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, left angle bracket21right-pointing angle bracket, and left angle bracket3right-pointing angle bracket 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, left angle bracket21right-pointing angle bracket, and left angle bracket3right-pointing angle bracket 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 left angle bracket21right-pointing angle bracket 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.