are larger than that in crystal A because crystal B contains higher content of Ga which has a larger covalent radius (0.126 nm) than Ge (0.122 nm). Besides, some other factors, such as the quality of crystals, could also affect the values. The Seebeck coefficient S versus the temperature is shown in Fig. 3(b). As can be seen from Fig. 3(a), there exists about 44% difference between the electrical conductivity of crystals A and B at 300 K. However, the S values and their temperature dependence of the two crystals are almost the same, different from what is expected that a trend similar to electrical conductivity should be observed. Such phenomenon is similar to what Toberer et al. have reported [9]. All Seebeck coefficients are negative and the absolute values increase with increasing temperature. The S value for the crystal A is −45 V/K at room temperature, similar to Saramat’s result [8]. The Seebeck coefficients of the samples do not reach their maximum values in the measured temperature range. The observed S value for crystal B is −151 V/K at 850 K, slightly lower than that of earlier report [8]. The calculated power factor (S2 ) is shown in Fig. 3(c). The power factor for crystal B is 15.8 W/(cm K2 ) at 850 K, much larger than that of crystal A, which is 11.3 W/(cm K2 ) at the same temperature. Comparing the trend of and S with earlier reports, [8,9] it is reasonable to extrapolate these values to 1000 K. The thermal conductivity is measured from 300 to 1000 K and shown in Fig. 4. The value of crystal A is lower, due to the lower electrical conductivity than that of crystal B. The value of thermal conductivity decreases with the increase of temperature before 900 K. The value for crystal B is 2.19 W/(m K) at room temperature and reaches its minimum of 1.43 W/(m K) at 900 K. The rise of around 900 K is considered to be caused by bipolar heat conduction that the minority charge carriers began to affect the transport by carrying heat in the same direction as the majority carriers [8]. However, the effect of the minority charge carriers on electrical conductivity could be ignored, so the temperature dependence of electrical conductivity keeps the same trend at high temperature as shown in Fig. 3(a). With the Wiedemann–Franz approximation, = l + LT, the lattice component of thermal conductivity l is estimated by taking Lorenz number L as 2.0 × 10−8 J2 /K2 C2 . At 300 K, the l is 1.30 W/(m K) for crystal A and 1.14 W/(m K) for crystal B. Such phenomenon should be associated with the different Ga/Ge ratios of the obtained crystals. For the type I clathrate compounds in the Ba–Ga–Ge system, it was reported that the value of atomic displacement parameters (ADP) at the Ba site in the tetrakaidecahedral cage was extraordinary large and could be enhanced with the increase in
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tion. It is expected to further improve the thermoelectric property of Ba8 Ga16 Ge30 crystal by optimizing the chemical composition through controlling the growth conditions. 4. Conclusions
Fig. 4. Temperature dependence of thermal conductivity (). The inset shows the temperature dependence of lattice thermal conductivity (l ).
Two Ba8 Ga16 Ge30 clathrate crystals were fabricated with Czochralski method. The elemental composition and thermoelectric properties were proved to be related to the growth conditions. The lower pulling rate and higher pressure lead to a higher Ga/Ge ratio in the grown crystals. The obtained Ba8 Ga16 Ge30 clathrate crystals show relatively good homogeneity in chemical composition. The higher Ga/Ge ratio leads to the larger electrical conductivity and similar Seebeck coefficient S, resulting in a larger power factor PF. The different lattice component of thermal conductivity l should also arouse from the shifted Ga/Ge ratio which results in the different ADP values of Ba atoms in the tetrakaidecahedral cage. All the disks cut from crystal B exhibit higher ZT values. The measured ZT is 0.93 at 850 K for crystal B. Using the extrapolated values, the maximum ZT value is expected to be able to reach 1.30 at 1000 K. Acknowledgements This work was partially supported by the National Basic Research Program of China (2007CB607503), the National High Technology Research and Development Program of China (2007AA03Z233) and the National Natural Science Foundation of China (50821004). References
Fig. 5. Temperature dependence of calculated dimensionless figure-of-merit ZT for sample A (), sample B () and their extrapolations up to 1000 K.
the Ga content because Ga had larger covalent radius than Ge [14]. A larger ADP of the guest atom was considered to lead to a more glasslike lattice thermal conductivity for clathrate [15]. So the l for crystal B is lower because B has a relatively higher Ga/Ge ratio than that of crystal A. Fig. 5 shows the temperature dependence of ZT for the crystals. The value for crystal A is smaller, which is 0.70 at 850 K, while crystal B exhibits higher ZT value. The calculated ZT for crystal B is 0.93 at 850 K and it could reach 1.30 around 1000 K with extrapola-
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