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Investigation of Al substitution on the thermoelectric properties of SrSi2
Materials Chemistry and Physics 137 (2012) 604e607
Contents lists available at SciVerse ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Investigation of Al substitution on the thermoelectric properties of SrSi2 Y.K. Kuo a, C.S. Lue b, *, G. Hsu b, J.Y. Huang c, H.L. Hsieh c a
Department of Physics, National Dong Hwa University, Hualien 97401, Taiwan Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan c New Material Research & Development Department, China Steel Corporation, Kaohsiung 81233, Taiwan b
h i g h l i g h t s < Doping of Al onto the Si sites causes a decrease in the electrical resistivity. < Low-temperature lattice thermal conductivity reduces with increasing Al content. < Variation of the Seebeck coefficient is understood as the hole-doping effect.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 January 2012 Received in revised form 21 September 2012 Accepted 17 October 2012
We report the results of aluminum substitution on the temperature-dependent electrical resistivity, Seebeck coefficient, as well as thermal conductivity of SrSi2xAlx alloys with 0 x 0.20. It is found that the substitution of Al onto the Si sites of SrSi2 causes a significant decrease in the electrical resistivity and the Seebeck coefficient. The observations are associated with the downward shift of the Fermi level, due to hole-doping via Al substitution within a rigid-band scenario. The low-temperature thermal conductivity decreases markedly with increasing Al content. Analysis of the lattice thermal conductivity from the contribution of various thermal scattering mechanisms reveals that the reduction in the lattice thermal conductivity mainly arises from the grain-boundary and point-defect scattering of the phonons through chemical substitution. Ó 2012 Elsevier B.V. All rights reserved.
Keywords: A. Alloys B. Arc discharges D. Thermal properties D. Transport properties
1. Introduction Silicides with semiconducting or semimetallic properties have attracted considerable attention due to their practical applications in electronics and thermoelectrics [1e4]. Strontium disilicide SrSi2 was characterized as a narrow gap semiconductor based on the negative temperature coefficient of resistivity (TCR) while other measurements and band structure calculations indicated semimetallic behavior with a pseudogap in the vicinity of the Fermi level (EF) [5e9]. This material has been considered as a promising candidate for advanced thermoelectric applications through chemical substitution. For example, the thermoelectric figure-of-merit ZT ¼ 0.4 at room temperature has been achieved in the Sr1xYxSi2 system [10], which is one order of magnitude larger than that of stoichiometric SrSi2. This encouraging finding suggests that tuning the electronic band structure by suitable alloying with other
* Corresponding author. Tel.: þ886 6 2757575; fax: þ886 6 2747995. E-mail address: [email protected] (C.S. Lue). 0254-0584/$ e see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matchemphys.2012.10.009
elements may lead to a substantial enhancement on their thermoelectric performance [11]. In this study, to ascertain the effect of Al substitution on the thermoelectric properties of SrSi2, the electrical resistivity (r), Seebeck coefficient (S), and thermal conductivity (k) measurements were performed on the SrSi2xAlx samples, with x varying from 0 to 0.2. We observed a large enhancement of the electrical conductivity accompanied by a significant decrease of the Seebeck coefficient. The observations are attributed to a downward shift of the Fermi level from the pseudogap, due to the hole-doping effect via Al substitution based on a rigid-band picture. An analysis of the lattice thermal conductivity (kL) further indicated that both grainboundary and point-defect scattering of the phonons play important roles for the reduction of kL. 2. Experiment and discussion Polycrystalline SrSi2xAlx compounds were prepared by arcmelting the appropriate proportion of elements Sr (99.9%), Al (99.99%), and Si (99.999%) under an inert atmosphere of argon. Due to the volatility of Sr at high temperatures, we added with excess Sr
Y.K. Kuo et al. / Materials Chemistry and Physics 137 (2012) 604e607
to compensate the weight loss during each melting process, assuming that the weight loss arose entirely from the Sr element. The resulting ingots were melted several times to improve the homogeneity. The structure of these alloys was examined by the powder X-ray diffraction measurement using conventional Cu-Ka radiations. Electrical resistivity measurements were performed by a standard dc four-terminal method during the warming process. Thermal conductivity and Seebeck coefficient measurements were performed simultaneously in a close-cycle helium refrigerator by the heat pulse technique. Samples were cut into a rectangular parallelepiped shape of typical size of 1.5 1.5 5 mm3. Thin differential thermocouple junctions were fixed at the two ends of the sample using thermal epoxy. To measure the Seebeck emf, thin copper leads were placed on the specimen near to the thermocouple junctions using silver paste. One end of the sample was mounted on a copper block and a small chip resistor was fixed at the other end of the sample, which serves as a heater. The temperature difference was controlled to be less than 1 K to minimize the heat loss through radiation, and the sample space is maintained in a good vacuum (104 torr) during experiments. All data were recorded at a slow warming rate of about 20 K h1. The more details of the measurement techniques can be found elsewhere [12,13]. Fig. 1(a) demonstrates the room-temperature X-ray diffraction (XRD) patterns of the powder specimens in the range of 10 2q 80 . Each XRD result can be indexed according to the expected P4332 structure (No. 212). The variation of lattice constant as a function of Al concentration is shown in Fig. 1(b) It is clearly seen that the lattice constant monotonically increases with x,
605
indicating that the Si sites are successfully replaced by Al atoms, according to Vegard’s law. The evolution of the electrical resistivity of SrSi2xAlx is illustrated in Fig. 2. It is apparent that the substitution of Al onto the Si sites effectively reduces the electrical resistivity in SrSi2xAlx. Such a trend is attributed to a downward shift of EF from the valley of the pseudogap, as Si has one more electron in its valence shell than Al. As a consequence, EF moves to the position with larger density of states (DOS), leading to the reduction in the magnitude of the electrical resistivity. A further interpretation will be given below in accordance with the features of the Seebeck coefficient. The temperature dependence of the Seebeck coefficient for SrSi2xAlx is presented in Fig. 3. The positive sign of Seebeck coefficient for all materials over the measured temperature range indicates that predominant charge carriers for the thermal transport are holes. Among these SrSi2xAlx samples, the magnitude of S is drastically reduced with introducing Al content, similar to the trend of the electrical resistivity. For x ¼ 0.06, the magnitude of S at room temperature reduces to 63 mV K1 and tends to decrease with further increasing x in the SrSi2xAlx system. The Seebeck coefficient is an essential physical property in evaluating the potential performance of thermoelectric materials, as it is highly sensitive to the electronic structure. For ordinary metals and semimetals, the Seebeck coefficient at a temperature T is described by Mott’s formula [14]
SðTÞfT
vlnsðEÞ ; vE E¼EF
(1)
where s(E) is the electrical conductivity as a function of energy. In general, s(E) is proportional to the corresponding Fermi level DOS, N(EF), and a large Seebeck coefficient is normally connected to a low N(EF) coupled with its steep slope, vN(E)/vE, near EF. Therefore, the observed trend that the decrease in S with increasing x in the SrSi2xAlx alloys can be associated with an increase of N(EF). This is realized as the fact that the replacement of Si by Al effectively donates holes into the system, moving EF to the position with higher DOS from the dip of the pseudogap. It is worthwhile mentioning that the present low-temperature transport behavior of SrSi2 is different from that reported by Imai et al. which indicates a semiconducting character [5]. The discrepancy is mainly due to different amounts of impurities and/ or defects in the samples. These extrinsic effects would have a dramatic influence on the corresponding transport and
Fig. 1. (a) Powder X-ray diffraction patterns of the SrSi2xAlx samples. Impurity peaks marked by asterisks were identified to be due to other minor phases. (b) Lattice constant a as a function of aluminum concentration x.
Fig. 2. Temperature dependence of measured electrical resistivity r(T) for SrSi2xAlx.
606
Y.K. Kuo et al. / Materials Chemistry and Physics 137 (2012) 604e607
resistivity and the Lorentz number Lo attains the Sommerfields value of 2.45 108 WU K2 under the assumption that inelastic electron scattering processes are absent. The lattice thermal conductivity, kL, is obtained by subtracting the electronic part from the total measured conductivity and the result is presented in Fig. 5. In order to clarify the origin of the significant reduction of kL, we modeled the T-dependent kL using the Debye approximation. In the model of Debye approximation, kL is written as [16]
qZD =T kB T 3 x4 ex kL ¼ dx; 1 2p2 v Z s ðex 1Þ2 kB
0
Fig. 3. Temperature variation of the Seebeck coefficient for SrSi2xAlx over the temperature range 10 K T 300 K.
thermoelectric behavior, particularly in the SrSi2 sample. The high sensitivity with extrinsic impurities and/or additional spin-orbital coupling effect has been widely studied in the series of topological insulators. For example, the electronic structures of the Zintl phase compounds Sr2Sn and Sr2Pb were proposed to possess narrow semiconducting gaps with considering the spin-orbital coupling effects [15]. It is general agreement that a pure topological insulator is not a good thermoelectric material while the imperfect one usually exhibits promising thermoelectric performance. With this respect, the currently explored electronic features of SrSi2xAlx are quite similar to the topological insulators in some aspects. Fig. 4 displays the measured total thermal conductivity for SrSi2xAlx over the temperature range of 10 K T 300 K. The low temperature k exhibits similar behavior for all alloys where a sharp rise is followed by a broad peak around 30 K and then gradually decreases with lowering temperature. The characteristic peak in k is commonly seen in solids due to the reduction of thermal scattering at low temperatures. The maximum in k occurs when the phonon mean free path is comparable to crystal site distance. For ordinary metals or semimetals, the total thermal conductivity is generally expressed as a sum of electronic and lattice terms. The electronic thermal conductivity, ke, can be estimated by the WiedemanneFranz law: ke ¼ LoT/r. Here r is the dc electrical
Fig. 4. Temperature dependence of the total thermal conductivity k(T) for SrSi2xAlx.
(2)
P
where x ¼ Zu=kB T is a dimensionless quantity, u is the phonon frequency, Z is the reduced Planck constant, kB is the Boltzmann constant, qD is the Debye temperature, v is the average phonon velocity, and s1 P is the phonon scattering relaxation rate and is given by Eq. (3) as
s1 ¼ P
v þ Au4 þ Bu2 TeðqD =3TÞ ; L
(3)
where the coefficients v/L, A, and B are fitting parameters. The terms in Eq. (3) represent the scattering rates for the grainboundary, point-defect, and phonon Umklapp scattering, respectively. In general, the grain-boundary scattering is a dominant mechanism for the low-temperature kL, while the Umklapp procedure is important at high temperatures. The point-defect scattering, on the other hand, has a strong influence on the appearance of the shape and position of the phonon peak occurring in the intermediate temperature regime. The low-T peak in kL is very sensitive to various mechanisms of phonon scattering in crystalline solids. In general, the height of this peak reduces with increasing phonon scattering rates. Except the grain-boundary, point-defect, and phonon Umklapp scattering as given in Eq. (3),
Fig. 5. Lattice thermal conductivity for SrSi2xAlx as a function of temperature. Each solid curve represents the calculated kL using Eqs. (2) and (3).
Y.K. Kuo et al. / Materials Chemistry and Physics 137 (2012) 604e607 Table 1 Fitting parameters of the lattice thermal conductivity determined from Eqs. (2) and (3). Sample x x x x
¼ ¼ ¼ ¼
0 0.06 0.15 0.20
v/L (106 s1)
A (1042 s3)
B (1017 s K1)
4.1 19 33 123
6.7 4.4 5.8 6.8
1.1 1.4 1.2 1.9
another important mechanism in this regard is scattering of phonons by impurities, where the scattering rate is independence of temperature. All these scattering processes should be taken into account by using Matthiessen’s rule. The fitting curves were drawn in Fig. 5. It is noted that the discrepancy between the measured data and the fit at high temperatures may be attributed to radiation losses during experiments, temperature dependence of the Lorentz number, and the undetermined Debye temperatures for the Al-doped compounds. This discrepancy, however, has little effect on the following discussion. The optimized fitting parameters are tabulated in Table 1. As one can see, the Umklapp coefficient B scatters around in these samples. On the other hand, a systematic increase of v/L is found except for the stoichiometric SrSi2 alloy, indicative of the growing importance of the grain-boundary scattering with increasing Al concentration. It is well-established that the phonongrain boundary scattering is a dominant mechanism in reducing the lattice thermal conductivity in silicon-germanium based thermoelectric alloys [17]. In general, the enhancement in v/L with increasing Al concentration could be connected to the reduction in the grain size L if the average phonon velocity (or Debye temperature) does not vary greatly upon Al substitution. However, our SEM images on these materials indicate no consistent variation in L. With this respect, it is very likely that the obtained enhancement in v/L is mainly associated with the increase of the phonon velocity instead of the reduction of the grain size as increasing Al concentration in the present SrSi2xAlx series. Also the magnitude of A gradually increases with increasing x in the SrSi2xAlx system. According to the model proposed by Klemens [18], the prefactor A is associated with the concentration of point defects in the sample. Therefore, the parameter A increasing with x suggests that the reduction of the phonon peak via Al substitution is strongly related to the appearance of point defects. We argue that these point defects are not originated from the mass fluctuations between Si and Al, since their atomic size and mass differences are less than 4%. Rather, other lattice imperfections, such as vacancies, are introduced with Si substitution, which in turn give rise to a considerable amount of point defects to the substituted samples. From the application viewpoint, the efficiency of a thermoelectric material is characterized by the dimensionless ZT value. While the electrical resistivity of SrSi2xAlx exhibits an encouraging decrease with increasing Al concentration, the thermoelectric
607
performance is hampered by the reduction of the Seebeck coefficient through Al doping. Also the thermal conductivity at high temperatures in the SrSi2xAlx system remains high. As a consequence, the corresponding ZT value reduces rather than enhances in these SrSi2xAlx alloys. 3. Conclusions A systematic study of the thermoelectric properties on SrSi2xAlx (x ¼ 0e0.20) was performed. Upon Al substitution for Si, the SrSi2xAlx alloys exhibit a significant reduction in both r and S, due to the hole-doping effect on the substituted samples. Such observations were connected to the shift of EF within the rigid-band scenario. Furthermore, the effect of Al substitution is strongly related to the appearance of point defects, which causes a drastic reduction in the low-T lattice thermal conductivity. Since the holedoping effect on the SrSi2 system becomes a drawback of the ZT enhancement, an important issue which should be considered in future studies is the effect of electron-doping on the thermoelectric performance of the SrSi2 system. Acknowledgments We are grateful for the support from the National Science Council of Taiwan for financially supporting this research under contract Nos. NSC-101-2112-M-006-009-MY2 (CSL) and NSC-1002628-M-259-002-MY3 (YKK). Partial support was provided by China Steel Corporation under project No. RE100705. References [1] T.M. Tritt, M. Kanatzidis, H.B. Lyon Jr., G. Mahan, Symposium Proceedings of the Materials Research Society, Materials Research Society, Pittsburgh, 1997, p. 478. [2] C.S. Lue, Y.K. Kuo, C.L. Huang, W.J. Lai, Phys. Rev. B 69 (2004) 125111. [3] Silicides, in: L. Miglio, M. d’Heurle (Eds.), Fundamentals and Applications, World Scientific, Singapore, 2000. [4] C.S. Lue, P.C. Fang, A.C. Abhyanka, J.W. Lin, H.W. Lee, C.M. Chang, Y.K. Kuo, Intermetallics 19 (2011) 1448. [5] M. Imai, T. Naka, T. Furubayashi, H. Abe, T. Nakama, K. Yagasaki, Appl. Phys. Lett. 86 (2005) 032102. [6] K. Hashimoto, K. Kurosaki, Y. Imamura, H. Muta, S. Yamanaka, J. Appl. Phys. 102 (2007) 063703. [7] Y. Imai, A. Watanabe, Intermetallics 14 (2006) 666. [8] S. Brutti, D. Nguyen Manh, D.G. Pettifor, Intermetallics 14 (2006) 1472. [9] Z.J. Chen, D.B. Tian, J. Appl. Phys. 109 (2011) 033506. [10] C.S. Lue, M.D. Chou, N. Kaurav, Y.T. Chung, Y.K. Kuo, Appl. Phys. Lett. 94 (2009) 192105. [11] M. Imai, A. Sato, T. Kimura, T. Aoyagi, Thin Solid Films 519 (2011) 8496. [12] C.S. Lue, Y.K. Kuo, Phys. Rev. B 66 (2002) 085121. [13] C.S. Lue, C.F. Chen, J.Y. Lin, Y.T. Yu, Y.K. Kuo, Phys. Rev. B 75 (2007) 064204. [14] N.F. Mott, H. Jones, The Theory of the Properties of Metals, Clarendon Press, Oxford, 1936. [15] Y. Sun, X.-Q. Chen, C. Franchini, D. Li, S. Yunoki, Y. Li, Z. Fang, Phys. Rev. B 84 (2011) 165127. [16] J. Callaway, H.C. von Baeyer, Phys. Rev. 120 (1960) 1149. [17] C.M. Bhandarit, D.M. Rowe, J. Phys. D Appl. Phys. 16 (1983) L75. [18] P.G. Klemens, Proc. Phys. Soc. London Sect. A 68 (1959) 1113.
Contents lists available at SciVerse ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Investigation of Al substitution on the thermoelectric properties of SrSi2 Y.K. Kuo a, C.S. Lue b, *, G. Hsu b, J.Y. Huang c, H.L. Hsieh c a
Department of Physics, National Dong Hwa University, Hualien 97401, Taiwan Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan c New Material Research & Development Department, China Steel Corporation, Kaohsiung 81233, Taiwan b
h i g h l i g h t s < Doping of Al onto the Si sites causes a decrease in the electrical resistivity. < Low-temperature lattice thermal conductivity reduces with increasing Al content. < Variation of the Seebeck coefficient is understood as the hole-doping effect.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 January 2012 Received in revised form 21 September 2012 Accepted 17 October 2012
We report the results of aluminum substitution on the temperature-dependent electrical resistivity, Seebeck coefficient, as well as thermal conductivity of SrSi2xAlx alloys with 0 x 0.20. It is found that the substitution of Al onto the Si sites of SrSi2 causes a significant decrease in the electrical resistivity and the Seebeck coefficient. The observations are associated with the downward shift of the Fermi level, due to hole-doping via Al substitution within a rigid-band scenario. The low-temperature thermal conductivity decreases markedly with increasing Al content. Analysis of the lattice thermal conductivity from the contribution of various thermal scattering mechanisms reveals that the reduction in the lattice thermal conductivity mainly arises from the grain-boundary and point-defect scattering of the phonons through chemical substitution. Ó 2012 Elsevier B.V. All rights reserved.
Keywords: A. Alloys B. Arc discharges D. Thermal properties D. Transport properties
1. Introduction Silicides with semiconducting or semimetallic properties have attracted considerable attention due to their practical applications in electronics and thermoelectrics [1e4]. Strontium disilicide SrSi2 was characterized as a narrow gap semiconductor based on the negative temperature coefficient of resistivity (TCR) while other measurements and band structure calculations indicated semimetallic behavior with a pseudogap in the vicinity of the Fermi level (EF) [5e9]. This material has been considered as a promising candidate for advanced thermoelectric applications through chemical substitution. For example, the thermoelectric figure-of-merit ZT ¼ 0.4 at room temperature has been achieved in the Sr1xYxSi2 system [10], which is one order of magnitude larger than that of stoichiometric SrSi2. This encouraging finding suggests that tuning the electronic band structure by suitable alloying with other
* Corresponding author. Tel.: þ886 6 2757575; fax: þ886 6 2747995. E-mail address: [email protected] (C.S. Lue). 0254-0584/$ e see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matchemphys.2012.10.009
elements may lead to a substantial enhancement on their thermoelectric performance [11]. In this study, to ascertain the effect of Al substitution on the thermoelectric properties of SrSi2, the electrical resistivity (r), Seebeck coefficient (S), and thermal conductivity (k) measurements were performed on the SrSi2xAlx samples, with x varying from 0 to 0.2. We observed a large enhancement of the electrical conductivity accompanied by a significant decrease of the Seebeck coefficient. The observations are attributed to a downward shift of the Fermi level from the pseudogap, due to the hole-doping effect via Al substitution based on a rigid-band picture. An analysis of the lattice thermal conductivity (kL) further indicated that both grainboundary and point-defect scattering of the phonons play important roles for the reduction of kL. 2. Experiment and discussion Polycrystalline SrSi2xAlx compounds were prepared by arcmelting the appropriate proportion of elements Sr (99.9%), Al (99.99%), and Si (99.999%) under an inert atmosphere of argon. Due to the volatility of Sr at high temperatures, we added with excess Sr
Y.K. Kuo et al. / Materials Chemistry and Physics 137 (2012) 604e607
to compensate the weight loss during each melting process, assuming that the weight loss arose entirely from the Sr element. The resulting ingots were melted several times to improve the homogeneity. The structure of these alloys was examined by the powder X-ray diffraction measurement using conventional Cu-Ka radiations. Electrical resistivity measurements were performed by a standard dc four-terminal method during the warming process. Thermal conductivity and Seebeck coefficient measurements were performed simultaneously in a close-cycle helium refrigerator by the heat pulse technique. Samples were cut into a rectangular parallelepiped shape of typical size of 1.5 1.5 5 mm3. Thin differential thermocouple junctions were fixed at the two ends of the sample using thermal epoxy. To measure the Seebeck emf, thin copper leads were placed on the specimen near to the thermocouple junctions using silver paste. One end of the sample was mounted on a copper block and a small chip resistor was fixed at the other end of the sample, which serves as a heater. The temperature difference was controlled to be less than 1 K to minimize the heat loss through radiation, and the sample space is maintained in a good vacuum (104 torr) during experiments. All data were recorded at a slow warming rate of about 20 K h1. The more details of the measurement techniques can be found elsewhere [12,13]. Fig. 1(a) demonstrates the room-temperature X-ray diffraction (XRD) patterns of the powder specimens in the range of 10 2q 80 . Each XRD result can be indexed according to the expected P4332 structure (No. 212). The variation of lattice constant as a function of Al concentration is shown in Fig. 1(b) It is clearly seen that the lattice constant monotonically increases with x,
605
indicating that the Si sites are successfully replaced by Al atoms, according to Vegard’s law. The evolution of the electrical resistivity of SrSi2xAlx is illustrated in Fig. 2. It is apparent that the substitution of Al onto the Si sites effectively reduces the electrical resistivity in SrSi2xAlx. Such a trend is attributed to a downward shift of EF from the valley of the pseudogap, as Si has one more electron in its valence shell than Al. As a consequence, EF moves to the position with larger density of states (DOS), leading to the reduction in the magnitude of the electrical resistivity. A further interpretation will be given below in accordance with the features of the Seebeck coefficient. The temperature dependence of the Seebeck coefficient for SrSi2xAlx is presented in Fig. 3. The positive sign of Seebeck coefficient for all materials over the measured temperature range indicates that predominant charge carriers for the thermal transport are holes. Among these SrSi2xAlx samples, the magnitude of S is drastically reduced with introducing Al content, similar to the trend of the electrical resistivity. For x ¼ 0.06, the magnitude of S at room temperature reduces to 63 mV K1 and tends to decrease with further increasing x in the SrSi2xAlx system. The Seebeck coefficient is an essential physical property in evaluating the potential performance of thermoelectric materials, as it is highly sensitive to the electronic structure. For ordinary metals and semimetals, the Seebeck coefficient at a temperature T is described by Mott’s formula [14]
SðTÞfT
vlnsðEÞ ; vE E¼EF
(1)
where s(E) is the electrical conductivity as a function of energy. In general, s(E) is proportional to the corresponding Fermi level DOS, N(EF), and a large Seebeck coefficient is normally connected to a low N(EF) coupled with its steep slope, vN(E)/vE, near EF. Therefore, the observed trend that the decrease in S with increasing x in the SrSi2xAlx alloys can be associated with an increase of N(EF). This is realized as the fact that the replacement of Si by Al effectively donates holes into the system, moving EF to the position with higher DOS from the dip of the pseudogap. It is worthwhile mentioning that the present low-temperature transport behavior of SrSi2 is different from that reported by Imai et al. which indicates a semiconducting character [5]. The discrepancy is mainly due to different amounts of impurities and/ or defects in the samples. These extrinsic effects would have a dramatic influence on the corresponding transport and
Fig. 1. (a) Powder X-ray diffraction patterns of the SrSi2xAlx samples. Impurity peaks marked by asterisks were identified to be due to other minor phases. (b) Lattice constant a as a function of aluminum concentration x.
Fig. 2. Temperature dependence of measured electrical resistivity r(T) for SrSi2xAlx.
606
Y.K. Kuo et al. / Materials Chemistry and Physics 137 (2012) 604e607
resistivity and the Lorentz number Lo attains the Sommerfields value of 2.45 108 WU K2 under the assumption that inelastic electron scattering processes are absent. The lattice thermal conductivity, kL, is obtained by subtracting the electronic part from the total measured conductivity and the result is presented in Fig. 5. In order to clarify the origin of the significant reduction of kL, we modeled the T-dependent kL using the Debye approximation. In the model of Debye approximation, kL is written as [16]
qZD =T kB T 3 x4 ex kL ¼ dx; 1 2p2 v Z s ðex 1Þ2 kB
0
Fig. 3. Temperature variation of the Seebeck coefficient for SrSi2xAlx over the temperature range 10 K T 300 K.
thermoelectric behavior, particularly in the SrSi2 sample. The high sensitivity with extrinsic impurities and/or additional spin-orbital coupling effect has been widely studied in the series of topological insulators. For example, the electronic structures of the Zintl phase compounds Sr2Sn and Sr2Pb were proposed to possess narrow semiconducting gaps with considering the spin-orbital coupling effects [15]. It is general agreement that a pure topological insulator is not a good thermoelectric material while the imperfect one usually exhibits promising thermoelectric performance. With this respect, the currently explored electronic features of SrSi2xAlx are quite similar to the topological insulators in some aspects. Fig. 4 displays the measured total thermal conductivity for SrSi2xAlx over the temperature range of 10 K T 300 K. The low temperature k exhibits similar behavior for all alloys where a sharp rise is followed by a broad peak around 30 K and then gradually decreases with lowering temperature. The characteristic peak in k is commonly seen in solids due to the reduction of thermal scattering at low temperatures. The maximum in k occurs when the phonon mean free path is comparable to crystal site distance. For ordinary metals or semimetals, the total thermal conductivity is generally expressed as a sum of electronic and lattice terms. The electronic thermal conductivity, ke, can be estimated by the WiedemanneFranz law: ke ¼ LoT/r. Here r is the dc electrical
Fig. 4. Temperature dependence of the total thermal conductivity k(T) for SrSi2xAlx.
(2)
P
where x ¼ Zu=kB T is a dimensionless quantity, u is the phonon frequency, Z is the reduced Planck constant, kB is the Boltzmann constant, qD is the Debye temperature, v is the average phonon velocity, and s1 P is the phonon scattering relaxation rate and is given by Eq. (3) as
s1 ¼ P
v þ Au4 þ Bu2 TeðqD =3TÞ ; L
(3)
where the coefficients v/L, A, and B are fitting parameters. The terms in Eq. (3) represent the scattering rates for the grainboundary, point-defect, and phonon Umklapp scattering, respectively. In general, the grain-boundary scattering is a dominant mechanism for the low-temperature kL, while the Umklapp procedure is important at high temperatures. The point-defect scattering, on the other hand, has a strong influence on the appearance of the shape and position of the phonon peak occurring in the intermediate temperature regime. The low-T peak in kL is very sensitive to various mechanisms of phonon scattering in crystalline solids. In general, the height of this peak reduces with increasing phonon scattering rates. Except the grain-boundary, point-defect, and phonon Umklapp scattering as given in Eq. (3),
Fig. 5. Lattice thermal conductivity for SrSi2xAlx as a function of temperature. Each solid curve represents the calculated kL using Eqs. (2) and (3).
Y.K. Kuo et al. / Materials Chemistry and Physics 137 (2012) 604e607 Table 1 Fitting parameters of the lattice thermal conductivity determined from Eqs. (2) and (3). Sample x x x x
¼ ¼ ¼ ¼
0 0.06 0.15 0.20
v/L (106 s1)
A (1042 s3)
B (1017 s K1)
4.1 19 33 123
6.7 4.4 5.8 6.8
1.1 1.4 1.2 1.9
another important mechanism in this regard is scattering of phonons by impurities, where the scattering rate is independence of temperature. All these scattering processes should be taken into account by using Matthiessen’s rule. The fitting curves were drawn in Fig. 5. It is noted that the discrepancy between the measured data and the fit at high temperatures may be attributed to radiation losses during experiments, temperature dependence of the Lorentz number, and the undetermined Debye temperatures for the Al-doped compounds. This discrepancy, however, has little effect on the following discussion. The optimized fitting parameters are tabulated in Table 1. As one can see, the Umklapp coefficient B scatters around in these samples. On the other hand, a systematic increase of v/L is found except for the stoichiometric SrSi2 alloy, indicative of the growing importance of the grain-boundary scattering with increasing Al concentration. It is well-established that the phonongrain boundary scattering is a dominant mechanism in reducing the lattice thermal conductivity in silicon-germanium based thermoelectric alloys [17]. In general, the enhancement in v/L with increasing Al concentration could be connected to the reduction in the grain size L if the average phonon velocity (or Debye temperature) does not vary greatly upon Al substitution. However, our SEM images on these materials indicate no consistent variation in L. With this respect, it is very likely that the obtained enhancement in v/L is mainly associated with the increase of the phonon velocity instead of the reduction of the grain size as increasing Al concentration in the present SrSi2xAlx series. Also the magnitude of A gradually increases with increasing x in the SrSi2xAlx system. According to the model proposed by Klemens [18], the prefactor A is associated with the concentration of point defects in the sample. Therefore, the parameter A increasing with x suggests that the reduction of the phonon peak via Al substitution is strongly related to the appearance of point defects. We argue that these point defects are not originated from the mass fluctuations between Si and Al, since their atomic size and mass differences are less than 4%. Rather, other lattice imperfections, such as vacancies, are introduced with Si substitution, which in turn give rise to a considerable amount of point defects to the substituted samples. From the application viewpoint, the efficiency of a thermoelectric material is characterized by the dimensionless ZT value. While the electrical resistivity of SrSi2xAlx exhibits an encouraging decrease with increasing Al concentration, the thermoelectric
607
performance is hampered by the reduction of the Seebeck coefficient through Al doping. Also the thermal conductivity at high temperatures in the SrSi2xAlx system remains high. As a consequence, the corresponding ZT value reduces rather than enhances in these SrSi2xAlx alloys. 3. Conclusions A systematic study of the thermoelectric properties on SrSi2xAlx (x ¼ 0e0.20) was performed. Upon Al substitution for Si, the SrSi2xAlx alloys exhibit a significant reduction in both r and S, due to the hole-doping effect on the substituted samples. Such observations were connected to the shift of EF within the rigid-band scenario. Furthermore, the effect of Al substitution is strongly related to the appearance of point defects, which causes a drastic reduction in the low-T lattice thermal conductivity. Since the holedoping effect on the SrSi2 system becomes a drawback of the ZT enhancement, an important issue which should be considered in future studies is the effect of electron-doping on the thermoelectric performance of the SrSi2 system. Acknowledgments We are grateful for the support from the National Science Council of Taiwan for financially supporting this research under contract Nos. NSC-101-2112-M-006-009-MY2 (CSL) and NSC-1002628-M-259-002-MY3 (YKK). Partial support was provided by China Steel Corporation under project No. RE100705. References [1] T.M. Tritt, M. Kanatzidis, H.B. Lyon Jr., G. Mahan, Symposium Proceedings of the Materials Research Society, Materials Research Society, Pittsburgh, 1997, p. 478. [2] C.S. Lue, Y.K. Kuo, C.L. Huang, W.J. Lai, Phys. Rev. B 69 (2004) 125111. [3] Silicides, in: L. Miglio, M. d’Heurle (Eds.), Fundamentals and Applications, World Scientific, Singapore, 2000. [4] C.S. Lue, P.C. Fang, A.C. Abhyanka, J.W. Lin, H.W. Lee, C.M. Chang, Y.K. Kuo, Intermetallics 19 (2011) 1448. [5] M. Imai, T. Naka, T. Furubayashi, H. Abe, T. Nakama, K. Yagasaki, Appl. Phys. Lett. 86 (2005) 032102. [6] K. Hashimoto, K. Kurosaki, Y. Imamura, H. Muta, S. Yamanaka, J. Appl. Phys. 102 (2007) 063703. [7] Y. Imai, A. Watanabe, Intermetallics 14 (2006) 666. [8] S. Brutti, D. Nguyen Manh, D.G. Pettifor, Intermetallics 14 (2006) 1472. [9] Z.J. Chen, D.B. Tian, J. Appl. Phys. 109 (2011) 033506. [10] C.S. Lue, M.D. Chou, N. Kaurav, Y.T. Chung, Y.K. Kuo, Appl. Phys. Lett. 94 (2009) 192105. [11] M. Imai, A. Sato, T. Kimura, T. Aoyagi, Thin Solid Films 519 (2011) 8496. [12] C.S. Lue, Y.K. Kuo, Phys. Rev. B 66 (2002) 085121. [13] C.S. Lue, C.F. Chen, J.Y. Lin, Y.T. Yu, Y.K. Kuo, Phys. Rev. B 75 (2007) 064204. [14] N.F. Mott, H. Jones, The Theory of the Properties of Metals, Clarendon Press, Oxford, 1936. [15] Y. Sun, X.-Q. Chen, C. Franchini, D. Li, S. Yunoki, Y. Li, Z. Fang, Phys. Rev. B 84 (2011) 165127. [16] J. Callaway, H.C. von Baeyer, Phys. Rev. 120 (1960) 1149. [17] C.M. Bhandarit, D.M. Rowe, J. Phys. D Appl. Phys. 16 (1983) L75. [18] P.G. Klemens, Proc. Phys. Soc. London Sect. A 68 (1959) 1113.