Crystal chemistry of zirconosilicates and their analogs: topological classification of MT frameworks and suprapolyhedral invariants

The first attempt is undertaken to consider systematically topological structures of zirconosilicates and their analogs (60 minerals and 34 synthetic phases), where the simplest structure units are MO₆ octahedra and TO₄ tetrahedra united by vertices ([TO₄]:[MO₆] = 1:1-6:1). A method of analysis and classification of mixed three-dimensional MT frameworks by topological types with coordination sequences {N_k} is developed, which is based on the representation of crystal structure as a finite `reduced' graph. The method is optimized for the frameworks of any composition and complexity and implemented within the TOPOS3.2 program package. A procedure of hierarchical analysis of MT-framework structure organization is proposed, which is based on the concept of polyhedral microensemble (PME) being a geometrical interpretation of coordination sequences of M and T nodes. All 12 theoretically possible PMEs of MT₆ polyhedral composition are considered where T is a separate and/or connected tetrahedron. Using this methodology the MT frameworks in crystal structures of zirconosilicates and their analogs were analyzed within the first 12 coordination spheres of M and T nodes and related to 41 topological types. The structural correlations were revealed between rosenbuschite, lavenite, hiortdahlite, woehlerite, siedozerite and the minerals of the eudialyte family.