Fragment Hamiltonian model potential for nickel: metallic character and defects in crystalline lattices

Abstract

The Fragment Hamiltonian (FH) model is introduced as the basis for a new class of atomistic potentials that may be viewed as generalizations of the embedded atom method (EAM) and related atomistic potentials. Many metals and alloys have been successfully modeled by this method and other related methods, but the nature of the metallic character in the models has been lost. Here we attempt to recover this character, at a qualitative level, by defining an embedding energy as a function of two variables through the FH model. One of these variables, called the ionicity, is associated with the established concept of background density in EAM models. The FH embedding energy is composed of two types of energies, one for energies of different states of an atom and the other for hopping energies that transform an atom from one state to another. A combination of the energies for the states of an atom yield a local gap energy that conforms to a generalized definition of the ‘Hubbard-U’ energy. The hopping energies compete with the gap energy to provide a notion of metallic behavior in an atomic-scale model. Lattices of nickel with different coordinations and spatial dimensions, elastic constants, energies for several types of defects in three-dimensional lattices and two surface energies are calculated to show the strengths and limitations of the current implementation and to explore their metallic character.