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(r pit ) 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.

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<p>During the dissolution at a calcite cleavage face, etch pits open around defects. Atomic steps moving outwards from these pit centres are currently considered the general driving mechanism of this dissolution process that results in heterogeneous material flux from the surface. This means that the defects that generate the etch pits are crucial for the surface evolution. Recent kinetic Monte Carlo (kMC) simulation results indicate that not only the density but also the spatial distribution of defects is critical for the influence on dissolution.</p><p>In kMC simulations used for crystal dissolution, defect positions are input and can be defined in various ways, e.g., at pre-defined coordinates or randomly drawn from a distribution. The user is free in defining the defects, although it can generally be considered reasonable to choose defect densities and distributions as close as possible to what is expected to occur in nature and technical systems.</p><p>The actual spatial distribution of screw dislocations in calcite and their influence on rate variability are still not entirely known. To make the calcite kMC simulations comparable with experimental results, we experimentally determined the etch pit distributions, analyzed them and subsequently used them as input for further kMC studies.</p><p>While the direct measurement of defects in the crystal structure is extremely difficult, the indirect approach of measuring etch pits that have formed around defect outcrops during the beginning of dissolution is more feasible. For this, cleaved calcite single crystals were etched using ultra-pure water for 3 to 4 hours to obtain a significant amount of etch pits on the surface. The topography of the crystal surfaces was analysed using Vertical Scanning Interferometry (VSI). The resulting topography maps were stitched to gain a larger area for better statistics, and the centres of visible etch pits marked. This generates two-dimensional point patterns that describe the actual defect distribution more accurately than purely randomly generated coordinates without further constraints.</p><p>Based on data analysis of the experiments, we will show the resulting point distributions and synthetic patterns with similar underlying statistics. Using these as input for modelling, we then calculate kMC simulations and geometrical models of a system close to the calcite single crystal from our experiment, and compare them also to simulations using different defect positions as input.</p>