The evolution of a polydisperse ensemble of ellipsoidal particles in the form of prolate and oblate ellipsoids of revolution

Abstract

The evolution of a polydisperse ensemble of prolate and oblate ellipsoidal crystals in a supercooled one-component melt is theoretically studied. The volume growth rates for prolate and oblate ellipsoids are analytically found and compared at the same melt supercooling. We show that prolate crystals evolve faster than the oblate ones and the difference between their growth rates increases with increasing the melt supercooling. Then taking these volume growth rates into account, we formulate the model describing the evolution of an ensemble of prolate/oblate ellipsoidal particles. The analytical solution to this integrodifferential model is found for two nucleation mechanisms in cases of prolate and oblate ellipsoids using the saddle-point method. Our solution demonstrates that an ensemble of prolate particles grows and removes the melt supercooling faster than an ensemble of oblate particles. As a result, the particle-volume distribution function for prolate crystals is shifted to larger crystal volumes than the same distribution for oblate crystals. Keeping this behavior in mind, we conclude that the shape of crystals plays a decisive role in the melt supercooling dynamics and their volume distribution.