Density of stacking faults and twin boundaries in ultrafine-grained materials determined by X-ray line profile analysis

Planar faults, especially stacking faults and twins, can play an important role in the defect structure of ultrafme-grained materials. X-ray line broadening and line shift caused by planar faults is highly anisotropic as a function of the hkl indices, the anisotropy being qualitatively different from both strain and size anisotropy. This makes it possible to distinguish the line broadening components corresponding to planar faults, dislocations and subgrain size. The numerical procedure, the CMWP (convolutional multiple whole profile) method for the evaluation of diffraction patterns based on the model of dislocations and grain size for strain and size broadening, has been extended for the evaluation of planar faults present concomitantly with dislocations and subgrains. The effect of planar faults on diffraction profiles has been evaluated numerically by using the DIFFAX software. About 15.000 diffraction profiles have been produced for intrinsic, extrinsic and twin faults as a function of different hkl indices and planar fault concentrations. It was found that the numerically calculated diffraction profiles can be well simulated by Lorentzian functions as far as down to 10⁴ relative intensities into the tails. Thus, about 15.000 simulated Lorentzians have been systematically parameterized for hkl fault types and fault densities, respectively, and the compiled parameter files have been incorporated into the CMWP numerical procedure; The dislocation structure, the subgrain size and size distribution and the densities of twin boundaries have been determined in specimens of Cu and Cu-Zn alloys processed by high-pressure torsion as a function of the distance along the radius of the samples.