Pile-ups in kink-chains

Abstract

Dislocation segments inclined at small angles to close-packed lattice directions in crystals with high Peierls energy contain a sequence of geometrical kinks. The distribution of these kinks under the action of an applied stress is studied. The segments are assumed to be pinned a distance L apart and the formation of kink-pairs is excluded. For kinks with finite width only numerical solutions are possible by minimizing the enthalpy. For abrupt kinks with nearest-neighbour interactions, analytical solutions are obtained. It turns out of that at a critical stress σ_cr there is a phase transition in the distribution. For σ < σ_cr the area A swept out by the kinks is proportional to σL ³ and independent of the number of kinks. For σ > σ_cr the kinks form a free pile-up, in which their separation distance decreases proportionally to . The changes in the area ΔA upon changes in stress Δσ are then independent of L but depend now on the number of kinks.