Eur. Phys. J. Special Topics 229, 2911–2921 (2020)
https://doi.org/10.1140/epjst/e2020-000050-1

Regular Article

Solute trapping phenomenon in binary systems and hodograph-equation within effective mobility approach

¹ University of Hassan II Casablanca, Faculty of Sciences Ben M’Sik, Department of Physics, Laboratory of Condensed Matter Physics (LPMC), BP 7955 Casablanca, Morocco
² Ural Federal University, Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, 620000 Ekaterinburg, Russia
³ Friedrich-Schiller-Universität-Jena, Faculty of Physics and Astronomy, Otto Schott Institute of Materials Research, 07743 Jena, Germany

^a e-mail: ahmedsalhoumi@gmail.com

Received: 29 March 2020
Accepted: 9 September 2020
Published online: 19 November 2020

Abstract

The phase field model is developed by the effective mobility approach to slow and rapid solidification. The phase field model equations are reduced to the hodograph equation for solid-liquid interface movement which is applied to the problem of solute trapping in a binary alloy. A specific method based on the one-point Cauchy problem is developed for solution of the hodograph equation with the solute diffusion equation. The method is tested in comparison with the rapid solidification of Si–0.1 at.% As alloy previously analyzed experimentally and using phase field modelling.