Kinetics of calcite growth: surface processes and relationships to macroscopic rate laws

Abstract

This study links classical crystal growth theory with observations of microscopic surface processes to quantify the dependence of calcite growth on supersaturation, σ, and show relationships to the same dependencies often approximated by affinity based expressions. In situ Atomic Force Microscopy was used to quantify calcite growth rates and observe transitions in growth processes on {10 1 4} faces in characterized solutions with variable σ. When σ < 0.8, growth occurs by step flow at surface defects, including screw dislocations. As σ exceeds 0.8, two-dimensional surface nucleation becomes increasingly important. The single sourced, single spirals that are produced at lower σ were examined to measure rates of step flow and the slopes of growth hillocks. These data were used to obtain the surface-normal growth rate, R m , by the pure spiral mechanism. The dependence of overall growth rate upon dislocation source structure was analyzed using the fundamentals of crystal growth theory. The resulting surface process-based rate expressions for spiral growth show the relationships between R m and the distribution and structures of dislocation sources. These theoretical relations are upheld by the process-based experimental rate data reported in this study. The analysis further shows that the dependence of growth rate on dislocation source structures is essential for properly representing growth. This is because most growth sources exhibit complex structures with multiple dislocations. The expressions resulting from this analysis were compared to affinity-based rate equations to show where popular affinity-based rate laws hold or break down. Results of this study demonstrate that the widely used second order chemical affinity-based rate laws are physically meaningful only under special conditions. The exponent in affinity-based expressions is dependent upon the supersaturation range used to fit data. An apparent second order dependence is achieved when solution supersaturations are very near equilibrium and growth occurs only by simple, single sourced dislocation spirals. These findings indicate the need to apply caution when deducing growth mechanisms and rate laws from temporal changes in bulk solution chemistry. Observations of various types of surface defects that give rise to step formation suggest that popular ‘rate laws’ are sample-dependent composites of rate contributions from each dislocation structure.