January 11, 2019
Journal Article

Adaptation of the GRAAL Model of Glass Reactivity to Accommodate Non-linear Diffusivity

Joseph Ryan
James Neeway
Sebastien Kerisit
Peter Rieke
In the GRAAL (Glass Reactivity with Allowance for the Alteration Layer) model comprises two differential equations that describe the rate of complete glass dissolution as well as the rate of growth of the partially altered gel layer. The model was modified by raising the unitless diffusion term by a power factor p. For a value of p = 1.0 the equations reduce to the original model where diffusivity in the gel layer is considered constant. With values of p > 1.0, the diffusivity is a non-linear, power function of the gel layer thickness. The modified model, GRAALP, was used to fit the long term alteration data for a series of sodium borosilicate glasses reported by Gin et al., J. Non-Crystalline Solids, 358 (2012) 2559 where glass alteration has slowed to a residual rate and growth of the gel layer has dominated alteration. The optimal value for the parameter p was found to vary significantly and could be correlated with glass composition. For the glasses containing both Ca and Al, a value of p = 3.0 was found most suitable and was reduced slightly to p = 2.6 if Ce was present in the glass. For glasses without Ca, the data followed the original GRAAL model with p = 1.0. In the absence of Al, glasses containing Ca and/or Zr were not as easily characterized. This findings point to a correlation between the residual alteration rate and glass composition. A power law dependence of diffusivity on local water content is proposed. This non-linear diffusion, in concert with water influx due to hydrolysis and removal of oxide species, can account for the formation of a distinct gel layer with a relatively sharp interface between gel and pristine glass.

Revised: January 11, 2019 | Published: December 15, 2018

Rieke P.C., S.N. Kerisit, J.V. Ryan, and J.J. Neeway. 2018. "Adaptation of the GRAAL Model of Glass Reactivity to Accommodate Non-linear Diffusivity." Journal of Nuclear Materials 512. PNNL-SA-130411. doi:10.1016/j.jnucmat.2018.09.058