Effects of the Grazing Incidence Geometry on X-ray Photon Correlation Spectroscopy Measurements

Abstract

X-ray photon correlation spectroscopy (XPCS) is a versatile tool to measure dynamics on the nanometer to micrometer scale in bulk samples. XPCS has also been applied in grazing incidence (GI) geometry to examine the dynamics of surface layers. However, considering GI scattering experiments more universally, the GI geometry leads to a superposition of signals due to reflection and refraction effects, also known from the distorted-wave Born approximation (DWBA). In this paper, the impact of these reflection and refraction effects on the correlation analysis is determined experimentally by measuring grazing incidence transmission XPCS (GT-XPCS) and grazing incidence XPCS (GI-XPCS) simultaneously for a thin film sample, showing non-equilibrium dynamics. The results of the GI and GT geometry comparisons are combined within the framework of the standardly applied, simplified DWBA. These calculations allow identifying the main contributions of the detected signal from the leading scattering terms along the out-of-plane direction q z , which dominate the measured intensity pattern on the detector. In combination with the calculation of the non-linear effect of refraction in GTSAXS and GISAXS, it is possible to identify experimental conditions that can be chosen to run experiments and data analysis as close as possible to transmission XPCS and to explain which limitations for data interpretations are observed. Consequently, the beam exposure can be significantly reduced by using GI geometry only. Calculations of experimental settings prior to experiments are detailed to determine suitable q z regions for a variety of material systems measured in bulk-sensitive GI-XPCS experiments, allowing us to determine the scaling behavior of typical decay times as a function of q that is comparable to the scaling behavior obtained in distortion-free GT-XPCS or transmission XPCS experiments.