Single crystals were deformed in uniaxial compression, and were investigated by means of X-ray line-profile analysis. The resultant statistical parameters of the dislocation pattern were compared to the fractal dimension of the dislocation network, as determined by applying the box-counting method to transmission electron micrographs. The correlation between the relative fluctuations of the dislocation density, and the fractal dimension of the dislocation pattern, was interpreted in terms of the generalized fractal composite model. The δ-parameter, which was related to the relative fluctuations of the dislocation density, decreased with increasing deformation while the fractal dimension which was deduced from transmission electron micrographs increased. Both results implied that the dislocation network tended to fill up the space homogeneously. For the present data, the relationship between δ and the fractal dimension, D, was described by D = 1.975-0.0354δ.

Characterization of Self-Similar Dislocation Patterns by X-Ray Diffraction. F.Székely, I.Groma, J.Lendvai: Physical Review B, 2000, 62[5], 3093-8