Interatomic Potentials for Atomistic Simulations
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MRS BULLETIN/FEBRUARY 1996
spanning the major classes of materials bonding: covalent, metallic, and ionic. The survey begins with a description of the type of interaction used in most pioneering computer simulations—the pair potential—in an article by Vaclav Vitek. From the perspective of one who has studied lattice defects using potentials spanning a wide range of sophistication, he argues that pairwise interactions are still appropriate for many atomistic studies. The next article, by Stephen Foiles, is an introduction to the embedded-atom method, in which a pair potential is augmented by a function of another pairwise sum. This surprisingly simple modification, which can be justified as an approximation to either density-functional theory or tight binding, has had a significant impact on the simulation of metals over the last decade. Marshall Stoneham, John Harding, and Tony Harker then describe the shell model, also a conceptually simple modification of a pair potential, which has become the standard approach for ceramics. They also discuss extensions to the basic shell model that show promise for treating systems with some metallic and covalent character. Donald Brenner describes the class of potentials based on the bond-order formalism. This approach, which is rooted in bonding concepts from the early days of quantum chemistry, has proved valuable for covalently bonded systems. The Tersoff form is one example. Brenner begins his article with a general introduction to potential-energy surfaces for systems making and breaking bonds. The set concludes with an introduction to the tight-binding method by Adrian
Sutton, Paul Godwin, and Andrew Horsfield. Tight binding, the most complex form considered here, holds an interesting position in the potential hierarchy. It is probably the simplest form that includes real quantum-mechanical effects such as resonance and electron delocalization, and it can be justified as an approximation to either density-functional theory or Hartree Fock theory. As such, it is currently the basis of considerable activity as a starting point from which more compact forms can be approximated. Though not discussed here, simulations using highly accurate, first-principles electronic-structure techniques are becoming more common. However, there will always be a need for lower complexity potentials such as those in the following articles. For example, for a given problem, substitution of a simpler (faster) potential allows one to obtain quick, qualitative results; to scan many cases to obtain trends; to investigate longer time scales; or to model a larger system. In addition to the excellent introductory treatments and historical perspective given in the articles collected here, the reader will also find views on remaining problems and future directions. The following summarizes this author's view of the future. The systems most in need of interatomic-potential development are those for which the bonding does not fall into one category. Examples include advanced intermetallics such as MoSi2,
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