Density fluctuations in vitreous SiO2 and GeO2

The early crystallite, random network and cybotactic theories of the structure of single component glasses, such as SiO2, differ in respect of their predictions concerning the frequency of occurrence and size of crystalline-like groupings within the vitreous network, and hence in the expected form of the spatial fluctuations in their average number density, rho degrees. The RMS fluctuations in average number density, <Delta rho(2) >(1/2), for vitreous SiO2 and GeO2 are calculated from the zero-Q limit of the static structure factor, S(Q), and it is shown that neither the early crystallite nor the cybotactic theory can be eliminated on the basis of small-Q scattering data. On the other hand, the devitrification behaviour for both glasses indicates the presence of potential crystallisation nuclei (cybotactic groupings) corresponding to the cristobalite polymorph, and hence clusters of 6-membered shortest path rings. An stimate is made as to the frequency of occurrence of crystalline-like clusters of 6-membered rings within a Zachariasen-Warren 'random' network, assuming that the density fluctuations for such a network follow a Gaussian distribution, and that the spatial distribution of the various sized rings is statistically random. Based on the shortest path ring statistics for the Evans & King random network model of vitreous silica, it is concluded that the frequency of occurrence of cybotactic groupings in vitreous SiO2 and GeO(2 )is higher than would be expected for a purely 'random' network.