The crystal structure of hexagonal barium titanate

The crystal structure of hexagonal barium titanate has been determined by X-ray methods. The unit cell, which contains six units of BaTiO₃, has a₀ = 5.735 A. and c₀ = 14.05 A. In the space group C6₃/mmc all the ions occur at special positions: 2 Ba at (b), 4 Ba at (f), 2 Ti at (a), 4 Ti at (f), 6 O at (h), and 12 O at (k). The structure is built up of six close-packed layers of Ba and O ions, each layer consisting of one Ba to three O ions, having the packing sequence ABCACB. The Ti ions are located in the oxygen octahedral holes between the layers. The structure is remarkable in that two-thirds of the TiO₆ octahedra occur in pairs which share a face to form Ti₂O₉ co-ordination groups. The compensating distortion which occurs in the Ti₂O₉ groups increases the Ti-Ti distance by 0.33 A. while the O-O distance in the shared face is decreased by 0.38 A. The existence of Ti₂O₉ groups in hexagonal barium titanate, an unusually stable substance under these circumstances, constitutes a notable exception to certain of Pauling's rules for complex ionic structures.