Structure types – a review

Abstract

Structures of binary inorganic AxBy compounds with A and B on two Wyckoff positions are characterized by the self‐coordination numbers Ti, i = 1–3, of A and B atoms. The T1 = 0–12 values of 122 structure types can be correlated with different topologies, A–A interactions and densities. High T1 values like T1 = 12 are obtained for fcc or hcp sphere packing with maximum density of A atoms and interstitial B atoms. Hexagonal or tetragonal layered compounds are recognized by the Ti values 6 6 6 or 4 4 4. The T1 = 2 values are found for chains, T1= 1 for ordered molecules like N2 or Br2. The A and B atoms of few compounds like NaCl or CsCl form a pc or bcc sphere packing. The T1 = 0 values of Na or Cs atoms indicate repulsive Na–Na or Cs–Cs interactions. Distorted structures of a structure type are recognized, if atoms with slightly different A–A or B–B distances are included in the proper coordination shells. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Characteristic Lattice Complexes

“…The x = 0.245 value of Ti atoms in the Ti 2 C structure (CdCl 2 antistructure type) is close to x = 1/4 of the (12 6 24) (Table 4) [19]. The NaZn 13 and CaCu 5 structures are examples of different neighborhoods of B particles. Different packings were also observed for micelles [20] in Wyckoff positions 225-a (12 6 24), 229-a (8 6 12), 223-ac (8 6 12 and 2 8 16) or 227-da (6 12 12 and 4 12 12).…”

“…The self-coordination numbers T 1 , T 2 , T 3 of 3D lattice complexes with zero or one parameters could be determined in a similar way as outlined for 2D structures [13] (Table 3). The cubic lattice complexes with variable x can degenerate at certain x values as was outlined for 2D complexes.…”

“…Most of the lattice complexes with 4 ≤ T 1 ≤ 12 are homogeneous sphere packings [8,13]. The nearest neighbors of layered structures or unstable sphere packings are on the meridian or one hemisphere.…”

Morphological lattice complexes

“…BiF 3 /AlFe 3 and (NH 4 ) 3 FeF 6 are examples with AB 3 stoichiometry, which can be found in Table 6 of [11]. The T i values of other A x B y compounds cannot be combined.…”

“…Characteristic lattice complexes of space group numbers 75 -230 with less than two parameters c/a, x, y or z were analyzed for maximum T i values [11] Binary or quasibinary compounds AB like NaCl or CaCO 3 were analyzed for morphological lattice complexes with self-coordination values T 1 T 2 T 3 of A and B and A + B for P = P A = P B (Table 2). Some formulas Cl 2 Cd or OCu 2 are written differently because of the increased T i values (12 6 24, S) of Cl or O atoms.…”