Global volume relaxations and phase stability in disordered Pd-Rh alloys

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Abstract
The energetics of disordered fcc-based Pd-Rh alloys are determined by a combination of a generalized Ising model and effective-pair and multisite interactions that are explicit functions of the alloy volume. The volume dependence of the interactions is incorporated in the method of direct configurational averaging, which is a real-space, Green-function technique for obtaining the interactions directly from their definition. The first two terms in the generalized Ising Hamiltonian (or cluster expansion), the so-called empty cluster and point interactions, may not be computed simply from one-electron energies; therefore, a technique is described to compute each of these terms from two contributions: (1) total energies of the pure elements, and (2) one-electron energies corresponding to the energy gained upon mixing the constituents of the alloy at a fixed volume. By using the volume-dependent interactions, the formation enthalpy, equilibrium volume, and bulk modulus are computed for the completely disordered alloy as a function of composition. The scheme of computing the volume-dependent interactions is compared with the results of the effective-cluster-interaction calculations from other Hamiltonians, and the results of this comparison explained in terms of the magnitude of the off-diagonal disorder present in each computation. The volume-dependent interactions are combined with the cluster-variation method to compute the solid-state portion of the Pd-Rh phase diagram, with no adjustable or experimentally determined parameters. The agreement between the theoretically predicted and experimentally determined diagrams is excellent.