Physical principles involved in anomalous X-ray scattering is discussed, by referring to the classical theory of forced vibrations of an oscillator. It is emphasized that the energy dissipation and the phase shift between force and displacement are an inseparable result due to friction. A brief historical review is given of studies of X-ray anomalous dispersion in these sixty years.
The anomalous scattering factors of X-rays have been described by the classical and quantum-field theory. Then the results are compared among three different calculations of f' (ω) and f″ (ω) for isolated atoms : (1) by Hönl (quantum theory), (2) by Parratt and Hempstead (semi-empirical theory) and (3) by Cromer and Liberman (relativistic quantum theory) . The fine structures of f' (ω) and f″ (ω) near the absorption edge are also reviewed from the viewpoint of the band theory and the dispersion relation.
A stress is put on the various methods of the relevant measurements rather than on the review of the measured values in comparison with the corresponding calculated values. The methods of the measurements are classified into two : (i) optical methods and (ii) intensity methods. Among the first methods, the older methods were only briefly referred to, and more recently published methods, particularly those with interferome-ters, are explained in details. The second methods include many varieties of experiments, but relatively new studies are explained in details, with the stress on the use of the white radiation. Finally, some studies which partially include computational procedures have been introduced.
Recent development of an energy-dispersive diffractometry with a solid-state detector made it possible to measure integrated reflecting intensities very near the absorption edge, which brought about several characteristic features for a perfect crystal. Some topics on the effects of anomalous scattering in a perfect crystal are discussed on the basis of the dynamical theory with reference to those in a mosaic crystal. The applications, such as determination of anomalous scattering factors f' and f'', are also briefly reviewed.
The real part of the anomalous dispersion of Si structure factor was measured by means of Pendellosung fringes. The experimental procedures are explained in detail. The tentative results are given for Si 220 reflection in the wavelength range from CuKα to AgKα lines. The results are in accordance with the theory of Cromer and Liberman
A review has been made on the following subjects: (1) The unique characteristics of the anomalous scattering in materials researches. (2) The comparison among three anomalous scattering among X-rays, neutrons and nuclear resonant gamma-rays. (3) A stress has been put on the use of the white radiation in the phase determining procedures. Some intrinsic limitations are also pointed out. (4) Miscellaneous applications which are not described in other articles in the present special issue.
A survey of the theory of diffraction symmetry involving anomalous scattering is given, and conditions for the occurrence of Bijvoet differences are discussed in detail. Some applications of Friedel-law violation, especially those to the determination of the space group and various kinds of Fourier techniques, are described.
Accuracy of the structural parameters determined by the least-squares refinements and the features of residual electron densities are affected by the errors both in the observed and calculated X-ray structure factors, as well as by the refinement procedures. These errors are summarized and discussed. Anomalous dispersion effect could be one of these error sources if it is not treated properly. Some successful examples are given, in which the absolute configuration of molecules composed of light atoms is determined by means of X-ray anomalous scattering.
We here review the effectiveness of the anomalous difference to the protein crystal analysis : the determination of the heavy atom coordinates, the refinement of them and the phase determination. We then cite our experience on the study of porcine two-zinc insulin crystal structure analysis at 4°C in the application of the single isomorphous replacement method using the anomalous scattering.
A review is reported on the absolute determination of polarity and on the antiparallel domain configuration of f erroelectric crystals, using the difference of integrated intensity between hkl and hkl reflections
The method to find the correction terms for the anomalous scattering is briefly surveyed in the angle-dispersive and the energy-dispersive methods on the powder sample. On the former, a special attention is payed to an influence of the multiplicity on the correction. On the latter, the anomalous scattering terms change from line to line as the X-ray energy of the Bragg peak changes. As a condition to determine the correction term and the temperature factors simultaneously, minimization of an average of Δ ρ (r) 2 in the unit cell is discussed.
Application of anomalous scattering to the determination of deviations from the perfect disorder or from the perfect order such as superlattice of alloys or inversibility of spinel are reviewed historically. Applications to the study of partial structure factors of amorphous and liquid alloys are also reviewed.