Continuous transformations are possible when free energies are concave with respect to an order parameter. Spinodes occur when the curvature of the free energy is zero and admit spinodal decomposition as a route to phase transformations that would otherwise require nucleation and growth of new phases. John W. Cahn’s classical analysis of the chemical spinodal with and without strain effects is a linear perturbation analysis about a quenched state for a conserved order parameter (composition).

A few reports of spinodal decomposition in ferroelectrics have appeared recently. Buse et al (2018) report an experimental observation of spinodal decomposition in BZT-BCT ferroelectric crystals during high temperature annealing based on composition modulations. Ke et al. (2020) predict phase decomposition by spinodal decomposition for nanodomain-in-microdomain structures in a model multi-phase ferroelectric in phase-field simulations. Enhanced piezoelectric performance has been reported for morphotropic phase boundary compositions with ferroelectric nanodomains, which could be achieved by a spinodal pathway. No general analysis of spinodal decomposition in ferroelectric crystals was found by the author in the literature.

Here the conditions for spinodal decomposition in a bulk ferroelectric are determined. The critical wavelength for stable perturbations is derived. Predictions are made for single phase ferroelectrics below the Curie temperature, T_c, for both first order and second order ferroelectric transitions. The ferroelectric multi-phase field model is used to make predictions for ferroelectrics that undergo ferroelectric-ferroelectric phase transformations at a morphotropic phase boundary at T_MPB. Specific predictions are made for tetragonal barium titanate and for tetragonal + rhombohedral BZT-50BCT using published model parameters.