Ion diffusion and mechanical losses in mixed alkali glasses

Based on general theoretical considerations we show that the fraction cV of vacant sites for the mobile ions in glasses should be small in order to understand the peculiar behavior of the internal friction in the mixed alkali effect. Moreover, for small cV, the steep fall of the conductivity in the dilute foreign alkali region can be explained by a trapping of vacancies induced by the minority ions. To demonstrate our general analysis we study a simple hopping model and show that it allows one to recover both the typical behavior of the internal friction (shifts of single and mixed alkali peak positions with the mixing ratio and associated changes in activation energies, changes of peak heights) and the typical behavior of tracer diffusion coefficients (drastic fall of mobility of one type of ion by replacement with a second type of mobile ion and associated changes in activation energies). Reasonable values of model parameters can be estimated from measured data and predictions are made for experiments.