The phenomenon of the diffraction of monochromatic x-radiation by a single crystal can be broken down for convenience into two somewhat separate aspects: the geometry of the distribution of the diffracted beams, and the relative intensities of the beams. The distribution geometry is a function of the lattice of the crystal only, and if it is properly recorded it supplies data for the unequivocal determination of the unit cell of the crystal. The relative intensities of the diffraction spectra, on the other hand, are functions of the positions of the atoms with respect to the lattice co-ordinate system. If both the intensities and the phases are known, data are at hand for an unequivocal determination of the positions of the atoms. It is unfortunate that, while the intensities of the spectra can be recorded, their phases cannot. For this reason it is not possible to fix the positions of the atoms in all crystal structures.
It is not the purpose of this publication to discuss all the methods of seeking solutions for crystal structures in the face of this difficulty. There is, however, one method with which it is concerned—that of cut and try. Although it is not always possible to derive the structure from its diffraction, it is always possible to predict the diffraction from the structure. A method has consequently arisen which consists of postulating a reasonable trial structure, computing the x-ray diffraction intensities to be expected from it, and comparing these . . . .