Jou D, Galenko P K
Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia, Spain
Physikalisch-Astronomische Fakultät, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany.
Philos Trans A Math Phys Eng Sci. 2018 Feb 28;376(2113). doi: 10.1098/rsta.2017.0203.
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'.
在标准描述中，主方程可通过应用完全局部热化假设进行粗粒化得到，该假设等同于局部热力学平衡。相比之下，快速转变在不存在局部平衡的情况下进行，且主方程必须在没有热化的情况下得到。在本工作中，针对具有两个序参量的系统，推导了一个非马尔可夫主方程，在特定的弛豫到局部热力学平衡的情况下，该方程可导出二元合金的双曲型演化方程。其中一个序参量是与原子组成相关的守恒序参量，另一个是非守恒序参量，与相场有关。当相变非常快以至于系统中两个连续的基本过程之间没有足够时间实现局部热化时，本文为快速相变的唯象相场模型提供了微观基础。在一个特定情况下，当弛豫到局部热化按指数规律进行时，所得到的粗粒化方程与双曲型相场模型相关。通过求解模型方程来展示枝晶快速生长过程中出现的溶质截留非平衡现象。本文是主题为“从原子界面到枝晶图案”的一部分。
