Decision tree driven construction of rate constant models: Identifying the “top-N” environment atoms that influence surface diffusion barriers in Ag, Cu, Ni, Pd and Pt

Abstract

The local chemical environment is known to influence the rate constants of thermally activated atomic-scale processes in materials. In situations where rate constants vary over several orders of magnitude, dynamical materials simulations often require accurate rate constant models that can rapidly predict the rate for vast number of environments. Deriving rate constant models by fitting to a database of barriers can be particularly challenging when several environment atoms are believed to affect the rate. Previously, artificial neural networks (ANN) and cluster expansion models (CEM) have been employed as rate constant models. We demonstrate that a decision tree (DT) can complement training of such models by providing useful inputs. DTs can be used to (i) determine the relevant chemical environment, (ii) estimate the accuracy expected from CEM/ANN, (iii) identify cluster sizes required in CEM or size of the input layer in ANN so that the CEM/ANN model can be trained in a single step, and (iv) determine the minimum amount of data required for accurate training. Using this strategy, we construct for the first time CEM and ANN models for the exchange move (surface diffusion of metal on metal) that are both compact and accurate. The use of DT has enabled inclusion of large clusters, as big as 11 atom clusters in the CEM. Our strategy paves way for coupling DT and CEM/ANN for building computationally inexpensive rate constant models.