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Quantitative Analysis of Correlated Atomic Displacements via Diffuse Electron Scattering

Momentum-resolved information on phonons can be inferred from neutron and X-ray scattering experiments by utilizing momentum conservation [1, 2]. In contrast to Bragg diffraction, thermal diffuse scattering intensities are distributed across reciprocal space and can deviate strongly from the isotropic Einstein model due to their dependence on correlated atomic displacements. Applications of electron diffraction to studies of phonon distribution have been limited by the detector dynamic range and detector sensitivity [3, 4]. Specifically, the intense direct beam and Bragg reflections make it difficult to normalize the intensity of the diffuse background to an absolute intensity scale. Therefore, it is difficult to obtain quantitative information that can be directly compared to theoretical predictions. With the development of new direct electron detectors, such as the Electron Microscopy Pixel Array Detector (EMPAD), which enable capturing single electrons with a dynamic range of 1,000,000:1 [5], detailed quantification of the full electron scatter distribution (diffuse and Bragg) became possible. In this presentation, we will discuss an approach to capture diffuse scattering and Bragg reflections on an absolute intensity scale using a Si single crystal as a testbed. We will show this can be achieved by shifting the diffraction information across an EMPAD. Even though the detector is only128x128 pixels in size, it can finely sample reciprocal space all the way out to the objective lens bore, as shown in Figure 1. Further, we will briefly discuss the methodology used to reconstruct the final diffraction pattern, particularly the need to account for shift errors introduced by hysteresis. We highlight how the diffuse scattering and the Bragg reflections can be normalized with respect to the incident beam, enabling direct comparison with theory. We will compare the experimental results to computed kinematical and dynamical thermal diffuse scatter distributions taking into account canonical ensembles of phonon displacements obtained ab initio , as shown in Figure 2(b,