Architecture of crystal structures from square planes.

The crystal structures of ordered b.c.c. (body-centered cubic), f.c. c. (face-centered cubic) or primitive cubic alloys AxBy 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 approximately 10 different combinations of structural units. The different combination mechanisms explain e.g. the shear structures of CuAu II or Nb(2)O(5) and the occurrence of vacancies in NaCl-related structures like NbO.