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

在介观尺度上对模式形成的理解上取得了很大进展，这与相场模型的发展有关，相场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，它是根据空间均匀的平衡场来表述的。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、各向异性和多取向。在过去的几年中，使用相场晶体（PFC）方法在减轻相场方法的上述固有局限性方面取得了进展。该模型在原子尺度上运行，并根据由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，当密度场是周期性的时，固体的自由能泛函最小。密度场的周期性自然导致了弹性效应、多晶取向以及位错的成核和运动。PFC模型可以通过对自由能泛函的适当近似，直接从经典动态密度泛函理论（DDFT）中导出。通过这个推导，给出了原子间势和PFC能量之间的联系，原则上允许参数化PFC来描述实际材料的成核。我们将使用PFC模型和扩展的PFC模型，结合流体流动和考虑限制几何来研究单系统和双系统的非均相成核。在系统的方法中，我们将使用串方法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，这需要使用高斯超级计算中心的超级计算中心JSC和HLRS进行高性能计算。

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.