Dissolution of minerals with rough surfaces

We study dissolution of minerals with initial rough surfaces using kinetic Monte Carlo simulations and a scaling approach. We consider a simple cubic lattice structure, a thermally activated rate of detachment of a molecule (site), and rough surface configurations produced by fractional Brownian motion algorithm. First we revisit the problem of dissolution of initial flat surfaces, in which the dissolution rate rF reaches an approximately constant value at short times and is controlled by detachment of step edge sites. For initial rough surfaces, the dissolution rate r at short times is much larger than rF; after dissolution of some hundreds of molecular layers, r decreases by some orders of magnitude across several time decades. Meanwhile, the surface evolves through configurations of decreasing energy, beginning with dissolution of isolated sites, then formation of terraces with disordered boundaries, their growth, and final smoothing. A crossover time to a smooth configuration is defined when r=1.5rF; the surface retreat at the crossover is approximately 3 times the initial roughness and is temperature-independent, while the crossover time is proportional to the initial roughness and is controlled by step-edge site detachment. The initial dissolution process is described by the so-called rough rates, which are measured for fixed ratios between the surface retreat and the initial roughness. The temperature dependence of the rough rates indicates control by kink site detachment; in general, it suggests that rough rates are controlled by the weakest microscopic bonds during the nucleation and formation of the lowest energy configurations of the crystalline surface. Our results are related to recent laboratory studies which show enhanced dissolution in polished calcite surfaces. In the application to calcite dissolution in alkaline environment, the minimal values of recently measured dissolution rate spectra give rF∼10-9 mol/(m2 s), and the calculated rate laws of our model give rough rates in the range 10-6-10-5 mol/(m2 s). This estimate is consistent with the range of calcite dissolution rates obtained in a recent work after treatment of literature data, which suggests the universal control of kink site dissolution in short term laboratory works. The weak effects of lattice size on our results also suggest that smoothing of mineral grain surfaces across geological times may be a microscopic explanation for the difference of chemical weathering rate of silicate minerals in laboratory and in the environment.