Pair Potentials in Atomistic Computer Simulations

Abstract

Computer modeling of crystal defects ranges at present from generic empirical investigations to first-principle quantum-mechanical calculations (see, for example, References 1–4). Descriptions of atomic interactions in terms of pair potentials dominated such studies until the early 1980s, and many fundamental features of lattice defects and interfaces were revealed in these calculations. The generic results of these studies withstood the test of time, and calculations employing more sophisticated schemes usually confirmed their validity. An early example goes back to the late 1950s when Vineyard and co-workers pioneered the very first computer simulations in their studies of radiation damage. Empirical pair potentials were used in these investigations in which many fundamental, generic aspects of the effect of irradiation of crystalline materials by energetic particles were discovered.Such simple treatments of atomic interactions may appear totally inadequate from the point of view of pure physics. However, it must be recognized that the purpose of the majority of atomistic studies of lattice defects has been to elucidate atomic structure and atomic-level properties in materials with given: (a) crystal structure, (b) elastic properties and possibly phonon spectra, (c) values of certain material parameters such as vacancy formation energies and stacking fault energies, and (d) in alloys, alloying and ordering energies, and possibly antiphase boundary energies. This is in contrast with ab initio studies, the objective of which is to determine all these properties from first principles. These goals of atomistic studies are, of course, the same for all semi-empirical approaches discussed in this collection of articles. In general, the validity of the structural features of lattice defects found in calculations using empirical schemes is best guaranteed if they can be related to fitted material properties and are not sensitively dependent on the deails of the fittings and functional forms employed.