Simulations of Dissolution of Initially Flat Calcite Surfaces: Retreat Velocity Control and Surface Roughness Scaling

Abstract

The far-from-equilibrium alkaline dissolution of initially flat and defect-free calcite surfaces is modeled with kinetic Monte Carlo simulations of site detachment from a Kossel crystal and with scaling approaches. The surface retreat velocity is strongly dependent on the detachment rate of the highest coordination sites, which represent molecules in the middle of (101̅4) terraces. The comparison with a recent velocity estimate from digital holographic microscopy predicts the removal rate of those molecules between 2 × 10–7 and 4 × 10–6 s–1 at room temperature, which improves a previous estimate from a grain dissolution model. The activation energy for this molecular-scale process is estimated as 92 ± 6 kJ/mol (assuming the same prefactor ∼3 × 1010 s–1 of kink and step sites). The areal density of nonterrace sites (mostly steps and kinks) is also related to that removal rate, so we propose that the measurement of this density may provide independent estimates of the above quantities. Arrhenius plots of the retreat velocities obtained in high-temperature simulations predict the (macroscopic) activation energy of 69 ± 4 kJ/mol for dissolution of smooth surfaces. We also show that the scaling of the surface roughness in time and size is the same as in the Kardar–Parisi–Zhang (KPZ) equation of kinetic roughening. However, room-temperature roughening of initially smooth calcite surfaces is so slow that it is unlikely to be observed in typical experimental times and the alkaline conditions modeled here. Since the rates in acidic media are larger and arguing that the microscopic symmetries of the molecule detachment processes should be preserved, we suggest the investigation of KPZ scaling under those conditions.

Competition between Kardar-Parisi-Zhang and Berezinskii-Kosterlitz-Thouless kinetic roughening on (001) singular surface: nucleation-limited steady crystal growth

“…The KPZ universality class is known to explain many non-equilibrium systems such as directed polymers and quantum systems 11,28,29 . However, in the case of crystal growth, the observed roughness exponents differ from those predicted by the KPZ model 11,26,30 , with the exception of several special surface systems [31][32][33] . Numerous studies have been conducted to determine why crystal surfaces do not become KPZ rough 26 .…”