Virtual-crystal approximation that works:: Locating a compositional phase boundary in Pb(Zr1-xTix)O3

We present a method for modeling disordered solid solutions, based on the virtual crystal approximation (VCA). The VCA is a tractable way of studying configurationally disordered systems; traditionally, the potentials which represent atoms of two or more elements are averaged into a composite atomic potential. We have overcome significant shortcomings of the standard VCA by developing a potential which yields averaged atomic properties. We perform the VCA on a ferroelectric oxide, determining the energy differences between the high-temperature rhombohedral, low-temperature rhombohedral, and tetragonal phases of Pb(Zr1-xTix)O-3 at x = 0.5 and comparing these results to superlattice calculations and experiment. We then use our method to determine the preferred structural phase at x = 0.4. We find that the low-temperature rhombohedral phase becomes the ground state at x = 0.4, in agreement with experimental findings.