CRYSTALLOGRAPHIC CONTROLS ON THE DISTRIBUTION OF MINERALS AMONGST THE SPACE GROUPS

The IMA’s online database of accepted minerals contains 4840 species for which space group symmetries have been defined. The vast majority of these minerals are monotypic while ~9% are polytypic. It has long been recognized that minerals are non-uniformly distributed among the space groups as well as their corresponding point groups and crystal systems. This non-uniformity is not, however, non-systematic. Rather, six general rules have been identified that strongly influence the distribution of known minerals. First, at the highest level, the 7 holohedral space groups are more populated than the 13 merohedral fixed-point-free (Bieberbachian) space groups. Second, within crystal systems, space groups with centrosymmetric geometries are more populated than enantiomorphic space groups. Additionally, the 11 chiral pairs are represented by few or no known species. Third, within any point group, space groups with high Wyckoff multiplicities are more densely populated than those with lower values. Fourth, within the 73 arithmetic space group classes, in most cases, non-symmorphic space groups are more richly populated than their linked symmorphic space group. Further, in those cases where both hemisymmorphic and asymmorphic analogs are present the asymmorphic space groups typically contain more species. Finally, in some point groups rich in space groups – such as the 222 and mm2 groups of the orthorhombic system – it is noted that minerals preferentially populate screw axis geometries over those with rotation axes. Future study may identify other similar subtle controls on the frequency distribution of minerals among the space groups. Given the rate of new mineral identification, it is likely that most, if not all, of the 37 space groups currently devoid of mineral examples will eventually be populated by future discoveries.