The growth of ellipsoidal crystals in supercooled and supersaturated liquids
Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Lenin ave., 51, 620000, Ekaterinburg, Russian Federation
Accepted: 21 March 2023
Published online: 11 April 2023
This review is devoted to the theory of nucleation and growth of the ellipsoidal crystals in supercooled melts and supersaturated solutions. We first outline the theory of single crystal growth in such systems and derive the growth rate of ellipsoidal particle volume as a function of the liquid supercooling/supersaturation and current volume. Then we formulate the mathematical models for the growth of polydisperse ensembles of ellipsoidal crystals in supercooled single-component and binary melts and supersaturated solutions. Methods for solving these models are further discussed and their approximate analytical solutions are given. A behaviour of analytical solutions and their comparison with experimental data are demonstrated. This review also allows one to visualize the common features and differences in the analytical description of the evolution of crystal ensembles in supercooled melts (one-component and binary) and supersaturated solutions.
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