ANALYSIS OF GROUP-SUBGROUP RELATIONSHIPS WITHIN BIMORPHIC MONOCLINIC MINERALS USING EDGE WEIGHTED DIRECTIONAL GRAPHS

Bimorphic monoclinic minerals exhibiting group-subgroup parings among their space groups are analyzed using edge weighted directional graphs, a mathematical approach that facilitates enhanced understanding of patterns and distributions of polymorphism. For simplicity, this preliminary analysis is limited to consideration of 59 known monoclinic mineral species exhibiting bimorphic pairings. Minerals of the monoclinic system were chosen because of the relative simplicity of the symmetries and structures present in the group-subgroup relationships as well as the frequency of occurrence and proportional distribution of bimorphic species among the system’s 13 space groups relative to that exhibited by the more common monomorphic monoclinic species. All of the 59 known bimorphic pairings exhibit supergroups drawn from the 2/m point group. Maximal subgroups of the klassengleiche type within the 2/m point group are found to be the most commonly occurring bimorphic pairing such that 8 of the 13 possible pairs are represented by 31 of the 59 known bimoprhic monoclinic minerals. Conversely, frequencies of pair occurrence and the number of minerals exhibiting those pairings are found to decrease with increasing magnitudes of symmetry difference between the supergroup and paired subgroup such that translationengleiche and general subgroup pairing are increasingly less common. The prevalence of bimorphism in pairings involving high-symmetry structures is a novel observation and suggests similarities in and differences between the crystallographic symmetry of space group pairings of bimorphic species is a significant factor influencing the occurrence of polymorphism.