TO A QUESTION OF SULFUR SITES IN CRYSTAL STRUCTURES OF TETRAHEDRITE GROUP MINERALS: RELATIONSHIPS BETWEEN OCCUPANCY, EFFECTIVE ION SIZES, AND UNIT CELL PARAMETERS

In this work, a crystal chemical analysis of the known experimentally deciphered crystal structures of tetrahedrite group minerals was carried out in order to reveal the relationships between the occupancies of anion crystallographic sites in the structures, their effective sizes and unit cell parameters. To achieve this aim, we analyzed the effective sizes of the 24g and 2a anion sites in 68 deciphered crystal structures of tetrahedrite group minerals according to the published data. The analysis was carried out using the TOPOSPro software package by partitioning the space into Voronoi–Dirichlet polyhedra (VDP). It has been shown theoretically for the first time that the content of a large sulfur ion and its deficiency affect the unit cell parameter. A linear correlation between the VDP volume of the anionic site of S^2– (24g) and the unit cell parameter in minerals of the tetrahedrite group was established, which shows that the anionic substructure dictates the structural motif in this class of compounds. It was found that the change in the VDP volumes of sulfur anions is associated with different occupancies of anionic sites. It is found that the formula (unit cell) of the compound contains fewer than 13 sulfur ions in almost all deciphered crystal structures of tetrahedrite group minerals. It was concluded that the calculated VDP volume of the 24g anionic position less than 22 ų indicates a significant deficit in the anionic substructure. It was shown that, using information about the VDP volumes of all anionic and cationic sites in the structure, it is possible to predict the unit cell parameters of minerals of the tetrahedrite group with an accuracy of 0.01 Å