Architecture of crystal structures from square planes

Abstract

The crystal structures of ordered b.c.c. (body-centered cubic), f.c.c. (face-centered cubic) or primitive cubic alloys A_xB_y and related NaCl, ZnS or CaF_2 derivative structures are characterized by the self-coordination numbers T_1, T_2 of the A atoms with A atoms. Structures with identical T_1 and T_2 values for all A atoms are at the corners of T_1 and T_2 structure maps, and can be analyzed for attractive or repulsive interactions of A atoms. Most observed structures are at the borders of the structure map and can be obtained by ∼10 different combinations of structural units. The different combination mechanisms explain e.g. the shear structures of CuAu II or \rm Nb_2O_5 and the occurrence of vacancies in NaCl-related structures like NbO.