Introduction to the Application and Limits of Anomalous X-ray Diffraction in the Determination of Partial Structure Factors*

The use of anomalous X-ray scattering to obtain the first differences and partial structure factors normally obtained with isotopic substitution neutron diffraction is described and compared with the neutron technique. Both the problems associated with the X-ray technique and the situations in which it is highly valuable are discussed. The availability of tunable, intense synchrotron radiation (SR) has made it possible to readily vary atomic form factors by varying the incident photon energy in X-ray scattering experiments. As a result, many isotopic substitution neutron diffraction techniques have become feasible, at least in principle, with X-rays. These include the determination of first differences [known as the differential structure factors (DSFs) and differential distribution functions (DDFs) of the differential anomalous scattering technique] and partial structure factors (PSFs) utilizing small-angle scattering and/or wide-angle scattering. There are, however, distinct differences between the X-ray and the neutron experiments. Some of these serve to limit the accuracy and utility of the SR-determined PSFs considerably and are discussed in Sec. 3. Others, discussed in Sec.5 make the X-ray approach applicable to materials systems which cannot be readily studied with isotopic substitution neutron diffraction. 2. Anomalous X-ray Scattering and Partial Structure Factors The atomic scattering factor is frequently expressed as: f(q,E)=f,(q)+f’(E)+ifyE), (1) where E is the photon energy, f. is the high photon energy limit off, given by the Fourier transform of the atom’s electron density, while f and f’ are the real and imaginary shifts arising from resonances when E is close to some excitation energy for atomic electrons. * Work supported by the U.S. Department of Energy under Contract DE-AC03-76SFOO515. Invited paper presented at Methods in the Detemhaation of Partial Structure Factors of Disordered Matter by Neutron & Anomalous X-ray Diffraction, Institut Max von Luue Paul Langevin, ESRF, Grenoble, FRANCE, September I O-I I, I992 f’ is simply related to the X-ray absorption coefficient, (T, by the relation