THE DENSITY OF 3-DIMENSIONAL NETS

Estimates for the density of periodic three-dimensional nets in Euclid ean three-dimensional space (R3) are derived. The analysis assumes tha t the nets tile triply periodic hyperbolic surfaces that are free of s elf-intersections (embedded in R3). Upper and lower bounds of the net density as a function of the average ring size on the surfaces are giv en. These geometrical relations are compared with framework densities of a range of silicon-rich zeolites, silica clathrasils and dense four -connected silicates in order to separate the roles of geometry and ch emistry in setting silicate densities. The data suggest that silica fr ameworks are constrained by an approximate requirement of constant are a per framework vertex in addition to the impositions of Euclidean thr ee-space and are thus hyperbolic two-dimensional (layer) structures.