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., domain and phase de-strain 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, coherent and incoherent de-strain within the de-strain model description, in a complete analogy to phase decomposition. The proposed de-strain model is validated using phase-field simulations and experimental observations of PbTiO_3 and BiFeO_3 thin films as examples. The de-strain model provides a simple tool to guide and design domain structures of ferroelastic systems.