Data-reduction procedure for correction of geometric factors in the analysis of specular X-ray reflectivity of small samples

Abstract

For small samples, the modification of the X-ray reflectivity (XRR) profile by the geometric factors due to the profile and size of the beam and the size of the sample is significant. These geometric factors extend the spill-over angle, which is often greater than the critical angle for small samples. To separate the geometric factors, it is necessary to know the spill-over angle. Since the geometric factors are smoothly varying functions and extend beyond the critical angle, it is impossible to determine the spill-over angle from the XRR profile of small samples. It is shown that the spill-over angle can be determined by comparing the normal XRR profile of a small sample with the XRR profile taken with a surface-contact knife edge on the same sample. Thus, a procedure has been developed for data reduction for small samples and validated with suitable experiments. Unlike the methods used hitherto, which have drawbacks, this is a self-consistent method for data reduction.

REFLEX: a program for the analysis of specular X-ray and neutron reflectivity data

“…In several commercial reflectometers, beam knife edges are used to reduce the beam footprint so that the plateau of total external reflection becomes more visible, and to improve the instrumental resolution. They also have the function of reducing the air scattering (Das et al, 2018). (a) A schematic drawing to calculate the reduced intensity which passes through a beam knife edge.…”

Depth-resolved oxidational studies of Be/Al periodic multilayers investigated by X-ray photoelectron spectroscopy

“…A common practice is to modify the experimentally observed XRR profile appropriately with various data processing procedures and then further fit it to a theoretical curve calculated using Parratt's recursive formalism, which helps to extract the numerical value of the thickness of the layers and period thickness. 25 The numerical method of this program was developed by Svechnikov. 26…”

11B4C containing Ni/Ti neutron multilayer mirrors

“…Where g(θ) is the attenuation factor due to the beam overspill effect, and R(θ) describes the reflectivity curve in absence of this factor. The factor g(θ) can be determined by considering the geometry of the beam which then reduces to [33] [34]:…”

“…Depending on the relevant features in the diffraction pattern, a good alignment of the sample can be extremely important. In particular a proper correction of the beam overspill effect is highly dependent on the alignment of the sample [33]. The NR measurements in this work have all been aligned using the same procedure.…”