Explaining Concepts and Applications of Second-Order X-Ray Diffuse Scattering in Materials Characterization

X-ray diffuse scattering (DS) generally arises from any departure that structures have from a perfectly regular atomic lattice. In crystals, thermal DS is caused by scattering from lattice vibrations and provides valuable information about the lattice dynamics of materials. Historically, DS was the first tool to determine phonon dispersion relations experimentally [1]. With the advent of synchrotron radiation technology, it has reemerged as a feasible method for studying phonons in contrast with inelastic X-ray and neutron scattering that require complex experimental equipment, long acquisition times, and, in the case of neutron scattering, large single crystals [2]. However, high-flux synchrotron X-rays, approaching 10¹⁵ ph/s/mm², in addition to zero noise area detectors, have also revealed a relatively unknown 2nd-order DS process, first called diffuse multiple scattering (DMS) [3], which appears as a kind of Kikuchi lines [4] for monochromatic X-rays. In recent years, accidental observation of DMS lines has become increasingly frequent for high-flux synchrotron beamline users working with monocrystalline materials such as epitaxy-based nanostructured devices. Although DMS lines carry intrinsic 3D information on structural and vibrational properties of the crystal lattice, their predictability and practical applications have been open to investigation for about a decade. In this work, we introduce the concept of bright and dark Bragg cones required to understand and describe DMS lines. The intensity distribution along DMS lines depends on the actual primary source of DS in the material, as demonstrated for isotropic DS plus truncation rod of a perfect semiconductor surface and a particular case of thermal DS in skutterudites [5,6] as obtained by first principle calculation. A survey is given on computer codes for 3D reciprocal space maps [7], thermal DS simulation, and prediction of the most visible and susceptible DMS lines.<br/><br/>Acknowledgments: FAPESP (2022/09531-8; 2021/01004-6) and CNPq (310432/2020-0).<br/><br/>[1] B. E. Warren. X-ray Diffraction. Dove, New York, 1990.<br/>[2] A. B. Mei et al. Reflection thermal diffuse x-ray scattering for quantitative determination of phonon dispersion relations. Phys. Rev. B 92, 174301 (2015). 10.1103/PhysRevB.92.174301<br/>[3] A. G. A. Nisbet, G. Beutier, F. Fabrizi, B. Moser, S. P. Collins. Diffuse Multiple Scattering. Acta Cryst. A 71, 20-25 (2015). 10.1107/S2053273314026515<br/>[4] D. A. Muller et al. Simulation of thermal diffuse scattering including a detailed phonon dispersion curve. Ultramicroscopy 86, 371-380 (2001). 10.1016/S0304-3991(00)00128-5<br/>[5] S. El Oualid et al. High Power Density Thermoelectric Generators with Skutterudites. Advanced Energy Materials 11, 2100580 (2021). 10.1002/aenm.202100580<br/>[6] A. Valério et al. Phonon scattering mechanism in thermoelectric materials revised via resonant x-ray dynamical diffraction. MRS Commun. 10, 265–271 (2020). 10.1557/mrc.2020.37<br/>[7] R. F. S. Penacchio et al. A simple recipe to create three-dimensional reciprocal space maps. ArXiv 2210.05427 (2022). 10.48550/arXiv.2210.05427 (https://github.com/rafaela-felix/rsm)