Configurational lattice dynamics: The phase diagram of Rh − Pd

Abstract

Free energies of Rh-Pd alloys as functions of both temperature and composition are calculated using quasiharmonic lattice dynamics. The free energy of the disordered solid is determined from an ensemble of a large number of randomly generated configurations. Both configurational and vibrational contributions to the entropy and enthalpy of mixing are taken into account. We study the convergence with the number of random configurations, and analyze the validity of the zero static internal stress approximation ZSISA, where only external strains are relaxed fully dynamically while internal stresses are relaxed in the static approximation. It is shown that the use of ZSISA allows an accurate calculation of free energies in a fraction of the time needed to carry out fully dynamic optimizations. From the values of free energies as functions of composition and temperature the phase diagram of Rh-Pd alloys is calculated, showing a good agreement with Monte Carlo simulations as well as with experiment. It is also shown that although free energies of mixing appear to be linear functions of temperature to a good approximation, the explicit expressions given by the configurational lattice dynamics method show that both enthalpies and entropies of mixing change appreciably with temperature.