Theoretical calculation of the phase diagram between one-dimensional long-period structures in the quasi binary sections: Pd3xRh3(1−x)V, Pt3xRh3(1−x)V, and Pt3VxTi(1−x)

The relative stabilities of L12, D022, D023, 〈21〉, and 〈3〉 structures in the Pd3V, Pt3V, Rh3V, and Pt3Ti compounds are investigated employing the Vienna ab initio simulation package. In the pseudobinary Pd3xRh3(1−x)V, Pt3xRh3(1−x)V, and Pt3VxTi(1−x) alloys, the energy differences from L12 of D022, D023, 〈21〉, and 〈3〉 structures are assumed to be linear as function of the number of electrons per atom. At T=0K, the resulting energy diagram shows that the equilibrium between the limiting binary phases is the most stable state. At high temperature, the Gibbs energy curves are computed assuming a Bragg and Williams entropy of mixing in the pseudobinary sections. The D023 and 〈21〉 structures are stabilized in the pseudobinary Pd3xRh3(1−x)V, Pt3xRh3(1−x)V, and Pt3VxTi(1−x) alloys. The phase diagram between the various structures is calculated in each pseudobinary section and compared with the experimental one.