Depth resolved grazing incidence neutron scattering experiments from semi-infinite interfaces: a statistical analysis of the scattering contributions

Abstract

Grazing incidence neutron scattering experiments offer surface sensitivity by reflecting from an interface at momentum transfers close to total external reflection. Under these conditions the penetration depth is strongly non-linear and may change by many orders of magnitude. This fact imposes severe challenges for depth resolved experiments, since the brilliance of neutron beams is relatively low in comparison to e.g. synchrotron radiation. In this article we use probability density functions to calculate the contribution of scattering at different distances from an interface to the intensities registered on the detector. Our method has the particular advantage that the depth sensitivity is directly extracted from the scattering pattern itself. Hence for perfectly known samples exact resolution functions can be calculated and visa versa. We show that any tails in the resolution function, e.g. Gaussian shaped, hinders depth resolved experiments. More importantly we provide means for a descriptive statistical analysis of detector images with respect to the scattering contributions and show that even for perfect resolution near surface scattering is hardly accessible.

BornAgain: software for simulating and fitting grazing-incidence small-angle scattering

“…Real-space characteristics like beam profile and finite sample surface will be added in future extensions for reflectometry (Section 8.1; compare Adlmann et al, 2018). Real-space characteristics like beam profile and finite sample surface will be added in future extensions for reflectometry (Section 8.1; compare Adlmann et al, 2018).…”

Exploring Hidden Local Ordering in Microemulsions with a Weak Directive Second Order Parameter

“…1 The experimental grazing incidence scattering patterns as a function of the different surfactants (C 8 E 3 , C 10 E 4 , C 12 E 5 ) (increasing emulsification efficiency from left to right) and the scattering depth Λ (indicated in the images). The errors of the scattering depths are 10, 26, 150 Å, and 10 µm according to resolution effects [34]. The "divergence" [35] of the scattering depth at the critical angle increases this error.…”

Π-GISANS: probing lateral structures with a fan shaped beam

“…For GISANS done in the traditional way a source size of 1.5 mm may be used whereas we use 15 cm, resulting in a potential gain in flux of two orders of magnitude. However, the large incident divergence results in a loss of depth sensitivity 19 . Still the method has all the advantages of neutron scattering experiments benefiting from isotope contrast variation, sensitivity to light elements and the capability to probe buried interfaces as well as the magnetic induction.…”