Shell model for BaTiO$_3$-Bi(Zn$_{1/2}$Ti$_{1/2})$O$_3$ perovskite solid solutions

Even though the composition of BaTiO$_3$-Bi(Zn$_{1/2}$Ti$_{1/2})$O$_3$ perovskite solid solutions is similar to other ferroelectric compounds, the dielectric response is unusual. Results of permittivity measurements as a function of temperature show a diffuse phase transition indicative of a weakly coupled relaxor behavior.\footnote{C. C. Huang and D. P. Cann, J. Appl. Phys. {\bf 104}, 024117 (2008)} To investigate the weakly coupled relaxor behavior in these materials at intermediate length scales we are developing a newly calibrated shell model based on first-principles supercell calculations of both the solid solution and its compositional endpoints. Initial results for its phase diagram will presented.