Nucleation and growth of ellipsoidal crystals in a supercooled binary melt

When considering the evolution of particulate assemblages in supercooled and supersaturated liquids, the shape of crystals often differs from spherical. Existing experiments show that evolved crystals often are ellipsoidal. Motivated by important applications in materials physics, chemistry, and biophysics, we develop here a growth theory of a polydisperse ensemble of ellipsoidal crystals in a binary supercooled melt. An integro-differential model of kinetic and balance equations supplemented by initial and boundary conditions that describe desupercooling dynamics and particle-volume distribution function with allowance for the ellipsoidal shape of growing crystals is formulated and solved analytically using the saddle-point technique for a Laplace-type integral. The distribution function increases up to the maximal volume of particles and shifts to larger crystal volumes with time. The solute concentration substantially changes the evolution of a particulate assemblage. The melt supercooling decays faster and the particle-volume distribution function is lower with increasing the initial solute concentration. The theory under consideration generalizes previously developed growth theories for spherical crystals in a binary melt (Alexandrov 2014 J. Phys. A: Math. Theor. 47 125102) and ellipsoidal crystals in a single-component melt (Nikishina and Alexandrov 2021 Phil. Trans. R. Soc. A 379 20200306).