Dielectric properties of the $Ba Ti O_3 - Bi (Zn_{\frac{1}{2}} Ti_{\frac{1}{2}}) 0_3$ solid solution from density-functional theory

Using density functional theory combined with the modern theory of polarization, we predict dielectric properties of $Ba Ti O_3$ and $Bi (Zn_{\frac{1}{2}} Ti_{\frac{1}{2}}) 0_3$ in solid solution. In particular, we study the effects of disorder on the system in the presence of a homogeneous finite electric field. We consider all unique configurations of the solid solution in a given supercell, computing the polarization resulting from a given applied field. This provides a statistical ensemble from which we predict the finite-temperature dielectric response. We will discuss the implications for uniform bulk solids and within polar nano-regions of a non-uniform solid.