Theory of strain phase separation and strain spinodal: Applications to ferroelastic and ferroelectric systems

In the well-known phase decomposition process, a phase with a homogeneous composition separates into two phases with different local compositions that can be geometrically determined by the common tangent construction on the molar free energy versus composition curves. Here we consider an analogous phase destrain process in which a phase with a homogeneous strain separates into two phases with different local strains that can be geometrically determined by the common tangent construction on the volume free energy density versus strain curves. There is also a complete analogy between compositional and strain spinodals. Within the phase destrain model, we provide a general thermodynamic formulation for the phase rule, lever rule, equilibrium conditions of chemical potential, and coherent/incoherent strain spinodals. Using the cubic to tetragonal ferroelastic/ferroelectric transition as an example, we study the possible strain phase separation and spinodal phenomena, and calculate the strain-strain and strain-temperature phase diagrams for the first-order proper, first-order improper, and second-order improper ferroelastic transitions. The proposed phase destrain theory complements the existing compositional phase separation theory and can serve as guidance for the analysis and design of multi-domain/multi-phase structures during any phase transitions associated with structural changes.