Influence of disorder on the diffusion of alkali ions in SiO 2- and GeO 2-glasses

Abstract

The frequency factor and activation energy for the diffusion of Na and K in SiO 2-glasses are strongly dependent on the concentration of Na 2O or K 2O respectively. A similar behavior was found for hydrogen diffusion in amorphous metals. In the last case the results are in agreement with theoretical calculations, if a Gaussian distribution of activation energies is assumed which arises from a similar distribution of the potential energy of hydrogen being in equilibrium sites. The equations derived were used in this study to describe the concentration dependence of Na and K diffusion in SiO 2 glasses, because these impurities are dissolved in randomly distributed interstices of different volume as well. The theory yields the two experimental facts that diffusion below the glass transformation temperature is governed by a single activation energy and that concentration profiles of the tracer atoms can be described by a constant diffusion coefficient. A comparison with low temperature results for Na diffusion shows they agree with theoretical predictions and yield the following parameters: most probable value of the activation energy = 59.4 kJ/mol, corresponding frequency factor = 2 × 10 −3 cm 2/s and half width of the Gaussian distribution = 25 kJ/mol. The model also predicts a minimum in plots of the chemical diffusivity versus concentration which is in agreement with experimental findings for sodium diffusion in GeO 2.