Crystal Dissolution Kinetics Studied by a Combination of Monte Carlo and Voronoi Methods

Abstract

Kinetic Monte Carlo (kMC) methods have been used extensively for the study of crystal dissolution kinetics and surface reactivity. A current restriction of kMC simulation calculations is their limitation in spatial system size. Here, we explore a new and very fast method for the calculation of the reaction kinetics of a dissolving crystal, capable of being used for much larger systems. This method includes a geometrical approach, the Voronoi distance map, to generate the surface morphology, including etch pit evolution, and calculation of reaction rate maps and rate spectra in an efficient way, at a calculation time that was about 1/180 of the time required for a kMC simulation of the same system size at one million removed atoms. We calculate Voronoi distance maps that are based on a distance metric corresponding to the crystal lattice, weighted additively in relation to stochastic etch pit depths. We also show how Voronoi distance maps can be effectively parameterized by kMC simulation results. The resulting temporal sequences of Voronoi maps provide kinetic information. By comparing temporal sequences of kMC simulation and Voronoi distance maps of identical etch pit distributions, we demonstrate the opportunity of making specific predictions about the dissolution reaction kinetics, based on rate maps and rate spectra. The dissolution of an initially flat Kossel crystal surface served as an example to show that a sequence of Voronoi calculations can predict dissolution kinetics based on the information about the distribution of screw defects. The results confirm that a geometrical relationship exists between the material flux from the surface at a certain point and the distance (or, when considering anisotropy, a function of distance) to the nearest defect. In this study, for the sake of comparability, the calculations are made using input parameters directly derived from the kMC models operating at the atomic scale. We show that, using values of v(rpit) and weighting factors obtained by kMC, the resulting surface morphologies and material flux are almost identical. This implies that discrete Voronoi calculations of starting and end points of the dissolution are sufficient to calculate material flux maps, without the time-consuming overhead of computing the interim reactions at the atomic-scale. This opens a promising new venue to efficiently upscale full-atomic kMC models to the continuum macroscopic level where reactive transport and Lattice Boltzmann calculations can be applied.