X-ray scattering by dislocations in crystals. General theory and application to screw dislocations

Line profiling of X-ray Bragg peaks has great potential for extracting meaningful physical parameters from work-hardened single-crystal samples; these include both dislocation densities and ordering lengths. However, a detailed reading of the existing literature uncovered shortcomings in the required theoretical understanding of scattering from dislocations. A mathematically rigorous theoretical framework is presented for understanding dislocation scattering; the procedure is based upon first principles of kinematic scattering and basic laws of probability theory. These results are then applied to the specific case of parallel screw dislocations. As expected from experimental measurements, the solution to this problem is neither Gaussian nor Lorentzian but is 'intermediate' between these distributions. Detailed computer simulations of the scattering are carried out and compared to the theoretical predictions. The predictions match the computer simulations with no adjustable parameters. Comparisons are also made to the work of previous authors.