Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes

Nanoscale surface pattern evolution in heteroepitaxial bimetallic films

Nanoscale self-assembly dynamics of submonolayer bimetallic films was studied through simulation of a coarse-grained mesoscopic model. Simulations predict a phase transition sequence (hexagonal→stripe→inverse hexagonal) consistent with experimental observations of Pb/Cu(111) heteroepitaxial growth. Post-transition ordering dynamics of hexagonal and inverse hexagonal patterns was simulated and quantified in order to predict pattern quality and evolution mechanisms. Correlation length scaling laws and nanoscale evolution mechanisms were predicted through simulation of experimentally relevant length (≈1 μm(2)) and time scales, with findings supporting evidence of universal pattern behavior with other hexagonal systems. Results provide detailed dynamics and structure of this novel self-assembly process applicable to the design and optimization of functional bimetallic materials, such as bimetallic catalysts.

Coarse-grained kinetic Monte Carlo models: Complex lattices, multicomponent systems, and homogenization at the stochastic level

On-lattice kinetic Monte Carlo (KMC) simulations have extensively been applied to numerous systems. However, their applicability is severely limited to relatively short time and length scales. Recently, the coarse-grained MC (CGMC) method was introduced to greatly expand the reach of the lattice KMC technique. Herein, we extend the previous spatial CGMC methods to multicomponent species and/or site types. The underlying theory is derived and numerical examples are presented to demonstrate the method. Furthermore, we introduce the concept of homogenization at the stochastic level over all site types of a spatially coarse-grained cell. Homogenization provides a novel coarsening of the number of processes, an important aspect for complex problems plagued by the existence of numerous microscopic processes (combinatorial complexity). As expected, the homogenized CGMC method outperforms the traditional KMC method on computational cost while retaining good accuracy.