Phase determination and Patterson maps from multiwave powder data

In the limit of unrestricted resolution, with Friedel pairs as the only coincidences, phase angles or signs can be determined uniquely from powder diffraction data using multiple-wavelength techniques. For a centrosymmetric structure one anomalously scattering species of atoms and data taken at two λ's are sufficient. In the acentric case one needs two different anomalous scatterers and measurements at three λ's. The anomalous scatterers can be localized from difference Patterson maps: their peaks can be discriminated against the peaks due to non-anomalous scatterers.