Contributions of the embedded-atom method to materials science and engineering
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Many-body potentials Atomic-scale computer simulations of materials such as Monte Carlo (MD) and molecular dynamics (MD) rely on a prescription of the energy in terms of the atomic positions, which is often referred to as the interatomic potential. In the early 1980s, however, the typical interatomic potential models used were pair potentials. As mentioned in the introductory article by Sinnott and Brenner in this issue of MRS Bulletin, pair potential models have well-known limitations in the description of crystalline solids. Further, the theoretical framework of pair potentials is based on bulk materials and so could only be applied to systems that did not contain surfaces and interfaces. Finally, there was an increasing interest in models that went beyond qualitative features and represented specific materials systems. Multiple approximations were proposed during the first half of the 1980s for the energy of a metallic system that provided a means to describe the energy of an inhomogeneous system. While the physical motivations differed, the energy expressions had similar mathematical forms. In particular, the energy expressions can be written in the form1,2 § · 1 E = ¦ F ¨ ¦ fij ( Rij ) ¸ + ¦ Vij ( Rij ) . i © j ¹ 2 ij
(1)
In this expression, i and j are indices referring to the atoms, Rij is the separation between atoms i and j, V is a pair interaction between atoms i and j, and the functions f and F have interpretations that depend on the different models as discussed later.
This form has one significant advantage: it can be applied to inhomogeneous problems. The sidebar discusses the consequences of this form for the energy. Here, we will briefly outline the reasoning that led various authors to propose Equation 1. In the process, the physical interpretation of the various terms in Equation 1 will be described. As will be seen, these interpretations of the terms are different. One route to Equation 1 starts with the concepts of the quasiatom theory of Stott and Zaremba3 and the effective medium theory of Norskov.4 These theories assert that the energy of light impurity atoms such as hydrogen is largely determined by the energy to embed that impurity into the local electron density, the embedding energy. Daw and Baskes5,6 extended this idea in a study of nickel and palladium hydrides by applying the embedding energy concept to both the host metal atoms as well as the impurities. This line of development led to the embedded-atom method (EAM)1 potentials. From the EAM perspective, the function F in Equation 1 is the embedding energy. The argument of F represents the local electron density in which the atom is placed. This is computed by a superposition of atomic-like electron densities. Thus, the functions fij are the electron density from atom j at the location of atom i. The remaining terms in the energy are contained in the pair interaction term V. Another route to Equation 1 starts with a tight-binding description of the electronic structure of a solid. A major component of the bonding of a solid results fro
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