Modeling ion-exchanged glass photonics: the modified quasi-chemical diffusion coefficient

A new description of concentration-dependent ion exchange is presented. A three-dimensional, quasi-chemical approximation is used to estimate the chemical potentials of the exchanging cations. The diffusion coefficient is then expressed as a function of the self-diffusion coefficients, excess interaction energy and cation-cation coordination. The modified quasichemical description results in excellent fits to experimentally determined concentration-dependent diffusion coefficients. It is shown to be useful for modeling the strong concentration-dependence of ion exchange as used in the development of glasses for micro- and gradient-index optics.