Calculation of the Scattering Factor from the Shell Model of Nanoscale Defects

Theoretical and experimental investigations have pointed out the formation of dilute polydisperse system of spherical particles with diffusion zones embedded in matrix in the nucleation and growth evolution stages due to quenching, irradiation and other special kinds of treatment of multicomponent materials. Small-angle neutron and X-ray scattering provide information about the chemical composition as well as about the size distribution of the nanoscale defects.
Unlike to the case of homogeneously structurized scattering objects the analytical solution for heterogeneous scattering objects has not yet well-established. The paper states that the present approaches do not account in full measure the interference between the scattering intensities from the core and shell. Therefore, a more accurate procedure to calculate the scattering factor from heterogeneous objects is worked out. It bases on the formalism of the pair distribution function and the Porod' formula.
The suggested approach is verified on homogeneous scattering objects and then is applied to the set of shell models with different parameters of structure. For the calculation a Visual-Fortran programme is worked out. It is found that the homogeneous model and shell models produce the same scattering factor.
Model of the polydisperse nanoscale defects in neutron irradiated reactor steel is considered as composites of iron core and vacancy enriched shell with different sizes. The fitting procedure to determine the parameters of the size distribution function of irradiation induced precipitates from the magnetic part of small-angle neutron scattering is worked out. The results well agree with results of investigation by other methods for VVER steels with small Cu-content.