The Jig-saw puzzle of crystal structures : alloys, superconducting oxides, semiconductors, ionic conductors, surface adsorbates and magnetic structures

The crystal structures of ordered bcc, fcc or primitive cubic alloys AXBy and related NaCl, ZnS or CaF2 derivative structures are characterized by the self-coordination numbers T1, T2 of the A atoms with A atoms. Structures with identical T1 , T2 values for all A atoms are at the corners of T1 , T2 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 different combinations of structural units . The combination mechanisms explain e.g. the shear structures of CuAu II or Nb 205 and the occurrence of vacancies in NaC1 related structures like NbO . Many other ordered structures like magnetic ordering, adatoms an metal surfaces, colloids and Clusters are analyzed by the same method . The very large numbers of possible structures are reduced to a smaller number of structures at the borders of the structure maps, which are stabilized by enthalpy. The other structures are stabilized by entropy. The T1 , T2 values of DNA sequences in different areas of the structure map are related with the evolutio