A Multilevel Analytical Theory for Prediction of Ferroelectric Perovskite Oxide Properties from Composition

Prediction of properties from composition is a fundamental goal of materials science that is particularly relevant for ferroelectric perovskite oxide solid solutions where compositional variation is a primary tool for material design. Design of ferroelectric oxide solid solutions has been guided by heuristics and first-principles and Landau-Ginzburg-Devonshire theoretical methods that become increasingly difficult to apply in ternary, quaternary, and quintary solid solutions. To address this problem, a multilevel model is developed for the prediction of the ferroelectric-to-paraelectric transition temperature (T_c ), coercive field (E_c ), and polarization (P) of PbTiO₃ -derived ferroelectric solid solutions from composition. The characteristics of the materials at different length scales, starting at the level of the electronic structure and chemical bonding of the constituent ions and ending at the level of collective behavior, are analytically related by using ferroelectric domain walls and cationic off-center displacements as the key links between the different levels of the model. The obtained composition-structure-property relationships provide a unified quantitatively predictive theory for understanding PbTiO₃ -derived solid solutions. Such a multilevel analytical modeling approach is likely to be generally applicable to different classes of ferroelectric perovskite oxides and to other functional properties, and to materials and properties beyond the field of ferroelectrics.