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

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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.