Mathematical modeling of the growth of an ellipsoidal particle in a supersaturated solution

Abstract

Based on experimental data showing that crystal shapes are often far from spherical, it becomes important to find another more accurate way of constructing a theory of crystal growth in supersaturated solutions. Very often, during the study of the evolution of crystals, one can notice that their shape in most cases is close to ellipsoidal. That is why, in this article, this case is considered when the crystals have an ellipsoidal shape. The growth of an individual ellipsoidal crystal in a supersaturated solution at the stage of phase transition was studied. The growth rate of the volume of an ellipsoidal crystal, as a function of the current volume of the particle and supersaturation, is found explicitly. A mathematical model describing the growth of an ensemble of ellipsoidal particles in a supersaturated liquid is formulated. The graph demonstrating the relationship between the growth rate of a particle and its volume is plotted and analyzed. It is shown that the amount of impurity essentially affects the growth rate of ellipsoidal crystals. This rate increases with increasing the impurity concentration in the supersaturated mixture.