  We present a new 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(Zr_{1-x}Ti_x)O_3 at x=0.5 and comparing these results to
superlattice calculations and experiment. We then use our new 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.
