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Substitute effects of Ga on AlB2-type superconductor CaAlSi
Physica C 406 (2004) 15–19 www.elsevier.com/locate/physc
Substitute effects of Ga on AlB2-type superconductor CaAlSi H.H. Sung, W.H. Lee
*
Department of Physics, National Chung Cheng University, Ming-Hsiung, Chia-Yi 621, Taiwan, ROC Received 9 January 2003; received in revised form 12 February 2004; accepted 16 February 2004 Available online 16 April 2004
Abstract We present the results of lattice parameters at room temperature and the static magnetic susceptibility between 1.8 and 9.0 K for a series of eleven polycrystalline Ca(Al1x Gax )Si samples with x ¼ 0:0–1.0. Variation of the lattice parameters reveals that there is a movement for c to increase, for a and v to decrease, linearly with increasing x. The superconducting phase diagram of Ca(Al1x Gax )Si shows that there is an explicit minimum Tc close to x ¼ 0:7. This demonstrates that the superconducting transition temperature of the pseudo-binary system Ca(Al1x Gax )Si is not a monotonic function of the lattice constants irrespective of the same valences of Ga and Al. 2004 Elsevier B.V. All rights reserved. PACS: 61.66.Fn; 74.70.Ad; 74.62.)c; 74.62.Dh Keywords: AlB2 -type structure; Superconductivity; Lattice parameter; Ca(Al1x Gax )Si
1. Introduction Research on the superconducting materials with AlB2 -type structure has been of current interest since the discovery of bulk superconductivity at 39 K in magnesium diboride, MgB2 [1]. Sr(Ga0:37 , Si0:63 )2 [2], Ca(Al0:5 , Si0:5 )2 [3], MI (MII0:5 , Si0:5 )2 (MI ¼ Sr and Ba, MII ¼ Al and Ga) [4], A(Ga2x Six ) (A ¼ Ca, Sr and Ba) [5,6] A(Al2x Six ) (A ¼ Ca, Sr) [7,8], Y2 PdGe3 [9–11] and Y(Pt0:5 Ge1:5 ) [12] are this class of pseudo-binary intermetallic compounds which have been discovered recently. Among these members of pseudo-binary supercon-
*
Corresponding author. Tel.: +886-5-272-0586; fax: +886-5272-0587. E-mail address: [email protected] (W.H. Lee).
ductors, CaAlSi has the highest superconducting transition temperature Tc 7:8 K. As reported earlier, the superconducting phase diagram of pseudo-binary systems, SrGax Si2x and CaAl2x Six , showed a non-monotonic Tc dependence of x. Because of the different valences of Ga (or Al) and Si, which results in a continuous shift of Fermi energy with the change of x, the rigid band model is not sufficient to account for the observations. It was suggested that the electronic structures of this class compounds should depend on more than just the valence electron density and the lattice parameters. The main aim of this study by Ga substitution at the Al-site in the CaAlSi system is to give further understanding of the effects of alloying as well as the expansion on the superconducting behavior of CaAlSi because the larger Gaþ3 -ions replace the smaller Alþ3 -ions in honeycomb layers.
0921-4534/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.02.175
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H.H. Sung, W.H. Lee / Physica C 406 (2004) 15–19
By considering (1) the size factor, (2) the electrochemical factor and (3) the relative valence effect of the two elements Al and Ga, it is believed that the extensive solid solutions are expected according to the Hume–Rothery theory of alloy phase formation [13]. 2. Experimental All samples were synthesized by arc melting together appropriate amounts of the components on a water-cooled Cu hearth in 1 atm of high-purity argon gas in which a Zr button used as an oxygen getter had been previously arc melted. The >2N purity Ca, 5N purity Al, 5N purity gallium and 6N purity Si were purchased from Alfa Aesar, a Johnson Matthey company. Due to sufficiently low vapor pressures of these elements at the melting temperature of the pseudo-binary compounds, evaporation losses can be neglected. A microcomputer controlled MXP3 diffractometer equipped with copper target and graphite monochromator for CuKa radiation was used to get the powder Xray diffraction (XRD) patterns at a scan rate of 0.4/min. The refined lattice parameters of the unit cell were determined from powder X-ray diffraction patterns by the method of least squares. Magnetic data were carried out in a quantum design SQUID magnetometer. The temperature dependence of magnetization was measured using zero-field cool-
Fig. 1. Room temperature powder X-ray difffraction patterns of Ca(Al1x Gax )Si (x ¼ 0, 0.2, 0.4, 0.6, 0.8 and 1.0) using CuKa radiation.
Table 1 Lattice parameters and Tc (10–90% values) in the series Ca(Al1x Gax )Si Composition ðxÞ a (A) c (A) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
4.184(10) 4.182(9) 4.177(8) 4.170(10) 4.159(9) 4.152(8) 4.147(8) 4.135(9) 4.128(8) 4.119(9) 4.118(8)
4.375(20) 4.392(20) 4.384(9) 4.388(9) 4.390(15) 4.402(7) 4.405(8) 4.414(9) 4.421(7) 4.414(20) 4.438(20)
3 ) v (A
Tc (K)
66.32(21) 66.52(22) 66.22(9) 66.09(8) 65.77(15) 65.71(7) 65.59(9) 65.35(8) 65.22(8) 64.85(24) 64.98(14)
6.53–7.13 6.16–6.54 5.30–5.60 4.10–4.78 3.67–4.51 3.15–3.73 3.01–3.45 2.40–3.0 2.80–3.24 2.82–3.34 3.20–4.05
The number given in the parentheses is the standard deviation in the least significant digit of the reported value.
H.H. Sung, W.H. Lee / Physica C 406 (2004) 15–19
17
ing (ZFC) process, i.e., the sample was initially cooled in zero field (actually 5 · 103 Oe) to 1.8 K and subsequently a small field (10 Oe) was then applied, and the ZFC curve was taken as a function of increasing temperature up to T > Tc . The transition width will be taken as 10–90% values and the midpoint of the transition will be taken as the bulk superconducting transition temperature Tc .
3. Results and discussion The observed powder X-ray diffraction patterns at room temperature for seven samples in the series Ca(Al1x Gax )Si with x ¼ 0:0, 0.2, 0.4, 0.6, 0.8 and 1.0 are shown in Fig. 1. The sharp peaks of each observed pattern can be all indexed in a hexagonal structure with space group P6/mmm. Some small amount of unindexed impurity phases of CaAl4x Six and CaAl2 Si2 are also observed, as previously pointed out by Imai et al. [3]. The refined lattice parameters a, c and the unit cell volume v are listed in Table 1 and replotted as a function of Ga concentration in Fig. 2(a) and (b). It was surprising that the crystallographic parameter c (a) increases (decreases) linearly with increasing x since earlier report showed that the lattice parameters (a and c) of the hexagonal unit cell of CaAl2x Six decrease with silicon content x due to the smaller Si-ions occupied the sites within the honeycomb planes. However, in Sr(Gax Si2x ) system [6], there was also an overall tendency for c to increase and for a to decrease with increasing x. Considering the valence of the Ga atom and its corresponding size of ionic radius, it is speculated that the substitutional replacements for Al atoms may serve to change the number of conduction electrons in the honeycomb layers which results in the decrease of lattice parameter a as well as the unit cell volume v. Though the origin of these anomalies observed in Ca(Al1x Gax )Si and Sr(Gax Si2x ) is not clearly known at present, it is expected that this abnormal phenomenon may also be reflected in the intrinsic electronic structure. Fig. 3(a) and (b) display the temperature dependence of the zero-field cooled magnetization for the eleven samples (x ¼ 0:0, 0.1, 0.2, 0.3, 0.4,
Fig. 2. Variation of lattice parameters vs Ga concentration in the series Ca(Al1x Gax )Si. (a) a, c vs x and (b) v vs x.
0.5, 0.6, 0.7, 0.8, 0.9 and 1.0) in the series Ca(Al1x Gax )Si measured in a field of 10 Oe between 1.8 and 9.0 K. All measurements were performed on bulk samples of about 0.1 g mass. From Fig. 3(a) and (b), it is noted that the shielding curves for constant field shift toward lower temperature with increasing Ga concentration up to x ¼ 0:7 then backward higher temperature. The ZFC curves for the eleven samples show sharp transition and reach saturation at the lower temperature, which is an indication of the sample homogeneity. In addition, these samples also show
18
H.H. Sung, W.H. Lee / Physica C 406 (2004) 15–19
Fig. 4. Superconducting transition temperature Tc as a function of Ga constituent in the series Ca(Al1x Gax )Si. The error bars attached to the data points measure the transition width (10– 90% values).
Fig. 3. Zero-field cooling magnetization data for eleven samples in the series Ca(Al1x Gax )Si. (a) x ¼ 0:0, 0.1, 0.2, 0.3, 0.4 ad 0.5 (b) x ¼ 0:6, 0.7, 0.8, 0.9 and 1.0.
large shielding signals, by comparison to the ideal value of 1=4p for a long cylinder, with apparent volume fractions above 100%. This phenomenon can be explained in terms of the shielding current and the estimated geometrical demagnetization factor n 0:5 for these two samples CaAlSi and Ca(Al0:9 Ga0:1 )Si because of their irregular shapes. The superconducting transition width (10–90% values) data thus obtained in the series Ca(Al1x Gax )Si are reported in Table 1. We note the transition point value obtained by magnetic measurement is slightly lower than the zero resistance temperature. For example, the zero resistance temperature for CaAlSi is about 7.6 K and the 10–90% value of magnetic transition is 6.53– 7.13 K. This is due to the phenomenon of surface
superconductivity in intermetallic compound [14,15]. Fig. 4 displays the superconducting phase diagram of Ca(Al1x Gax )Si. The error bars attached to the data in Fig. 4 express the width of the transitions as estimated from 90% to 10% magnetic change at Tc . As shown in Fig. 4, the Tc value clearly slides down as x increases from x ¼ 0 to around 0.7 then climbs up to x ¼ 1:0. This indicates that the superconducting transition temperature of the pseudo-binary system Ca(Al1x Gax )Si is not a monotonic function of the lattice constants a, c, v or the ratio c=a. The change in Tc may imply a change of the density of states at the Fermi energy. Therefore, band structure studies are necessary to gain more information regarding the relationship between the electronic structure and the superconducting phase diagram of Ca(Al1x Gax )Si.
4. Conclusion We have synthesized and studied the pseudobinary intermetallic compounds, Ca(Al1x Gax )Si, which are isostructural to the non-copper-oxide bulk superconductor MgB2 with Tc 39 K. In spite
H.H. Sung, W.H. Lee / Physica C 406 (2004) 15–19
of the larger size of Gaþ3 than Alþ3 , the lattice constant a and the unit cell volume v decrease with the increasing Ga concentration in the series Ca(Al1x Gax )Si, which is abnormal to the Vegard’s law. Both the lattice variations and the change of the average valence due to the Al, Ga and Si atoms arranged in chemically disordered honeycomb layers and atoms Ca interacted between them should affect the superconducting properties in these compounds Ca(Al1x Gax )Si.
Acknowledgements This work was supported by National Science Council of Republic of China under contract no. NSC92-2112-M194-010.
References [1] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akimitsu, Nature (London) 410 (2001) 63.
19
[2] M. Imai, E. Abe, J. Ye, K. Nishida, T. Kimura, K. Honma, H. Abe, H. Kitazawa, Phys. Rev. Lett. 87 (2001) 077003. [3] M. Imai, K. Nishida, T. Kimura, H. Abe, Appl. Phys. Lett. 80 (2002) 1019. [4] M. Imai, K. Nishida, T. Kimura, H. Kitazawa, H. Abe, H. Kit^ o, K. Yoshii, Physica C 382 (2002) 361. [5] M. Imai, K. Nishida, T. Kimura, H. Abe, Physica C 377 (2002) 96. [6] R.L. Meng, B. Lorenz, Y.S. Wang, J. Cmaidalka, Y.Y. Sun, Y.Y. Xue, J.K. Meen, C.W. Chu, Physica C 382 (2002) 113. [7] B. Lorez, J. Lenzi, J. Camaidalka, R.L. Meng, Y.Y. Sun, Y.Y. Xue, C.W. Chu, Physica C 383 (2002) 191. [8] B. Lorenz, J. Cmaidalka, R.L. Meng, C.W. Chu, Phys. Rev. B 68 (2003) 014512. [9] S. Majumdar, E.V. Sampathkumaran, Phys. Rev. B 63 (2001) 172407. [10] E.V. Sampathkumaran, S. Majumdar, W. Schneider, S.L. Molodtsov, C. Laubschat, Physica B 312–313 (2002) 152. [11] S. Takano, Y. Iriyama, Y. Kimishima, M. Uehara, Physica C 383 (2003) 295. [12] H. Kit^ o, Y. Takano, K. Togano, Physica C 377 (2002) 185. [13] L.H. Bennett (Ed.), Theory of alloy phase formation, Proceedings of a symposium at the 108th AIME Annual Meeting, New Orleans, LA, 1979. [14] D. Saint James, P.G. de Gennes, Phys. Lett. 7 (1963) 306. [15] J.G. Park, Phys. Rev. Lett. 16 (1966) 1196.
Substitute effects of Ga on AlB2-type superconductor CaAlSi H.H. Sung, W.H. Lee
*
Department of Physics, National Chung Cheng University, Ming-Hsiung, Chia-Yi 621, Taiwan, ROC Received 9 January 2003; received in revised form 12 February 2004; accepted 16 February 2004 Available online 16 April 2004
Abstract We present the results of lattice parameters at room temperature and the static magnetic susceptibility between 1.8 and 9.0 K for a series of eleven polycrystalline Ca(Al1x Gax )Si samples with x ¼ 0:0–1.0. Variation of the lattice parameters reveals that there is a movement for c to increase, for a and v to decrease, linearly with increasing x. The superconducting phase diagram of Ca(Al1x Gax )Si shows that there is an explicit minimum Tc close to x ¼ 0:7. This demonstrates that the superconducting transition temperature of the pseudo-binary system Ca(Al1x Gax )Si is not a monotonic function of the lattice constants irrespective of the same valences of Ga and Al. 2004 Elsevier B.V. All rights reserved. PACS: 61.66.Fn; 74.70.Ad; 74.62.)c; 74.62.Dh Keywords: AlB2 -type structure; Superconductivity; Lattice parameter; Ca(Al1x Gax )Si
1. Introduction Research on the superconducting materials with AlB2 -type structure has been of current interest since the discovery of bulk superconductivity at 39 K in magnesium diboride, MgB2 [1]. Sr(Ga0:37 , Si0:63 )2 [2], Ca(Al0:5 , Si0:5 )2 [3], MI (MII0:5 , Si0:5 )2 (MI ¼ Sr and Ba, MII ¼ Al and Ga) [4], A(Ga2x Six ) (A ¼ Ca, Sr and Ba) [5,6] A(Al2x Six ) (A ¼ Ca, Sr) [7,8], Y2 PdGe3 [9–11] and Y(Pt0:5 Ge1:5 ) [12] are this class of pseudo-binary intermetallic compounds which have been discovered recently. Among these members of pseudo-binary supercon-
*
Corresponding author. Tel.: +886-5-272-0586; fax: +886-5272-0587. E-mail address: [email protected] (W.H. Lee).
ductors, CaAlSi has the highest superconducting transition temperature Tc 7:8 K. As reported earlier, the superconducting phase diagram of pseudo-binary systems, SrGax Si2x and CaAl2x Six , showed a non-monotonic Tc dependence of x. Because of the different valences of Ga (or Al) and Si, which results in a continuous shift of Fermi energy with the change of x, the rigid band model is not sufficient to account for the observations. It was suggested that the electronic structures of this class compounds should depend on more than just the valence electron density and the lattice parameters. The main aim of this study by Ga substitution at the Al-site in the CaAlSi system is to give further understanding of the effects of alloying as well as the expansion on the superconducting behavior of CaAlSi because the larger Gaþ3 -ions replace the smaller Alþ3 -ions in honeycomb layers.
0921-4534/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.02.175
16
H.H. Sung, W.H. Lee / Physica C 406 (2004) 15–19
By considering (1) the size factor, (2) the electrochemical factor and (3) the relative valence effect of the two elements Al and Ga, it is believed that the extensive solid solutions are expected according to the Hume–Rothery theory of alloy phase formation [13]. 2. Experimental All samples were synthesized by arc melting together appropriate amounts of the components on a water-cooled Cu hearth in 1 atm of high-purity argon gas in which a Zr button used as an oxygen getter had been previously arc melted. The >2N purity Ca, 5N purity Al, 5N purity gallium and 6N purity Si were purchased from Alfa Aesar, a Johnson Matthey company. Due to sufficiently low vapor pressures of these elements at the melting temperature of the pseudo-binary compounds, evaporation losses can be neglected. A microcomputer controlled MXP3 diffractometer equipped with copper target and graphite monochromator for CuKa radiation was used to get the powder Xray diffraction (XRD) patterns at a scan rate of 0.4/min. The refined lattice parameters of the unit cell were determined from powder X-ray diffraction patterns by the method of least squares. Magnetic data were carried out in a quantum design SQUID magnetometer. The temperature dependence of magnetization was measured using zero-field cool-
Fig. 1. Room temperature powder X-ray difffraction patterns of Ca(Al1x Gax )Si (x ¼ 0, 0.2, 0.4, 0.6, 0.8 and 1.0) using CuKa radiation.
Table 1 Lattice parameters and Tc (10–90% values) in the series Ca(Al1x Gax )Si Composition ðxÞ a (A) c (A) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
4.184(10) 4.182(9) 4.177(8) 4.170(10) 4.159(9) 4.152(8) 4.147(8) 4.135(9) 4.128(8) 4.119(9) 4.118(8)
4.375(20) 4.392(20) 4.384(9) 4.388(9) 4.390(15) 4.402(7) 4.405(8) 4.414(9) 4.421(7) 4.414(20) 4.438(20)
3 ) v (A
Tc (K)
66.32(21) 66.52(22) 66.22(9) 66.09(8) 65.77(15) 65.71(7) 65.59(9) 65.35(8) 65.22(8) 64.85(24) 64.98(14)
6.53–7.13 6.16–6.54 5.30–5.60 4.10–4.78 3.67–4.51 3.15–3.73 3.01–3.45 2.40–3.0 2.80–3.24 2.82–3.34 3.20–4.05
The number given in the parentheses is the standard deviation in the least significant digit of the reported value.
H.H. Sung, W.H. Lee / Physica C 406 (2004) 15–19
17
ing (ZFC) process, i.e., the sample was initially cooled in zero field (actually 5 · 103 Oe) to 1.8 K and subsequently a small field (10 Oe) was then applied, and the ZFC curve was taken as a function of increasing temperature up to T > Tc . The transition width will be taken as 10–90% values and the midpoint of the transition will be taken as the bulk superconducting transition temperature Tc .
3. Results and discussion The observed powder X-ray diffraction patterns at room temperature for seven samples in the series Ca(Al1x Gax )Si with x ¼ 0:0, 0.2, 0.4, 0.6, 0.8 and 1.0 are shown in Fig. 1. The sharp peaks of each observed pattern can be all indexed in a hexagonal structure with space group P6/mmm. Some small amount of unindexed impurity phases of CaAl4x Six and CaAl2 Si2 are also observed, as previously pointed out by Imai et al. [3]. The refined lattice parameters a, c and the unit cell volume v are listed in Table 1 and replotted as a function of Ga concentration in Fig. 2(a) and (b). It was surprising that the crystallographic parameter c (a) increases (decreases) linearly with increasing x since earlier report showed that the lattice parameters (a and c) of the hexagonal unit cell of CaAl2x Six decrease with silicon content x due to the smaller Si-ions occupied the sites within the honeycomb planes. However, in Sr(Gax Si2x ) system [6], there was also an overall tendency for c to increase and for a to decrease with increasing x. Considering the valence of the Ga atom and its corresponding size of ionic radius, it is speculated that the substitutional replacements for Al atoms may serve to change the number of conduction electrons in the honeycomb layers which results in the decrease of lattice parameter a as well as the unit cell volume v. Though the origin of these anomalies observed in Ca(Al1x Gax )Si and Sr(Gax Si2x ) is not clearly known at present, it is expected that this abnormal phenomenon may also be reflected in the intrinsic electronic structure. Fig. 3(a) and (b) display the temperature dependence of the zero-field cooled magnetization for the eleven samples (x ¼ 0:0, 0.1, 0.2, 0.3, 0.4,
Fig. 2. Variation of lattice parameters vs Ga concentration in the series Ca(Al1x Gax )Si. (a) a, c vs x and (b) v vs x.
0.5, 0.6, 0.7, 0.8, 0.9 and 1.0) in the series Ca(Al1x Gax )Si measured in a field of 10 Oe between 1.8 and 9.0 K. All measurements were performed on bulk samples of about 0.1 g mass. From Fig. 3(a) and (b), it is noted that the shielding curves for constant field shift toward lower temperature with increasing Ga concentration up to x ¼ 0:7 then backward higher temperature. The ZFC curves for the eleven samples show sharp transition and reach saturation at the lower temperature, which is an indication of the sample homogeneity. In addition, these samples also show
18
H.H. Sung, W.H. Lee / Physica C 406 (2004) 15–19
Fig. 4. Superconducting transition temperature Tc as a function of Ga constituent in the series Ca(Al1x Gax )Si. The error bars attached to the data points measure the transition width (10– 90% values).
Fig. 3. Zero-field cooling magnetization data for eleven samples in the series Ca(Al1x Gax )Si. (a) x ¼ 0:0, 0.1, 0.2, 0.3, 0.4 ad 0.5 (b) x ¼ 0:6, 0.7, 0.8, 0.9 and 1.0.
large shielding signals, by comparison to the ideal value of 1=4p for a long cylinder, with apparent volume fractions above 100%. This phenomenon can be explained in terms of the shielding current and the estimated geometrical demagnetization factor n 0:5 for these two samples CaAlSi and Ca(Al0:9 Ga0:1 )Si because of their irregular shapes. The superconducting transition width (10–90% values) data thus obtained in the series Ca(Al1x Gax )Si are reported in Table 1. We note the transition point value obtained by magnetic measurement is slightly lower than the zero resistance temperature. For example, the zero resistance temperature for CaAlSi is about 7.6 K and the 10–90% value of magnetic transition is 6.53– 7.13 K. This is due to the phenomenon of surface
superconductivity in intermetallic compound [14,15]. Fig. 4 displays the superconducting phase diagram of Ca(Al1x Gax )Si. The error bars attached to the data in Fig. 4 express the width of the transitions as estimated from 90% to 10% magnetic change at Tc . As shown in Fig. 4, the Tc value clearly slides down as x increases from x ¼ 0 to around 0.7 then climbs up to x ¼ 1:0. This indicates that the superconducting transition temperature of the pseudo-binary system Ca(Al1x Gax )Si is not a monotonic function of the lattice constants a, c, v or the ratio c=a. The change in Tc may imply a change of the density of states at the Fermi energy. Therefore, band structure studies are necessary to gain more information regarding the relationship between the electronic structure and the superconducting phase diagram of Ca(Al1x Gax )Si.
4. Conclusion We have synthesized and studied the pseudobinary intermetallic compounds, Ca(Al1x Gax )Si, which are isostructural to the non-copper-oxide bulk superconductor MgB2 with Tc 39 K. In spite
H.H. Sung, W.H. Lee / Physica C 406 (2004) 15–19
of the larger size of Gaþ3 than Alþ3 , the lattice constant a and the unit cell volume v decrease with the increasing Ga concentration in the series Ca(Al1x Gax )Si, which is abnormal to the Vegard’s law. Both the lattice variations and the change of the average valence due to the Al, Ga and Si atoms arranged in chemically disordered honeycomb layers and atoms Ca interacted between them should affect the superconducting properties in these compounds Ca(Al1x Gax )Si.
Acknowledgements This work was supported by National Science Council of Republic of China under contract no. NSC92-2112-M194-010.
References [1] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akimitsu, Nature (London) 410 (2001) 63.
19
[2] M. Imai, E. Abe, J. Ye, K. Nishida, T. Kimura, K. Honma, H. Abe, H. Kitazawa, Phys. Rev. Lett. 87 (2001) 077003. [3] M. Imai, K. Nishida, T. Kimura, H. Abe, Appl. Phys. Lett. 80 (2002) 1019. [4] M. Imai, K. Nishida, T. Kimura, H. Kitazawa, H. Abe, H. Kit^ o, K. Yoshii, Physica C 382 (2002) 361. [5] M. Imai, K. Nishida, T. Kimura, H. Abe, Physica C 377 (2002) 96. [6] R.L. Meng, B. Lorenz, Y.S. Wang, J. Cmaidalka, Y.Y. Sun, Y.Y. Xue, J.K. Meen, C.W. Chu, Physica C 382 (2002) 113. [7] B. Lorez, J. Lenzi, J. Camaidalka, R.L. Meng, Y.Y. Sun, Y.Y. Xue, C.W. Chu, Physica C 383 (2002) 191. [8] B. Lorenz, J. Cmaidalka, R.L. Meng, C.W. Chu, Phys. Rev. B 68 (2003) 014512. [9] S. Majumdar, E.V. Sampathkumaran, Phys. Rev. B 63 (2001) 172407. [10] E.V. Sampathkumaran, S. Majumdar, W. Schneider, S.L. Molodtsov, C. Laubschat, Physica B 312–313 (2002) 152. [11] S. Takano, Y. Iriyama, Y. Kimishima, M. Uehara, Physica C 383 (2003) 295. [12] H. Kit^ o, Y. Takano, K. Togano, Physica C 377 (2002) 185. [13] L.H. Bennett (Ed.), Theory of alloy phase formation, Proceedings of a symposium at the 108th AIME Annual Meeting, New Orleans, LA, 1979. [14] D. Saint James, P.G. de Gennes, Phys. Lett. 7 (1963) 306. [15] J.G. Park, Phys. Rev. Lett. 16 (1966) 1196.