Eur. Phys. J. Special Topics 229, 2923–2935 (2020)
https://doi.org/10.1140/epjst/e2020-000113-3

Regular Article

How the shift in the phase transition temperature influences the evolution of crystals during the intermediate stage of phase transformations

Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Lenin avenue 51, Ekaterinburg 620000, Russia

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Received: 12 June 2020
Accepted: 11 September 2020
Published online: 19 November 2020

Abstract

The influence of the phase transition temperature shift on the growth dynamics of a polydisperse ensemble of spherical crystals in metastable melts and solutions is studied. This shift is connected with the Gibbs–Thomson effect and the attachment kinetics of atoms at the phase transition interfaces of evolving crystals. The nonlinear model of kinetic and balance equations with allowance for the particle “diffusion” term is solved analytically. The obtained solution is compared with the case when this temperature shift is not taken into account. It is shown that the Gibbs–Thomson and attachment kinetics effects slightly accelerate the system desupercooling for a single-component titanium melt. This shifts the particle-size distribution function and changes the shape of its tail, which is responsible for the concluding stage of Ostwald ripening.