Interatomic forces in relation to the theory of dislocations

Abstract

The early developments of the dislocation theory were mainly in the framework of the continuum theory of elasticity. However, the importance of understanding the dislocation cores became apparent as investigations turned away from materials with close-packed structures to materials with more complex crystal structures. A necessary precursor for theoretical studies of the atomic structure of dislocations and other lattice defects is an understanding of atomic interactions. Until recently pair potentials were used almost exclusively in such studies. In this paper we first discuss the origin, merits and limitations of pair potentials. In particular, we analyse which features of pair potentials, as well as of the problems studied, are most important for the success of such atomistic studies. This is then demonstrated on two examples: the core structures of screw dislocations in intermetallic compounds with the Ll₂ crystal structure and the cores of intrinsic grain-boundary dislocations. Finally we discuss possible future developments in dislocation studies, in particular the replacement of pair potentials by empirical many-body potentials and quantum-mechanically based total-energy calculations.