On the Theory of X-Ray Small-Angle Scattering

Abstract

It is pointed out that a Fourier inversion of the intensity distribution of x-ray scattering, taking the small-angle scattering alone, gives the electron density function of the continuum approximation. The procedure of including only the central scattering is practicable, when none of the peaks of the lattice diffraction occurs at such a small angle that their scattered intensity overlaps the central scattering. A general discussion of the choice of the sign of the phase factor in the Fourier transformation and of its experimental consequences is given. The analysis is applied to scattering in a supersaturated Al-Ag alloy and to a discussion of some of the approximate formulas used in fitting experimental data. When the electron density function of the scattering center has an odd symmetry with respect to one of the coordinate variables, conclusions can be drawn about the scattered intensity distribution without actually knowing the density function. The most interesting case of an odd symmetry is the edge dislocation. An experiment is suggested to reveal the pileup of dislocations as well as the aggregation of vacancies along the slip plane of a metal crystal deformed by a pure shear stress.