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

Abstract

The crystal structures of ordered bcc, fcc or primitive cubic alloys AXBy and related NaCl, ZnS or CaF 2 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 2 05 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 evolution .

Review: Different types of ordering

“…9a). The pc ordering of A and B can be found in NaCl (0 12 0 ; 1 structure) and in magnetic compounds RM like AuMn, β' -ZnMn, Pt 3 Fe or DyCrO 3 [17]. The spins with A = ↑ and B = ↓ direction of β'-ZnMn are aligned antiferromagnetically with positions of A and B as in NaCl.…”

Interactions in Sphere Packings

“…The ordering of A and B in two-dimensional A x B y was investigated for the two-dimensional square, hexagonal, honeycomb and kagomé nets by the following procedure [9][10][11]: (a) The size of the unit cell was increased in a systematic way [12] (Table 1) and the A and B positions occupied to a maximum of 50% at r = y/x = 1. (the probability to find an A particle in the i-th shell) [13] is used for the structure map [9]:…”

“…The structure maps of the different three-dimensional lattices or packings were obtained by the same procedure as outlined for the two-dimensional square and hexagonal nets [1][2][3][4]11]. The borders of the structure maps can be characterized by different linear relations of the T 1 and T 2 values [4,11] (Table 3).…”

“…The borders of the structure maps can be characterized by different linear relations of the T 1 and T 2 values [4,11] (Table 3).…”

“…The different 0 0 6 ; 5 (Al) and 3 0 6 ; 2 (B) values of the ph structure map [11] indicate repulsive interactions of A particles and attractive interactions of B particles. The A particles are separated with no contact to other A particles.…”