A phase diagram for epitaxial PbZr _1-xTi _xO ₃ thin films at the bulk morphotropic boundary composition

A phase diagram of temperature versus strain was constructed for a (001)-oriented PbZr _1-xTi _xO ₃ epitaxial single crystal thin film near the bulk morphotropic boundary composition (x = 0.47) on an (001)-oriented cubic substrate. The phase-field approach is employed. It is shown that a mixture of distorted rhombohedral, orthorhombic, and tetragonal phases exists under small values of strain, i.e., close to the in-plane clamped boundary condition. This result contradicts thermodynamic calculations assuming a single-domain state that predicted a single distorted rhombohedral phase under similar strains. Furthermore, it is demonstrated that under a large tensile strain current phase-field simulations showed a tetragonal phase with a ₁/a ₂ twin structures as the stable state whereas thermodynamic calculations predicted an orthorhombic phase.