Affiliation:
1. Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia, Spain
2. Physikalisch-Astronomische Fakultät, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany
Abstract
In standard descriptions, the master equation can be obtained by coarse-graining with the application of the hypothesis of full local thermalization that is equivalent to the local thermodynamic equilibrium. By contrast, fast transformations proceed in the absence of local equilibrium and the master equation must be obtained with the absence of thermalization. In the present work, a non-Markovian master equation leading, in specific cases of relaxation to local thermodynamic equilibrium, to hyperbolic evolution equations for a binary alloy, is derived for a system with two order parameters. One of them is a conserved order parameter related to the atomistic composition, and the other one is a non-conserved order parameter, which is related to phase field. A microscopic basis for phenomenological phase-field models of fast phase transitions, when the transition is so fast that there is not sufficient time to achieve local thermalization between two successive elementary processes in the system, is provided. In a particular case, when the relaxation to local thermalization proceeds by the exponential law, the obtained coarse-grained equations are related to the hyperbolic phase-field model. The solution of the model equations is obtained to demonstrate non-equilibrium phenomenon of solute trapping which appears in rapid growth of dendritic crystals.
This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.
Funder
Direccion General de Investigación of the Spanish Ministry of Economy and Competitiveness
Generalitat of Catalonia
RSF
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
9 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献