Crystallographic Basis for the Stability of Abundant (Popular) Structure Types

In compliance with the hypothesis that the crystal structure stability increases with a decrease in the degrees of freedom of the constituent atoms, we propose quantitative criteria for structures: the ratio between the amount of the degrees of freedom of atoms to their number in a primitive cell (S) and the fundamental volume (V*)–the quotient of the cell volume (asymmetric unit) and the order of the symmetry group (M) that is the general position multiplicity. The crystallographic analysis of diamond and spinel structure types and their comparative analysis with stability and packing criteria are performed. The study uses the findings from the analysis of abundant less symmetrical tourmaline and apatite structure types which confirm the existence of standard frameworks–symmetrical spatial configurations of atomic sites that can be taken by atoms of various types.