Grazing-incidence small-angle neutron scattering from structures below an interface

Abstract

Changes of scattering are observed as the grazing angle of incidence of an incoming beam increases and probes different depths in samples. A model has been developed to describe the observed intensity in grazing-incidence small-angle neutron scattering (GISANS) experiments. This includes the significant effects of instrument resolution, the sample transmission, which depends on both absorption and scattering, and the sample structure. The calculations are tested with self-organized structures of two colloidal samples with different size particles that were measured on two different instruments. The model allows calculations for various instruments with defined resolution and can be used to design future improved experiments. The possibilities and limits of GISANS for different studies are discussed using the model calculations.

Keywords: GISANS; colloidal particles; grazing-incidence small-angle neutron scattering; solid/liquid interfaces.

Figure 1

Schematic geometry of the GISANS experiment with a vertical sample holder (D22 and NG3-SANS). The dispersion is sealed between the silicon and sapphire crystals. is the incident angle of the beam; is the angle of the scattered beam on the horizontal plane; α is the angle of the scattered beam on the vertical plane. A scattered beam with is shown with red arrows and a scattered beam with in green.

Figure 2

Detector image recorded for PS11 latex in D₂O at , indicating scattering regions (NG3 SANS, NIST). The critical angle for this sample, measured with λ = 0.8 nm, was 0.7°. Streaking of the scattering around the labelled Bragg peaks shows the effect of instrument resolution. This effect is more pronounced with NG3 SANS than D22 owing to the slightly larger wavelength spread and better pixel resolution. The region around the transmitted beam shows the refraction and the scattered signal with clear diffraction peaks from a highly ordered sample structure, but these are subject to heavy multiple scattering. There is also strong diffuse background scattering from the sample cell and sealing ring in this region. In general, describing Q is complicated because of both refraction effects and the different origins of the scattering. The axes are labelled simply according to equations (6) and (8). The intensities are normalized and shown on a scale.

Figure 3

Scattering intensities recorded close to the critical angle from 9 wt% PS3 latex in D₂O against a silicon surface with D22. Density measurements showed that the particles were dispersed in a 15:85 mixture of H₂O:D₂O. Using the scattering length density of this combination the critical angle measured with λ = 1.4 nm was 0.8°. The rectangles around the first-order Bragg peaks represent the regions of interest chosen to estimate the relative intensities plotted in Fig. 5. The intensities are normalized to the measurement time and shown on a scale. The vertical strip along the central part of on the right side of the figure shows the integrated peaks as an example for = 1.07.

Figure 4

SLD profile for a dispersion of particles with radius R, lattice parameter a, and a gap between the structure and interface labelled as , in D₂O next to a silicon surface. Note that is defined as the distance between the centre of the first layer of particles and the interface.

Figure 5

Relative GISANS intensity calculated by the model for PS3 latex with lattice parameter a at different separations z from the interface are shown with lines and the experimental data from two measurements of the same sample are shown as scattered points with error bars (top figure). The corresponding penetration depth at each angle is represented in the bottom plot with (dashed line) and without (solid line) wavelength spread.