Variations on the theme of closest packing: The structural chemistry of barium titanate compounds

The crystal structures of most barium titanates can be described as hexagonal closest packings consisting of atoms of Ba and O and of vacancies between them. The pseudohexagonal cell constants of these compounds are close to the ideal hexagonal values. The most common stacking is the six-layer sequence (hcc)₂. The mean diameter of a closest packed particle in these packings is 2.85 Å, while the mean thickness of a layer is 2.33 Å. The recognition of this closest packing principle has been helpful in the solution of many of the crystal structures of this group. With the exception of BaTi₄O₉, all the barium titanates which are usually classified as tunnel structures or Wadsley-Andersson phases can be described as cubic closest packings. The deviations of the pseudocubic phases from the ideal cubic values are larger than in the pseudohexagonal cases. A few of the barium titanates are related to the so-called 3.0-Å phases based on the rutile-type octahedral chain. These structures are characterized by having two almost closest packed corrugated layers at right angles to each other. The structures of a number of compounds in which the Ti⁴⁺ atoms are replaced partly by Ti³⁺, Al, Pt⁴⁺, or Li are based on principles similar to those of the barium titanates proper. The mean TiO distances in the coordination octahedra of the barium titanates depend strongly on the distortions of the octahedra.