One-dimensional dislocations - III. Influence of the second harmonic term in the potential representation, on the properties of the model

Abstract

In the previous one-dimensional dislocation model, a single sinusoidal term was taken to represent the potential energy of the deposit as a function of its position on the substrate. In this model a more general representation of the potential, containing a second harmonic term as well, is used, and it is shown that the solution in this case is also expressible in terms of elliptic integrals. The displacements corresponding to a sequence of dislocations (or a single one) are calculated. The work done in generating a single dislocation by a force on a free end is derived and the stability conditions for such a chain determined. It turns out that the properties of single dislocations, especially as concerns their application to misfitting monolayers and oriented overgrowth, remain almost uninfluenced, unless the amplitude of the second harmonic term is so large as to produce a new minimum and provided the overall amplitude of the potential energy is taken to be constant. When the amplitude of the second harmonic term is large, so that the potential curve has a second minimum, a complete dislocation splits up into two halves which are the one-dimensional analogues of Shockley’s ‘half-dislocations’ in close-packed lattices. The equilibrium separation of the two halves, as well as the stability conditions for the existence of a single half, are determined.