Multiscale modeling based on phase-field approaches: consistency analysis regarding growth and melting kinetics in metals

该项目处理多尺度建模的核心挑战之一，即如何弥合原子和宏观方法之间的差距，以确保所有级别的描述在数量上彼此一致。这项任务是针对一种很有前途的多尺度方法进行的：结合分子动力学（MD）和相场（PF）模拟的分层耦合方法。一致性分析是通过对所考虑的生长和熔化动力学建模方法的定量预测进行详细比较来实现的。后者是材料物理中典型的多尺度问题。MD模拟提供了构建多尺度模型所需的物理量。最重要的是体积自由能和固液界面自由能，它们的计算需要使用特殊的方法。要研究的单原子和二元体系是Fe， Al， NiZr和NiAl，它们在文献中有可靠的电位。第一个项目期间产生了一些重要的发现，特别是关于固液界面的扩散、界面厚度各向异性以及它们对生长和熔化动力学的决定性影响。这些见解导致了现象学PF模型设计的改进，从而提高了MD/PF耦合的预测精度。第二个项目期旨在理解这些见解之间的明显相关性，并将它们建立在定量定律和可能的普遍行为中。特别地，我们分析了晶体影响液体扩散的相关长度的温度依赖性和各向异性。潜在的动力各向异性预计与结构界面厚度各向异性有关，这是我们在第一个项目期间为bcc Iron证明的一个概念。本文将研究这种各向异性概念在fcc金属和合金中的推广，并通过将MD与PF模型相结合来评估其可靠性。了解不同的结构和动态界面各向异性是准确预测枝晶和共晶等界面形态动态的先决条件。鉴于所获得的见解，我们重新审视了一些经典的生长模型，试图合理化它们在描述合金结晶行为方面的失败。

The project deals with one of the central challenges in multiscale modeling, namely how to bridge the gap among atomistic and macroscopic approaches in order to ensure that the descriptions at all levels are quantitatively consistent with each other. This task is carried out for one of the promising multiscale methods: The hierarchical coupling approach that combines molecular dynamics (MD) with phase-field (PF) simulations. The consistency analysis is achieved by detailed comparisons of quantitative predictions of the considered modeling methods for the growth and melting kinetics. The latter are typical multiscale problems in material physics. The MD simulations provide the physical quantities needed for the construction of the multiscale models. Of central importance are the bulk free energy and the solid-liquid interfacial free energy whose calculation requires the use of special methods. The monatomic and binary systems to be investigated are Fe, Al, NiZr and NiAl, for which reliable potentials are available in the literature. The first project period led to essential findings concerning, in particular, the diffusion at the solid-liquid interface, the interfacial thickness anisotropy, and their determining influence on the growth and melting kinetics. These insights resulted in improvements of the design of the phenomenological PF model leading to enhancements of the prediction accuracy of the MD/PF coupling. The second project period is aimed at understanding the apparent correlation between these insights and establishing them in quantitative laws and possible universal behaviour. In particular, we analyze the temperature dependence and anisotropy of the correlation length over which the crystal affects the liquid diffusion. The underlying dynamical anisotropy is expected to be connected with the structural interface-thickness anisotropy, a concept that we demonstrated for bcc Iron in the first project period. A generalization of this anisotropy concept to fcc metals and alloys will be here investigated and its reliability assessed by linking MD to PF modeling. Understanding the different structural and dynamical interface anisotropies is a prerequisit to accurately predict the dynamics of interface morphologies like dendrites and eutectics. In the light of the gained insights, we revisit some classical growth models in an attempt to rationalize their failings to describe crystallization behaviour in alloys.