Periodic arrays of identical ions packed with 10, 11, and 12 nearest neighbors

The relationships between 10, 11, and 12 coordination identical-sphere packing arrangements are discussed. Primitive tetragonal packing, which is adopted with minor distortions by rutile, has 11 coordination and may be regarded as an intimate intergrowth of close packing (12 coordination) and body-centered tetragonal (10 coordination) packing. Several other known and postulated structures are shown to represent different arrangements of the 50-50 intergrowth of c-axis square channel and c-axis strings of edge-shared octahedra typical of body-centered tetragonal packing and close packings, respectively. Partial cation occupancy of the square channels in such anion arrays would provide conduction pathways for small cations such as Li⁺. It is also shown that body-centered tetragonal packing is an intermediate of cubic and hexagonal close packing.