8 - Monte Carlo method in two-dimensional materials

Abstract

Two-dimensional films are increasingly utilized for solving stability related problems, for instance, in the rapidly emerging body of work related to battery interfaces. With experimental evidences pointing towards some sort of mechanistic advantage in utilizing smooth 2D surfaces or films on various electrode interfaces, a combination of Monte Carlo and Molecular Dynamics simulations can help lay out the fundamental science of such nanoscale interfaces. In this chapter, we first explore the concepts behind the formulation of Metropolis Monte Carlo method, before delving into its application in a relevant area which enables us to study the interfacial mechanics involved in stabilizing the extremely failure-prone silicon based anodes in otherwise very high capacity Li-ion batteries, utilizing 2D materials. However, such MC based MD approaches require short time steps, limiting the simulation time scale, and reling on the accuracy of the interatomic potentials. These limitations call for an increased utility of kinetic Monte Carlo(KMC) methods. This becomes the subject of our subsequent discussion, where we fall back on stochastic algorithm and basic problem-specific codes to build on the concept of state to state dynamics as utilized by the KMC method, rather than tracing particles' trajectory through the vibrational periods. By permitting only infrequent events to be tracked, KMC traces simulations for longer timescales. As an example, problem of Langmuir adsorption on a unit lattice is elaborated and explanation is further extended to site specificity in a 2D lattice of graphene.