One challenge impeding the analysis of terabyte scale X-ray scattering data from the Linac Coherent Light Source (LCLS) is determining the number of clusters required for the execution of traditional clustering algorithms. Here, we demonstrate that the previous work using bi-cross validation to determine the number of singular vectors directly maps to the spectral clustering problem of estimating both the number of clusters and hyperparameter values. Applying this method to LCLS X-ray scattering data enables the identification of dropped shots without manually setting boundaries on detector fluence and provides a path toward identifying rare and anomalous events.

Single crystals of Sm0.55Sr0.45Mn0.4Fe0.6O3 were grown by an optical floating zone technique in an oxygen atmosphere. The powder X-ray diffraction pattern for the grown crystal revealed single-crystalline nature. The lattice parameters and atomic structure were refined and indexed using a General Structure Analysis System (GSAS) to an orthorhombic structure with lattice parameters a = 5.4415 (32) Å, b = 7.6994 (27) Å, c = 5.43868 (28) Å, and space group Pnma.

A two-dimensional (2D) diffraction pattern is an image representing the diffraction intensity distribution over the detected area. For data evaluations of various materials characterization, such as phase identification, stress, texture, and crystal size, this distribution is further converted into the intensity distribution over 2θ or γ angles. For many applications, especially phase analysis and structure refinement, it is crucial for the two-dimensional (2D) pattern to have a large 2θ range sufficient to cover as many diffraction rings as necessary. The 2θ range covered by a 2D detector is determined by the size of the detector active area and the detector distance from the sample. In order to expand the 2θ coverage with a given 2D detector, one may collect several 2D frames at various swing angles and then merge the multiple frames, or scan the 2D detector over the desired 2θ range during the data collection. This paper introduces the geometry and algorithms to produce accurate 2D diffraction patterns with expanded 2θ coverages from multiple images or scanned images.