Density-functional study of the Ba$_{x}$Bi$_{(1-x)}$(M$_{(1-x)/2})$Ti$_{(1+x)/2}$O$_3$ perovskite solid solution

Using density-functional theory we predict properties of the solid solution perovskites Ba$_{x}$Bi$_{(1-x)}$(M$_{(1-x)/2})$Ti$_{(1+x)/2}$O$_3$ where M is Mg, Ni or Zn. These properties are strongly affected by the presence of both A-site and B-site disorder. We study all distinct orderings within a given $2\times2\times2$ supercell.