Rethinking Classical Crystal Growth Models through Molecular Scale Insights: Consequences of Kink-Limited Kinetics

Abstract

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.

Rapid Screening of Calcium Carbonate Precipitation in the Presence of Amino Acids: Kinetics, Structure, and Composition

“…Raman spectra were obtained from single crystals (rather than polycrystals) in the range 1050 to 1150 cm 1 are seen across Asp, Gly and Asn, but are most marked with Asp ( Figure 6b). This is consistent with occlusion being promoted both at higher [Asp] and higher supersaturations, where the latter correlates with an increase in the density of step edges and kink sites, 49 which translates into higher occlusion levels.…”

Growth and Dissolution of Calcite in the Presence of Adsorbed Stearic Acid

“…Here, the SI has been calculated for each brine dilution studied using the PHREEQC 37 At high saline concentrations (down to _ × 2 diluted brines), not only calcite but also 24 , allowing the formation of relatively regular steps (Figure 2A-B). In contrast, Sr 2+ ions follow the step-pinning model, resulting in a highly irregular growth process 22 as visible in Figure 2D-E. Both ions are, to a certain extent, incorporated in the newly formed crystal 47 .…”

Kinetics and mechanisms of cadmium carbonate heteroepitaxial growth at the calcite (101¯4) surface

“…Additionally, the critical supersaturation for 2D nucleation can be correlated to mineral solubility whereby higher critical supersaturations are required for minerals with low solubilities (De Yoreo and Vekilov, 2003). This effect stems from the fact that 2D nucleation requires the creation of step edges, which means that the free energy barrier for 2D nucleation increases with increasing step edge energy, and that a lower solubility translates to a higher step edge energy (Christoffersen et al, 1991) as well as a lower equilibrium kink density (De Yoreo et al, 2009). This effect is likely to also contribute to the large difference in critical supersaturations between pure calcite growth and otavite growth on calcite.…”

“…It is well accepted that the growth process proceeds by the attachment of growth units to the growing crystal and that the attachment occurs predominantly at kink sites. If it is assumed that steps have a high density of kinks and that step propagation is limited only by the kinetics of solute attachment and detachment at kink sites, the rate of step advancement is predicted to be linearly proportional to the difference between the actual and equilibrium concentrations of the solute, (C À C e ), by (Teng et al, 1999;De Yoreo and Vekilov, 2003;De Yoreo et al, 2009):…”