A structure hierarchy for silicate minerals: chain, ribbon, and tube silicates. (26th April 2020) - Day, Maxwell C.; Hawthorne, Frank C.
Abstract: A structure hierarchy is developed for chain-, ribbon- and tube-silicate based on the connectedness of one-dimensional polymerisations of (TO4 ) n − tetrahedra, where T = Si 4+ plus P 5+, V 5+, As 5+, Al 3+, Fe 3+, B 3+, Be 2+, Zn 2+ and Mg 2+ . Such polymerisations are described by a geometrical repeat unit (with ng tetrahedra) and a topological repeat unit (or graph) (with nt vertices). The connectivity of the tetrahedra (vertices) in the geometrical (topological) repeat units is denoted by the expression c Tr ( c Vr ) where c is the connectivity (degree) of the tetrahedron (vertex) and r is the number of tetrahedra (vertices) of connectivity (degree) c in the repeat unit. Thus c Tr = 1 Tr1 2 Tr2 3 Tr3 4 Tr4 ( c Vr = 1 Vr1 2 Vr2 3 Vr3 4 Vr4 ) represents all possible connectivities (degrees) of tetrahedra (vertices) in the geometrical (topological) repeat units of such one-dimensional polymerisations. We may generate all possible c Tr ( c Vr ) expressions for chains (graphs) with tetrahedron (vertex) connectivities (degrees) c = 1 to 4 where r = 1 to n by sequentially increasing the values of c and r, and by ranking them accordingly. The silicate ( sensu lato ) units of chain-, ribbon- and tube-silicate minerals are identified and associated with the relevant c Tr ( c Vr ) symbols. Following description and association with the relevant c Tr ( c Vr ) symbols of the silicate units in all chain-, ribbon- and tube-silicate minerals, the minerals are arranged into decreasing O:T ratio from 3.0 to 2.5, an arrangement that reflects their increasing structural connectivity. Considering only the silicate component, the compositional range of the chain-, ribbon- and tube-silicate minerals strongly overlaps that of the sheet-silicate minerals. Of the chain-, ribbon- and tube-silicates and sheet silicates with the same O:T ratio, some have the same c Vr symbols (vertex connectivities) but the tetrahedra link to each other in different ways and are topologically different. The abundance of chain-, ribbon- and tube-silicate minerals decreases as O:T decreases from 3.0 to 2.5 whereas the abundance of sheet-silicate minerals increases from O:T = 3.0 to 2.5 and decreases again to O:T = 2.0. Some of the chain-, ribbon- and tube-silicate minerals have more than one distinct silicate unit: (1) vinogradovite, revdite, lintisite (punkaruaivite) and charoite have mixed chains, ribbons and/or tubes; (2) veblenite, yuksporite, miserite and okenite have clusters or sheets in addition to chains, ribbons and tubes. It is apparent that some chain-ribbon-tube topologies are favoured over others as of the ~450 inosilicate minerals, ~375 correspond to only four topologically unique graphs, the other ~75 minerals correspond to ~46 topologically unique graphs.