Strain phase separation: Formation of ferroelastic domain structures

Phase decomposition is a well-known process leading to the formation of two-phase mixtures. Here we show that a strain imposed on a ferroelastic crystal promotes the formation of mixed phases and domains, i.e., strain phase separation with local strains determined by a common tangent construction on the free energy versus strain curves. It is demonstrated that a domain structure can be understood using the concepts of domain/phase rule, lever rule, and coherent and incoherent strain phase separation, in a complete analogy to phase decomposition. The proposed strain phase separation model is validated using phase-field simulations and experimental observations of PbTiO3 and BiFeO3 thin films as examples. The proposed model provides a simple tool to guide and design domain structures of ferroelastic systems.