Analytical model of electric field assisted ion diffusion into glass containing two indigenous mobile species, with application to poling

An analytical model of electric field assisted diffusion of ions into glass is extended to include two indigenous mobile ion species that are initially uniformly distributed within the glass. A quasi-stationary state solution that includes diffusion effects and is applicable when the invasive ions have a lower mobility than the two indigenous species is presented. It is relevant to the electrical poling of soda-lime and borosilicate glasses with concentrations of mobile ions (Na+, K+) that are processed with a non-blocking anode where hydrogen ion injection occurs. The model is compared with numerical solutions based on the drift-diffusion equations and Poisson's equation and shows good agreement. The increase in the concentration of the indigenous species with the lower mobility (K+) below the poled layer within a pile-up region is accurately modelled.