A new embedded-atom method approach based on the pth moment approximation

Abstract

Large scale atomistic simulations with suitable interatomic potentials are widely employed by scientists or engineers of different areas. The quick generation of high-quality interatomic potentials is urgently needed. This largely relies on the developments of potential construction methods and algorithms in this area. Quantities of interatomic potential models have been proposed and parameterized with various methods, such as the analytic method, the force-matching approach and multi-object optimization method, in order to make the potentials more transferable. Without apparently lowering the precision for describing the target system, potentials of fewer fitting parameters (FPs) are somewhat more physically reasonable. Thus, studying methods to reduce the FP number is helpful in understanding the underlying physics of simulated systems and improving the precision of potential models. In this work, we propose an embedded-atom method (EAM) potential model consisting of a new manybody term based on the pth moment approximation to the tight binding theory and the general transformation invariance of EAM potentials, and an energy modification term represented by pairwise interactions. The pairwise interactions are evaluated by an analytic-numerical scheme without the need to know their functional forms a priori. By constructing three potentials of aluminum and comparing them with a commonly used EAM potential model, several wonderful results are obtained. First, without losing the precision of potentials, our potential of aluminum has fewer potential parameters and a smaller cutoff distance when compared with some constantly-used potentials of aluminum. This is because several physical quantities, usually serving as target quantities to match in other potentials, seem to be uniquely dependent on quantities contained in our basic reference database within the new potential model. Second, a key empirical parameter in the embedding term of the commonly used EAM model is found to be related to the effective order of moments of local density of states. This may provide a way to improve the precision of EAM potentials further through more precise approximations to tight binding theory. In addition, some critical details about construction procedures are discussed.