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Laue diffraction pattern9/2/2023 We conclude by developing structural models from two experimental data sets where the total film thickness (calculated from the period of the Kiessig oscillations) is different from the thickness derived from the period of the Laue oscillations (defined as the product of the number of coherently diffracting unit cells and the c-axis lattice parameter). We illustrate how the interaction between reflectivity and diffraction effects cause the asymmetry in Laue intensities around the central Bragg reflection and use simulations to show the impact of structural imperfections on the intensities of Laue oscillations. Next, we discuss the origin of Laue oscillations and use examples to demonstrate how Laue oscillation intensities calculated using the Laue function differ from experimental patterns. Examples show how to extract structural information from experimental data. We begin this section with a short review of the physical origin of Kiessig fringes and show how increasing the structural complexity of films affects the intensity of the fringes with increasing angle using simulations. Further efforts are required to create simulation software that enables the development of atom-level structural descriptions of films using the intensities of Kiessig fringes and Laue oscillations. The second example involves a more complex example where these two phenomena are both important in the same angular regions. The first example illustrates an approach to simultaneously model reflectivity and diffraction patterns when these two phenomena are relatively uncoupled. This paper addresses this challenge by presenting a summary of the relevant physical phenomena, showing how structural features in films impact the intensity and number of both Kiessig fringes and Laue oscillations that are observed, and provides examples of developing a structural model from experimental data. The extraction of structural information from Laue oscillations has been challenging due to the lack of a discussion of all relevant physical phenomena in a single reference that relates structural parameters to Laue intensities and provides examples illustrating the development of structural models from experimental data. In addition, the number of Laue oscillations observed on either side of the Bragg reflection varies significantly from sample to sample, ,, ,, ,, ,, ,, ,, ,, ,, ,, ,, ,, ,. The Laue function results in symmetric intensities of satellite reflections on either side of the Bragg maxima, but an asymmetric distribution of intensities on each side is also frequently observed. Furthermore, the intensity of experimental Laue oscillations often differs from those predicted from the Laue function. In these reports, differences between the total film thickness calculated from Kiessig fringes in the XRR data and the thickness of the crystalline layers obtained via the Laue oscillations were found. There are only a few reports in the literature where both the oscillations in the X-ray reflectivity (XRR) at low diffraction angles and the Laue oscillations observed in the vicinity of a Bragg reflection are used to detect potential excess material. The thickness obtained in this manner is often taken to be the total film thickness, which assumes that there is no additional thickness from amorphous or non-crystallographically aligned layers present above and/or below the diffracting crystal. The most common quantitative analysis of Laue oscillations utilizes an equation derived from the Laue interference function to extract the total thickness of the crystalline phase, ,, ,, ,, ,. While it is true that Laue oscillations are a qualitative indicator of sample quality, the presence of Laue oscillations also provides an opportunity to gain significant structural information about films. ![]() The presence of Laue oscillations is frequently used as evidence of “the high crystallinity of samples”, “the uniformity of the film and smoothness of the interfaces”, or that “the out-of-plane order is high and coherent over the entire film thickness”. Generally, the presence of Laue oscillations are taken as confirmation that grown films are of high quality, homogenous, contain only the targeted compound, and have smooth and planar top and bottom interfaces, ,, ,, ,,. First predicted by Max von Laue, the Laue interference function relates the number of unit cells in the diffracting crystal to the distribution of diffracted intensity. Laue oscillations result from the incomplete destructive interference of a finite number of unit cells and occur when a sample consists of domains with the same number of unit cells across most of the area being probed.
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