Ab initio study of Cu diffusion in α-cristobalite

We have studied the geometries, formation energies, migration barriers and diffusion of a copper interstitial with different charge states with and without an external electric field in the α-cristobalite crystalline form of SiO₂ using ab initio computer simulation. The most stable state almost throughout the band gap is charge q = + 1. The height of the migration barrier depends slightly on the charge state and varies between 0.11 and 0.18 eV. However, the charge has a strong influence on the shape of the barrier, as metastable states exist in the middle of the diffusion path for Cu with q = + 1. The heights and shapes of barriers also depend on the density of SiO ₂, because volume expansion has a similar effect to increase the positive charge on Cu. Furthermore, diffusion coefficients have been deduced from our calculations according to transition-state theory and these calculations confirm the experimental result that oxidation of Cu is a necessary condition for diffusion. Our molecular dynamics simulations show a similar ion diffusion, and dependence on charge state. These simulations also confirm the fact that diffusion of ions can be directly simulated using ab initio molecular dynamics.