A continuum model for heterogeneous nucleation - atomistic simulations on diffusive time scales

异相成核的连续体模型 - 扩散时间尺度上的原子模拟

• 批准号: 50868377
• 负责人: Professor Dr. Axel Voigt
• 金额: --
• 依托单位: Professur für Wissenschaftliches Rechnen und Angewandte Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2007
• 资助国家: 德国
• 起止时间: 2006-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/50868377?language=en
• 关键词: continuum; model; heterogeneous; nucleation; atomistic

Much progress in the understanding of pattern formation on mesoscopic scales is associated with the development of phase field (PF) models, which use a so-called phase field variable to describe the thermodynamic state of a system. A weakness of the traditional PF methodology is that it is formulated in terms of fields that are spatially uniform in equilibrium. This eliminates many physical features that arise due to the periodic nature of crystalline phases, including elastic and plastic deformation, anisotropy and multiple orientations. Over the past several years, progress towards alleviating the aforementioned inherent limitations of the phase-field approach have been made using a phase-field-crystal (PFC) approach. This model operates on an atomistic scale and describes the evolution of the atomic density ρ of a system according to dissipative dynamics driven by free energy minimization. In the PFC approach the free energy functional of a solid is minimized when the density field is periodic. The periodic nature of the density field naturally gives rise to elastic effects, multiple crystal orientations and the nucleation and motion of dislocations. The PFC model can be directly derived from classical dynamic density functional theory (DDFT) by appropriate approximations of the free energy functional. With this derivation a link between inter-atomic potentials and PFC energy is given, which in principle allows to parametrize PFC to describe nucleation of real materials. We will use the PFC model and extensions of the PFC model, incorporating fluid flow and considering confined geometries to study heterogeneous nucleation for single and binary systems. Within a systematic approach, using the string method, we will compute stable nuclei and nucleation barriers for various systems which will be compared with experimental data and other microscopic modeling approach. Especially for 3d computations this requires high performance computing for which the supercomputing centers JSC and HLRS of the Gauss Center for Supercomputing will be used.

在介观尺度上对图案形成的理解的许多进展与相场（PF）模型的发展有关，该模型使用所谓的相场变量 来描述系统的热力学状态。传统PF方法的一个弱点是，它是制定在平衡的空间均匀的领域。这消除了由于结晶相的周期性而产生的许多物理特征，包括弹性和塑性变形、各向异性和多个取向。在过去几年中，已经使用相场晶体（PFC）方法在减轻相场方法的上述固有限制方面取得了进展。该模型在原子尺度上运行，并根据自由能最小化驱动的耗散动力学描述系统的原子密度ρ的演化。在PFC方法中，当密度场为周期性时，固体的自由能泛函最小。密度场的周期性自然会引起弹性效应、多晶向以及位错的成核和运动。PFC模型可以直接从经典的动态密度泛函理论（DDFT）的自由能泛函的适当近似。通过这种推导，给出了原子间势和PFC能量之间的联系，这在原则上允许参数化PFC来描述真实的材料的成核。我们将使用PFC模型和PFC模型的扩展，结合流体流动和考虑受限的几何形状来研究单一和二元体系的非均质成核。在一个系统的方法中，使用弦方法，我们将计算各种系统的稳定核和成核势垒，并将其与实验数据和其他微观建模方法进行比较。特别是对于3D计算，这需要高性能计算，为此将使用高斯超级计算中心的超级计算中心JSC和HLRS。