X-ray determination of dislocation density and arrangement in plastically deformed copper

Using the kinematical theory of X-ray scattering by crystals with dislocations as developed by Krivoglaz et al. and Wilkens, the dislocation content of compressed copper single and polycrystals was investigated by means of profile analysis of selected diffraction peaks. Measurements of radial intensity distributions I(2θ) were performed with a double-crystal spectrometer in the case of the single crystals and with conventional polycrystal diffractometers in the case of the polycrystals. Additionally, the misorientations Θ occurring within the dislocation cell structure because of the accumulation of excess dislocations of one sign were investigated by means of rocking curves of the single-crystal reflections and by evaluation of electron backscattering patterns (EBSPs). Within a wide deformation range, the mean total dislocation density ρ_d can be related well to the flow stress via the Taylor relationship. Assuming a random distribution of the misorientations Θ between adjacent dislocation cells, the evaluation of the rocking curves gives mean values 〈|Θ|〉 much smaller than those determined by EBSP analysis. For this reason, a model of a dislocation cell structure with restrictedly correlated misorientations, which leads to better agreement of the X-ray and the EBSP data, is proposed.