Determination of ferroelectric compositional phase transition using   novel virtual crystal approach
  We employ a new method for studying compositionally disordered ferroelectric oxides. This method is based on the virtual crystal approximation (VCA), in which two or more component potentials are averaged into a composite atomic potential. In our method, we construct a virtual atom with the correctly averaged atomic size and atomic eigenvalues. We have used our new method to study the composition dependent phase transition in Pb(Zr_{1-x}Ti_x)O_3 lying between x=0.5 and x=0.4. We correctly predict the experimentally determined phase transition from the tetragonal phase to a low-temperature rhombohedral phase between these two compositions. 
Nicholas J. Ramer and Andrew M. Rappe