Solute trapping phenomenon in binary systems and hodograph-equation within effective mobility approach
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part of Springer Nature, 2020 https://doi.org/10.1140/epjst/e2020-000050-1
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
Solute trapping phenomenon in binary systems and hodograph-equation within effective mobility approach A. Salhoumi1,a , D.V. Alexandrov2 , and P.K. Galenko2,3 1
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University of Hassan II Casablanca, Faculty of Sciences Ben M’Sik, Department of Physics, Laboratory of Condensed Matter Physics (LPMC), BP 7955 Casablanca, Morocco Ural Federal University, Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, 620000 Ekaterinburg, Russia Friedrich-Schiller-Universit¨ at-Jena, Faculty of Physics and Astronomy, Otto Schott Institute of Materials Research, 07743 Jena, Germany 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.
1 Introduction It is well-known that phase field theory plays a highly important role in description of transport processes together with the analysis of phase transformations in materials sciences [1–6]. To describe the slow and fast interfaces propagating into a metastable media, a class of hyperbolic equations of the phase field theory is considered which describe the time delay due to relaxation toward local thermodynamic equilibrium. This relaxation is described by the introducing the solute diffusion flux and gradient flow as fast thermodynamic variables in addition to the set of standard slow thermodynamic variables such as phase field variable, internal energy and chemical potential. The relaxation time of fast variables is comparable with the time of local solidification and describes temporal relaxation to the local thermodynamic equilibrium giving the system to be nonergodic [7]. As the result the phase field equations are found from the kinetic energy and extended mobility approaches [8–10]. After averaging procedure, the hyperbolic phase field equation is reduced to the hodograph equation which is considered as generalized Gibbs–Thomson equation realizing a connection of the interface acceleration and velocity with the interface curvature and driving force [11]. a
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The European Physical Journal Special Topics
The predictions of kinetic energy and effective mobility approaches have been tested against molecular dynamics simulation data [12]. In the present work, we analyze the phenomenon of solute trapping by the rapidly moving interface during solidif
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