A first-principles-derived scheme that incorporates ferroelectric and antiferrodistortive degrees of freedom is developed to study finite-temperature properties of $\mathrm{Pb}({\mathrm{Zr}}_{1-x}{\mathrm{Ti}}_x){\mathrm{O}}_3$ solid solution near its morphotropic phase boundary. The use of this numerical technique (i) resolves controversies about the monoclinic ground state for some Ti compositions, (ii) leads to the discovery of an overlooked phase, and (iii) yields three multiphase points that are each associated with four phases. Additional neutron diffraction measurements strongly support some of these predictions.

• Received 14 July 2006

DOI:https://doi.org/10.1103/PhysRevLett.97.157601