https://doi.org/10.1140/epjs/s11734-025-02068-y
Regular Article
Evolution of a polydisperse ensemble of crystals in a supercooled binary melt
Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin ave., 51, 620000, Ekaterinburg, Russian Federation
a
dmitri.v.alexandrov@gmail.com
Received:
3
June
2025
Accepted:
13
November
2025
Published online:
20
November
2025
Motivated by important applications in condensed matter physics, we describe the nucleation and evolution of crystals in a supercooled binary liquid taking fluctuations in particle growth rates into account. An integro-differential system of balance and kinetic equations is formulated and analytically solved with allowance for the diffusion of crystal-radius distribution in the space of particle sizes. The dynamics of melt temperature, supercooling, solute concentration, and crystal-radius distribution function are found for various nucleation kinetics and crystal growth laws. The theory under consideration can be used for the description of one- and two-step nucleation mechanisms. Numerical examples based on the developed theory are given and analyzed. The theory is compared with the experimental data.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
