What Determines the Rate of Growth of Crystals from Solution?

Abstract

Crystallization from solution underlies numerous laboratory, industrial, geological, and biological processes. The interface between a crystal and the solution is smooth and comprised of singular crystal faces. On such smooth interfaces, the locations at which a molecule from the solution can associate to the crystal, the kinks, are few and located along the edges of unfinished crystalline layers, the steps. The rate of step propagation, and through it, the rate of growth of a crystal from solution, is determined by the kink density and by the kinetics of incorporation into the kinks. In turn, the latter depends on the free energy barriers for incorporation. Here, three mechanisms of generation of kinks are discussed: by thermal fluctuations of the steps, by one-dimensional nucleation of new crystalline rows, and by association to the steps of two-dimensional clusters, preformed on the terraces between the steps. The latter two mechanisms only operate in the cases where the kink density, determined by the thermal fluctuations, is low. The rate of incorporation into kinks follows Kramers-type kinetics, in which the transition over the free energy barrier is governed by diffusion in the solution, in contrast to the Eyring-type transition state, which decays due to the vibrations of the activated complex. Finally, the barrier is not due to stretched bonds between the incoming molecules and the kink but rather corresponds to the destruction of the shell of structured water around both the kink and the incoming molecule. The latter two insights allow rationalization of the effects of additives on crystallization kinetics, especially those employed in biological regulation in living organisms.