One of the most important techniques for determining the atomic structure of a material is X-ray diffraction. One of the great problems of the technique, however, is the fact that only the intensity of the diffraction pattern can be measured, not its phase. The inverse problem, of determining the structure from the pattern thus contains ambiguities that must be resolved by other means. Quantitative X-ray analysis provides one way to resolve this phase problem: mixing the material in question with a material of known structure yields interferences that can be analyzed to yield the unknown...