Crystallographic Orientation Relationships Between Hexagonal and Tetragonal Barium Titanate

The high-temperature hexagonal (h) phase has been found to retain metastability at room temperature and co-exist with the room-temperature tetragonal (t) phase in hot-pressed BaTiO₃ ceramics. The crystallographic orientation relationships between two polytypes have been analyzed by TEM and selected-area diffraction patterns (SADPs). The relationships are illustrated using transformation matrices for both the forward h→t phase transformation ( M _f) and the backward t→h phase transformation ( M _b) based on two independent microstructures containing h-particle in t-matrix and t-particle in h-matrix, respectively. Self-consistent transformation matrices are derived from the coincident reflections in corresponding SADPs. The forward and backward matrices are inverse matrix to each other.