A kinetic model for crystal growth from aqueous solution in the presence of impurity

Abstract

A mathematical model describing crystal growth rates from aqueous solution as a function of impurity concentration is presented. The model assumes that the step velocity decreases linearly with increasing surface coverage ( θ eq) by impurities adsorbed on the growing crystal, and a proportionality constant α is introduced to take into account the effectiveness of the impurity. When α > 1, the step velocity is stopped at θ eq < 1 (incomplete coverage of the active sites for adsorption). In the case of α = 1, the velocity reaches zero just at θ eq = 1, and for α < 1, it never becomes zero even at θ eq = 1 (complete coverage) but approaches a limiting value. The Langmuir adsorption isotherm is used to relate the relative step velocity with the impurity concentration in solution. Three typical cases reported in the literature, each previously explained with a different model, are shown to be described satisfactorily with this new single model. The value of α is changed by stereochemical factors and decreases as the supersaturation is increased. The supersaturation effect is explained with the aid of the Cabrera-Vermilyea model.