Direct methods for the determination of atomic-scale structure of amorphous solids (X-ray, electron, and neutron scattering)

Abstract: The atomic-scale structure of amorphous solids can be determined from the X-ray, electron, or neutron scattering pattern. The atomic distribution function ϱ ( r ) or the pair correlation function g ( r ) = ϱ ( r )/ ϱ 0 , were ϱ 0 is the average atomiic density, is related to the interference function or structure factor I ( K ) by a Fourier transformation. Unfortunately, I ( K ) is not directly accessible from the scattering experiment, but can be deduced from the scattering pattern after suitable corrections for polarization, absorption, inelastic scattering, multiple scattering, and static approximation, and after normalization to absolute units. In multicomponent systems, the coherent scattering function per atom I a ( K ) is a weighted sum of the partial interference functions I ij ( K ), which represent the Fourier transforms of ϱij ( r ), the number of j -type atoms per unit volume at a distance r from an i -type atom. It is also possible to express I a ( K ) as a weighted sum of number-concentration structure factors I NC ( K ), which are associated with the number-number (density), number-concentration, and concentration-concentration correlations. The long-wavelength limit of the functions I NC ( CK ) can be expressed in terms of the various thermodynamic quantities and their variation with composition. In binary allos, three partial functions are required to describe the atomic arrangements. These functions can be obtained by varying the atomic scattering factors f i through choic of three different radiations (X-rays, electrons, and neutrons), or isotopes in neutron scattering, or anomalous dispersion in X-ray scattering. The latest developments in the experimental techniques for the determination of the interference function I ( K ) are presented, and examples of the scattering patterns of metallic glasses are given, which were obtained by the conventional, variable 2θ technique, and by the variable λ technique. Attempts are discussed to deduce the partial interference functions in binary systems from several scattering experiments, and to determine concentration fluctuations in binary alloys.