Determination of the dispersive correction f'(E) to the atomic form factor from X-ray reflection

Abstract

It is shown in this paper that the reflectivity of X-rays at smooth and fiat surfaces gives the dispersive correction f′(E) to the atomic form factor with an accuracy comparable to that obtained by X-ray interferometry. A detailed set of values of f′(E) in the energy range 7–27 keV is given for Ni, Cu, CuO, Ta, LiTaO3, Pt and Au, together with the corresponding linear absorption coefficients μ/ρ. Whenever comparison is possible the values of f′(E) agree very well with those obtained by interferometry or by Kramers–Kronig transformation. Data calculated according to Cromer & Liberman [J. Chem. Phys. (1970). 53, 1891–1898] agree well with our data far from absorption edges. At the edges there are substantial differences because the calculations do not take into account the structure of the edges, their chemical shift in compounds and the EXAFS structure above the edges. Below absorption edges the values of f′(E) for metals and their oxides are equal, provided the chemical shift in the position of the edges is taken care of. This feature is interesting in anomalous scattering experiments, where the variation off' with energy is used to vary the scattering contrast of a given atomic species. Once f′(E) is known, X-ray reflectivity measurements can be used to determine the density and the thickness of layers on fiat substrates. In addition, the roughness of the air-layer and layer-substrate interfaces have been determined with high precision in the metals and oxides mentioned above.