High-energy x-ray diffraction from surfaces and nanoparticles

Abstract

High-energy surface-sensitive x-ray diffraction (HESXRD) is a powerful high-energy photon technique (E g 70 keV) that has in recent years proven to allow a fast data acquisition for the 3D structure determination of surfaces and nanoparticles under in situ and operando conditions. The use of a large-area detector facilitates the direct collection of nearly distortion-free diffraction patterns over a wide $q$ range, including crystal truncation rods perpendicular to the surface and large-area reciprocal space maps from epitaxial nanoparticles, which is not possible in the conventional low-photon energy approach ($E=10\ensuremath{-}20\phantom{\rule{0.16em}{0ex}}\mathrm{keV}$). Here, we present a comprehensive mathematical approach, explaining the working principle of HESXRD for both single-crystal surfaces and epitaxial nanostructures on single-crystal supports. The angular calculations used in conventional crystal truncation rod measurements at low-photon energies are adopted for the high-photon-energy regime, illustrating why and to which extent large reciprocal-space areas can be probed in stationary geometry with fixed sample rotation. We discuss how imperfections such as mosaicity and finite domain size aid in sampling a substantial part of reciprocal space without the need of rotating the sample. An exact account is given of the area probed in reciprocal space using such a stationary mode, which is essential for in situ or operando time-resolved experiments on surfaces and nanostructures.