CECAM - Multiscale Modeling of Heterogeneous Nucleation and Structure Formation in Colloids and Metals

When a system undergoes a first order phase transition, the transformation process is usually initiated at the walls or on top of a substrate. Hence the structure and chemical nature of the walls have a direct influence on the morphology of the final aggregates observed after transformation. Employing the wall properties, the physics of the corresponding interfaces, the boundary and respective contact angle conditions in order to produce specific morphologies is an important target in the engineering of materials, e.g. in systems such as metals and colloids. The micro-structure depends on the nucleation events and, in turn, determines the mechanical properties of the material. Hence, a better understanding of the scale-bridging process of nucleation and micro-structure evolution is essential for the design of new materials. Modern techniques of modeling and simulation can provide a deeper understanding and insight into these processes and enable a careful investigation of the interactions and dependences among the various length scales. Since the effects occur on a large range of length scale, the aim of this workshop is to bring together researchers working on atomistic and mesoscopic modeling methods. As nucleation is by definition a non-equilibrium process which involves the crossing of at least one large free energy barrier, it poses challenges both, from the point of view of the basic theoretical description as well as simulation algorithms. Atomistic simulations cannot cover the time-scales necessary to go from fluctuations in the metastable phase via the nucleation process to the subsequent growth of the stable phase. The first part, the nucleation problem, can be addressed by modern methods for rare event sampling. It has been studied both, in terms of algorithms which are based on a free energy landscape picture (e.g. Wang-Landau Sampling [1] and Umbrella Sampling [2]), as well as by methods that allow to access full non-equilibrium, such as transition path sampling [3] or forward flux sampling [4,5]. However, both types of approaches suffer from certain drawbacks: Free energy landscape based methods require the choice of a reaction coordinate, which is often difficult to determine a priori [6-9]. Transition path sampling and related methods do not require this kind of ``intuition'' about the system, but they are computationally much more expensive and have therefore until very recently been limited to studies of small systems [10-19]. Also the second part, the connection of modeling on the microscopic scale to coarse-grained models of structure formation has, to our understanding, not been addressed sufficiently yet. A powerful methodology describing phase transition phenomena and micro-structure formation processes is the phase-field approach (see recent reviews [20,21]). This approach has been used to model solidification, micro-structure formation in solids, and motion of grain boundaries. The micro-structure responses to the shape of the nuclei, to the characteristic properties of the substrate and of the heterogeneous nucleation process can systematically be investigated using phase-field simulations. Phase-field models include formulations for the case of a pure substance [22], for multicomponent systems [23-25], for polycrystalline structures [26,27] as well as for phase transitions where multiple different phases are involved: eutectic [28-30], peritectic [29], and monotectic [31] systems. Despite all the progress of the phase-field approach in recent years, quantitative simulations are still limited to the knowledge of intrinsic materials properties. Such properties as e.g. the interfacial energy or kinetic coefficients and their anisotropies are determined by effects and structures on atomic length and time scales. In order to provide quantitative modeling, a bottom-up approach is required. The authors of Ref. [32] have suggested a combined approach where the properties of the solid-liquid interface are determined by molecular dynamics simulations and then transferred as input parameters into phase-field modeling. This has been the most efficient way to link the scales in a quantitative way, although the ultimate goal of materials simulation is to use a concurrent multiscale approach which is still a big challenge.

Multiscale Modeling of Heterogeneous Nucleation and Structure Formation in Colloids and Metals

CECAM-ETHZ, Zurich, Switzerland

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