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

This study links classical crystal growth theory with observations of micro scopic surface processes to quantify the dependence of calcite growth on su persaturation, sigma, and show relationships to the same dependencies often approximated by affinity based expressions. In situ Atomic Force Microscop y was used to quantify calcite growth rates and observe transitions in grow th processes on {10 (1) over bar4} faces in characterized solutions with va riable sigma. When sigma < 0.8, growth occurs by step flow at, surface defe cts, including screw dislocations. As <sigma> exceeds 0.8, two-dimensional surface nucleation becomes increasingly important. The single sourced, sing le spirals that are produced at lower sigma were examined to measure rates of step flow and the slopes of growth hillocks. These data were used to obt ain 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 su rface process based rate expressions for spiral growth show the relationshi ps between R-m and the distribution and structures of dislocation sources. These theoretical relations are upheld by the process-based experimental ra te data reported in this study. The analysis further shows that the depende nce of growth rate on dislocation source structures is essential for proper ly 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 when popul ar affinity-based rare laws hold or break down. Results of this study demonstrate that the widely used second order chemica l affinity-based rate laws are physically meaningful only under special con ditions. The exponent in affinity-based expressions is dependent upon the s upersaturation range used to fit data. An apparent second order dependence is achieved when solution supersaturations are very near equilibrium and gr owth occurs only by simple, single sourced dislocation spirals. These findi ngs 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 contributio ns from each dislocation structure. Copyright (C) 2000 Elsevier Science Ltd .