First-principles study of lattice instabilities in Ba_xSr_(1-x)TiO_3
  Using first-principles calculations based on a variational density functional perturbation theory, we investigate the lattice dynamics of solid solutions of barium and strontium titanates. Averaging the information available for the related pure compounds yields results equivalent to those obtained within the virtual crystal approximation, providing frequencies which are a good approximation to those computed for a (111) ordered supercell. Using the same averaging technique we report the evolution of the ferroelectric and antiferrodistortive instabilities with composition. 
Ph. Ghosez, D. Desquesnes, X. Gonze, and K. M. Rabe