Crystallography of (111) twins in BaTiO₃

Abstract

A transmission electron microscopy study has revealed (111) twins in cubic/tetragonal BaTiO₃ ceramics. The relation between the lattices in the bicrystal is described by a coincident site lattice cell with Σ = 3. By considering the structure of BaTiO₃, the formation of a twin can be understood as a shear operation with (111) planes successively translated by ⅓[1ζ2] vectors. Because of the small tetragonal distortion at room temperature, an α-δ fringe contrast is observed at the twin boundary for reflections which coincide, in the cubic phase, for matrix and twin. In the tetragonal phase, (111) planes parallel to the twin boundary remain parallel for matrix and twin. From structure images the width of the interface in the tetragonal phase is estimated to be less than three unit cells. The distortion of planes near the interface is caused by the presence of the tetragonal phase. For the structural model of an ideally coherent interface, a (Ba-O₃) plane is proposed. This preserves the Ti-O octahedra at the interface by the formation of a Ti₂O₉ structural unit which is also found in the hexagonal form of BaTiO₃. Possible formation mechanisms of twins are discussed.