Strain phase equilibria and phase-field method of ferroelectric polydomain: A case study of monoclinic K_xNa_1 −xNbO₃ thin films

Knowledge of the thermodynamic equilibria and domain structures of ferroelectrics is critical to establishing their structure–property relationships that underpin their applications from piezoelectric devices to nonlinear optics. Here, we establish the strain condition for strain phase separation and polydomain formation and analytically predict the corresponding domain volume fractions and wall orientations of, relatively low symmetry and theoretically more challenging, monoclinic ferroelectric thin films by integrating thermodynamics of ferroelectrics, strain phase equilibria theory, microelasticity, and phase-field method. Using monoclinic K_xNa_1 −xNbO₃(0.5 < x < 1.0) thin films as a model system, we establish the polydomain strain–strain phase diagrams, from which we identify two types of monoclinic polydomain structures. The analytically predicted strain conditions of formation, domain volume fractions, and domain wall orientations for the two polydomain structures are consistent with phase-field simulations and in good agreement with experimental results in the literature. The present study demonstrates a general, powerful analytical theoretical framework to predict the strain phase equilibria and domain wall orientations of polydomain structures applicable to both high- and low-symmetry ferroelectrics and provide fundamental insights into the equilibrium domain structures of ferroelectric K_xNa_1 −xNbO₃ thin films that are of technology relevance for lead-free dielectric and piezoelectric applications.