Structural prototypes of disordered ferroelectric phases

We generalize our previous work on microscopic structural prototypes, first applied to the paraelectric phase of BaTiO₃ [PRR 4, L012042 (2022)], to its lower-symmetry tetragonal and orthorhombic phases, both possessing a degree of disorder seen in diffuse x-ray experiments [Acta Cryst. A 26, 244 (1970)]. As these lower-symmetry phases can host many more symmetry-allowed distortions in a supercell of a given volume than the cubic paraelectric phase, we show how we can streamline the analysis and filter admissible candidates using symmetry-constrained primitive cell instabilities before optimizing the structures with density functional theory. These prototypes are designed to serve as minimal models which can be used to faithfully represent these phases in calculations, and to be metastable: i.e. are local minima of the potential-energy landscape and possess no structural instabilities. The analysis is further extended to other ferroelectric titanates and niobates, finding that the ferroelectric prototypes consist of the primitive-cell polar mode with small distortions associated with primitive-cell instabilities. While these prototypes are nearly degenerate in energy with the unstable primitive cells, the small distortions surprisingly lead to dynamically stable structures.