Rethinking classical crystal growth models through molecular scale insights: Consequences of kink-limited kinetics

The classical terrace-ledge-kink model of crystal growth is widely used to interpret mineral formation in biological and geological systems. A key assumption underlying application of the model is that thermal fluctuations of steps are sufficiently rapid to produce an abundance of kink sites for attachment of growth units. High-resolution in situ atomic force microscopy (AFM) studies and kinetic Monte Carlo simulations of step-edge structure and dynamics show this physical picture to be invalid for the common mineral calcite whose steps exhibit low kink density and weak step edge fluctuations. As a consequence, interactions of impurities with calcite step edges cannot be interpreted with traditional thermodynamic models based on minimization of the Gibbs free energy. Instead, impurity-step interactions follow a different mechanism determined by the kinetics of attachment and detachment. Step advance is unimpeded when the creation of new kinks by attachment of growth units to the step outpaces binding of impurities to the newly created kinks. This kink-limited model offers a plausible explanation for reports of "kinetic disequilibrium" of trace element signatures. Moreover, because kink density is tied to crystal solubility, these findings argue for a theory based on weak fluctuations to interpret growth of many common crystalline phases of importance in geochemical, biological, and technological settings.