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 an applied stress was studied. The segments were assumed to be pinned a distance, L, apart and the formation of kink-pairs was excluded. Numerical solutions alone were possible, by minimizing the enthalpy, for kinks having a finite width. Analytical solutions were obtained for abrupt kinks with nearest-neighbour interactions,. 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 was independent of the number of kinks. For σ > σcr, the kinks formed a free pile-up in which their separation distance decreased in proportion to 1/√k. 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