Investigation of the strain field of bismuth in lead by diffuse elastic neutron scattering

The calculation of the intensity of diffuse X-ray scattering by interstitials involves the evaluation of a crystal structure factor which accounts for both the configuration of the interstitial atom and the distortion of the surrounding lattice. The lattice-distortion field surrounding an interstitial may be calculated using a Green's function lattice-statics approach described in earlier work [Benedek, R. & Ho, P. S. (1973). J. Phys. F: Metal Phys. 3, 1285-1295]. In this approach, several atoms in the vicinity of the interstitial (the interstitial 'core') are treated formally on the same footing as the interstitial itself. Once the Green's function calculation of the lattice distortion field is performed the structure factor can be evaluated as follows. The contribution from the interstitial core is calculated explicitly using the coreatom displacements. The contribution from the remainder of the lattice is expressed in terms of 'Kanzaki forces' and certain 'virtual' displacements of core atoms, both of which are by-products of the Green's function calculation. Using this approach numerical calculations of diffuse scattering by selfinterstitial atoms in tungsten were performed. Based on the results, typical features of the Huang scattering, small-angle scattering, and scattering far from reciprocal-lattice points are discussed. The sensitivity of the calculations to the interatomic potential are also discussed.