The Origin of the Crystallographic Pedigree

The origin of the crystallographic pedigree [Haisa (1978). Acta Cryst. A34, 753-759] is shown to be the Fm3m family, by examining crystal structures of chemical elements and compounds. The family is maintained by making the most of the relevant symmetry sites over the structures of a (Strukturbericht A 1), ab (B1), ac (C1), abc (L21), abd, ae, abe, ace (Jll), abce (J21), abcde, bcef (D89), abcef (H5s), cdf, bdef (D8a), abdeJ; acefh (D84), ai (D2y), abcg], abdfk and abcejl types in Wyckoff notation. The descent in site symmetry from O h to its subgroups may be caused by the balance of the interactions between the neighbors of atomic contents which can be estimated from the lifting of the degeneracy of the nearest-neighbor distances, or the coordination index. When the interactions become out of balance, a descent of the space group through Pm3m, Im3m and P63/mmc to their subgroups occurs to form the crystallographic pedigree.