• powder diffraction;
  • normal equations;
  • charge density

Under the experimental condition that all Bragg peaks in a powder X-ray diffraction (PXRD) pattern have the same shape, one can readily obtain the Bragg intensities without fitting any parameters. This condition is fulfilled at the P02.1 beamline at PETRA III using the seventh harmonic from a 23 mm-period undulator (60 keV) at a distance of 65 m. For grain sizes of the order of 1 µm, the Bragg peak shape in the PXRD is entirely determined by the diameter of the capillary containing the powder sample and the pixel size of the image plate detector, and consequently it is independent of the scattering angle. As an example, a diamond powder has been chosen and structure factors derived which are in accordance with those calculated from density functional theory methods of the WIEN2k package to within an accuracy that allows a detailed electron density analysis.