Origin of the phase separation into B2 and L2 1 ordered phases in X–Al–Ti (X: Fe, Co, and Ni) alloys based on the first-principles cluster variation method

The phase separation behaviors from a single B2 ordered phase into two separate B2 and L21 ordered phases in X-Al-Ti (X: Fe, Co, and Ni) alloys are analyzed utilizing the cluster variation method (CVM), based on interaction energies derived from electronic band structure calculations. A cubic approximation of the CVM is adopted for X2Al2-x Ti x ([Formula: see text]) alloys limiting the interchange between Al and Ti atoms on the [Formula: see text]- and [Formula: see text]-sublattices of an L21 ordered structure with X atoms fixed on the [Formula: see text]-sublattice. The phase stabilities of the B2 and L21 structures are examined, and phase diagrams at the pseudo-binary section, XAl-XTi, are determined. The two-phase regions of the B2 and L21 phases (i.e. phase separation behavior) are successfully produced in Co- and Ni-Al-Ti alloy systems, and no phase separation is observed in the Fe-Al-Ti alloy. The origins of phase separation in the Co- and Ni-Al-Ti alloys are mechanical instability and a combination of mechanical instability and chemical repulsions of unlike pairs, respectively.