Crystal Growth from Aqueous Solution in the Presence of Structured Impurities

Abstract

A kinetic model describing crystal growth from aqueous solution in the presence of structured impurities is developed on a generalization in the spirit of the Davey and Mullin model. The proposed theoretical framework combines (i) an analytical expression for the step velocity, where this quantity decreases linearly with increasing surface coverage (Îeq) by impurities adsorbed on the growing crystal, and (ii) a new adsorption isotherm equation Îeq(CI) (CI is the concentration of impurities) in which the adsorbate can occupy more than one adsorption site (structured impurity). The formalism leads to the exact adsorption isotherm of linear rods in one dimension and provides a close approximation for two-dimensional systems accounting for multisite occupancy. Moreover, the model is capable of predicting the effect of size/shape of the impurities from parameters having a precise physical meaning. These parameters can be obtained from thermodynamic experiments and are related directly to the spatial configuration of the impurity molecules in the adsorbed state. The theoretical results are contrasted with Monte Carlo simulations and experimental data of the relative growth rates of the {100} faces of KBr crystals in the presence of impurity molecules (linear aliphatic carboxylic acids) of different sizes. A good agreement between theory, simulations, and experiments is found.