Coordination sequences of zeolites revisited: asymptotic behaviour for large distances

The coordination sequences of several zeolite frameworks (faujasite, Linde type-A, KFI, sodalite and analcime) have been obtained by direct counting until at least the 23rd coordination sphere. This allows us to study the asymptotic behaviour of the number of sites in the ith shell, Ni, for high values of i. In all cases, Ni adapts well to a parabolic law, Ni=ai2+b, as expected for three-dimensional lattices. The constant a, which ranges from 1.43 for faujasite to 2.40 for analcime, is typical for each framework, and is directly related to the topological density of these materials. For the faujasite framework, we find a modulation superimposed on the parabolic dependence, which is associated with the particular connectivity of this structure.