A new embedded-atom method approach based on thepth 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.

Improved embedded-atom model potentials of Pb at high pressure: application to investigations of plasticity and phase transition under extreme conditions

“…In comparison, expression (3) does not suffer from this problem. Besides, expression (3) could produce similar curve shapes as expression (2) within a range between about 2 e r / on the low-density side and F 2 0 / on the high-density side that validated for the latter [38], and thereby could correctly reproduce the universal relation between binding energy and interatomic separation in the valid range. For the reasons, we use expression (3) to construct the EAM potentials of Pb in the present work.…”

“…In such expression, n serves as a potential parameter, F 0 and e r are the embedding energy and electron density at atom l under equilibrium states, respectively. If the averaged pth rather than the second moment approximations to the tightbinding theory is employed, the bonding term could be expressed as [38] F F p , 3…”

“…If parts of the nodes are chosen to be r , i e then equilibrium equation, binding energy equation as well as equations representing other physical properties should also be satisfied. These equations help reduce quantities of potential parameters and greatly improve the efficiency for potential developments (more technique details could be found in [38]). Consequently, only N 4 parameters are independent.…”

Response embedded atom model potential of Pb at finite temperature: application on the dislocation mobility

“…where g g k , , g 0 are the parameters of the model. Since the polynomial spline function does not have to be limited by the analytical form and has sufficient flexibility, the response function and the pairwise interaction are also fitted by a standard cubic spline function in this potential, and the pairwise interaction [27][28][29] is defined as…”