Relaxor ferroelectrics can be categorized into single-phase relaxors, reentrant relaxors, and polymorphic relaxors in terms of domain structure features. Among these, polymorphic relaxors with nanodomains in at least two different phases exhibit superior energy storage/electrocaloric properties compared with the other two types of relaxors. However, it has remained unclear how polymorphic relaxors form because of limitations in characterization techniques and, more importantly, a lack of theoretical models. In this work, we develop a phase-field model of polymorphic relaxors based on a perovskite-structured binary ferroelectric system with a cubic (C) to tetragonal (T) transition at one end and a C to rhombohedral (R) transition at the other, incorporating both the nanoscale compositional heterogeneity arising from the random distribution of substituted ions and the local electric fields generated by heterovalent ion substitution. Based on this model, we reproduce the domain structure features as well as the dielectric permittivity behavior and construct a complete phase diagram for polymorphic relaxors, all of which are consistent with experimental observations. Further analysis shows that composition near the morphotropic phase boundary (MPB) and strong local electric fields are the critical dual factors driving the formation of polymorphic relaxors. Once the two necessary conditions are not simultaneously satisfied, either single-phase relaxors or reentrant relaxors occur. This work unravels the origin of polymorphic relaxor formation by developing a phase-field model of polymorphic relaxors, which provides a theoretical foundation for the design of relaxors with enhanced performance.

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• Dielectric properties
• Ferroelectric domains
• Ferroelectricity
• Relaxor ferroelectrics
• Phase-field modeling