Analytical explicit expressions have been derived for multiple‐scattering effects under assumptions which are usually fulfilled in small‐angle scattering. The expressions are used to evaluate quantitatively distortions of scattering patterns caused by multiple scattering. The distortions are discussed in terms of changes of the forward‐scattering cross section, the radius of the gyration, the integrated intensity, the Porod region and Porod constant. In addition, the analytical expressions have been used to calculate the scattering cross section of the sample from scattering patterns which are strongly affected by multiple scattering.

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The use of neutrons in small-angle scattering has opened a wide field of applications for investigations in magnetism, polymeric science, for certain problems in biology, and in metallurgy. In the first part, this review deals with the experimental aspects of neutron small-angle scattering. In particular, the compensation of the relatively small luminosity of neutron sources as compared to X-ray tubes will be discussed in detail. This is mainly achieved by large beam cross sections, leading to correspondingly long instruments, and by an optimization of the intensity with respect to the different contributions to the resolution width of the scattering vector K(~: = 27r0/2, 0 = scattering angle, 2 = wavelength). Instruments which have been developed along these lines are described, especially the 40 m instrument in Ji~lich and the 80 m instrument at the high-flux reactor in Grenoble. The Grenoble instrument covers a range of scattering vectors between 1 .~-1 and 3.10 -4 A-~; the maximum possible resolution is about 10 -4 A-1. Typical applications are reviewed and discussed, namely those dealing with (i) density and compositional fluctuations in solids (alloys, defect clusters, dislocations, grains), (ii) magnetic inhomogeneities in solids (alloys, magnetic domains), (iii) flux-line lattices in type-II superconductors (form factors, imperfections and morphology), (iv) polymers in the solid state, and (v) biological substances.

Numerical diffuse scattering calculations are carried out for interstitial dislocation loops on {ill} planes in aluminum using numerical displacement fields calculated for an elastically isotropic medium. Calculations are performed along selected directions near the (400), (200), (220). and (222)

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