The classical Peierls theory of dislocations was critically examined and was shown to contain a number of inconsistencies. In the case of narrow-core dislocations, the classical theory led to a gross over-estimation of the barrier to dislocation motion. A new semi-discrete theory was presented here which corrected the inconsistencies of the classical theory and furnished results which were markedly similar, both qualitatively and quantitatively, to those of atomistic calculations. This theory provided a link between accurate nm-scale quantum mechanical calculations of dislocation-core energetics and mesoscale continuum descriptions. Although analytical solution was no longer feasible, the model was numerically efficient and could be extended so as to deal with various complex dislocation processes such as cross-slip, dislocation intersection and non-planar cores.

Semidiscrete Variational Peierls Framework for Dislocation Core Properties. V.V.Bulatov, E.Kaxiras: Physical Review Letters, 1997, 78[22], 4221-4