Phase stability of Ni2(Mn1-xFex)Ga: A first-principles study

Ni-2(Mn1-xFex)Ga ferromagnetic shape memory alloy shows unusual composition-dependent martensitic transformation temperature (T-M), namely, T-M decreases with increasing e/a ratio. In hope of understanding this unusual behavior, we investigated the composition dependence of the heat of formation (H-f) and shear elastic modulus (C') of the cubic austenite as well as the stability of the five-layer modulated (5M) tetragonal martensite relative to the austenite, using first-principles exact muffin-tin orbital method in combination with coherent potential approximation. Our calculations demonstrated that H-f of the austenite increases with the Fe content x. C' increases slightly with x up to 0.05 but decreases thereafter. The composition dependence of both H-f and C' cannot fully account for the trend of T-M against x although such correlations have been proposed in literature for other Ni-Mn-Ga based alloys. The structure of 5M martensite phase of Ni-2(Mn1-xFex)Ga with 0 < x < 0.2 is determined by optimizing both the shear (changing c/a) and wavelike shuffle of atoms in (110) planes along [1 (1) over bar0] direction adopting the experimentally determined modulation function. The energy difference Delta E-AM between the austenite and 5M phases decreases with increasing x up to 0.05, following the lower Delta E-AM corresponding to lower T-M rule. However, with x larger than 0.05, Delta E-AM increases, against the experimental T-M similar to x behavior. We propose that, if taking the temperature effect and the spin-orbital coupling into account, the Delta E-AM similar to x curve might be altered and may explain the unusual composition dependence of Ni-2(Mn1-xFex)Ga.