A cluster expansion model for predicting activation barrier of atomic processes

We introduce a procedure based on cluster expansion models for predicting the activation barrier of atomic processes encountered while studying the dynamics of a material system using the kinetic Monte Carlo (KMC) method. Starting with an interatomic potential description, a mathematical derivation is presented to show that the local environment dependence of the activation barrier can be captured using cluster interaction models. Next, we develop a systematic procedure for training the cluster interaction model on-the-fly, which involves: (i) obtaining activation barriers for handful local environments using nudged elastic band (NEB) calculations, (ii) identifying the local environment by analyzing the NEB results, and (iii) estimating the cluster interaction model parameters from the activation barrier data. Once a cluster expansion model has been trained, it is used to predict activation barriers without requiring any additional NEB calculations. Numerical studies are performed to validate the cluster expansion model by studying hop processes in Ag/Ag(100). We show that the use of cluster expansion model with KMC enables efficient generation of an accurate process rate catalog.