First-principles study of phase equilibria in Cu-Pt-Rh disordered alloys.

Phase stability of Cu-Pt-Rh ternary disordered alloys is examined by a combination of cluster expansion techniques and Monte Carlo statistical simulation based on first-principles calculation. The sign of pseudo-binary ECIs indicates that neighboring Cu and Pt strongly prefer unlike-atom pairs, Pt and Rh weakly prefer unlike-atom pairs, and Cu and Rh atoms prefer like-atom pairs, indicating that the ternary alloy retains the ordering tendency of the constituent binary alloys. The formation energy of a random alloy at T = 1200 K exhibits a negative sign for a wide range of Pt-rich compositions, while at Pt-poor compositions of x≤0.25, the formation energy has a positive value. Calculated affinities for the random alloy show the variety of energetically favored bonds for the alloy: Cu-Pt bonds in both first-and second-nearest neighbor (1-NN and 2-NN) are energetically preferred for all the composition range, the Pt-Rh bond in 1-NN is preferred at Pt-rich compositions, the Pt-Rh in 2-NN and Rh-Cu in 1-NN bonds are unfavored for all compositions, and the Rh-Cu bond in 2-NN is unfavored for Pt-poor compositions. We elucidate that the ordering tendency of 1-NN and 2-NN Cu-Pt, 2-NN Pt-Rh and 1-NN Cu-Rh atoms in constituent binary alloys is retained for the whole composition range of Cu-Pt-Rh ternary alloys, while that of 1-NN Pt-Rh and 2-NN Cu-Rh atoms significantly depends on composition.