Analysis of Field-Assisted Binary Ion Exchange

A differential equation was derived for ionic migration in a system with two mobile ions. Stationary solutions were obtained for the case where the slower ion follows the faster, which reduce to those obtained when diffusion is ignored. When the faster ion is "behind" the slower no stationary solutions are possible, but the diffusion term is not important for this case and appropriate solutions are readily obtained. However, by taking account of diffusion at the boundaries, where it is important, infinite gradients are avoided and concentration equilibrium is permitted at the glass-salt interface. The concentration distributions predicted from this approach are compared with those measured on glass that has been ion exchanged with electric field assistance. Although the agreement is reasonable, there is some discrepancy, due in part to the assumption of concentration-independent species mobility.