During plastic deformation of crystalline materials, the collective dynamics of interacting dislocations gave rise to various patterning phenomena. A crucial and still open question was whether the long range dislocation-dislocation interactions which did not have an intrinsic range could lead to spatial patterns which may exhibit well-defined characteristic scales. It was demonstrated for a general model of two-dimensional dislocation systems that spontaneously emerging dislocation pair correlations introduce a length scale which was proportional to the mean dislocation spacing. General properties of the pair correlation functions were derived, and explicit calculations were performed for a simple special case, viz pair correlations in single-glide dislocation dynamics. It was shown that in this case the dislocation system exhibited a patterning instability leading to the formation of walls normal to the glide plane. The results were analyzed in terms of their general implications for dislocation patterning.

Statistical Dynamics of Dislocation Systems - the Influence of Dislocation-Dislocation Correlations. M.Zaiser, M.C.Miguel, I.Groma: Physical Review B, 2001, 64[22], 224102 (9pp)