The magnitude and direction of polarization within alloys of the tetragonally distorted Bi (Zn1/2 Ti1/2) O3 (BZT) and the rhombohedrally oriented (Bi1/2 Sr1/2) (Zn1/2 Nb1/2) O3 are explored using density functional theory. For compositions with 50% of BZT, we find that the polarization is mainly in the  direction. Conversely, for low concentrations of BZT the polarization is rhombohedrally oriented. Based on these results we propose a phase diagram with a monoclinic phase that appears when the BZT concentration is roughly 50%. At this concentration, the material may have a useful piezoelectric response.