Materials Transactions, Vol. 44, No. 1 (2003) pp. 204 to 210 #2003 The Japan Institute of Metals EXPRESS REGULAR ARTICLE Valence Electron Concentration and Phase Transformations of Shape Memory Alloys Ni–Mn–Ga–X Kenichi Yamaguchi1;*, Shoji Ishida1 and Setsuro Asano2 1Department of Physics, Faculty of Science, Kagoshima University, Kagoshima, 890-0065 Japan 2The Graduate School of=College of Arts and Sciences, The University of Tokyo, Tokyo, 153-0041 Japan In the Ni2MnGa based alloys with additions of transition element Ni–Mn–Ga–X, the martensitic transformation temperature TM was observed as a function of the valence electron concentration per atom e=a. The TMðe=aÞ strongly depends on e=a and increases with increasing e=a. In this paper, to examine the effect of Xatom on the phase transformation in Ni–Mn–Ga–Xalloys, the electronic structures for six systems were calculated for four phases, that is, the paramagnetic cubic, the paramagnetic monoclinic, the ferromagnetic cubic and the ferromagnetic monoclinic phases. Moreover, the total energy differences ÁEðe=aÞ between two phases among four phases were calculated as a function of e=a. The variations of TMðe=aÞ were predicted by the difference ÁEðe=aÞ between the cubic and monoclinic structures in a ferromagnetic state. It was found that their correspondence is good for some systems and that the features of TMðe=aÞ reflect the changes of the density of states of Xatoms. (Received October 9, 2002; Accepted December 13, 2002) Keywords: shape memory, martensitic transformation temperature, valence electron concentration, electronic structure, total energy, nickel, manganese, gallium, Curie temperature 1. Introduction martensitic phase in the range e=a < 7:62, (II) paramagnetic parent phase , (ferromagnetic parent phase) , ferromag- Many researchers have reported on the crystal structures netic martensitic phase in the range 7:62 < e=a < 7:65 and and the phase transformations of the Ni–Mn–Ga alloys. The (III) paramagnetic parent phase , paramagnetic martensitic tetragonal structure was observed in the martensitic phase phase , ferromagnetic martensitic phase in the range around valence electron concentration e=a ¼ 7:50 (stoichio- 7:65 < e=a.12) The symbol ‘‘,’’ denotes the process of metric Ni2MnGa). On the other hand, the orthorhombic and transformation between two phases. monoclinic structures were observed.1–4) For example, the Previously, paying attention to only two systems in a orthorhombic structure was observed at the e=a ¼ 7:635 and ferromagnetic state, the authors calculated total energy the monoclinic structures at e=a ¼ 7:64, 7.67, 7.72 and differences ÁE between the cubic and monoclinic structures 7.78.2,3) It was also reported that the tetragonal phase in the as a function of e=a and related the ÁE with the e=a 5) 13) lower e=a can be suppressed by Ni excess. Furthermore, it is dependence of TM. It was found that ÁEðe=aÞ changes like also predicted theoretically that the tetragonal and orthor- a straight line in the range e=a ¼ 7:50{7:625 for the case hombic structures may be metastable and the monoclinic where Xatoms occupy Ni sites, while like a parabolic line in structure is the most stable state among these structures for the range e=a ¼ 7:625{7:77 for the case where Xatoms 6) Ni2:17Ni0:83Ga and Ni2(Pd0:17Ni0:83)Ga. Thus, it is possible occupy Mn sites. The characteristic behavior of ÁEðe=aÞ is for the monoclinic structure to appear in martensitic phase in similar to the behavior of TMðe=aÞ of Ni2:16ÀxCoxMn0:84Ga, wide e=a range. Ni2:20ÀzFezMn0:80Ga and Ni2:16Mn0:84ÀyCoyGa. However, for The martensitic transformation temperature TM and the Ni2þxMn1ÀxGa, the correspondence between ÁEðe=aÞ and Curie temperature Tc for Ni2MnGa (e=a ¼ 7:50) are 202 and TMðe=aÞ is good in the range e=a ¼ 7:50{7:625 but not good 7) 376 K, respectively. The various values of TM were in the range e=a > 7:625. observed in the wide range from 175 to 626 K in the range In this paper, new four systems and a paramagnetic state 8–10) e=a ¼ 7:45{8:10. For Ni–Mn–Ga alloys, Tc decreases will be considered to investigate in more detail the effect of X 5,9) and TM increases with increasing e=a. They merge in the atom on the phase transformation in Ni–Mn–Ga–Xsystems. range e=a ¼ 7:635{7:70. It was also shown that TM is lower than Tc in the lower e=a and higher than Tc in the higher 2. Crystal Structure and Method of Calculation 5,9) e=a. Moreover, Xin et al. reported that the values of TM for ferromagnetic alloys Ni–Mn–Ga are higher than 300 K and As described in the previous section, it was reported lower than Tc and that TM is represented by the equation theoretically that the monoclinic structure is the most stable 11) TM ¼ 702:5ðe=aÞÀ5067 K as a function of e=a. These among the cubic, tetragonal, orthorhombic and monoclinic results indicate that the martensitic transformation occurs in a structures for Ni2:17Ni0:83Ga and Ni2(Pd0:17Ni0:83)Ga. Then, ferromagnetic phase for the lower e=a and in a paramagnetic we consider the cubic structure and the monoclinic structure state for the higher e=a. as the parent phase and the martensitic phase, respectively. Moreover, Tsuchiya et al. reported three types of trans- The symmetry of the monoclinic structure is lower than that formations: (I) paramagnetic parent phase , ferromagnetic of the cubic structure. The cubic structure is treated as a parent phase , intermediate phase , ferromagnetic monoclinic structure with an angle of shown in Fig. 1 to calculate under the same condition. The angle is 71.565 *Graduate Student, Kagoshima University. and 98.461 or the cubic structure and the monoclinic Valence Electron Concentration and Phase Transformations of Shape Memory Alloys Ni–Mn–Ga–X205 (a) Monoclinic Structure Ni y=1 plane Mn Ga Mn,Ga : y=0 or 1 y=3/4 plane Ni : y=1/4 2 Cubic Structure 3 1 4 3 y=1/2 plane Mn(2) 3 1 y=0 plane 1 y=1/4 Ni(1) Mn(1) (b) y z Monoclinic Structure x Mn, Ga : y=1/2 Fig. 2 Monoclinic structure. The monoclinic structure has twenty-four Ni : y=3/4 atoms in the unit cell, which corresponds to the observed monoclinic structure having the shuffling of 6 layers of (2 2 0) planes. 2 Cubic Structure 4 2 circles, solid circle and circle with slants denote Ni, Mn and 4 3 Ga, respectively. The Mn(1), Mn(2) and Ni(1) are the sites 4 where Xatoms occupy. Recently, it was confirmed that the 1 monoclinic structure is equivalent to the tetragonal structure 14) 2 of the named of 2M. The alloy where a sixth of Mn atoms of Ni2MnGa were Fig. 1 Relation between the cubic and monoclinic structures of Ni–Mn– replaced with Ni atoms was described as Ni2:17Ni0:83Ga in the Ga–Xalloy. The constituent atoms on the y ¼ 0 and y ¼ 1=4 planes are 6) shown in (a) and ones on y ¼ 1=2 and y ¼ 3=4 planes in (b). The numbers previous papers. In this paper, the alloy is described as denote the atomic sites in the monoclinic structure. The cubic structure is Ni2(X1=6Mn5=6)Ga where the Ni atoms at the Mn(1) sites are treated as the monoclinic structure with an angle of ¼ 71:565. described in parentheses with the Mn atoms. Here, we consider six systems of Ni–Mn–Ga–Xalloys where Ni or Mn atoms in Ni2MnGa or Ni2(Ni1=6Mn5=6)Ga are replaced with 6) structure of Ni2:17Ni0:83Ga. When we assume that y-axis is other transition element. They are listed in Table 1, where the vertical to this paper, Mn and Ga atoms are located on the name of the systems, the molecular formula and atoms at the y ¼ 0 (or 1) and 1=2 planes and Ni atoms on the y ¼ 1=4 and Mn(1), Mn(2) and Ni(1) sites are shown. For example, in 3=4 planes shown in Fig. 1. Each of nickel, manganese and (Ni5=6X1=6)2(Ni1=6Mn5=6)Ga, Ni atoms are replaced with X gallium in Ni2MnGa has the four different atomic sites in the atoms and Mn(1) atoms with Ni atoms. The s-Nm1-n1 and s- unit cell with the P2/m symmetry of the tenth space group. Nm1-m2 are new notation for sys-N1 and sys-M2 in the For example, the sites of Ni and Mn atoms are distinguished previous paper, respectively.13) When transition elements are by such as the symbols of Ni(1), Mn(1) and Mn(2). The chosen as the Xatoms, these alloys are in the range of Ni(1), Mn(1) and Mn(2) are located at the 2j, 1a and 1f sites. e=a ¼ 7:50{7:77. When we cannot choose a real element as The monoclinic structure has twenty-four atoms in the unit the Xatom for the special value of e=a, we adopt an artificial cell, which corresponds to the observed monoclinic structure atom. For example, the artificial atom is described like Z27.5 having the shuffling of 6 layers of (2 2 0) planes.2) This where the number of 27.5 means the atomic number and the monoclinic structure is shown in Fig. 2 and the symbols open number of electrons. Table 1 Six systems classified by the site of Xatom (Mn or Ni site) in the shape memory alloys Ni–Mn–Ga–X.The symbols, the molecular formula used in this paper are listed.