X-ray diffraction (XRD) is a standard method for quantitative material analysis in areas like crystallography, chemistry, or biochemistry: X-Ray exposure yields intensity distributions that depend on the molecular structure and that can be measured with high precision over a certain range of diffraction angles. Material parameters are then obtained by suitable parameter estimation methods. The talk presents the resulting class of typically ill-conditioned constrained inverse problems and reports on the development and implementation of a real time solution algorithm. Main components of the algorithm include a Levenberg-Marquardt method, an aggressive truncated CG method featuring special projection techniques, and sparse linear algebra exploiting the specific Jacobian structure. The post-optimality analysis includes a detection of modeling redundancy and a covariance computation based on an SVD or a QR decomposition with pivoting. Computational results for a benchmark problem will be presented.