- Email: [email protected]
Phase equilibria and stability of B2 and L21 ordered phases in the vicinity of half-metallic composition of Co–Cr–Ga Heusler alloy system
Journal of Alloys and Compounds 403 (2005) 161–167
Phase equilibria and stability of B2 and L21 ordered phases in the vicinity of half-metallic composition of Co–Cr–Ga Heusler alloy system K. Kobayashi a , R. Kainuma a,b , K. Fukamichi b , K. Ishida a,b,∗ a
Core Research for Evolutional Science and Technology (CREST)-Japan Science and Technology Agency (JST), Department of Materials Science, Graduate School of Engineering, Tohoku University, Aoba-yama 6-6-02, Sendai 980-8579, Japan b Department of Materials Science, Graduate School of Engineering, Tohoku University, Aoba-yama 6-6-02, Sendai 980-8579, Japan Received 28 March 2005; received in revised form 14 May 2005; accepted 17 May 2005 Available online 19 July 2005
Abstract Recently, half-metallic properties have been extensively investigated from theoretical and practical viewpoints. In the present study, the phase equilibria, A2/B2 and B2/L21 order–disorder transition, and ferromagnetic/paramagnetic transition in the Co-rich portion, that is, in the vicinity of half-metallic composition, for Co–Cr–Ga system were examined by electron probe microanalysis (EPMA), differential scanning calorimetric (DSC) measurement, and transmission electron microscope (TEM). The compositions of the ␥ (A1; fcc-Co), ␣ (A2; bcc-Cr),  (B2; CoGa), (A3; hcp-Co), and (D8b ) phases in equilibrium, the critical compositions corresponding to the A2/B2 continuous order–disorder transition, and the critical temperatures of the B2/L21 order–disorder transition and the paramagnetic/ferromagnetic transition in the L21 phase region have been determined. It has been confirmed that the  single-phase region at 1000 ◦ C exists in a wide composition range, and the B2/L21 order–disorder transition temperature is higher than that of the Co–Cr–Al system. Furthermore, it has been disclosed that the phase stability of the CoGa B2 phase, estimated from the Bragg–Williams–Gorsky (BWG) calculation as a linear extrapolation of the continuous order–disorder transition temperatures, is lower than that of CoAl. © 2005 Elsevier B.V. All rights reserved. Keywords: B2 and L21 -type phase; Order–disorder transition; Phase equilibrium
1. Introduction Half-metallic ferromagnets (HMFs) are currently interesting in the field of spintronics in order to realize spin-dependent devices with high performance, and many L21 (full-Heusler)-type HMFs have been extensively studied from both theoretical and experimental viewpoints [1–5]. Recent band calculations have shown clear evidence for the HMFs from the electronic structures of L21 and B2-type Co2 CrAl alloys [6–9]. However, experimental values of the saturation magnetic moment, Ms , and the spin polarization of the L21 and B2-type Co2 CrAl alloys are much lower than the theoretical values [10,11]. Recently, it has been demonstrated ∗
Corresponding author. Tel.: +81 22 217 7323; fax: +81 22 217 7322. E-mail address: [email protected] (K. Ishida).
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.05.009
that an inevitable A2 + B2 spinodal decomposition which appears in the Cr-rich portion of Co2 Cr1−x Fex Al alloys significantly reduces the half-metallic magnetic properties [12]. Furthermore, we have pointed out from the investigations of magnetic properties and electronic structures that the Co2 CrGa Heusler alloy is a promising candidate for applications to spintronic devices because of its halfmetallic property with 95% of spin polarization [13]. Since half-metallic properties including spin polarization strongly depend on the crystal structure [14] and the degree of order [9,15], detailed information on the phase stability is useful for realizing HMF characteristics. Therefore, the quantitative analysis on the phase equilibria among the phases appearing in the Co-rich part of Co–Cr–Ga system is important. Fig. 1 shows binary phase diagrams of the Co–Cr [16], Co–Ga [17], and Cr–Ga [18] systems and isothermal section
162
K. Kobayashi et al. / Journal of Alloys and Compounds 403 (2005) 161–167
distance in the A2 and B2 phases [20,21]. All the transformation temperatures were determined from differential scanning calorimetric (DSC; Netzsch) measurements with heating and cooling rates of 5 ◦ C/min. For transmission electron microscopic (TEM) examination, thin foils were prepared from the as-quenched alloys by jet-polishing in a solution of 20 pct perchloric acid in ethanol. Electron diffractions and TEM observations were carried out with a JEM2000EX.
3. Results and discussion 3.1. Determination of phase boundaries
Fig. 1. Co–Cr–Ga isothermal section diagram of 800 ◦ C [19] and binary phase diagrams constituting the ternary system [16–18].
of Co–Cr–Ga ternary phase diagram at 800 ◦ C reported by Markiv and Rachinskij [19], which is the only one report for the phase diagram in the whole range of composition. In the present study, the phase equilibria of 800, 1000, and 1100 ◦ C and the stability of B2 and L21 phase are investigated for the Co-rich portion of Co–Cr–Ga system which exhibits excellent half-metallic properties with a high spin polarization of about 95% [13].
Fig. 2(a and b) shows optical micrographs observed in the Co–35 at.%Cr–15 at.%Ga and Co–50 at.%Cr–10 at.%Ga specimens annealed at 800 ◦ C for 28 days and 1000 ◦ C for 7 days, respectively. Each specimen shows typical  (B2) + (A3) + (D8b ) and  (B2) + ␥ (A1) + (D8b ) three-phase microstructures which are large enough to be quantitatively analyzed by the EPMA. All the results of phase equilibria of 800, 1000, and 1100 ◦ C obtained from the multi-phase alloys determined by the EPMA are given in Table 1, and the isothermal section diagrams of the Co–Cr–Ga system at 800, 1000, and 1100 ◦ C are shown in Fig. 3, together with the previous experimental data in the Co–Cr system [22]. The solubility of A1 and A3 phases at 800 ◦ C extends to the Ga-rich direction as shown in Fig. 3, inconsistent with the previously reported data [19] in Fig. 1. These differences would
2. Experimental procedures The alloys were prepared from high purity Co (99.9%), Cr (99.2%), and Ga (99.9999%) by induction furnace melting under an argon gas atmosphere. The preparation of diffusion couples and the examination of phase equilibria were carried out in almost the same way as described in our previous works [20,21]. The diffusion couples or multi-phase specimens were sealed in quarts tubes to prevent oxidation after wrapped in molybdenum foil to prevent reaction with the tubes. Heat treatment for equilibration was carried out for more than 2 h at 1100 ◦ C, 1 day at 1000 ◦ C, and 28 days at 800 ◦ C, respectively. After the heat treatment, the alloys were quenched into ice water. Microstructural observations were carried out with an optical microscope. The equilibrium compositions were measured by an electron probe microanalysis method (EPMA; JEOL JXA8100) and were determined by more five calibrated data by a ZAF (Z: atomic number, absorption, and fluorescence) correction for each phase. The critical compositions of the continuous A2/B2 ordering transition were determined from the concentration–penetration curves obtained for each element of the diffusion couples utilizing the difference in the composition gradient versus
Fig. 2. Optical micrographs of the Co–Cr–Ga alloys (a) Co–35 at.%Cr– 15 at.%Ga quenched from 800 ◦ C and (b) Co–50 at.%Cr–10 at.%Ga quenched from 1000 ◦ C.
K. Kobayashi et al. / Journal of Alloys and Compounds 403 (2005) 161–167
163
Table 1 Phase equilibria among  (B2), ␥ (A1), ␣ (A2), (A3), and (D8b ) phases in the Co–Cr–Ga system Temperature (◦ C)
 (at.%)
␥ (at.%)
␣ (at.%)
(at.%)
(at.%)
Cr
Ga
Cr
Ga
Cr
Ga
Cr
Ga
Cr
Ga
800 – – – – – – –
7.5 8.2 15.8 28.6 24.2 28.9 – –
30.2 30.3 28.1 23.4 25.5 22.9 – –
11.3 12.8 – – – – – –
14.7 14.4 – – – – – –
– – – – – – – –
– – – – – – – –
– – 22.1 31.1 29.1 31.4 31.6 32.2
– – 12.8 11.6 12.3 11.4 11.2 7.1
– – – – – 53.7 52.8 54.5
– – – – – 6.3 6.4 2.9
1000 – – – – – – – – – – –
8.0 8.5 16.2 28.8 31.9 36.6 44.3 49.8 35.7 – – –
28.5 28.6 26.5 22.2 20.0 18.0 14.1 10.5 10.7 – – –
10.9 11.9 20.2 30.3 31.5 32.8 34.5 38.0 – 35.9 – –
17.3 17.2 15.9 14.3 13.7 13.3 12.1 9.6 – 6.3 – –
– – – – – – – – – – 62.8 78.5
– – – – – – – – – – 3.7 2.2
– – – – – – – – – – – –
– – – – – – – – – – – –
– – – – – – – 54.2 53.5 52.0 71.5 65.0
– – – – – – – 6.1 6.4 3.4 5.1 1.9
1100 – – – – – – – – –
8.6 16.8 29.6 37.9 42.9 44.5 45.4 47.9 – –
27.9 25.8 21.1 16.2 13.5 12.3 10.5 9.8 – –
11.6 20.3 29.5 32.6 35.2 35.8 37.1 38.0 37.9 –
18.4 17.1 15.8 13.7 12.1 11.2 9.8 9.2 5.9 –
– – – – – – – – – 65.5
– – – – – – – – – 1.6
– – – – – – – – – –
– – – – – – – – – –
– – – – – – – – 53.6 74.3
– – – – – – – – 3.3 2.2
Fig. 3. Isothermal section diagrams of the Co–Cr–Ga system at 800, 1000, and 1100 ◦ C, together with the previous experimental data for Co–Cr system [22].
164
K. Kobayashi et al. / Journal of Alloys and Compounds 403 (2005) 161–167 /␥
Fig. 4. Concentration-penetration profile for Cr and Ga obtained from the Co–49.7 at.%Cr–9.6 at.%Ga (␣; A2)/Co–19.9 at.%Cr–38.3 at.%Ga (; B2) diffusion couple heat-treated at 1100 ◦ C for 2 h.
be arised from the uncertainty of phase boundaries estimated by the microstructural observations in the previous study. It is also confirmed that the B2 phase region at 1000 ◦ C is much wider than that of Co–Cr–Al system [23]. It has been reported in the Co–Cr–Al system that the miscibility gap between A2 and B2 phases exists in a wide concentration range and the continuous A2/B2 ordering transition starts to appear at above 1200 ◦ C [23]. In the present study, the critical compositions of the continuous A2/B2 ordering transition of Co–Cr–Ga system were determined using the concentration–penetration curves obtained for each element of the diffusion couples. Fig. 4 shows the concentration–penetration curves for Cr and Ga obtained from the Co–49.7 at.%Cr–9.6 at.%Ga (␣; A2)/Co–9.9 at.%Cr–8.3 at.%Ga (; B2) diffusion couple heat-treated at 1100 ◦ C for 2 h. Singularities in both the Ga and Cr profiles are observed at about 19 at.%Ga and 43 at.%Cr of the distance x ≈ 55 m. Such a singularity in a concentration profile is attributed to the large difference in the diffusivity of each element in the ␣ (A2) and  (B2) phases, and the concentrations of the singular point correspond to a critical concentration of order–disorder transition. All the results of the critical composition of the A2/B2 order–disorder transition determined from the singularities of the diffusion couples are given in Table 2 and Fig. 3, respectively. From the isothermal section diagrams at 1000 and 1100 ◦ C shown in Fig. 3, it is clear that the continuous ordering reaction strongly affects the ␣ (A1)  (B2) phase equilibrium, changing the tie-line direction between the  and ␥ phases drastically at the critical ␣ (A2)/ (B2) transition boundary /␥ in the bcc phase. The values of partition coefficients KCr and
␣/␥
␣/␥
KGa (or KCr and KGa ) of elements Cr and Ga between the  (or ␣) and ␥ phases are plotted in Fig. 5, respectively, where /␥ /␥  ␥ KCr is, for example, defined as KCr = KCr /KCr , the ratio  ␥ of Cr contents xCr and xCr in the  and ␥ phases in equilibrium. In the /␥ phase equilibrium of the composition range ␥ /␥ below xCr = 30 at.%, the KCr is smaller than 1.0 (␥ former) /␥ and the KGa is larger than 1.0 ( former), that is, Cr and Ga concentrate into the ␥ and  phases and stabilize the ␥ and  phases, respectively. However, in the vicinity of the criti␥ cal A2/B2 ordering transition boundary located at xCr = 34 and 33 at.% at 1000 and 1100 ◦ C, respectively, the plots of partition coefficients versus Cr content of the equilibrating ␥ phase exhibit singularities and Cr drastically changes from ␥ former to  (␣) former. Such a peculiar behavior of the partition coefficient due to continuous ordering of a bcc phase has also been reported for the Co–Cr–Al and Fe–Ni–Si systems [23,24]. This effect is brought about by the free energy change in the bcc phase due to ordering contributions. 3.2. Stability of L21 phase The selected area diffraction pattern (SADP) with the ¯ matrix zone axis and TEM darkspecimen tilted to the [0 1 1] field image taken from a (1 1 1)L21 reflection for the Co2 CrGa alloy are shown in Fig. 6. Note that the quenching temperature is lower than the reported data and the anti-phase domain (APD) size becomes much smaller, compared with the previous result [25]. From the SADP, the crystal structure of the alloy quenched from 900 ◦ C was identified as the L21 type, and the anti-phase domain boundaries (APBs) of the L21 phase without any precipitates can be confirmed in the TEM dark-field image, showing that transition from the B2 to L21 phase occurs during quenching. It is suggested that the transition temperature from the B2 to L21 phase is lower than 900 ◦ C from the SADP and TEM dark-field image. Therefore, the concentration dependence of the metastable transition temperature from the B2 to L21 phase and the paramagnetic/ferromagnetic transition temperature were determined by the DSC curves to examine the stability of ferromagnetic L21 -type phase. Fig. 7 shows typical heating and cooling curves obtained from the Co–26 at.%Cr–24 at.%Ga specimen. The Curie temperature, Tc , of the L21 phase and metastable transition temperature from the B2 to L21 phase, TtB2/L21 , are detected to be about 219 and 785 ◦ C, respectively. All the results obtained from the DSC analyses are listed in Table 3 and plotted in Fig. 8 for the isoplethal sections of CoCrGa ternary phase
Table 2 Critical compositions of the ␣ (A2)/ (B2) continuous order–disorder transition determined by the diffusion couples in the Co–Cr–Ga system Diffusion temperature (◦ C)
1000 1100 1100
Contents of couple (at.%)
40.3 Cr–19.0 Ga/49.7 Cr–9.6 Ga 19.9 Cr–38.3 Ga/49.7 Cr–9.6 Ga 19.9 Cr–38.3 Ga/40.0 Cr–10.0 Ga
Diffusion time (h)
24 2 2
Critical composition Cr (at.%)
Ga (at.%)
46.5 42.5 38.1
14.0 19.2 17.8
K. Kobayashi et al. / Journal of Alloys and Compounds 403 (2005) 161–167
165
Fig. 5. Partition coefficients of Cr and Ga between the ␥ (A1) and ␣ (A2) or  (B2) phases vs. the Cr content of the equilibrating ␥ phase.
diagram at 50 at.% Co, together with the previous experimental data [13]. The temperatures of Tc and the TtB2/L21 increase with the Ga content, and the maxima of Tc and TtB2/L21 are converged to the stoichiometric content of Co2 CrGa. It is also shown that the measured TtB2/L21 curve is in good agreement with the Bragg–Williams–Gorsky (BWG) approximation [26–28], where the calculated TtB2/L21 is described by a parabolic curve as a function of atomic content, and the maximum TtB2/L21 is at the stoichiometric (Co2 CrGa) composition. Consequently, the L21 -type single-phase alloys in the Co–Cr–Ga system can be easily obtained by quenching, in contrast to the Co–Cr–Al alloy system which exhibits an inevitable A2 + B2 spinodal decomposition. Fig. 7. DSC traces of Co–26 at.%Cr–24 at.%Ga alloy.
3.3. Stability of B2 phase The miscibility gaps between the ␣ (A2) and  (B2) phases in the Co–Cr–Al system [23] and the A2/B2 order–disorder transition lines in the Co–Cr–Ga and Co–Cr–Al systems are shown in Fig. 9. The formation of a miscibility gap island due to the A2/B2 ordering reaction as shown in Fig. 9 has been reported in Co–Fe–Al [29,30], Co–Mn–Al [31], Ni–Fe–Al [21,32], Ni–Cr–Al [33], and Ni–Mn–Al [31] systems. Thermodynamic calculation has shown that the ordering is greatly related to the formation of a miscibility gap island [34], where a miscibility gap island is induced by the presence of an especially stable phase, such as CoAl and NiAl B2 phases. The reason why no miscibility gap island appears in the present alloy system would be related to the low stability of stoichiometric CoGa B2 phase, which will be discussed
Table 3 The Curie temperature, Tc , and the metastable transition temperature from the B2 to L21 phase TtB2 /L21 obtained from the DSC experiments
¯ matrix Fig. 6. Selected area diffraction pattern (SADP) tilted to the [0 1 1] zone axis: (a) TEM dark-field image taken from (1 1 1)L21 reflection; (b) of the Co2 CrGa alloy, quenching from 900 ◦ C [25].
Chemical composition (at.%)
Temperature (◦ C)
Cr
Ga
Tc
TtB2/L21
20 22 26
30 28 24
167 190 219
749 771 785
166
K. Kobayashi et al. / Journal of Alloys and Compounds 403 (2005) 161–167
Fig. 8. Vertical section diagram of 50 at.% Co in the Co–Cr–Ga ternary system, together with the previous experimental data [13].
in connection with the next figure. Fig. 10 shows the vertical section diagrams of the CoGa–Cr and CoAl–X (X = Cr, Fe) [23,30] pseudo-binary systems. The critical transition A2/B2 temperature from the A2 to B2 phase, Tc , of the stoichiometric CoAl or CoGa compound can be estimated by the Bragg–Williams–Gorsky (BWG) calculation [26–28] as a linear extrapolation of the continuous order–disorder transition temperatures [23] as shown in Fig. 7 when the exchange interactions of Co–X, Al–X, and Ga–X are less than the half of that between Co and Al or Ga. In an assumption of the low interchange energies of Co–X, Al–X, and Ga–X bonding in A2/B2 bcc phase, Tc of CoGa is estimated to be ≈2550 K by a parabolic extrapolation of the continuous order–disorder transition boundaries in the isothermal section diagram at 1100 ◦ C as shown in Fig. 3, almost consistent with the estimated value about 2400 K using the calculated enthalpy of formation for the CoGa intermediate phases at 1100 K of A2/B2 H ≈ −40 kJ/mol [35]. On the other hand, Tc of CoAl is about 3250 K [23], much higher than that of CoGa.
Fig. 9. Phase stability of the A2 disordered phase in the  (B2) phase of the Co–Cr–Al [23] and Co–Cr–Ga systems.
Fig. 10. Vertical section diagrams of the CoGa–Cr and CoAl–X (X = Cr, Fe) [23,30] pseudo-binary systems.
4. Summary The phase equilibria, A2/B2 and B2/L21 order–disorder transition, and ferromagnetic/paramagnetic transition in the vicinity of half-metallic composition for the Co–Cr–Ga system were examined. Main results obtained from the compositions of the ␥ (A1), ␣ (A2),  (B2), (A3), and (D8b ) phases in equilibrium, the critical compositions corresponding to the A2/B2 continuous order–disorder transition, and the critical temperatures of the B2/L21 order–disorder transition and the paramagnetic/ferromagnetic transition in the L21 phase region are as follows: 1. The phase equilibria among the ␥, ␣, , , and phases at 800, 1000, and 1100 ◦ C in the Co-rich corner of the Co–Cr–Ga system were experimentally determined. 2. The A2/B2 continuous order–disorder transition determined by a diffusion couple technique strongly influences the phase equilibrium between the ␥ and  or ␣ phases. 3. The  (B2) phase region at 1000 ◦ C is much wider than that of Co–Cr–Al system, and the solubilities of the ␥ and phases extend to the Ga-rich direction, compared with the previously reported data at 800 ◦ C. 4. No miscibility gap island was observed in the present study, in contrast to many Ni–Al and Co–Al systems because of a low stability of stoichiometric CoGa  (B2) phase. 5. Both the Curie temperature, Tc , and the order–disorder transition temperature from the B2 to L21 phase TtB2/L21
K. Kobayashi et al. / Journal of Alloys and Compounds 403 (2005) 161–167
have a maximal value at the stoichiometric content corresponding to Co2 CrGa. Acknowledgement The authors are very grateful to Professor K. Inomata of Tohoku University for many helpful discussions during this work. References [1] J. K¨ubler, A.R. Williams, C.B. Sommers, Phys. Rev. B 28 (1983) 1745. [2] S. Ishida, S. Sugimura, S. Fujii, S. Asano, J. Phys. Condens. Matter 3 (1991) 5793. [3] S. Ishida, D. Fujii, S. Kashiwagi, S. Asano, J. Phys. Soc. Jpn. 64 (1995) 2152. [4] H.J. Elmers, G.H. Fecher, D. Valdaitsev, S.A. Nepijko, A. Gloskovskii, G. Jakob, G. Sch¨onhense, S. Wurmehl, T. Block, C. Felser, P.-C. Hsu, W.-L. Tsai, S. Cramm, Phys. Rev. B 67 (2003) 104412. [5] T. Block, C. Felser, G. Jakob, J. Ensling, B. M¨uhling, P. G¨utlich, R.J. Cava, J. Solid State Chem. 176 (2003) 646. [6] I. Galanakis, P.H. Dederichs, N. Papanikolaou, Phys. Rev. B 66 (2002) 174429. [7] A. Kellou, N.E. Fenineche, T. Grosdidier, H. Aourag, C. Coddet, J. Appl. Phys. 94 (32) (2003) 3292. [8] S. Ishida, S. Kawakami, S. Asano, Mater. Trans. JIM 45 (2004) 1065. [9] Y. Miura, K. Nagano, M. Shirai, J. Appl. Phys. 95 (2004) 7225. [10] K.H.J. Buschow, P.G. van Engen, J. Magn. Magn. Mater. 25 (1981) 90. [11] S. Okamura, R. Goto, N. Tezuka, S. Sugimoto, K. Inomata, Jpn. J. Appl. Phys. 28 (2004) 172. [12] K. Kobayashi, R. Kainuma, K. Ishida, R.Y. Umetsu, T. Oyamada, A. Fujita, K. Fukamichi, Appl. Phys. Lett. 85 (2004) 4684.
167
[13] R.Y. Umetsu, K. Kobayashi, R. Kainuma, A. Fujita, K. Fukamichi, K. Ishida, A. Sakuma, Appl. Phys. Lett. 85 (2004) 2011. [14] D. Orgassa, H. Fujiwara, T.C. Schulthess, W.H. Butler, Phys. Rev. B 60 (1999) 13237. [15] Y. Miura, K. Nagao, M. Shirai, Phys. Rev. B 69 (2004) 144413. [16] H. Okamoto, et al. (Eds.), Desk Handbook Phase Diagrams for Binary Alloys, ASM International, Material Park, OH, 2000, p. 245. [17] H. Okamoto, et al. (Eds.), Desk Handbook Phase Diagrams for Binary Alloys, ASM International, Material Park, OH, 2000, p. 247. [18] H. Okamoto, et al. (Eds.), Desk Handbook Phase Diagrams for Binary Alloys, ASM International, Material Park, OH, 2000, p. 266. [19] V.J. Markiv, V.G. Rachinskij, Dopovidi Akademii Nauk Ukrains’koi RSR, Seriya A, Fiziko–Matematichni Ta Tekhnichni Nauki 40 (1978) 278. [20] R. Kainuma, K. Urushiyama, K. Ishikawa, C.C. Jia, I. Ohnuma, K. Ishida, Mater. Sci. Eng. A239–240 (1997) 235. [21] S.M. Hao, K. Ishida, T. Nishizawa, Metall. Trans. A 15A (1984) 1819. [22] K. Oikawa, G.W. Qin, T. Ikeshoji, R. Kainuma, K. Ishida, Acta Mater. 50 (2002) 2223. [23] K. Ishikawa, M. Ise, I. Ohnuma, R. Kainuma, K. Ishida, Ber. BunsenGes. Phys. Chem. 102 (1998) 1206. [24] O. Ikeda, Y. Himuro, I. Ohnuma, R. Kainuma, K. Ishida, J. Alloys Compd. 268 (1998) 130. [25] K. Kobayashi, R. Y. Umetsu, K. Oikawa, A. Fujita, R. Kainuma, K. Fukamichi, K. Ishida, J. Alloys Compd., in press. [26] V.S. Gorsky, Z. Phys. 50 (1928) 64. [27] W.L. Bragg, E.J. Williams, Proc. R. Soc. A145 (1934) 699. [28] W.L. Bragg, E.J. Williams, Proc. R. Soc. A151 (1935) 540. [29] T. Kozakai, T. Miyazaki, J. Mater. Sci. 29 (1994) 652. [30] M. Ise, R. Kainuma, H. Ohtani, K. Ishida, The Annual Fall Meeting of the JIM, Fukuoka, October 1994 (Abstract 338). [31] R. Kainuma, M. Ise, K. Ishikawa, I. Ohnuma, K. Ishida, J. Alloys Compd. 269 (1998) 173. [32] A.J. Bradlay, J. Iron Steel Inst. 168 (1951) 233, ibid. 171 (1952) 41. [33] P. Villars, A. Prince, H. Okamoto, Handbook of Ternary Alloy Phase Diagram 3, ASM International, 1995, p. 3149. [34] T. Nishizawa, S.M. Hao, M. Hasebe, K. Ishida, Acta Metall. 31 (1983) 1403. [35] X. Su, J.-C. Tedenak, Intermetallics 13 (2005) 467.
Phase equilibria and stability of B2 and L21 ordered phases in the vicinity of half-metallic composition of Co–Cr–Ga Heusler alloy system K. Kobayashi a , R. Kainuma a,b , K. Fukamichi b , K. Ishida a,b,∗ a
Core Research for Evolutional Science and Technology (CREST)-Japan Science and Technology Agency (JST), Department of Materials Science, Graduate School of Engineering, Tohoku University, Aoba-yama 6-6-02, Sendai 980-8579, Japan b Department of Materials Science, Graduate School of Engineering, Tohoku University, Aoba-yama 6-6-02, Sendai 980-8579, Japan Received 28 March 2005; received in revised form 14 May 2005; accepted 17 May 2005 Available online 19 July 2005
Abstract Recently, half-metallic properties have been extensively investigated from theoretical and practical viewpoints. In the present study, the phase equilibria, A2/B2 and B2/L21 order–disorder transition, and ferromagnetic/paramagnetic transition in the Co-rich portion, that is, in the vicinity of half-metallic composition, for Co–Cr–Ga system were examined by electron probe microanalysis (EPMA), differential scanning calorimetric (DSC) measurement, and transmission electron microscope (TEM). The compositions of the ␥ (A1; fcc-Co), ␣ (A2; bcc-Cr),  (B2; CoGa), (A3; hcp-Co), and (D8b ) phases in equilibrium, the critical compositions corresponding to the A2/B2 continuous order–disorder transition, and the critical temperatures of the B2/L21 order–disorder transition and the paramagnetic/ferromagnetic transition in the L21 phase region have been determined. It has been confirmed that the  single-phase region at 1000 ◦ C exists in a wide composition range, and the B2/L21 order–disorder transition temperature is higher than that of the Co–Cr–Al system. Furthermore, it has been disclosed that the phase stability of the CoGa B2 phase, estimated from the Bragg–Williams–Gorsky (BWG) calculation as a linear extrapolation of the continuous order–disorder transition temperatures, is lower than that of CoAl. © 2005 Elsevier B.V. All rights reserved. Keywords: B2 and L21 -type phase; Order–disorder transition; Phase equilibrium
1. Introduction Half-metallic ferromagnets (HMFs) are currently interesting in the field of spintronics in order to realize spin-dependent devices with high performance, and many L21 (full-Heusler)-type HMFs have been extensively studied from both theoretical and experimental viewpoints [1–5]. Recent band calculations have shown clear evidence for the HMFs from the electronic structures of L21 and B2-type Co2 CrAl alloys [6–9]. However, experimental values of the saturation magnetic moment, Ms , and the spin polarization of the L21 and B2-type Co2 CrAl alloys are much lower than the theoretical values [10,11]. Recently, it has been demonstrated ∗
Corresponding author. Tel.: +81 22 217 7323; fax: +81 22 217 7322. E-mail address: [email protected] (K. Ishida).
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.05.009
that an inevitable A2 + B2 spinodal decomposition which appears in the Cr-rich portion of Co2 Cr1−x Fex Al alloys significantly reduces the half-metallic magnetic properties [12]. Furthermore, we have pointed out from the investigations of magnetic properties and electronic structures that the Co2 CrGa Heusler alloy is a promising candidate for applications to spintronic devices because of its halfmetallic property with 95% of spin polarization [13]. Since half-metallic properties including spin polarization strongly depend on the crystal structure [14] and the degree of order [9,15], detailed information on the phase stability is useful for realizing HMF characteristics. Therefore, the quantitative analysis on the phase equilibria among the phases appearing in the Co-rich part of Co–Cr–Ga system is important. Fig. 1 shows binary phase diagrams of the Co–Cr [16], Co–Ga [17], and Cr–Ga [18] systems and isothermal section
162
K. Kobayashi et al. / Journal of Alloys and Compounds 403 (2005) 161–167
distance in the A2 and B2 phases [20,21]. All the transformation temperatures were determined from differential scanning calorimetric (DSC; Netzsch) measurements with heating and cooling rates of 5 ◦ C/min. For transmission electron microscopic (TEM) examination, thin foils were prepared from the as-quenched alloys by jet-polishing in a solution of 20 pct perchloric acid in ethanol. Electron diffractions and TEM observations were carried out with a JEM2000EX.
3. Results and discussion 3.1. Determination of phase boundaries
Fig. 1. Co–Cr–Ga isothermal section diagram of 800 ◦ C [19] and binary phase diagrams constituting the ternary system [16–18].
of Co–Cr–Ga ternary phase diagram at 800 ◦ C reported by Markiv and Rachinskij [19], which is the only one report for the phase diagram in the whole range of composition. In the present study, the phase equilibria of 800, 1000, and 1100 ◦ C and the stability of B2 and L21 phase are investigated for the Co-rich portion of Co–Cr–Ga system which exhibits excellent half-metallic properties with a high spin polarization of about 95% [13].
Fig. 2(a and b) shows optical micrographs observed in the Co–35 at.%Cr–15 at.%Ga and Co–50 at.%Cr–10 at.%Ga specimens annealed at 800 ◦ C for 28 days and 1000 ◦ C for 7 days, respectively. Each specimen shows typical  (B2) + (A3) + (D8b ) and  (B2) + ␥ (A1) + (D8b ) three-phase microstructures which are large enough to be quantitatively analyzed by the EPMA. All the results of phase equilibria of 800, 1000, and 1100 ◦ C obtained from the multi-phase alloys determined by the EPMA are given in Table 1, and the isothermal section diagrams of the Co–Cr–Ga system at 800, 1000, and 1100 ◦ C are shown in Fig. 3, together with the previous experimental data in the Co–Cr system [22]. The solubility of A1 and A3 phases at 800 ◦ C extends to the Ga-rich direction as shown in Fig. 3, inconsistent with the previously reported data [19] in Fig. 1. These differences would
2. Experimental procedures The alloys were prepared from high purity Co (99.9%), Cr (99.2%), and Ga (99.9999%) by induction furnace melting under an argon gas atmosphere. The preparation of diffusion couples and the examination of phase equilibria were carried out in almost the same way as described in our previous works [20,21]. The diffusion couples or multi-phase specimens were sealed in quarts tubes to prevent oxidation after wrapped in molybdenum foil to prevent reaction with the tubes. Heat treatment for equilibration was carried out for more than 2 h at 1100 ◦ C, 1 day at 1000 ◦ C, and 28 days at 800 ◦ C, respectively. After the heat treatment, the alloys were quenched into ice water. Microstructural observations were carried out with an optical microscope. The equilibrium compositions were measured by an electron probe microanalysis method (EPMA; JEOL JXA8100) and were determined by more five calibrated data by a ZAF (Z: atomic number, absorption, and fluorescence) correction for each phase. The critical compositions of the continuous A2/B2 ordering transition were determined from the concentration–penetration curves obtained for each element of the diffusion couples utilizing the difference in the composition gradient versus
Fig. 2. Optical micrographs of the Co–Cr–Ga alloys (a) Co–35 at.%Cr– 15 at.%Ga quenched from 800 ◦ C and (b) Co–50 at.%Cr–10 at.%Ga quenched from 1000 ◦ C.
K. Kobayashi et al. / Journal of Alloys and Compounds 403 (2005) 161–167
163
Table 1 Phase equilibria among  (B2), ␥ (A1), ␣ (A2), (A3), and (D8b ) phases in the Co–Cr–Ga system Temperature (◦ C)
 (at.%)
␥ (at.%)
␣ (at.%)
(at.%)
(at.%)
Cr
Ga
Cr
Ga
Cr
Ga
Cr
Ga
Cr
Ga
800 – – – – – – –
7.5 8.2 15.8 28.6 24.2 28.9 – –
30.2 30.3 28.1 23.4 25.5 22.9 – –
11.3 12.8 – – – – – –
14.7 14.4 – – – – – –
– – – – – – – –
– – – – – – – –
– – 22.1 31.1 29.1 31.4 31.6 32.2
– – 12.8 11.6 12.3 11.4 11.2 7.1
– – – – – 53.7 52.8 54.5
– – – – – 6.3 6.4 2.9
1000 – – – – – – – – – – –
8.0 8.5 16.2 28.8 31.9 36.6 44.3 49.8 35.7 – – –
28.5 28.6 26.5 22.2 20.0 18.0 14.1 10.5 10.7 – – –
10.9 11.9 20.2 30.3 31.5 32.8 34.5 38.0 – 35.9 – –
17.3 17.2 15.9 14.3 13.7 13.3 12.1 9.6 – 6.3 – –
– – – – – – – – – – 62.8 78.5
– – – – – – – – – – 3.7 2.2
– – – – – – – – – – – –
– – – – – – – – – – – –
– – – – – – – 54.2 53.5 52.0 71.5 65.0
– – – – – – – 6.1 6.4 3.4 5.1 1.9
1100 – – – – – – – – –
8.6 16.8 29.6 37.9 42.9 44.5 45.4 47.9 – –
27.9 25.8 21.1 16.2 13.5 12.3 10.5 9.8 – –
11.6 20.3 29.5 32.6 35.2 35.8 37.1 38.0 37.9 –
18.4 17.1 15.8 13.7 12.1 11.2 9.8 9.2 5.9 –
– – – – – – – – – 65.5
– – – – – – – – – 1.6
– – – – – – – – – –
– – – – – – – – – –
– – – – – – – – 53.6 74.3
– – – – – – – – 3.3 2.2
Fig. 3. Isothermal section diagrams of the Co–Cr–Ga system at 800, 1000, and 1100 ◦ C, together with the previous experimental data for Co–Cr system [22].
164
K. Kobayashi et al. / Journal of Alloys and Compounds 403 (2005) 161–167 /␥
Fig. 4. Concentration-penetration profile for Cr and Ga obtained from the Co–49.7 at.%Cr–9.6 at.%Ga (␣; A2)/Co–19.9 at.%Cr–38.3 at.%Ga (; B2) diffusion couple heat-treated at 1100 ◦ C for 2 h.
be arised from the uncertainty of phase boundaries estimated by the microstructural observations in the previous study. It is also confirmed that the B2 phase region at 1000 ◦ C is much wider than that of Co–Cr–Al system [23]. It has been reported in the Co–Cr–Al system that the miscibility gap between A2 and B2 phases exists in a wide concentration range and the continuous A2/B2 ordering transition starts to appear at above 1200 ◦ C [23]. In the present study, the critical compositions of the continuous A2/B2 ordering transition of Co–Cr–Ga system were determined using the concentration–penetration curves obtained for each element of the diffusion couples. Fig. 4 shows the concentration–penetration curves for Cr and Ga obtained from the Co–49.7 at.%Cr–9.6 at.%Ga (␣; A2)/Co–9.9 at.%Cr–8.3 at.%Ga (; B2) diffusion couple heat-treated at 1100 ◦ C for 2 h. Singularities in both the Ga and Cr profiles are observed at about 19 at.%Ga and 43 at.%Cr of the distance x ≈ 55 m. Such a singularity in a concentration profile is attributed to the large difference in the diffusivity of each element in the ␣ (A2) and  (B2) phases, and the concentrations of the singular point correspond to a critical concentration of order–disorder transition. All the results of the critical composition of the A2/B2 order–disorder transition determined from the singularities of the diffusion couples are given in Table 2 and Fig. 3, respectively. From the isothermal section diagrams at 1000 and 1100 ◦ C shown in Fig. 3, it is clear that the continuous ordering reaction strongly affects the ␣ (A1)  (B2) phase equilibrium, changing the tie-line direction between the  and ␥ phases drastically at the critical ␣ (A2)/ (B2) transition boundary /␥ in the bcc phase. The values of partition coefficients KCr and
␣/␥
␣/␥
KGa (or KCr and KGa ) of elements Cr and Ga between the  (or ␣) and ␥ phases are plotted in Fig. 5, respectively, where /␥ /␥  ␥ KCr is, for example, defined as KCr = KCr /KCr , the ratio  ␥ of Cr contents xCr and xCr in the  and ␥ phases in equilibrium. In the /␥ phase equilibrium of the composition range ␥ /␥ below xCr = 30 at.%, the KCr is smaller than 1.0 (␥ former) /␥ and the KGa is larger than 1.0 ( former), that is, Cr and Ga concentrate into the ␥ and  phases and stabilize the ␥ and  phases, respectively. However, in the vicinity of the criti␥ cal A2/B2 ordering transition boundary located at xCr = 34 and 33 at.% at 1000 and 1100 ◦ C, respectively, the plots of partition coefficients versus Cr content of the equilibrating ␥ phase exhibit singularities and Cr drastically changes from ␥ former to  (␣) former. Such a peculiar behavior of the partition coefficient due to continuous ordering of a bcc phase has also been reported for the Co–Cr–Al and Fe–Ni–Si systems [23,24]. This effect is brought about by the free energy change in the bcc phase due to ordering contributions. 3.2. Stability of L21 phase The selected area diffraction pattern (SADP) with the ¯ matrix zone axis and TEM darkspecimen tilted to the [0 1 1] field image taken from a (1 1 1)L21 reflection for the Co2 CrGa alloy are shown in Fig. 6. Note that the quenching temperature is lower than the reported data and the anti-phase domain (APD) size becomes much smaller, compared with the previous result [25]. From the SADP, the crystal structure of the alloy quenched from 900 ◦ C was identified as the L21 type, and the anti-phase domain boundaries (APBs) of the L21 phase without any precipitates can be confirmed in the TEM dark-field image, showing that transition from the B2 to L21 phase occurs during quenching. It is suggested that the transition temperature from the B2 to L21 phase is lower than 900 ◦ C from the SADP and TEM dark-field image. Therefore, the concentration dependence of the metastable transition temperature from the B2 to L21 phase and the paramagnetic/ferromagnetic transition temperature were determined by the DSC curves to examine the stability of ferromagnetic L21 -type phase. Fig. 7 shows typical heating and cooling curves obtained from the Co–26 at.%Cr–24 at.%Ga specimen. The Curie temperature, Tc , of the L21 phase and metastable transition temperature from the B2 to L21 phase, TtB2/L21 , are detected to be about 219 and 785 ◦ C, respectively. All the results obtained from the DSC analyses are listed in Table 3 and plotted in Fig. 8 for the isoplethal sections of CoCrGa ternary phase
Table 2 Critical compositions of the ␣ (A2)/ (B2) continuous order–disorder transition determined by the diffusion couples in the Co–Cr–Ga system Diffusion temperature (◦ C)
1000 1100 1100
Contents of couple (at.%)
40.3 Cr–19.0 Ga/49.7 Cr–9.6 Ga 19.9 Cr–38.3 Ga/49.7 Cr–9.6 Ga 19.9 Cr–38.3 Ga/40.0 Cr–10.0 Ga
Diffusion time (h)
24 2 2
Critical composition Cr (at.%)
Ga (at.%)
46.5 42.5 38.1
14.0 19.2 17.8
K. Kobayashi et al. / Journal of Alloys and Compounds 403 (2005) 161–167
165
Fig. 5. Partition coefficients of Cr and Ga between the ␥ (A1) and ␣ (A2) or  (B2) phases vs. the Cr content of the equilibrating ␥ phase.
diagram at 50 at.% Co, together with the previous experimental data [13]. The temperatures of Tc and the TtB2/L21 increase with the Ga content, and the maxima of Tc and TtB2/L21 are converged to the stoichiometric content of Co2 CrGa. It is also shown that the measured TtB2/L21 curve is in good agreement with the Bragg–Williams–Gorsky (BWG) approximation [26–28], where the calculated TtB2/L21 is described by a parabolic curve as a function of atomic content, and the maximum TtB2/L21 is at the stoichiometric (Co2 CrGa) composition. Consequently, the L21 -type single-phase alloys in the Co–Cr–Ga system can be easily obtained by quenching, in contrast to the Co–Cr–Al alloy system which exhibits an inevitable A2 + B2 spinodal decomposition. Fig. 7. DSC traces of Co–26 at.%Cr–24 at.%Ga alloy.
3.3. Stability of B2 phase The miscibility gaps between the ␣ (A2) and  (B2) phases in the Co–Cr–Al system [23] and the A2/B2 order–disorder transition lines in the Co–Cr–Ga and Co–Cr–Al systems are shown in Fig. 9. The formation of a miscibility gap island due to the A2/B2 ordering reaction as shown in Fig. 9 has been reported in Co–Fe–Al [29,30], Co–Mn–Al [31], Ni–Fe–Al [21,32], Ni–Cr–Al [33], and Ni–Mn–Al [31] systems. Thermodynamic calculation has shown that the ordering is greatly related to the formation of a miscibility gap island [34], where a miscibility gap island is induced by the presence of an especially stable phase, such as CoAl and NiAl B2 phases. The reason why no miscibility gap island appears in the present alloy system would be related to the low stability of stoichiometric CoGa B2 phase, which will be discussed
Table 3 The Curie temperature, Tc , and the metastable transition temperature from the B2 to L21 phase TtB2 /L21 obtained from the DSC experiments
¯ matrix Fig. 6. Selected area diffraction pattern (SADP) tilted to the [0 1 1] zone axis: (a) TEM dark-field image taken from (1 1 1)L21 reflection; (b) of the Co2 CrGa alloy, quenching from 900 ◦ C [25].
Chemical composition (at.%)
Temperature (◦ C)
Cr
Ga
Tc
TtB2/L21
20 22 26
30 28 24
167 190 219
749 771 785
166
K. Kobayashi et al. / Journal of Alloys and Compounds 403 (2005) 161–167
Fig. 8. Vertical section diagram of 50 at.% Co in the Co–Cr–Ga ternary system, together with the previous experimental data [13].
in connection with the next figure. Fig. 10 shows the vertical section diagrams of the CoGa–Cr and CoAl–X (X = Cr, Fe) [23,30] pseudo-binary systems. The critical transition A2/B2 temperature from the A2 to B2 phase, Tc , of the stoichiometric CoAl or CoGa compound can be estimated by the Bragg–Williams–Gorsky (BWG) calculation [26–28] as a linear extrapolation of the continuous order–disorder transition temperatures [23] as shown in Fig. 7 when the exchange interactions of Co–X, Al–X, and Ga–X are less than the half of that between Co and Al or Ga. In an assumption of the low interchange energies of Co–X, Al–X, and Ga–X bonding in A2/B2 bcc phase, Tc of CoGa is estimated to be ≈2550 K by a parabolic extrapolation of the continuous order–disorder transition boundaries in the isothermal section diagram at 1100 ◦ C as shown in Fig. 3, almost consistent with the estimated value about 2400 K using the calculated enthalpy of formation for the CoGa intermediate phases at 1100 K of A2/B2 H ≈ −40 kJ/mol [35]. On the other hand, Tc of CoAl is about 3250 K [23], much higher than that of CoGa.
Fig. 9. Phase stability of the A2 disordered phase in the  (B2) phase of the Co–Cr–Al [23] and Co–Cr–Ga systems.
Fig. 10. Vertical section diagrams of the CoGa–Cr and CoAl–X (X = Cr, Fe) [23,30] pseudo-binary systems.
4. Summary The phase equilibria, A2/B2 and B2/L21 order–disorder transition, and ferromagnetic/paramagnetic transition in the vicinity of half-metallic composition for the Co–Cr–Ga system were examined. Main results obtained from the compositions of the ␥ (A1), ␣ (A2),  (B2), (A3), and (D8b ) phases in equilibrium, the critical compositions corresponding to the A2/B2 continuous order–disorder transition, and the critical temperatures of the B2/L21 order–disorder transition and the paramagnetic/ferromagnetic transition in the L21 phase region are as follows: 1. The phase equilibria among the ␥, ␣, , , and phases at 800, 1000, and 1100 ◦ C in the Co-rich corner of the Co–Cr–Ga system were experimentally determined. 2. The A2/B2 continuous order–disorder transition determined by a diffusion couple technique strongly influences the phase equilibrium between the ␥ and  or ␣ phases. 3. The  (B2) phase region at 1000 ◦ C is much wider than that of Co–Cr–Al system, and the solubilities of the ␥ and phases extend to the Ga-rich direction, compared with the previously reported data at 800 ◦ C. 4. No miscibility gap island was observed in the present study, in contrast to many Ni–Al and Co–Al systems because of a low stability of stoichiometric CoGa  (B2) phase. 5. Both the Curie temperature, Tc , and the order–disorder transition temperature from the B2 to L21 phase TtB2/L21
K. Kobayashi et al. / Journal of Alloys and Compounds 403 (2005) 161–167
have a maximal value at the stoichiometric content corresponding to Co2 CrGa. Acknowledgement The authors are very grateful to Professor K. Inomata of Tohoku University for many helpful discussions during this work. References [1] J. K¨ubler, A.R. Williams, C.B. Sommers, Phys. Rev. B 28 (1983) 1745. [2] S. Ishida, S. Sugimura, S. Fujii, S. Asano, J. Phys. Condens. Matter 3 (1991) 5793. [3] S. Ishida, D. Fujii, S. Kashiwagi, S. Asano, J. Phys. Soc. Jpn. 64 (1995) 2152. [4] H.J. Elmers, G.H. Fecher, D. Valdaitsev, S.A. Nepijko, A. Gloskovskii, G. Jakob, G. Sch¨onhense, S. Wurmehl, T. Block, C. Felser, P.-C. Hsu, W.-L. Tsai, S. Cramm, Phys. Rev. B 67 (2003) 104412. [5] T. Block, C. Felser, G. Jakob, J. Ensling, B. M¨uhling, P. G¨utlich, R.J. Cava, J. Solid State Chem. 176 (2003) 646. [6] I. Galanakis, P.H. Dederichs, N. Papanikolaou, Phys. Rev. B 66 (2002) 174429. [7] A. Kellou, N.E. Fenineche, T. Grosdidier, H. Aourag, C. Coddet, J. Appl. Phys. 94 (32) (2003) 3292. [8] S. Ishida, S. Kawakami, S. Asano, Mater. Trans. JIM 45 (2004) 1065. [9] Y. Miura, K. Nagano, M. Shirai, J. Appl. Phys. 95 (2004) 7225. [10] K.H.J. Buschow, P.G. van Engen, J. Magn. Magn. Mater. 25 (1981) 90. [11] S. Okamura, R. Goto, N. Tezuka, S. Sugimoto, K. Inomata, Jpn. J. Appl. Phys. 28 (2004) 172. [12] K. Kobayashi, R. Kainuma, K. Ishida, R.Y. Umetsu, T. Oyamada, A. Fujita, K. Fukamichi, Appl. Phys. Lett. 85 (2004) 4684.
167
[13] R.Y. Umetsu, K. Kobayashi, R. Kainuma, A. Fujita, K. Fukamichi, K. Ishida, A. Sakuma, Appl. Phys. Lett. 85 (2004) 2011. [14] D. Orgassa, H. Fujiwara, T.C. Schulthess, W.H. Butler, Phys. Rev. B 60 (1999) 13237. [15] Y. Miura, K. Nagao, M. Shirai, Phys. Rev. B 69 (2004) 144413. [16] H. Okamoto, et al. (Eds.), Desk Handbook Phase Diagrams for Binary Alloys, ASM International, Material Park, OH, 2000, p. 245. [17] H. Okamoto, et al. (Eds.), Desk Handbook Phase Diagrams for Binary Alloys, ASM International, Material Park, OH, 2000, p. 247. [18] H. Okamoto, et al. (Eds.), Desk Handbook Phase Diagrams for Binary Alloys, ASM International, Material Park, OH, 2000, p. 266. [19] V.J. Markiv, V.G. Rachinskij, Dopovidi Akademii Nauk Ukrains’koi RSR, Seriya A, Fiziko–Matematichni Ta Tekhnichni Nauki 40 (1978) 278. [20] R. Kainuma, K. Urushiyama, K. Ishikawa, C.C. Jia, I. Ohnuma, K. Ishida, Mater. Sci. Eng. A239–240 (1997) 235. [21] S.M. Hao, K. Ishida, T. Nishizawa, Metall. Trans. A 15A (1984) 1819. [22] K. Oikawa, G.W. Qin, T. Ikeshoji, R. Kainuma, K. Ishida, Acta Mater. 50 (2002) 2223. [23] K. Ishikawa, M. Ise, I. Ohnuma, R. Kainuma, K. Ishida, Ber. BunsenGes. Phys. Chem. 102 (1998) 1206. [24] O. Ikeda, Y. Himuro, I. Ohnuma, R. Kainuma, K. Ishida, J. Alloys Compd. 268 (1998) 130. [25] K. Kobayashi, R. Y. Umetsu, K. Oikawa, A. Fujita, R. Kainuma, K. Fukamichi, K. Ishida, J. Alloys Compd., in press. [26] V.S. Gorsky, Z. Phys. 50 (1928) 64. [27] W.L. Bragg, E.J. Williams, Proc. R. Soc. A145 (1934) 699. [28] W.L. Bragg, E.J. Williams, Proc. R. Soc. A151 (1935) 540. [29] T. Kozakai, T. Miyazaki, J. Mater. Sci. 29 (1994) 652. [30] M. Ise, R. Kainuma, H. Ohtani, K. Ishida, The Annual Fall Meeting of the JIM, Fukuoka, October 1994 (Abstract 338). [31] R. Kainuma, M. Ise, K. Ishikawa, I. Ohnuma, K. Ishida, J. Alloys Compd. 269 (1998) 173. [32] A.J. Bradlay, J. Iron Steel Inst. 168 (1951) 233, ibid. 171 (1952) 41. [33] P. Villars, A. Prince, H. Okamoto, Handbook of Ternary Alloy Phase Diagram 3, ASM International, 1995, p. 3149. [34] T. Nishizawa, S.M. Hao, M. Hasebe, K. Ishida, Acta Metall. 31 (1983) 1403. [35] X. Su, J.-C. Tedenak, Intermetallics 13 (2005) 467.