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Electronic and crystal structures of thermoelectric CaMgSi intermetallic compound
Journal of Electron Spectroscopy and Related Phenomena 206 (2016) 18–23
Contents lists available at ScienceDirect
Journal of Electron Spectroscopy and Related Phenomena journal homepage: www.elsevier.com/locate/elspec
Electronic and crystal structures of thermoelectric CaMgSi intermetallic compound Hidetoshi Miyazaki a,∗ , Manabu Inukai a , Kazuo Soda b , Nobufumi Miyazaki c , Nozomu Adachi c , Yoshikazu Todaka c , Yoichi Nishino a a
Department of Frontier Materials, Nagoya Institute of Technology, Nagoya 466-8555, Japan Department of Quantum Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan c Department of Mechanical Engineering, Toyohashi University of Technology, Toyohashi 441-8580, Japan b
a r t i c l e
i n f o
Article history: Received 9 July 2015 Received in revised form 23 October 2015 Accepted 3 November 2015 Available online 10 November 2015 Keywords: CaMgSi compound Thermoelectric materials Synchrotron radiation Photoemission spectroscopy X-ray powder diffraction
a b s t r a c t We investigated the electronic and crystal structures of a new thermoelectric material, CaMgSi compound, by using synchrotron radiation photoemission spectroscopy (SR-PES), synchrotron radiation X-ray powder diffraction (SR-XRD) measurements, and electronic band structure calculation to understand the way leading to improvement in the thermoelectric properties of this material. Electronic band structure calculation of the CaMgSi compound using the crystal structure determined from SR-XRD measurement showed a semi-metallic electronic structure with a pseudo-gap at the Fermi level. In contrast to the predicted semi-metallic electronic structure, the SR-PES results showed a small semiconductor-like gap at the Fermi level. This result revealed that the CaMgSi compound is a Mott-type insulator owing to strongly correlated electrons effect in the Ca 3d and Mg 3p states being well hybridized with those in the Si 3p states. The observed electronic structure of the CaMgSi compound suggests that an optimal carrier doping exists to best control the n- and p-type thermoelectric properties and enhance the power factors. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Thermoelectric materials have attracted considerable attention as viable materials for direct conversion of thermal energy into electrical energy. In principle, the performance of thermoelectric materials is determined by their dimensionless figure of merit ZT = S2 T/, where S is the Seebeck coefficient, is the electrical conductivity, is the thermal conductivity, and T is the absolute temperature. Given this relation, high performance of n- and p-type thermoelectric materials should exhibit high Seebeck coefficients, large electrical conductivities, and low thermal conductivities. Since Mg2 Si-based compounds do not include the rare-metal or heavy atoms and show high-performance of the thermoelectric properties, they are well- known candidates for thermoelectric materials with high economic performance and environmental harmonization [1–6]. Indeed, Mg2 Si-based compounds also have the lower density (1.88 g/cm3 ) [2] compared to Bi–Te compounds (7.86 g/cm3 ) [7], which are the conventional thermoelectric
∗ Corresponding author. Tel.: +81 52 735 5394; fax: +81 52 735 5247. E-mail address: [email protected] (H. Miyazaki). http://dx.doi.org/10.1016/j.elspec.2015.11.002 0368-2048/© 2015 Elsevier B.V. All rights reserved.
materials. Previous studies of n- and p-type thermoelectric properties of the Mg2 Si-based compounds have reported a ZT of 1.22 at 800 K and 0.11 at 873 K in Mg2.10 Si0.49 Sn0.5 Sb0.01 [5] and Mg2 SiAg0.01 [4] compounds, respectively. The lower p-type thermoelectric performance compared to the n-type one is a disadvantage of this otherwise promising material. Recently, Todaka et al. investigated the thermoelectric properties of various Ca–Mg–Si compounds, in which one Mg atom in the Mg2 Si compound was substituted by a Ca atom, and suggested the existence of a CaMgSi phase with high p-type thermoelectric performance [8]. However, it is still unclear whether the high ptype thermoelectric property of the CaMgSi phase originates from composition deviation or the intrinsic electronic structure. A band structure calculation predicts the stoichiometric CaMgSi compound to have a semi-metallic electronic structure with a narrow pseudo-gap of ∼2.0 eV at the Fermi energy (EF ) [9]. In metallic systems, the S may be given a following formula [10]:
2 kB2 S (T ) = T 3 −e
∂ ln (E) ∂E
(1) E=EF
H. Miyazaki et al. / Journal of Electron Spectroscopy and Related Phenomena 206 (2016) 18–23
19
where (E) denotes the electrical conductivity at a particular energy, E. Since (E) is proportional to the density of states (DOS), N(E), the above formula can be written as: S (T ) =
2 kB2 T 3 −e
1 ∂N (E) N (E) ∂E
(2) E=EF
Large value of S arises from a low N(E) coupled with a steep slope, ∂N(E)/∂E, at EF . Since the DOS rises sharply on both sides of the pseudo-gap, we expect the absolute value of S to be well enhanced and its sign to be controlled by carrier doping, such as offstoichiometry or doping another element. Therefore, the CaMgSi compound with a pseudo-gap is one of extremely promising candidates for a next generation thermoelectric material. Only a few studies have reported detailed crystal and electronic structures for the stoichiometric CaMgSi compound [9], despite the potential of this information suggests strategies to improve the thermoelectric properties. Synchrotron radiation powder diffraction (SR-XRD) and photoemission spectroscopy (SR-PES) have shown the detailed crystal and electronic structures. Hard X-ray photoemission spectroscopy (HAX-PES) with photoelectron emitted angle dependence returns information about the topmost surface layer and intrinsic bulk electronic structure [11]. Topmost surface layer property, such as surface oxide layer thickness, is important for p–n junctions in thermoelectric devices made with these materials because it is related to the electrical resistivity of the interface between the electrode and materials. Therefore, we performed high-resolution SR-XRD measurement to determine the detailed crystal structure of CaMgSi compound and SR-PES measurements at various excitation energies to investigate its electronic structure. 2. Experimental and theoretical procedures A stoichiometric CaMgSi compound was fabricated by the powder metallurgical process. Mechanical ball-milling (MM) yielded finely pulverized and homogenized CaMgSi powders. Appropriate amounts of CaH2 (99%, 200 m), Mg (99.9%, <150 m) and Si (99.9%, 5 m) powders were mixed and milled in a planetary ball mill with a 500 ml capacity SUS304 pot and SUJ2 balls at Ar gas atmosphere. MM was performed at 125 rpm for 72 ks with 6 × 102 s rests every hour. A disk of CaMgSi compound was sintered from the prepared powderes by pulse-current sintering (PCS) process in a graphite mold at 1273 K for 1.2 ks in Ar gas and at 1273 K for 1.2 ks in vacuum under a uniaxial pressure of 50 MPa. Samples for SR-PES and SR-XRD measurements were cut from the disk with a SiC blade and they were again crushed to obtain a powder composed of particles with diameters smaller than 45 m for SR-XRD measurement. High-resolution SR-XRD measurement was carried out at 300 K using the BL02B2 beamline (wavelength = 0.045993 nm) at the SPring-8 synchrotron radiation facility in Japan [12]. The wavelength was precisely calibrated using a CeO2 standard sample. A Rietveld analysis using the RIETAN-FP package [13] characterized the detailed crystal structure of the CaMgSi compound. Electronic band structure of the CaMgSi compound was calculated with the WIEN2k package for full potential linearized augmented plane wave method and generalized gradient approximation [14]. The values determined from SR-XRD measurement were used as the CaMgSi compound lattice parameters. The convergence energy was set to 0.0001 Ry. HAX-PES and soft X-ray PES (SX-PES) measurements were performed at the BL47XU [11] and BL27SU [15] beamlines of SPring-8, respectively. Clean surface for the HAX-PES measurement was obtained by ex-situ fracturing with a knife edge and immediately installing the sample in the HAX-PES chamber. Clean surface for the SX-PES measurement was obtained by in-situ fracturing with
Fig. 1. Synchrotron radiation X-ray powder diffraction patterns (cross symbol) of wide (a) and narrow ranges (b) for CaMgSi compound at 300 K. The thin line, dots, and vertical bars indicate the fitting, residual, and CaMgSi phase results, respectively, calculated by Rietveld analysis. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
a knife edge at 10 K under an ultra-high vacuum. HAX-PES and SX-PES measurements were recorded at room temperature and 10 K, respectively. The Fermi level and total energy resolution were determined by the Fermi edge of evaporated gold films. The total energy resolutions of the HAX-PES and SX-PES measurements were set to 260 meV and 200 meV at the excitation photon energies (h) of 7942 eV and 1000 eV, respectively. 3. Results and discussion Fig. 1 shows the SR-XRD pattern of the CaMgSi compound. Since several diffraction peaks could not be explained by the TiNiSi-type (Space group: No. 62) crystal structure, we performed a multiphase analysis to determine other phases, such as oxides, carbides, and hydroxides, and their respective volume fractions. Table 1 shows the converged results of the SR-XRD pattern for the CaMgSi compound evaluated by the Rietveld analysis. The reliability factors, namely Rwp , Rp , Re , and s, are sufficiently small to justify this fitting result.
Table 1 Reliability factors (Rwp , Re and s), refined lattice parameter (a, b, c, ˛, ˇ, and ), isotropic displacement parameters (B), and occupancies determined for CaMgSi compound by Rietveld analysis. Rwp
Rp
Re
s
6.944
4.818
2.336
2.972
a (nm)
b (nm)
c (nm)
˛ (◦ )
ˇ (◦ )
(◦ )
0.74666
0.44224
0.82958
90.0
90.0
90.0
Atom
Ca
Mg
Si
x y z B (Å2 ) Occupancy
0.019 0.250 0.680 1.109 0.985
0.146 0.250 0.065 0.947 1.012
0.270 0.250 0.386 0.827 0.994
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Table 2 Composition table of powdered CaMgSi compound determined by Rietveld analysis. Components
at.%
CaMgSi MgCN2 MgCO3 MgO CaSiO3 CaSi CaMgSiO6
86.7 3.9 2.7 2.1 1.8 1.7 1.2
The Rietveld analysis revealed that the powdered CaMgSi contained several other phases: MgCN2 , MgCO3 , MgO CaSiO3 , CaSi, and CaMgSiO6 , listed in Table 2. Since the volume fractions of the other phases are small and the diffraction peaks do not overlap the CaMgSi phase, the other phases did not affect the fitting results for the CaMgSi compound. However, it is not clear whether the other phases developed during the compound fabrication or powdered sample preparation for SR-XRD measurement. We will discuss this further in the context of the HAXPES measurement. The obtained
Fig. 2. Calculated density of states (DOS) and partial DOS of CaMgSi using experimental lattice parameters, as shown in Table 1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. Hard X-ray wide photoemission spectrum of CaMgSi compound at an excitation photon energy of h = 7942 eV. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
lattice parameters of the CaMgSi compound are very similar to previously reported result [9]. We performed the electronic band structure calculation using the lattice parameters and atomic configurations obtained here, shown in Table 1. Fig. 2 shows the calculated DOS for the CaMgSi compound and partial DOS of each component. Owing to the strong hybridization between the Ca 3d-Si 3p and Mg 3p-Si 3p states, the electronic structure of the CaMgSi compound is semi-metallic with a pseudo-gap at EF . This result is consistent with previous report [9]. However, the strong hybridization between each component may lead to unexpected strongly correlated electrons effects, may change its electronic structure in this compound. Therefore, we performed photoemission spectroscopy on the CaMgSi compound to directly determine the electronic structure. Fig. 3 shows a typical wide photoemission spectrum for the CaMgSi compound with h = 7942 eV. Most peaks are attributed to the valence band, core levels, and Auger emission lines of the constituent Ca, Mg and Si elements. Since only C and O 1s lines were observed in the wide photoemission spectrum, the MM and PCS processes did not supply other contaminants, such as Fe, Cr, and Ni. To determine the carbon and oxide contributions to the SR-XRD result and to distinguish the surface and bulk electronic structures of the CaMgSi compound, we measured the take-off angle dependence of the photoemission spectra of Ca, Mg, and Si 1s states, as shown in Fig. 4(a1, a2), (b1, b2) and (c1, c2), respectively. A 90◦ take-off angle corresponds to the surface normal. Each spectrum was decomposed into two components. The higher binding energy peaks were attributed to CaO, MgO, and SiO2 , and the lower binding energy peaks to the bulk components of the CaMgSi compound. The oxide components of each constituent element increased with decreasing take-off angle. This indicates the surface of the CaMgSi compound is covered with oxides. SR-XRD results also indicate a second phase of carbides, oxides, and nitrides in the CaMgSi compound. The C 1s line was only observed as an impurity in the wide photoemission spectra (Fig. 1). The intensity of C 1s line was much smaller than that of the O 1s lines, and the core level of each constituent element only contains two peaks (Fig. 4). Therefore, since the carbides, and nitrides of Ca, Mg and Si were not observed in the photoemission spectra, they developed during the powder preparation process for the SR-XRD measurements. Since the topmost oxide layer thickness affects the electrode/material interface electrical resistivity, knowledge of the topmost oxide layer is important in fabricating a p–n junction for a thermoelectric device. We estimated the thickness of the topmost oxide layers from the take-off angle dependence of the intensity ratio between the bulk and oxide component signals. The take-off angle dependences of the intensity ratios for the Ca, Mg, and Si 1s states are shown in Fig. 5(a1), (b1), and (c1). A simple bulk-surface double layer model with a constant surface oxide layer thickness,
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Fig. 4. Angle-resolved and single shot of 2D images of Ca 1s (a1, a2), Mg 1s (b1, b2), and Si 1s (c1, c2) states of CaMgSi compound for h = 7942 eV. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
d, was applied to determine the inelastic electron mean free path (IMFP) for CaMgSi, bulk , and for the oxide,surface , at the measured kinetic energy [16], Ibulk 1 nbulk bulk = Isurface nsurface surface exp d/surface sin − 1 d = surface sin ln
n I bulk bulk surface nsurface surface Ibulk
(3)
+1
(4)
here nsurface and nbulk denote atomic densities in the oxide layer and bulk components, respectively. The IMFPs of each component were calculated by the Tanuma–Powell–Penn TPP2 M formula using the QUASES code [17–19] at the measured kinetic energy of h = 7942 eV. Using the above mentioned parameters, the thicknesses of the oxide layer of each take-off angle were estimated by Eq. (4). The calculated oxide thicknesses for Ca, Mg, and Si are plotted as functions of the take-off angle in Fig. 5(a2), (b2), and (c2), respectively. The average thicknesses of CaO, MgO, and SiO2 layer between 35◦ and 85◦ were estimated to be 2.8 nm, 2.3 nm, 5.8 nm, respectively. As shown in Fig. 5(a1), (b1), and (c1), since the
intensity ratios of each element are consistent with the estimated thicknesses, these fitting results are reasonable and there is almost no oxygen or carbon in the CaMgSi compound. Since the oxide layer thicknesses correspond to several monolayers of the oxides, the oxide layer on the CaMgSi surface would negligibly increase the interface electrical resistivity. Fig. 6 shows the valence band photoemission spectra in a wide binding energy range for h = 1000 eV and 7942 eV, as well as the calculated DOS of the CaMgSi compound. While the peak widths of the spectra are broader than that of the calculated DOS, the overall spectral shapes are consistent with the DOS. The peaks and shoulders are observed around 1.8 eV, 2.2 eV, 3.8 eV, and 7.5 eV. The peak height between EF and 3.2 eV for h = 7942 eV is suppressed than that for h = 1000 eV. On the other hand, the peak height between 5 eV and 10 eV for h = 7942 eV is higher than that for h = 1000 eV. There are two reasons why the photoemission spectrum changes with h. One reason is the change in probing depth of the photoelectrons due to the kinetic energy dependence of the IMFP [20], and the other is the difference between the photon energy dependent atomic cross sections of the elements [21]. Since
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Fig. 5. Take-off angle dependence of the intensity ratio between surface oxide and bulk components of Ca 1s (a1), Mg 1s (b1), and Si 1s (c1) states. Calculated thickness of the surface oxide layer for each take-off angle of Ca 1s (a2), Mg 1s (b2), and Si 1s (c2) states. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. The valence band photoemission spectra and calculated DOS of CaMgSi compound with h = 1000 eV and 7942 eV. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the IMFPs of the valence electron (EB = 0 eV) at h = 1000 eV and 7942 eV calculated by QUASES code are about 2.7 nm and 15 nm, respectively, the change in overall valence band spectra may be attributed to the different probing depths. When the photon energy increased from 1000 eV to 7942 eV, the atomic cross-sections of the s states mainly enhance compared to that of the p states [21]. As a result, the partial DOS originating from the Mg 3p, and Si 3p states should be suppressed compared to that originating from the Ca 4s, Mg 3s and Si 3s states and hence the states near EF are attributed to the Mg 3p, and Si 3p states. This hypothesis is consistent with the calculated partial DOS for each component, shown in Fig. 2. Therefore, the differences of the photoemission spectra between h = 1000 eV and 7942 eV mainly originate from the difference in cross sections for the excitation energies. Fig. 7 shows the valence band spectra near EF of the CaMgSi compound and Au film for h = 1000 eV and 7942 eV. In the case of h = 7942 eV, the photoemission spectrum shows a clear narrow gap of about 0.26 eV, which is inconsistent with the semi-metallic electronic structure predicted by the band structure calculation. On the other hand, for h = 1000 eV, the photoemission spectra are consistent with the semi-metallic electronic structure. Since the intensity at EF gradually decreases with increasing h, the
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Thus, hole- and electron-doping of a fourth element, for example substitution of K or Sc for Ca or Mg, and Al or P for Si, is an effective way to improve the thermoelectric properties of the CaMgSi compound. 4. Conclusion We investigated the electronic and crystal structures of the new thermoelectric CaMgSi compound by SR-PES and SR-XRD measurements, and electronic band structure calculation. We found the compound to have a semiconductor-like electronic structure with a band gap of 0.26 eV at the Fermi level. Thus, we expect to be able to improve the thermoelectric properties of CaMgSi-based compounds by controlling the position of the Fermi level through electron- and hole-doping. Acknowledgements
Fig. 7. The valence band photoemission spectra near EF for CaMgSi compound and Au film with h = 1000 eV (a), and 7942 eV (b). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
observed intensity of the photoemission spectra for h = 1000 eV is attributed to the surface state [20]. Therefore, the observed unexpected semiconductor-like pseudo-gap is an intrinsic electronic structure. Similar inconsistencies have been observed for the transition metal oxides and MgO and explained by the Mott–Hubbard insulator model [22,23]. According to the Mott–Hubbard model, the effect of strongly correlated electrons creates a large repulsive Coulomb interaction that separates the DOS into an upper Hubbard band in the unoccupied region and a lower Hubbard band in the occupied region. Since the Ca 3d–Si 3p and Mg 3p–Si 3p states are strongly hybridized to each other from the band structure calculation in the CaMgSi compound, CaMgSi compound has a narrow band gap at EF . However, because the thermal broadening of the electronic state (4kB T [20]) is larger than the gap size above room temperature, the semiconductor-like gap is filled and the electronic structure of the CaMgSi compound near EF is expected to have the pseudo-gap. A pseudo-gap and narrow band gap around EF are advantageous to thermoelectric materials. It is argued that a large value and sign of S arise from a low DOS, N(E), coupled with a steep slope, ∂N(E)/∂E, at EF , and electrical conductivity, , is proportional to N(E) [10]. Since the DOS rises on both sides of the pseudo-gap and narrow band gap, we expect the absolute value of S and to be large and the sign of S to be controlled by hole- or electrondoping. In fact, in the case of Heusler-type Fe2 VAl based compound with a small pseudo-gap around EF , hole- and electron-doped compounds, such as Fe2 V1-y Tiy Al [24] and Fe2 VAl1-y Siy [25], exhibit large S from 70 V/K for the p-type to −130 V/K for the n-type, as well as a large . Since the partial DOS of the valence and conduction bands are other components, the carrier doping of the off-stoichiometric cases could change their electronic structure.
We would like to thank Dr. Muro, Dr. Sugimoto and Dr. Ikenaga for their technical support in the SX-PES, HAX-PES and SR-XRD measurements. SX-PES (Proposal nos. 2014A1485 and 2014A1160), HAX-PES (Proposal no. 2014A1160) and SR-XRD (Proposal nos. 2013B1783 and 2014A1494) measurements were performed at the SPring-8 synchrotron facility with the approval of the Japan Synchrotron Radiation Research Institute (JASRI). This study was partly supported by JSPS KAKENHI Grand-in-Aid for Scientific Research (B) (No. 23360279) and Young Scientists (B) (No. 24760536). References [1] M.W. Heller, G.C. Danielson, J. Phys. Chem. Solids 23 (1962) 601. [2] L.F. Mondolfo, Aluminum Compound: Structure and Properties, Butterworth & Co (Publishers) Ltd, London, 1976, pp. 566. [3] J. Tani, H. Kido, Physica B: Condens. Matter 223 (2005) 364. [4] T. Sakamoto, T. Iida, A. Matsumoto, Y. Honda, T. Nemoto, J. Sato, T. Nakalima, H. Taguchi, Y. Takanashi, J. Electron. Mater. 39 (2010) 1708. [5] W. Liu, X. Tang, H. Li, J. Sharp, X. Zhou, C. Uher, Chem. Mater. 23 (2011) 5256. [6] K. Kambe, H. Udono, J. Electron. Mater. 43 (2014) 2212. [7] G.R. Miller, C. Li, J. Phys. Chem. Solids 26 (1965) 173. [8] Y. Niwa, Y. Todaka, T. Masuda, T. Kawai, M. Umemoto, Mater. Trans. 50 (2009) 1725. [9] J.B. Whalen, J.V. Zaikina, R. Achey, R. Stillwell, H. Zhou, C.R. Wiebe, S.E. Latturner, Chem. Mater. 22 (2010) 1846. [10] N.F. Mott, H. Jones, The Theory of the Properties of Metals and Compounds, Clarendon Press, Oxford, 1936. [11] E. Ikenaga, M. Kobata, H. Matsuda, T. Sugiyama, H. Daimon, K. Kobayashi, J. Electron Spectrosc. Relat. Ph. 190 (2013) 180. [12] E. Nishibori, M. Takata, K. Kato, M. Sakata, Y. Kubota, S. Aoyagi, Y. Kuroiwa, M. Yamakata, N. Ikeda, Nucl. Instrum. Methods Phys. Res., Sect. A 467-468 (2001) 1045. [13] F. Izumi, K. Momma, Solid State Phenom. 130 (2007) 15. [14] P. Blaha, K. Schwarz, P.I. Sorantin, S.B. Trickey, Comput. Phys. Commun. 59 (1990) 399. [15] H. Ohashi, E. Ishiguro, H. Okumura, A. Hiraya, Y. Senba, K. Okada, N. Saito, I. Suzuki, K. Ueda, T. Ibuki, S. Nagaoka, I. Koyano, T. Ishikawa, Nucl. Instrum. Methods A 467–468 (2001) 533536. [16] J.M. Hill, D.G. Royce, C.S. Fadley, L.F. Wagner, Chem. Phys. Lett. 44 (1976) 225. [17] A. Jablonski, H. Ebel, Surf. Interface Anal. 11 (1988) 627. [18] A. Jablonski, Surf. Interface Anal. 15 (1990) 559. [19] S. Tanuma, C.J. Powell, D.R. Penn, Surf. Interface Anal. 21 (1994) 165. [20] S. Hüfner, Photoelectron Spectroscopy, third ed., Springer-Verlag, Berlin, 2003. [21] J.J. Yeh, I. Lindau, At. Data Nucl. Data Tables 32 (1985) 1. [22] M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70 (1998) 1039. [23] H.J. Im, M. Tsunekawa, T. Sakurada, M. Iwataki, K. Kawata, T. Watanabe, K. Takegahara, H. Miyazaki, M. Matsunami, T. Hajiri, S. Kimura, Phys. Rev. B: Condens. Matter 88 (2013) 205133. [24] H. Matsuura, Y. Nishino, U. Mizutani, S. Asano, J. Jpn. Inst. Met. 66 (2002) 767. [25] H. Kato, M. Kato, Y. Nishino, U. Mizutani, S. Asano, J. Jpn. Inst. Met. 65 (2001) 652.
Contents lists available at ScienceDirect
Journal of Electron Spectroscopy and Related Phenomena journal homepage: www.elsevier.com/locate/elspec
Electronic and crystal structures of thermoelectric CaMgSi intermetallic compound Hidetoshi Miyazaki a,∗ , Manabu Inukai a , Kazuo Soda b , Nobufumi Miyazaki c , Nozomu Adachi c , Yoshikazu Todaka c , Yoichi Nishino a a
Department of Frontier Materials, Nagoya Institute of Technology, Nagoya 466-8555, Japan Department of Quantum Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan c Department of Mechanical Engineering, Toyohashi University of Technology, Toyohashi 441-8580, Japan b
a r t i c l e
i n f o
Article history: Received 9 July 2015 Received in revised form 23 October 2015 Accepted 3 November 2015 Available online 10 November 2015 Keywords: CaMgSi compound Thermoelectric materials Synchrotron radiation Photoemission spectroscopy X-ray powder diffraction
a b s t r a c t We investigated the electronic and crystal structures of a new thermoelectric material, CaMgSi compound, by using synchrotron radiation photoemission spectroscopy (SR-PES), synchrotron radiation X-ray powder diffraction (SR-XRD) measurements, and electronic band structure calculation to understand the way leading to improvement in the thermoelectric properties of this material. Electronic band structure calculation of the CaMgSi compound using the crystal structure determined from SR-XRD measurement showed a semi-metallic electronic structure with a pseudo-gap at the Fermi level. In contrast to the predicted semi-metallic electronic structure, the SR-PES results showed a small semiconductor-like gap at the Fermi level. This result revealed that the CaMgSi compound is a Mott-type insulator owing to strongly correlated electrons effect in the Ca 3d and Mg 3p states being well hybridized with those in the Si 3p states. The observed electronic structure of the CaMgSi compound suggests that an optimal carrier doping exists to best control the n- and p-type thermoelectric properties and enhance the power factors. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Thermoelectric materials have attracted considerable attention as viable materials for direct conversion of thermal energy into electrical energy. In principle, the performance of thermoelectric materials is determined by their dimensionless figure of merit ZT = S2 T/, where S is the Seebeck coefficient, is the electrical conductivity, is the thermal conductivity, and T is the absolute temperature. Given this relation, high performance of n- and p-type thermoelectric materials should exhibit high Seebeck coefficients, large electrical conductivities, and low thermal conductivities. Since Mg2 Si-based compounds do not include the rare-metal or heavy atoms and show high-performance of the thermoelectric properties, they are well- known candidates for thermoelectric materials with high economic performance and environmental harmonization [1–6]. Indeed, Mg2 Si-based compounds also have the lower density (1.88 g/cm3 ) [2] compared to Bi–Te compounds (7.86 g/cm3 ) [7], which are the conventional thermoelectric
∗ Corresponding author. Tel.: +81 52 735 5394; fax: +81 52 735 5247. E-mail address: [email protected] (H. Miyazaki). http://dx.doi.org/10.1016/j.elspec.2015.11.002 0368-2048/© 2015 Elsevier B.V. All rights reserved.
materials. Previous studies of n- and p-type thermoelectric properties of the Mg2 Si-based compounds have reported a ZT of 1.22 at 800 K and 0.11 at 873 K in Mg2.10 Si0.49 Sn0.5 Sb0.01 [5] and Mg2 SiAg0.01 [4] compounds, respectively. The lower p-type thermoelectric performance compared to the n-type one is a disadvantage of this otherwise promising material. Recently, Todaka et al. investigated the thermoelectric properties of various Ca–Mg–Si compounds, in which one Mg atom in the Mg2 Si compound was substituted by a Ca atom, and suggested the existence of a CaMgSi phase with high p-type thermoelectric performance [8]. However, it is still unclear whether the high ptype thermoelectric property of the CaMgSi phase originates from composition deviation or the intrinsic electronic structure. A band structure calculation predicts the stoichiometric CaMgSi compound to have a semi-metallic electronic structure with a narrow pseudo-gap of ∼2.0 eV at the Fermi energy (EF ) [9]. In metallic systems, the S may be given a following formula [10]:
2 kB2 S (T ) = T 3 −e
∂ ln (E) ∂E
(1) E=EF
H. Miyazaki et al. / Journal of Electron Spectroscopy and Related Phenomena 206 (2016) 18–23
19
where (E) denotes the electrical conductivity at a particular energy, E. Since (E) is proportional to the density of states (DOS), N(E), the above formula can be written as: S (T ) =
2 kB2 T 3 −e
1 ∂N (E) N (E) ∂E
(2) E=EF
Large value of S arises from a low N(E) coupled with a steep slope, ∂N(E)/∂E, at EF . Since the DOS rises sharply on both sides of the pseudo-gap, we expect the absolute value of S to be well enhanced and its sign to be controlled by carrier doping, such as offstoichiometry or doping another element. Therefore, the CaMgSi compound with a pseudo-gap is one of extremely promising candidates for a next generation thermoelectric material. Only a few studies have reported detailed crystal and electronic structures for the stoichiometric CaMgSi compound [9], despite the potential of this information suggests strategies to improve the thermoelectric properties. Synchrotron radiation powder diffraction (SR-XRD) and photoemission spectroscopy (SR-PES) have shown the detailed crystal and electronic structures. Hard X-ray photoemission spectroscopy (HAX-PES) with photoelectron emitted angle dependence returns information about the topmost surface layer and intrinsic bulk electronic structure [11]. Topmost surface layer property, such as surface oxide layer thickness, is important for p–n junctions in thermoelectric devices made with these materials because it is related to the electrical resistivity of the interface between the electrode and materials. Therefore, we performed high-resolution SR-XRD measurement to determine the detailed crystal structure of CaMgSi compound and SR-PES measurements at various excitation energies to investigate its electronic structure. 2. Experimental and theoretical procedures A stoichiometric CaMgSi compound was fabricated by the powder metallurgical process. Mechanical ball-milling (MM) yielded finely pulverized and homogenized CaMgSi powders. Appropriate amounts of CaH2 (99%, 200 m), Mg (99.9%, <150 m) and Si (99.9%, 5 m) powders were mixed and milled in a planetary ball mill with a 500 ml capacity SUS304 pot and SUJ2 balls at Ar gas atmosphere. MM was performed at 125 rpm for 72 ks with 6 × 102 s rests every hour. A disk of CaMgSi compound was sintered from the prepared powderes by pulse-current sintering (PCS) process in a graphite mold at 1273 K for 1.2 ks in Ar gas and at 1273 K for 1.2 ks in vacuum under a uniaxial pressure of 50 MPa. Samples for SR-PES and SR-XRD measurements were cut from the disk with a SiC blade and they were again crushed to obtain a powder composed of particles with diameters smaller than 45 m for SR-XRD measurement. High-resolution SR-XRD measurement was carried out at 300 K using the BL02B2 beamline (wavelength = 0.045993 nm) at the SPring-8 synchrotron radiation facility in Japan [12]. The wavelength was precisely calibrated using a CeO2 standard sample. A Rietveld analysis using the RIETAN-FP package [13] characterized the detailed crystal structure of the CaMgSi compound. Electronic band structure of the CaMgSi compound was calculated with the WIEN2k package for full potential linearized augmented plane wave method and generalized gradient approximation [14]. The values determined from SR-XRD measurement were used as the CaMgSi compound lattice parameters. The convergence energy was set to 0.0001 Ry. HAX-PES and soft X-ray PES (SX-PES) measurements were performed at the BL47XU [11] and BL27SU [15] beamlines of SPring-8, respectively. Clean surface for the HAX-PES measurement was obtained by ex-situ fracturing with a knife edge and immediately installing the sample in the HAX-PES chamber. Clean surface for the SX-PES measurement was obtained by in-situ fracturing with
Fig. 1. Synchrotron radiation X-ray powder diffraction patterns (cross symbol) of wide (a) and narrow ranges (b) for CaMgSi compound at 300 K. The thin line, dots, and vertical bars indicate the fitting, residual, and CaMgSi phase results, respectively, calculated by Rietveld analysis. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
a knife edge at 10 K under an ultra-high vacuum. HAX-PES and SX-PES measurements were recorded at room temperature and 10 K, respectively. The Fermi level and total energy resolution were determined by the Fermi edge of evaporated gold films. The total energy resolutions of the HAX-PES and SX-PES measurements were set to 260 meV and 200 meV at the excitation photon energies (h) of 7942 eV and 1000 eV, respectively. 3. Results and discussion Fig. 1 shows the SR-XRD pattern of the CaMgSi compound. Since several diffraction peaks could not be explained by the TiNiSi-type (Space group: No. 62) crystal structure, we performed a multiphase analysis to determine other phases, such as oxides, carbides, and hydroxides, and their respective volume fractions. Table 1 shows the converged results of the SR-XRD pattern for the CaMgSi compound evaluated by the Rietveld analysis. The reliability factors, namely Rwp , Rp , Re , and s, are sufficiently small to justify this fitting result.
Table 1 Reliability factors (Rwp , Re and s), refined lattice parameter (a, b, c, ˛, ˇ, and ), isotropic displacement parameters (B), and occupancies determined for CaMgSi compound by Rietveld analysis. Rwp
Rp
Re
s
6.944
4.818
2.336
2.972
a (nm)
b (nm)
c (nm)
˛ (◦ )
ˇ (◦ )
(◦ )
0.74666
0.44224
0.82958
90.0
90.0
90.0
Atom
Ca
Mg
Si
x y z B (Å2 ) Occupancy
0.019 0.250 0.680 1.109 0.985
0.146 0.250 0.065 0.947 1.012
0.270 0.250 0.386 0.827 0.994
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Table 2 Composition table of powdered CaMgSi compound determined by Rietveld analysis. Components
at.%
CaMgSi MgCN2 MgCO3 MgO CaSiO3 CaSi CaMgSiO6
86.7 3.9 2.7 2.1 1.8 1.7 1.2
The Rietveld analysis revealed that the powdered CaMgSi contained several other phases: MgCN2 , MgCO3 , MgO CaSiO3 , CaSi, and CaMgSiO6 , listed in Table 2. Since the volume fractions of the other phases are small and the diffraction peaks do not overlap the CaMgSi phase, the other phases did not affect the fitting results for the CaMgSi compound. However, it is not clear whether the other phases developed during the compound fabrication or powdered sample preparation for SR-XRD measurement. We will discuss this further in the context of the HAXPES measurement. The obtained
Fig. 2. Calculated density of states (DOS) and partial DOS of CaMgSi using experimental lattice parameters, as shown in Table 1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. Hard X-ray wide photoemission spectrum of CaMgSi compound at an excitation photon energy of h = 7942 eV. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
lattice parameters of the CaMgSi compound are very similar to previously reported result [9]. We performed the electronic band structure calculation using the lattice parameters and atomic configurations obtained here, shown in Table 1. Fig. 2 shows the calculated DOS for the CaMgSi compound and partial DOS of each component. Owing to the strong hybridization between the Ca 3d-Si 3p and Mg 3p-Si 3p states, the electronic structure of the CaMgSi compound is semi-metallic with a pseudo-gap at EF . This result is consistent with previous report [9]. However, the strong hybridization between each component may lead to unexpected strongly correlated electrons effects, may change its electronic structure in this compound. Therefore, we performed photoemission spectroscopy on the CaMgSi compound to directly determine the electronic structure. Fig. 3 shows a typical wide photoemission spectrum for the CaMgSi compound with h = 7942 eV. Most peaks are attributed to the valence band, core levels, and Auger emission lines of the constituent Ca, Mg and Si elements. Since only C and O 1s lines were observed in the wide photoemission spectrum, the MM and PCS processes did not supply other contaminants, such as Fe, Cr, and Ni. To determine the carbon and oxide contributions to the SR-XRD result and to distinguish the surface and bulk electronic structures of the CaMgSi compound, we measured the take-off angle dependence of the photoemission spectra of Ca, Mg, and Si 1s states, as shown in Fig. 4(a1, a2), (b1, b2) and (c1, c2), respectively. A 90◦ take-off angle corresponds to the surface normal. Each spectrum was decomposed into two components. The higher binding energy peaks were attributed to CaO, MgO, and SiO2 , and the lower binding energy peaks to the bulk components of the CaMgSi compound. The oxide components of each constituent element increased with decreasing take-off angle. This indicates the surface of the CaMgSi compound is covered with oxides. SR-XRD results also indicate a second phase of carbides, oxides, and nitrides in the CaMgSi compound. The C 1s line was only observed as an impurity in the wide photoemission spectra (Fig. 1). The intensity of C 1s line was much smaller than that of the O 1s lines, and the core level of each constituent element only contains two peaks (Fig. 4). Therefore, since the carbides, and nitrides of Ca, Mg and Si were not observed in the photoemission spectra, they developed during the powder preparation process for the SR-XRD measurements. Since the topmost oxide layer thickness affects the electrode/material interface electrical resistivity, knowledge of the topmost oxide layer is important in fabricating a p–n junction for a thermoelectric device. We estimated the thickness of the topmost oxide layers from the take-off angle dependence of the intensity ratio between the bulk and oxide component signals. The take-off angle dependences of the intensity ratios for the Ca, Mg, and Si 1s states are shown in Fig. 5(a1), (b1), and (c1). A simple bulk-surface double layer model with a constant surface oxide layer thickness,
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Fig. 4. Angle-resolved and single shot of 2D images of Ca 1s (a1, a2), Mg 1s (b1, b2), and Si 1s (c1, c2) states of CaMgSi compound for h = 7942 eV. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
d, was applied to determine the inelastic electron mean free path (IMFP) for CaMgSi, bulk , and for the oxide,surface , at the measured kinetic energy [16], Ibulk 1 nbulk bulk = Isurface nsurface surface exp d/surface sin − 1 d = surface sin ln
n I bulk bulk surface nsurface surface Ibulk
(3)
+1
(4)
here nsurface and nbulk denote atomic densities in the oxide layer and bulk components, respectively. The IMFPs of each component were calculated by the Tanuma–Powell–Penn TPP2 M formula using the QUASES code [17–19] at the measured kinetic energy of h = 7942 eV. Using the above mentioned parameters, the thicknesses of the oxide layer of each take-off angle were estimated by Eq. (4). The calculated oxide thicknesses for Ca, Mg, and Si are plotted as functions of the take-off angle in Fig. 5(a2), (b2), and (c2), respectively. The average thicknesses of CaO, MgO, and SiO2 layer between 35◦ and 85◦ were estimated to be 2.8 nm, 2.3 nm, 5.8 nm, respectively. As shown in Fig. 5(a1), (b1), and (c1), since the
intensity ratios of each element are consistent with the estimated thicknesses, these fitting results are reasonable and there is almost no oxygen or carbon in the CaMgSi compound. Since the oxide layer thicknesses correspond to several monolayers of the oxides, the oxide layer on the CaMgSi surface would negligibly increase the interface electrical resistivity. Fig. 6 shows the valence band photoemission spectra in a wide binding energy range for h = 1000 eV and 7942 eV, as well as the calculated DOS of the CaMgSi compound. While the peak widths of the spectra are broader than that of the calculated DOS, the overall spectral shapes are consistent with the DOS. The peaks and shoulders are observed around 1.8 eV, 2.2 eV, 3.8 eV, and 7.5 eV. The peak height between EF and 3.2 eV for h = 7942 eV is suppressed than that for h = 1000 eV. On the other hand, the peak height between 5 eV and 10 eV for h = 7942 eV is higher than that for h = 1000 eV. There are two reasons why the photoemission spectrum changes with h. One reason is the change in probing depth of the photoelectrons due to the kinetic energy dependence of the IMFP [20], and the other is the difference between the photon energy dependent atomic cross sections of the elements [21]. Since
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Fig. 5. Take-off angle dependence of the intensity ratio between surface oxide and bulk components of Ca 1s (a1), Mg 1s (b1), and Si 1s (c1) states. Calculated thickness of the surface oxide layer for each take-off angle of Ca 1s (a2), Mg 1s (b2), and Si 1s (c2) states. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. The valence band photoemission spectra and calculated DOS of CaMgSi compound with h = 1000 eV and 7942 eV. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the IMFPs of the valence electron (EB = 0 eV) at h = 1000 eV and 7942 eV calculated by QUASES code are about 2.7 nm and 15 nm, respectively, the change in overall valence band spectra may be attributed to the different probing depths. When the photon energy increased from 1000 eV to 7942 eV, the atomic cross-sections of the s states mainly enhance compared to that of the p states [21]. As a result, the partial DOS originating from the Mg 3p, and Si 3p states should be suppressed compared to that originating from the Ca 4s, Mg 3s and Si 3s states and hence the states near EF are attributed to the Mg 3p, and Si 3p states. This hypothesis is consistent with the calculated partial DOS for each component, shown in Fig. 2. Therefore, the differences of the photoemission spectra between h = 1000 eV and 7942 eV mainly originate from the difference in cross sections for the excitation energies. Fig. 7 shows the valence band spectra near EF of the CaMgSi compound and Au film for h = 1000 eV and 7942 eV. In the case of h = 7942 eV, the photoemission spectrum shows a clear narrow gap of about 0.26 eV, which is inconsistent with the semi-metallic electronic structure predicted by the band structure calculation. On the other hand, for h = 1000 eV, the photoemission spectra are consistent with the semi-metallic electronic structure. Since the intensity at EF gradually decreases with increasing h, the
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Thus, hole- and electron-doping of a fourth element, for example substitution of K or Sc for Ca or Mg, and Al or P for Si, is an effective way to improve the thermoelectric properties of the CaMgSi compound. 4. Conclusion We investigated the electronic and crystal structures of the new thermoelectric CaMgSi compound by SR-PES and SR-XRD measurements, and electronic band structure calculation. We found the compound to have a semiconductor-like electronic structure with a band gap of 0.26 eV at the Fermi level. Thus, we expect to be able to improve the thermoelectric properties of CaMgSi-based compounds by controlling the position of the Fermi level through electron- and hole-doping. Acknowledgements
Fig. 7. The valence band photoemission spectra near EF for CaMgSi compound and Au film with h = 1000 eV (a), and 7942 eV (b). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
observed intensity of the photoemission spectra for h = 1000 eV is attributed to the surface state [20]. Therefore, the observed unexpected semiconductor-like pseudo-gap is an intrinsic electronic structure. Similar inconsistencies have been observed for the transition metal oxides and MgO and explained by the Mott–Hubbard insulator model [22,23]. According to the Mott–Hubbard model, the effect of strongly correlated electrons creates a large repulsive Coulomb interaction that separates the DOS into an upper Hubbard band in the unoccupied region and a lower Hubbard band in the occupied region. Since the Ca 3d–Si 3p and Mg 3p–Si 3p states are strongly hybridized to each other from the band structure calculation in the CaMgSi compound, CaMgSi compound has a narrow band gap at EF . However, because the thermal broadening of the electronic state (4kB T [20]) is larger than the gap size above room temperature, the semiconductor-like gap is filled and the electronic structure of the CaMgSi compound near EF is expected to have the pseudo-gap. A pseudo-gap and narrow band gap around EF are advantageous to thermoelectric materials. It is argued that a large value and sign of S arise from a low DOS, N(E), coupled with a steep slope, ∂N(E)/∂E, at EF , and electrical conductivity, , is proportional to N(E) [10]. Since the DOS rises on both sides of the pseudo-gap and narrow band gap, we expect the absolute value of S and to be large and the sign of S to be controlled by hole- or electrondoping. In fact, in the case of Heusler-type Fe2 VAl based compound with a small pseudo-gap around EF , hole- and electron-doped compounds, such as Fe2 V1-y Tiy Al [24] and Fe2 VAl1-y Siy [25], exhibit large S from 70 V/K for the p-type to −130 V/K for the n-type, as well as a large . Since the partial DOS of the valence and conduction bands are other components, the carrier doping of the off-stoichiometric cases could change their electronic structure.
We would like to thank Dr. Muro, Dr. Sugimoto and Dr. Ikenaga for their technical support in the SX-PES, HAX-PES and SR-XRD measurements. SX-PES (Proposal nos. 2014A1485 and 2014A1160), HAX-PES (Proposal no. 2014A1160) and SR-XRD (Proposal nos. 2013B1783 and 2014A1494) measurements were performed at the SPring-8 synchrotron facility with the approval of the Japan Synchrotron Radiation Research Institute (JASRI). This study was partly supported by JSPS KAKENHI Grand-in-Aid for Scientific Research (B) (No. 23360279) and Young Scientists (B) (No. 24760536). References [1] M.W. Heller, G.C. Danielson, J. Phys. Chem. Solids 23 (1962) 601. [2] L.F. Mondolfo, Aluminum Compound: Structure and Properties, Butterworth & Co (Publishers) Ltd, London, 1976, pp. 566. [3] J. Tani, H. Kido, Physica B: Condens. Matter 223 (2005) 364. [4] T. Sakamoto, T. Iida, A. Matsumoto, Y. Honda, T. Nemoto, J. Sato, T. Nakalima, H. Taguchi, Y. Takanashi, J. Electron. Mater. 39 (2010) 1708. [5] W. Liu, X. Tang, H. Li, J. Sharp, X. Zhou, C. Uher, Chem. Mater. 23 (2011) 5256. [6] K. Kambe, H. Udono, J. Electron. Mater. 43 (2014) 2212. [7] G.R. Miller, C. Li, J. Phys. Chem. Solids 26 (1965) 173. [8] Y. Niwa, Y. Todaka, T. Masuda, T. Kawai, M. Umemoto, Mater. Trans. 50 (2009) 1725. [9] J.B. Whalen, J.V. Zaikina, R. Achey, R. Stillwell, H. Zhou, C.R. Wiebe, S.E. Latturner, Chem. Mater. 22 (2010) 1846. [10] N.F. Mott, H. Jones, The Theory of the Properties of Metals and Compounds, Clarendon Press, Oxford, 1936. [11] E. Ikenaga, M. Kobata, H. Matsuda, T. Sugiyama, H. Daimon, K. Kobayashi, J. Electron Spectrosc. Relat. Ph. 190 (2013) 180. [12] E. Nishibori, M. Takata, K. Kato, M. Sakata, Y. Kubota, S. Aoyagi, Y. Kuroiwa, M. Yamakata, N. Ikeda, Nucl. Instrum. Methods Phys. Res., Sect. A 467-468 (2001) 1045. [13] F. Izumi, K. Momma, Solid State Phenom. 130 (2007) 15. [14] P. Blaha, K. Schwarz, P.I. Sorantin, S.B. Trickey, Comput. Phys. Commun. 59 (1990) 399. [15] H. Ohashi, E. Ishiguro, H. Okumura, A. Hiraya, Y. Senba, K. Okada, N. Saito, I. Suzuki, K. Ueda, T. Ibuki, S. Nagaoka, I. Koyano, T. Ishikawa, Nucl. Instrum. Methods A 467–468 (2001) 533536. [16] J.M. Hill, D.G. Royce, C.S. Fadley, L.F. Wagner, Chem. Phys. Lett. 44 (1976) 225. [17] A. Jablonski, H. Ebel, Surf. Interface Anal. 11 (1988) 627. [18] A. Jablonski, Surf. Interface Anal. 15 (1990) 559. [19] S. Tanuma, C.J. Powell, D.R. Penn, Surf. Interface Anal. 21 (1994) 165. [20] S. Hüfner, Photoelectron Spectroscopy, third ed., Springer-Verlag, Berlin, 2003. [21] J.J. Yeh, I. Lindau, At. Data Nucl. Data Tables 32 (1985) 1. [22] M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70 (1998) 1039. [23] H.J. Im, M. Tsunekawa, T. Sakurada, M. Iwataki, K. Kawata, T. Watanabe, K. Takegahara, H. Miyazaki, M. Matsunami, T. Hajiri, S. Kimura, Phys. Rev. B: Condens. Matter 88 (2013) 205133. [24] H. Matsuura, Y. Nishino, U. Mizutani, S. Asano, J. Jpn. Inst. Met. 66 (2002) 767. [25] H. Kato, M. Kato, Y. Nishino, U. Mizutani, S. Asano, J. Jpn. Inst. Met. 65 (2001) 652.