Asymmetrical relaxation of simpleE’centers in silicon dioxide isomorphs

We have reanalyzed the Feigl-Fowler-Yip model of the positively charged oxygen vacancy ($E_1^{\mathcal{’}}$ center) in crystalline α-quartz. By performing molecular-orbital calculations on vacancy clusters of higher symmetry than that of α-quartz, we find that the asymmetrical relaxation evident in previous calculations is absent for purely $C_{2v}$ symmetry, except for clusters with expanded vacancies. A cluster with the symmetry of β-cristobalite also does not relax asymmetrically. We further find that the degree of asymmetrical relaxation is a continuous function of the degree of asymmetry of the initial cluster. A simple modification of the standard pseudo-Jahn-Teller Hamiltonian, originally proposed by Schirmer, accounts for these effects as well as for certain experimental observations. We expect that in the case of similar defects in silica glasses the initial asymmetry of the site will be sufficient for asymmetrical relaxation to take place. An important result of these calculations is that only one asymmetrical potential well is predicted to exist for the $E_1^{\mathcal{’}}$ center in α-quartz.