First-principles investigations of the five-layer modulated martensitic structure in Ni2Mn(AlxGa1−x) alloys

In this paper, the five-layer modulated (5M) martensitic structures of Ni2Mn(AlxGa1−x), with x = 0, 0.1 and 0.2, are investigated by the use of the exact muffin-tin orbital method in combination with the coherent potential approximation. The 5M martensite is modeled by varying c/a (shear) and wave-like displacements of the atoms on (1 1 0) plane (shuffle) scaled by η according to Martynov and Kokorin (J. Phys. III 2, 739 (1992)). For Ni2MnGa, we obtain 5M martensite with equilibrium c/a of 0.92 and η of 0.08, in reasonable agreement with the experiment results (0.94 and 0.06, respectively). c/a and η are linearly coupled to each other. Al-doping increases c/a and decreases η, but the linear c/a ∼ η coupling remains. Comparing the total energies of the 5M martensite and L21 austenite, we find that the martensite is more stable than the austenite. Al-doping increases the relative stability of the austenite and finally becomes energetically degenerated with the 5M martensite at an Al atomic fraction (x) of about 0.26. The relative phase stability is analyzed based on the calculated density of states. The calculated total magnetic moments μ0 as a function of c/a exhibit a maximum around the equilibrium c/a. Al-doping reduces μ0.