Characterizing short-range vs. long-range spatial correlations in dislocation distributions

Hard X-ray diffraction experiments have provided evidence of a strongly heterogeneous distribution of dislocation densities along the axis of cylindrical ice single crystals oriented for basal slip in torsion creep. The dislocation arrangements showed a complex scale-invariant character, which was analyzed by means of statistical and multifractal techniques. A trend to decreasing autocorrelation of the dislocation distribution was observed as deformation proceeds. At low strain levels, long-range spatial correlations control the distribution, but short-range correlations in relation with cross-slip progressively prevail when strain increases. This trend was reproduced by a model based on field dislocation dynamics, a theory accounting for both long-range elastic interactions and short-range interactions through transport of dislocation densities.