Simple kinetic Monte Carlo models for dissolution pitting induced by crystal defects

Abstract

The solid-on-solid kinetic Monte Carlo model of Lasaga and Blum [Geochim. Cosmochim. Acta 50, 2363 (1986)] for dislocation-controlled etch-pit growth has been extended to the growth of etch pits under the control of multiple dislocations and point defects. This required the development of algorithms that are O(10(3))-O(10(4)) times faster than primitive kinetic Monte Carlo models for surfaces with areas in the range of 1024 x 1024-4096 x 4096 lattice sites. Simulations with multiple line defects indicate that the surface morphology coarsens with increasing time and that the coarsening is more pronounced for large bond-breaking activation energies. For small bond breaking activation energies dissolution enhanced by line defects perpendicular to the dissolving surface results in pits with steep sides terminated by deep narrow hollow tubes (nanopipes). Larger bond breaking activation energies lead to shallow pits without deep nanopipes, and if the bond breaking activation energy is large enough, step flow is the primary dissolution mechanism, and pit formation is suppressed. Simplified models that neglect the far field strain energy density but include either a rapidly dissolving core or an initially empty core lead to results that are qualitatively similar to those obtained using models that include the effects of the far field stress and strain. Simulations with a regular array of line defects show that microscopic random thermal fluctuations play an important role in the coarsening process.

Method to account for arbitrary strains in kinetic Monte Carlo simulations

“…For example, in thin film growth, lattice mismatches lead to strains and eventually different film morphologies 15 . The effect of externally applied strain has also been shown to enhance the rate of material dissolution and the formation of etch pits 16 , modify the diffusion rate of impurities in nanowires 17 , and qualitatively change the behavior of both atom detachment from a step, and dimer dissociation of Ag on an Ag(100) surface 18 . Another source of strain that is commonly discounted in kMC simulations is thermal expansion: the rate catalog is often based on defect properties calculated in a constant volume ensemble, using the lattice parameter computed at T = 0 K 19,20 .…”

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

“…Although kMC programs can be sped up and the system size can be increased, for example by parallelizing the code, the parallel algorithms have a number of efficiency and scalability drawbacks [34], as well as theoretical issues, such as obeying detailed balance principle [35]. Kossel-type kMC models in the literature have typically sizes up to 4000 × 4000 atoms [15]. State of the art kMC simulations (usually using a cluster or computation center) of real minerals typically have the size of a few hundred units in each direction.…”

“…The KMC method showed its efficiency in explaining and predicting surface topography and reactivity, and, given the molecular reaction rates correctly, kinematics of reactive features, such as steps and etch pits [15] and material flux rates [36,38]. Running a KMC solver, however, at any required (x, y, z, t) point can be very time consuming and overall challenging and impractical.…”

“…Here r crit is the critical distance at which the hollow core opens, and reflects the material, solution chemistry, saturation state and other environmental parameters. We chose not to use the more accurate but also more complicated formulations for the stepwave velocity also given by Lasaga and Luttge [15] including ∆G and strain parameters, because the strain influence is largest close to the defects, where the Voronoi approach does not make any statement anyway. This was deemed appropriate given the trial basis of this Voronoi model.…”

“…Kinetic Monte Carlo simulation techniques have been used to analyze crystal surface reaction kinetics and topography (e.g., [13][14][15]). The analysis of kMC simulation results using the rate spectra concept towards an improved predictability of surface kinetics is promising [11].…”