Virtual-crystal approximation that works: Locating a compositional phase boundary in Pb„Zr1ÀxTix...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(Zr12xTix)O3 at x50.5 and comparing these results to superlattice calculations and experiment. We then use our method to determine the preferred structural phase at x50.4. We find that the low-temperature rhombohedral phase becomes the ground state at x50.4, in agreement with experimental findings.