It was recalled that dislocation segments, inclined at small angles to close-packed lattice directions in crystals with a high Peierls energy, contained a sequence of geometrical kinks. The distribution of these kinks under the action of an applied stress was studied. The segments were assumed to be pinned a distance, L, apart and the formation of kink-pairs was excluded. For kinks with a finite width, only numerical solutions were possible by minimizing the enthalpy. For abrupt kinks with nearest-neighbour interactions, analytical solutions were obtained. It was found that, at a critical stress, σcr, there was a phase transition in the distribution. For σ < σcr, the area, A, swept out by the kinks was proportional to σL3 and independent of the number of kinks. For σ > σcr, the kinks formed a free pile-up, in which their separation decreased in proportion to 1/√k. The changes in area, ΔA, with changes in stress, Δσ, were then independent of L but now depended upon the number of kinks.

Pile-Ups in Kink-Chains. G.Schoeck: Philosophical Magazine Letters, 2008, 88[1], 83-9