There is no remarkeable influence of the lattice vibrations on D even if the windows are so small that the potential threshold hinderes the diffusion of guest molecules. In the cation free form the Al atoms are replaced by additional Si atoms and the sodium and calcium ions are missing. The elasticity of the lattice is realized by a harmonic central force model. The elasticity of the angles is realized by additional fictive forces between oxygens that are separeted by only one T atom. Click to magnify.
Large sigma means small window.
The window that connects two adjacent cavities in the zeolite can be characterized by two slightly different diameters. This figure shows the probability distribution for the instantaneous values of the two window diameters defined in figure 15 for two special cases. One case is the lattice with Si, Al and the other one the pure silicon version. The dashed lines indicate the values of the two diameters which result if the lattice coordinates of the NaA are taken from the literature. D is extremely sentitive with respect to the window diameter in this system since the particle size and the window diameter are nearly the same.