A novel viewpoint on the Cu-Au phase diagram: The interplay between fixed ising energies and elastic effects

Phase Stability and Diagrams from First Principles

First principles theories of alloy phase equilibrium have been successfully used in recent years to compute temperature-composition phase diagrams for solid state phases. One particular approach, originating with the successful phenomenological Ising models to describe the alloy Hamiltonian, uses a cluster expansion of the configurational energy in terms of short-ranged pair and many-body interactions. The approach is deeply rooted in our ability to compute accurate total energies of relatively complex compounds, using density functional theory in the local approximation, from which effective interactions may be obtained. Fundamental aspects of the method which include convergence of the cluster expansion, treatment of the configurational entropy and description of vibrational modes are reviewed. Applications of the theory are given for binary alloys in the Ru-Zr-Nb system using the Linear Muffin Tin Orbital method for the total energy calculations, the Cluster Variation method for the description of the configurational entropy, and the Debye-Gruneisen approximation for the vibrational modes. The results are used to compute the equilibrium phase diagram for the Zr-Nb system and to assess current experimental data on phase stability in the Ru-Nb system. In the latter case, the calculations indicate that the DO19 structure is a likely candidate structure for the experimentally observed hexagonal-based compound Ru3Nb. Investigation of the energies and interactions of tetragonal structures as a function of the c/a ratio suggest the L10 structure as a likely candidate for the observed tetragonal phase near 1:1 stoichiometry.