Anomalous scatterers in X-ray diffraction and the use of several wavelengths.

An x-ray diffraction experiment involving crystals containing anomalous scatterers is analyzed to determine what information is available when two or more different wavelengths are employed and the positions of the atoms scattering anomalously are not known. It is found from an algebraic analysis of the structure factor equations for individual reflections that, if there is only one type of anomalous scatterer, a two-wavelength experiment can determine separately the intensities of scattering from the nonanomalously and anomalously scattering atoms, and also certain phase differences. This information is obtained with a twofold ambiguity which can be resolved by carrying out the experiment at a third wavelength. The separate intensities may be used for direct phase determination. In addition, special types of Fourier maps may be computed and are discussed in some detail.