Algorithms for calculations of homologue order N in the homologous series of sulfosalts

Homologous series are series of compounds built on exactly the same crystal chemical principles, the members of which differ by the volume of certain, incrementally growing structure portions. They are especially common and productive among complex sulfides of As, Sb, Bi with Pb, Tl, Ag, Cu, Fe, etc., known under a collective name of As, Sb, or Bi sulfosalts. Individual members are best diagnosed by single-crystal diffraction which, however, may be difficult to perform for many natural materials because of grain size and intergrowths. The algorithms derived and/or collected here use the incremental changes in chemical composition that are connected with the above incremental changes in crystal structure for determination of the homologue order N and of the mineral species in question. Twelve different sulfosalt series as well as different approaches to the joint problem of homologue order combined with cation substitutions or anion vacancies are treated in detail.