Origin of the Phase Separation into B2 and L21 Ordered Phases in the X-Al-Ti (X: Fe, Co, and Ni) Alloys from the First-principles Cluster Variation Method

Abstract: The phase separation behaviors from the single B2 ordered phase into the two separate B2 and L2$1$ ordered phases in the X-Al-Ti (X: Fe, Co, and Ni) alloys are analyzed using the cluster variation method (CVM) with the interaction energies evaluated from the electronic band structure calculations. The cubic approximation of the CVM is employed for the X$_2$Al${2-x}$Ti$_x$ ($0 \leq x \leq 2$) alloys limiting an interchange between Al and Ti atoms on the $\alpha$- and $\beta$-sublattices of the L2$_1$ ordered structure with the X atoms fixed on the $\gamma$-sublattice. The phase stabilities of the B2 and L2$_1$ structures are examined, and the phase diagrams at the pseudo-binary section, XAl-XTi, are determined. The two-phase regions of B2 and L2$_1$ phases, i.e., phase separation behavior, are successfully produced in both Co- and Ni-Al-Ti alloy systems, whereas no phase separation is predicted in the Fe-Al-Ti alloy. The origin of the phase separation in the Co- and Ni-Al-Ti alloys is, respectively, attributed to the mechanical instability and the combination of mechanical instability and chemical repulsions of unlike pairs.