Theory ofAl2O3incorporation inSiO2

Abstract

Different possible forms of ${\mathrm{Al}}_2{\mathrm{O}}_3$ units in a ${\mathrm{SiO}}_2$ network are studied theoretically within the framework of density-functional theory. Total-energy differences between the various configurations are obtained, and simple thermodynamical arguments are used to provide an estimate of their relative importance at different Al concentrations. Some experimentally accessible quantities (hyperfine parameters, electric-field gradient tensors, and core-level chemical shifts) are derived, and compared with experimental data where available. The results show that Al ions at low ${\mathrm{Al}}_2{\mathrm{O}}_3$ concentrations will be present as isolated impurities bound to three or four O atoms, whereas at higher concentrations clusters consisting of four Al ions will form. In these clusters both four- and five-coordinated Al can occur, but no energetic preference for the five-coordinated state is found.