A dislocation-dipole in one dimensional lattice model

A family of equilibria corresponding to dislocation-dipole, with variable separation between the two dislocations of opposite sign, is constructed in a one dimensional lattice model. A suitable path connecting certain members of this family is found which exhibits the familiar Peierls relief. A landscape for the variation of energy has been presented to highlight certain sequential transition between these equilibria that allows an interpretation in terms of quasi-statically separating pair of dislocations of opposite sign from the viewpoint of closely related Frenkel-Kontorova model. Closed form expressions are provided for the case of a piecewise-quadratic potential wherein an analysis of the effect of an intermediate spinodal region is included.