Probability distributions of mineral dissolution rates: the role of lattice defects

Abstract

The correct quantification of mineral dissolution rates is a critical task for macroscopic reactive transport modeling. Previous studies showed a substantial rate variability of about two orders of magnitude, which cannot be explained by variance of external environmental parameters alone. If the rate cannot be predicted as a constant parameter, then the critical question is whether it can be predicted as a stable reproducible probability distribution. Although a large variety of factors may contribute to the overall variance across the scales, the effect of defect density and defect spatial distribution can be considered as one of the key variance sources. Here, we tested the reproducibility of probability distributions for Kossel crystals with a different amount and spatial configurations of lattice dislocations. We ran several tests on systems with the same configurations and calculated the probabilities of material flux. Surprisingly, we discovered that the density of dislocations has minimal impact on the probability distributions. However, the spatial location of dislocations has a substantial influence on the rate distributions reproducibility. In cases where multiple etch pits operate simultaneously, reproducible rate distributions are found regardless of the number of dislocations. In cases where dislocations formed clusters, one large etch pit controlled the entire surface, and sets of reproducible probability distributions were detected. Then, more complex statistical behavior is expected, since the result is path-dependent. These results have serious consequences for the implementation of rate distributions in reactive transport models. Further studies, however, are needed to provide clear guidance on relating surface morphologies, dislocation distributions, and dissolution rate variance. The role of material-specific properties, such as crystallographic structure and bonding, in rate distributions, should be additionally addressed. The role of grain boundaries, crystal size and crystal habit, including nanoparticulate forms, in rate variance, also should be addressed for practical applications.