Phase-Field Modeling of Ferroic Domains in Strained Structures

Application of lattice strain via epitaxial growth of perovskite oxide ferroelectric and multiferroic films and superlattices on compliant lattice-mismatched substrates is an important strain-engineering technique to tune their dielectric and piezoelectric properties. Both first principles calculations of electronic structures and phenomenological models based on Ginzburg–Landau–Devonshire (GLD) theory have been used to predict the effect of strain-tuning on structure-property relations in ferroics. In this chapter, we focus on the application of phenomenological GLD models for predicting phase transitions and domain structure evolution in strained ferroelectrics. First we describe key crystallographic and thermodynamic aspects of the mean-field GLD theory of ferroics. Next we describe phase-field models of ferroelectrics. GLD theory forms the basis of phase-field models of domain structure evolution of ferroelectrics. Phase-field models assume a diffuse interface between coexisting phases and avoid explicit tracking of interface. Thus, complex domain morphology in ferroics during paraelectric to ferroelectric phase transition can be conveniently simulated using these models. Here we provide the recipe to performphase-field simulations of strained ferroics to predict their structure-property relations as a function of external electromechanical loading. We also provide a few examples of phase-field implementation and conclude by summarizing the future scope of these models.