MAD techniques applied to powder data: finding the structure given the substructure

The joint probability distribution function method is applied to multiple-wavelength anomalous dispersion (MAD) powder data. The distributions are calculated by assuming prior knowledge of the scattering intensities at two wavelengths and of the anomalous-scatterer substructure. The method leads to formulas estimating the full structure phases and their reliability. The procedure has been applied to two structures, one unknown and one known; the second was used as a control for the phasing procedure. In spite of the unavoidable peak overlapping in the diffraction pattern, the formulas proved to be very effective. Combined with a new algorithm for phase extension, they enabled the solution of both crystal structures.