Isomorphic representations of hyperfine structure of binary silicates by interior stress, vibrational wavenumber and spacial fractional dimension

Abstract

Stress index of tetrahedron (SIT) was defined to describe the topological connectivities among various silicon-oxygen tetrahedra (SiOT) in anionic clusters of binary silicate crystals, glasses and melts. It was found that the value of SIT was well correlated with the wavenumber of Raman active symmetric stretching vibration of non-bridging oxygen of SiOT. And also the spatial fractional dimension of hyperfine structure was introduced while comparative analysis being made with the value of SIT. It can be concluded that the concepts of SIT, vibrational wavenumber and spatial fractional dimension were inherently and holographically correlated and exhibit isomorphic representations of complex structure of binary silicates. Experimental Raman spectra of binary silicates with different alkali cation were investigated. It was demonstrated that alkali cation has little effect on the vibrational wavenumber of symmetric stretching of non-bridging oxygen (NBO) of SiOT, but remarkably affects its Raman active optical cross section, as was consensus resulted from ab initio calculation. It also can be concluded that the spatial fractional dimension of binary silicate is predominantly determined by the hyperfine structure of the anionic clusters and little affected by alkali cation, although the species of anionic clusters and their distributions were originally assigned by the content of alkali oxides.