Dislocation Cell Formation in Metals

TLDR: In this article, it is shown that an array of dislocations, modelled by parallel screw dislocation, of uniform density, is unstable, and that the instability grows ultimately into a dislocation cell structure and the cell size is given by the dominant wavelength of the density modulation.

Abstract: It is shown by an analysis similar to that for the spinodal decomposition of a supersaturated solution that an array of dislocations, modelled by parallel screw dislocations, of uniform density, is unstable; the dislocations move to form a structure having a modulated dislocation density. It is suggested that the instability grows ultimately into a dislocation cell structure and that the cell size is given by the dominant wavelength of the density modulation. This wavelength λm is found to be proportional to ρ−1/2 and furthermore the wavelength is given by λm ≈ Kc·ρ−1/2=rc, where Kc is a constant, ρ is the dislocation density and rc is defined as a dislocation‐dislocation interaction distance. Data in the literature relating to cell size are shown to support this result. Restrictions on the applicability of the analysis are discussed.