Stuffed Derivatives of Close-Packed Structures

Decades ago Buerger described and later Palmer reviewed stuffed silica crystal structures widely used by mineralogists. Many publications and books have discussed common crystal structures in terms of close-packing of one set of atoms or ions (P sites) with other atoms or ions in tetrahedral (T) or octahedral (O) sites. Douglas and Ho described many minerals and compounds as having filled or partially filled layers in the regular pattern, PTOT. In the cubic close-packed (ccp) structure twelve neighbors of an atom form a cuboctahedron with six O and eight T voids. Filling all O sites as in NaCl, all T sites as in CaF₂, or all O and T sites as in BiLi₃ of a cuboctahedron formed by one set of ions gives structures with no loss of symmetry. More complex structures are described also. In the hexagonal close-packed (hcp) structure twelve neighbors of an atom form a 14-sided polyhedron described as a twinned cuboctahedron. For NiAs, the 14-sided polyhedron is formed by As atoms with Ni atoms filling O sites, but these O sites are aligned at the same packing positions without screening. The NiAs structure is uncommon. ReO₂ has O sites half-filled by Re atoms and staggered to avoid close pairs of Re atoms. Pairs of T sites above and below P layers are very close without screening, so close that both of these sites cannot be filled without interference or chemical bonding. For those based on hcp only the PT structure with full layers is common, not PO, PTT, or PTOT. These severe limitations can be predicted from considerations given here. The concept of stuffing the 14-sided polyhedron for ccp structures shows the great variety of combinations of filled and partially filled P, T, and O layers and the polyhedron for hcp shows the severely limited combinations.