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Synthesis and thermoelectric properties of microstructural Heusler Fe2VAl alloy
Journal of Alloys and Compounds 461 (2008) 423–426
Synthesis and thermoelectric properties of microstructural Heusler Fe2VAl alloy M. Mikami ∗ , A. Matsumoto, K. Kobayashi National Institute of Advanced Industrial Science and Technology, 2266-98 Anagahora, Shimoshidami, Moriyama, Nagoya, Aichi 463-8560, Japan Received 16 November 2006; accepted 4 July 2007 Available online 10 July 2007
Abstract A Fe2 VAl sintered alloy with fine microstructure was synthesized to evaluate the effect of grain size on thermoelectric properties. Fine powder was first prepared by mechanical alloying. Secondly, to suppress grain growth during heat treatment, the powder was sintered rapidly using pulsecurrent sintering. Bulk material consisting of 200–300 nm grains was obtained. Compared to the arc-melted sample consisting of 100–400 m grains, the thermal conductivity was reduced by phonon scattering at grain boundaries. The microstructural modification had little effect on the magnitude of the Seebeck coefficient. The reduction of electrical conductivity by the increase of the number of grain boundaries was less than that of thermal conductivity. Therefore, the thermoelectric figure of merit was improved. © 2007 Published by Elsevier B.V. Keywords: Heusler alloy; Mechanical alloying; Pulse-current sintering; Thermoelectric properties
1. Introduction A Heusler alloy, Fe2 VAl, is a promising candidate for thermoelectric power generation near room temperature because of its high thermoelectric power factor compared to a Bi–Te system [1–5]. In the Fe2 VAl system, the electrical conductivity and the Seebeck coefficient (S) are enhanced simultaneously by the off-stoichiometry of Al content or the element partial substitution, such as Si or Ge for the Al site and Ti for the V site [2–4]. The thermoelectric power factor reaches 5.9 × 10−3 W/m K2 at 300 K [4]. In addition, because of its high mechanical strength and excellent resistance to oxidation and corrosion, a durable thermoelectric module can be fabricated using this alloy. The thermoelectric figure of merit (Z) of this alloy is poor, however, because of its high thermal conductivity (κ): ca. 26 W/m K. The thermoelectric energy conversion efficiency is lower than that of state-of-the-art thermoelectric materials. Reduction of κ is therefore required for practical applications. Recently, Nishino et al. found that κ is reduced considerably by heavy element partial substitution such as Ge for the Al ∗
Corresponding author. Tel.: +81 52 736 7204; fax: +81 52 736 7202. E-mail address: [email protected] (M. Mikami).
0925-8388/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.jallcom.2007.07.004
site and Ir for the V site [4,6]. Their investigations were performed on an arc-melted specimen consisting of large grains of several hundred micrometers. For that reason, the effect of phonon scattering at grain boundaries, which also contributes to the reduction of κ, was not included in their results. In this study, we prepared a sintered Fe2 VAl0.9 Si0.1 sample. This composition exhibits the highest thermoelectric power factor in an n-type Fe2 VAl system [2]. Bulk material having a submicrometer-scale microstructure was synthesized using pulse-current sintering technique with fine powder prepared by mechanical alloying. The microstructural effects on thermoelectric properties were investigated in comparison to an arc-melted sample consisting of submillimeter-sized grains. 2. Experimental Using mechanical alloying (MA), Fe2 VAl0.9 Si0.1 powder was prepared, yielding finely pulverized and homogenized particles. Appropriate amounts of Fe (99.9%), V (99.9%), Fe–Al (99.9%), and Si (99.9%) powders were mixed and milled in a planetary ball mill with a 500-ml-capacity Cr steel pot and balls. In the milling system, the pot rotates on its axis against the direction of orbital motion and air is blown to cool the pot. The pot was back-filled with a purified Ar gas atmosphere at 500 Torr after creating a vacuum. A total mass of 400 g of 10-mm-diameter Cr steel balls was inserted with 30 g of mixed powder into the pot: MA was performed at 170 rpm for 200 h.
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M. Mikami et al. / Journal of Alloys and Compounds 461 (2008) 423–426 in an arc furnace under argon atmosphere. For homogeneity, the samples were turned over and melted several times. Then the samples were annealed at 1273 K for 48 h and at 673 K for 6 h under vacuum to obtain the homogenized and the Heusler-structured material. The sample was cut to appropriate shapes for measurements of thermoelectric properties. Crystallographic structure analysis was performed with X-ray diffractometry (XRD) using Cu K␣ radiation. The microstructure was observed using a scanning electron microscope (SEM). The value of ρ was measured in a He atmosphere between 350 and 750 K using a conventional four-probe DC technique. S was calculated from a plot of thermoelectric voltage against the temperature difference. Also, κ was evaluated from the density (D), thermal diffusivity (α), and heat capacity (Cp ) with the relationship κ = DαCp . Of those parameters, D was measured using the Archimedes method; α and Cp was estimated using the laser flash method.
3. Results and discussion
Fig. 1. XRD patterns (Cu K␣ radiation) diffracted from (a) the PCSFe2 VAl0.9 Si0.1 sample sintered at 1273 K, (b) at 1223 K, (c) at 1173 K, and (d) from the mechanically alloyed powder (200 h).
The MA powder was sintered rapidly using pulse-current sintering technique (PCS) to suppress grain growth during heat treatment and to obtain a fine microstructural bulk material. The prepared powder was put into a graphite mold and sintered at 1173–1273 K for 3 min in vacuum under uniaxial pressure of 40 MPa. A pulse current was applied during heat treatment. The heating and cooling rate was 100 K/min. The total PCS processing time was then less than 30 min, which was a very short operation compared to that of the conventional sintering process, which requires at least several hours. The obtained bulk samples with 10-mm-diameter and a thickness of 1.5–2.2 mm were used for measurement of κ and were cut into a bar shape with a typical size of (1.5–2.2 mm) × 2 mm × 9.5 mm for measurement of electrical resistivity (ρ) and S. For comparison, an arc-melted sample was synthesized in the same composition as the PCS sample. The MA powder was solidified using PCS and melted
The XRD measurement was performed on the MA powder and the PCS samples. Fig. 1d shows the XRD pattern, which indicates that the MA powder forms Fe based solid solution, although diffraction peaks tend to shift toward the lower 2θ angle compared to the pure bcc-Fe diffraction pattern because of the dispersion of V and Al. No trace of an impurity phase or secondary phase, such as the oxides and the remaining raw materials, was observed. After sintering, peaks from the Heusler-type (L21 ) structure appear in a lower 2θ angle such as 1 1 1 and 2 0 0, as shown in Fig. 1. This result indicates that the Heusler structural Fe2 VAl alloy is obtained even though the PCS operation time is very short. Scanning electron microscope images of the MA powder and the fracture transverse sections of PCS samples are shown in Fig. 2. The average particle size of MA powder is 7 m. Fig. 2a shows that these particles consist of agglomerated flakes. In the PCS sample sintered at 1173 K (Fig. 2b), the edge of grains is obscure compared to those of samples sintered at 1223
Fig. 2. SEM images of (a) the mechanically alloyed powder (200 h), (b) the fracture cross-sections of the PCS-Fe2 VAl0.9 Si0.1 sample sintered at 1173 K, (c) at 1223 K, and (d) at 1273 K.
M. Mikami et al. / Journal of Alloys and Compounds 461 (2008) 423–426
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Fig. 3. Relationship of thermal conductivity and sintering temperature in the PCS-Fe2 VAl0.9 Si0.1 sample. The dashed line indicates the value in the arc-melted sample.
Fig. 5. Temperature dependence of electrical resistivity in the PCSFe2 VAl0.9 Si0.1 sample sintered at 1273 K (), at 1223 K (♦), at 1273 K (), and in the arc-melted sample (䊉).
and 1273 K (Fig. 2c and d). Therefore, grain growth seems to proceed at a slow pace at 1173 K. The grain sizes increase concomitant with the increased sintering temperature and become about 100–200 and 200–300 nm, respectively, at sintering temperatures of 1223 and 1273 K. These grain sizes are much smaller than the arc-melted specimen consisting of large grains of several hundred micrometers. These results of XRD and SEM observation confirm that the Heusler Fe2 VAl alloy having submicron-sized microstructure was obtained using PCS with MA powder. Fig. 3 shows that the value of κ decreases concomitant with the decrease in the sintering temperature. The reduction of κ is assumed to be related to the decreased density and the increased number of grain boundaries. Fig. 4 shows that the density decreases along with the decrease in the sintering temperature, which indicates that the sintered sample contains vacancies that prevent thermal conduction, especially in the sample sintered at lower temperatures. Grain boundaries, which also prevent thermal conduction by phonon scattering, increase numerically with the decrease in the sintering temperature because of the reduction of grain size, as mentioned above. We were unable
to clarify the main reason for reduction of κ. However, κ of the sample sintered at 1273 K, which is almost fully densified, is much lower than that of the arc-melted sample consisting of grains of 100–400 m. Therefore, we propose that the grain size reduction is effective for reduction of κ. Fig. 5 represents the temperature dependence of ρ. The magnitude of ρ decreases with the increase in the sintering temperature. We propose that this result is also related to the change in the samples’ microstructure. One reason for the reduction of ρ is that the increase in the grain size, as mentioned above, reduces the number of grain boundaries, at which additional energy is required for carrier travelling. The second is that the increased density, as shown in Fig. 4, contributes to reduction of ρ. It is noteworthy that the magnitude of ρ in the arc-melted sample is greater than in the sintered sample at temperatures greater than 650 K. Because the sample was exposed to the high temperature by arc melting, the composition might change slightly by evaporation or oxidation of the specific element such as Al, which has the lowest vapor pressure among elements containing the Fe2 VAl0.9 Si0.1 alloy. Reportedly, the small deviation of
Fig. 4. Relationship of the density and sintering temperature in the PCSFe2 VAl0.9 Si0.1 sample. The dashed line indicates the value in the arc-melted sample.
Fig. 6. Temperature dependence of the Seebeck coefficient in the PCSFe2 VAl0.9 Si0.1 sample sintered at 1273 K (), at 1223 K (♦), at 1273 K (), and in the arc-melted sample (䊉).
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Fig. 7. Temperature dependence of power factor in the PCS-Fe2 VAl0.9 Si0.1 sample sintered at 1273 K (), at 1223 K (♦), at 1273 K (), and in the arc-melted sample (䊉).
Fig. 6 represents the temperature dependence of S. Unlike κ and ρ, the value of S is almost equal in every sample, although some variations are apparent, especially at lower temperatures. For that reason, the change in the microstructure has little effect on the S value. The absolute value of S increases with the decrease of the temperature and reaches 120–140 V/K at 350 K. The thermoelectric power factor (PF = S2 /ρ) was calculated from measured ρ and S values (Fig. 7). The PF of each sample increases with decreasing temperature. The magnitude of PF is enhanced by the increased sintering temperature because of the reduction of ρ. The PF of the PCS sample sintered at 1273 K is almost identical to that of the arc-melted sample, although the grain size of the PCS samples is much smaller than that of the arc-melted sample. Finally, Z was calculated from measured thermoelectric properties (Fig. 8). Because the modification of microstructure had little effect on the S value and the reduction of κ was greater than the increase of ρ, Z was improved. 4. Conclusions A Heusler Fe2 VAl alloy having submicrometer-sized microstructure was obtained using PCS with fine powder prepared by MA. The PF of the sintered alloy consisting of grains of 200–300 nm was comparable to the arc-melted sample consisting of grains of 100–400 m. However, the value of κ of the sintered alloy was much smaller than that of the arc-melted sample because of phonon scattering at grain boundaries. Therefore, the modification of microstructure improved the thermoelectric figure of merit. References
Fig. 8. Relationship of the thermoelectric figure of merit and sintering temperature in the PCS-Fe2 VAl0.9 Si0.1 sample. The dashed line indicates the value in the arc-melted sample.
composition influences the transport properties in the Fe2 VAl system [1,4]. Consequently, we presume that the slight difference in composition between the sintered and the arc-melted sample causes the change of the temperature dependence of ρ.
[1] Y. Nishino, Mater. Trans. 42 (2001) 902–910. [2] H. Kato, M. Kato, Y. Nishino, U. Mizutani, S. Asano, J. Jpn. Inst. Metals 65 (2001) 652–656. [3] H. Matsuura, Y. Nishino, U. Mizutani, S. Asano, J. Jpn. Inst. Metals 66 (2002) 767–771. [4] Y. Nishino, S. Deguchi, U. Mizutani, Phys. Rev. B 74 (2006), 115115-1-6. [5] Y. Nishino, Phys. Rev. B 63 (2001), 233303-1-4. [6] The data were presented in the domestic conference of 2005 Fall Annual Meeting of the Japan Institute of Metals.
Synthesis and thermoelectric properties of microstructural Heusler Fe2VAl alloy M. Mikami ∗ , A. Matsumoto, K. Kobayashi National Institute of Advanced Industrial Science and Technology, 2266-98 Anagahora, Shimoshidami, Moriyama, Nagoya, Aichi 463-8560, Japan Received 16 November 2006; accepted 4 July 2007 Available online 10 July 2007
Abstract A Fe2 VAl sintered alloy with fine microstructure was synthesized to evaluate the effect of grain size on thermoelectric properties. Fine powder was first prepared by mechanical alloying. Secondly, to suppress grain growth during heat treatment, the powder was sintered rapidly using pulsecurrent sintering. Bulk material consisting of 200–300 nm grains was obtained. Compared to the arc-melted sample consisting of 100–400 m grains, the thermal conductivity was reduced by phonon scattering at grain boundaries. The microstructural modification had little effect on the magnitude of the Seebeck coefficient. The reduction of electrical conductivity by the increase of the number of grain boundaries was less than that of thermal conductivity. Therefore, the thermoelectric figure of merit was improved. © 2007 Published by Elsevier B.V. Keywords: Heusler alloy; Mechanical alloying; Pulse-current sintering; Thermoelectric properties
1. Introduction A Heusler alloy, Fe2 VAl, is a promising candidate for thermoelectric power generation near room temperature because of its high thermoelectric power factor compared to a Bi–Te system [1–5]. In the Fe2 VAl system, the electrical conductivity and the Seebeck coefficient (S) are enhanced simultaneously by the off-stoichiometry of Al content or the element partial substitution, such as Si or Ge for the Al site and Ti for the V site [2–4]. The thermoelectric power factor reaches 5.9 × 10−3 W/m K2 at 300 K [4]. In addition, because of its high mechanical strength and excellent resistance to oxidation and corrosion, a durable thermoelectric module can be fabricated using this alloy. The thermoelectric figure of merit (Z) of this alloy is poor, however, because of its high thermal conductivity (κ): ca. 26 W/m K. The thermoelectric energy conversion efficiency is lower than that of state-of-the-art thermoelectric materials. Reduction of κ is therefore required for practical applications. Recently, Nishino et al. found that κ is reduced considerably by heavy element partial substitution such as Ge for the Al ∗
Corresponding author. Tel.: +81 52 736 7204; fax: +81 52 736 7202. E-mail address: [email protected] (M. Mikami).
0925-8388/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.jallcom.2007.07.004
site and Ir for the V site [4,6]. Their investigations were performed on an arc-melted specimen consisting of large grains of several hundred micrometers. For that reason, the effect of phonon scattering at grain boundaries, which also contributes to the reduction of κ, was not included in their results. In this study, we prepared a sintered Fe2 VAl0.9 Si0.1 sample. This composition exhibits the highest thermoelectric power factor in an n-type Fe2 VAl system [2]. Bulk material having a submicrometer-scale microstructure was synthesized using pulse-current sintering technique with fine powder prepared by mechanical alloying. The microstructural effects on thermoelectric properties were investigated in comparison to an arc-melted sample consisting of submillimeter-sized grains. 2. Experimental Using mechanical alloying (MA), Fe2 VAl0.9 Si0.1 powder was prepared, yielding finely pulverized and homogenized particles. Appropriate amounts of Fe (99.9%), V (99.9%), Fe–Al (99.9%), and Si (99.9%) powders were mixed and milled in a planetary ball mill with a 500-ml-capacity Cr steel pot and balls. In the milling system, the pot rotates on its axis against the direction of orbital motion and air is blown to cool the pot. The pot was back-filled with a purified Ar gas atmosphere at 500 Torr after creating a vacuum. A total mass of 400 g of 10-mm-diameter Cr steel balls was inserted with 30 g of mixed powder into the pot: MA was performed at 170 rpm for 200 h.
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M. Mikami et al. / Journal of Alloys and Compounds 461 (2008) 423–426 in an arc furnace under argon atmosphere. For homogeneity, the samples were turned over and melted several times. Then the samples were annealed at 1273 K for 48 h and at 673 K for 6 h under vacuum to obtain the homogenized and the Heusler-structured material. The sample was cut to appropriate shapes for measurements of thermoelectric properties. Crystallographic structure analysis was performed with X-ray diffractometry (XRD) using Cu K␣ radiation. The microstructure was observed using a scanning electron microscope (SEM). The value of ρ was measured in a He atmosphere between 350 and 750 K using a conventional four-probe DC technique. S was calculated from a plot of thermoelectric voltage against the temperature difference. Also, κ was evaluated from the density (D), thermal diffusivity (α), and heat capacity (Cp ) with the relationship κ = DαCp . Of those parameters, D was measured using the Archimedes method; α and Cp was estimated using the laser flash method.
3. Results and discussion
Fig. 1. XRD patterns (Cu K␣ radiation) diffracted from (a) the PCSFe2 VAl0.9 Si0.1 sample sintered at 1273 K, (b) at 1223 K, (c) at 1173 K, and (d) from the mechanically alloyed powder (200 h).
The MA powder was sintered rapidly using pulse-current sintering technique (PCS) to suppress grain growth during heat treatment and to obtain a fine microstructural bulk material. The prepared powder was put into a graphite mold and sintered at 1173–1273 K for 3 min in vacuum under uniaxial pressure of 40 MPa. A pulse current was applied during heat treatment. The heating and cooling rate was 100 K/min. The total PCS processing time was then less than 30 min, which was a very short operation compared to that of the conventional sintering process, which requires at least several hours. The obtained bulk samples with 10-mm-diameter and a thickness of 1.5–2.2 mm were used for measurement of κ and were cut into a bar shape with a typical size of (1.5–2.2 mm) × 2 mm × 9.5 mm for measurement of electrical resistivity (ρ) and S. For comparison, an arc-melted sample was synthesized in the same composition as the PCS sample. The MA powder was solidified using PCS and melted
The XRD measurement was performed on the MA powder and the PCS samples. Fig. 1d shows the XRD pattern, which indicates that the MA powder forms Fe based solid solution, although diffraction peaks tend to shift toward the lower 2θ angle compared to the pure bcc-Fe diffraction pattern because of the dispersion of V and Al. No trace of an impurity phase or secondary phase, such as the oxides and the remaining raw materials, was observed. After sintering, peaks from the Heusler-type (L21 ) structure appear in a lower 2θ angle such as 1 1 1 and 2 0 0, as shown in Fig. 1. This result indicates that the Heusler structural Fe2 VAl alloy is obtained even though the PCS operation time is very short. Scanning electron microscope images of the MA powder and the fracture transverse sections of PCS samples are shown in Fig. 2. The average particle size of MA powder is 7 m. Fig. 2a shows that these particles consist of agglomerated flakes. In the PCS sample sintered at 1173 K (Fig. 2b), the edge of grains is obscure compared to those of samples sintered at 1223
Fig. 2. SEM images of (a) the mechanically alloyed powder (200 h), (b) the fracture cross-sections of the PCS-Fe2 VAl0.9 Si0.1 sample sintered at 1173 K, (c) at 1223 K, and (d) at 1273 K.
M. Mikami et al. / Journal of Alloys and Compounds 461 (2008) 423–426
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Fig. 3. Relationship of thermal conductivity and sintering temperature in the PCS-Fe2 VAl0.9 Si0.1 sample. The dashed line indicates the value in the arc-melted sample.
Fig. 5. Temperature dependence of electrical resistivity in the PCSFe2 VAl0.9 Si0.1 sample sintered at 1273 K (), at 1223 K (♦), at 1273 K (), and in the arc-melted sample (䊉).
and 1273 K (Fig. 2c and d). Therefore, grain growth seems to proceed at a slow pace at 1173 K. The grain sizes increase concomitant with the increased sintering temperature and become about 100–200 and 200–300 nm, respectively, at sintering temperatures of 1223 and 1273 K. These grain sizes are much smaller than the arc-melted specimen consisting of large grains of several hundred micrometers. These results of XRD and SEM observation confirm that the Heusler Fe2 VAl alloy having submicron-sized microstructure was obtained using PCS with MA powder. Fig. 3 shows that the value of κ decreases concomitant with the decrease in the sintering temperature. The reduction of κ is assumed to be related to the decreased density and the increased number of grain boundaries. Fig. 4 shows that the density decreases along with the decrease in the sintering temperature, which indicates that the sintered sample contains vacancies that prevent thermal conduction, especially in the sample sintered at lower temperatures. Grain boundaries, which also prevent thermal conduction by phonon scattering, increase numerically with the decrease in the sintering temperature because of the reduction of grain size, as mentioned above. We were unable
to clarify the main reason for reduction of κ. However, κ of the sample sintered at 1273 K, which is almost fully densified, is much lower than that of the arc-melted sample consisting of grains of 100–400 m. Therefore, we propose that the grain size reduction is effective for reduction of κ. Fig. 5 represents the temperature dependence of ρ. The magnitude of ρ decreases with the increase in the sintering temperature. We propose that this result is also related to the change in the samples’ microstructure. One reason for the reduction of ρ is that the increase in the grain size, as mentioned above, reduces the number of grain boundaries, at which additional energy is required for carrier travelling. The second is that the increased density, as shown in Fig. 4, contributes to reduction of ρ. It is noteworthy that the magnitude of ρ in the arc-melted sample is greater than in the sintered sample at temperatures greater than 650 K. Because the sample was exposed to the high temperature by arc melting, the composition might change slightly by evaporation or oxidation of the specific element such as Al, which has the lowest vapor pressure among elements containing the Fe2 VAl0.9 Si0.1 alloy. Reportedly, the small deviation of
Fig. 4. Relationship of the density and sintering temperature in the PCSFe2 VAl0.9 Si0.1 sample. The dashed line indicates the value in the arc-melted sample.
Fig. 6. Temperature dependence of the Seebeck coefficient in the PCSFe2 VAl0.9 Si0.1 sample sintered at 1273 K (), at 1223 K (♦), at 1273 K (), and in the arc-melted sample (䊉).
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Fig. 7. Temperature dependence of power factor in the PCS-Fe2 VAl0.9 Si0.1 sample sintered at 1273 K (), at 1223 K (♦), at 1273 K (), and in the arc-melted sample (䊉).
Fig. 6 represents the temperature dependence of S. Unlike κ and ρ, the value of S is almost equal in every sample, although some variations are apparent, especially at lower temperatures. For that reason, the change in the microstructure has little effect on the S value. The absolute value of S increases with the decrease of the temperature and reaches 120–140 V/K at 350 K. The thermoelectric power factor (PF = S2 /ρ) was calculated from measured ρ and S values (Fig. 7). The PF of each sample increases with decreasing temperature. The magnitude of PF is enhanced by the increased sintering temperature because of the reduction of ρ. The PF of the PCS sample sintered at 1273 K is almost identical to that of the arc-melted sample, although the grain size of the PCS samples is much smaller than that of the arc-melted sample. Finally, Z was calculated from measured thermoelectric properties (Fig. 8). Because the modification of microstructure had little effect on the S value and the reduction of κ was greater than the increase of ρ, Z was improved. 4. Conclusions A Heusler Fe2 VAl alloy having submicrometer-sized microstructure was obtained using PCS with fine powder prepared by MA. The PF of the sintered alloy consisting of grains of 200–300 nm was comparable to the arc-melted sample consisting of grains of 100–400 m. However, the value of κ of the sintered alloy was much smaller than that of the arc-melted sample because of phonon scattering at grain boundaries. Therefore, the modification of microstructure improved the thermoelectric figure of merit. References
Fig. 8. Relationship of the thermoelectric figure of merit and sintering temperature in the PCS-Fe2 VAl0.9 Si0.1 sample. The dashed line indicates the value in the arc-melted sample.
composition influences the transport properties in the Fe2 VAl system [1,4]. Consequently, we presume that the slight difference in composition between the sintered and the arc-melted sample causes the change of the temperature dependence of ρ.
[1] Y. Nishino, Mater. Trans. 42 (2001) 902–910. [2] H. Kato, M. Kato, Y. Nishino, U. Mizutani, S. Asano, J. Jpn. Inst. Metals 65 (2001) 652–656. [3] H. Matsuura, Y. Nishino, U. Mizutani, S. Asano, J. Jpn. Inst. Metals 66 (2002) 767–771. [4] Y. Nishino, S. Deguchi, U. Mizutani, Phys. Rev. B 74 (2006), 115115-1-6. [5] Y. Nishino, Phys. Rev. B 63 (2001), 233303-1-4. [6] The data were presented in the domestic conference of 2005 Fall Annual Meeting of the Japan Institute of Metals.