|Space group||136 P4_2/mnm D4h14|
|Coordination||see the comment below|
|PDB files||C4 (the most symmetric form), unit cell, X backbone|
|Substances||dioxides and difluorides (see the table below)|
Component A is a metal or semiconductor, X is something like oxygen or fluoride. The crystal has ion-covalent bonding, where X cations tend to form close-packed structure and A tend to have optimal coordination. From these reasons the optimal value of parameters are c/a=2-sqrt(2) and xi=1-1/sqrt(2) (pdb). At this point the packing factor of X-backbone (pdb) has local maximum (δ=4(3sqrt(2)-4)=0.971, z=11) and the coordination polyhedron of A atom is an octahedron AX6. Now we must take into account that the placement of A atoms into octahedral voids of X-backbone expands those octahedra in the direction of minimal resistance. Looking at the next coordination sphere we see that 4 X atoms in AX6 octahedron have 3 X atoms in behind and 2 X atoms have only one. Therefore in this direction the octahedron AX6 will be expanded in a way preserving the A-X distances. Lighter elements have more rigid covalent bonds so the corresponding crystals are less deformed (e.g. for TiO2 δ=0.73). This all is illustrated in the diagram below.
Note that the nearest higher symmetry is I4/mmm when xi=1/4 (Wyckoff position 2b) but it is energetically unfavourable.