Diffusion of calcium and barium in alkali alkaline-earth silicate glasses

Abstract

Diffusion of the radioactive isotopes ⁴⁵Ca and ¹³³Ba in alkali alkaline-earth silicate glasses of compositions ₂O·2CaO·4SiO₂ with  = Li, K, Cs and K₂O·2BaO·4SiO₂ was investigated at temperatures below the respective glass-transition temperatures. The diffusion profiles of the radiotracers were recorded by means of an ion-beam sputtering technique in conjunction with activity measurements. Analysis of the Ca and Ba profiles is based on the thin-film solution of the diffusion equation and a contribution which takes into account the instrumental broadening of the profiles caused by sputtering effects. The diffusion coefficients of the alkaline-earth ions were determined down to values of as low as 10⁻²¹ m² s⁻¹. Our diffusion data enables us to determine accurate values for the activation enthalpy of diffusion and the pre-exponential factor. The activation enthalpies reveal a distinct correlation with the radius ratio of the alkaline-earth ions to the alkali ions and show that the alkaline-earth ions are most mobile when the radii of the alkaline-earth and alkali ions are similar. The diffusion study strongly supports recent results from mechanical loss spectroscopy. A simple model is proposed which qualitatively explains the correlation of the alkaline-earth mobility with the radius ratio of the cations.