Quantitative analysis of hyperbolic frameworks silicate densities

7 Quantitative analysis of hyperbolic frameworks silicate densities 

Wide-pore zeolites must have a low framework density (FD), equal to the number of tetrahedral T atoms (silicon or aluminium) per lOOOA. Two questions arise naturally in this context. What sets the framework density What is the minimum FD achievable for a hydrophobic zeolite These are difficult questions to answer within the standard three-dimensional Euclidean view of these frameworks. However, within a two-dimensional hyperbolic perspective, they are readily answered. 

The latter view recognises that infinite crystalline frameworks are tesselations of periodic hyperbolic surface, as in Figs. 2.9. To many, this is an excessively complex description. However, this description does yield new insights into the nature of these covalent frameworks. 

Define the average value of the Gaussian curvature (see section 1.9) by 

Here D is the area (in A2) per vertex of the framework e.g. per Si02 group for 

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