Differential X-ray diffraction: a theoretical basis for a technique based on wavelength variation

Differential diffraction is an extension of spectrum-subtraction techniques of spectroscopy to X-ray powder diffraction. In differential diffraction two patterns are taken for the same material under different conditions. The patterns are then subtracted to obtain information helpful in characterizing the material. Examples of exploitable effects are density, magnetism, particle size, preferred orientation and absorption. One application of differential diffraction is the identification of phases in mixtures. If differential diffraction techniques could be used to label each diffraction line in a pattern with the elements of the compound giving rise to that particular line, phase characterization of mixtures would be greatly simplified. One possible way to accomplish this labeling is to take advantage of the pronounced change in absorption that occurs near the absorption edge of an element. A theory is presented for a differential diffraction technique based on wavelength variation that will allow diffraction peaks to be labeled with elemental information. Patterns are calculated for a binary mixture of CuO and NiO using wavelengths chosen to straddle an absorption edge for Ni. The absorption effects make it easy to use the difference pattern to separate and identify the two phases present. Extension of this method to more complex multiphase mixtures would necessitate additional patterns and require solution through factor analysis.