Extracting single crystal diffraction pattern from powder diffraction by intensity correlation functions

We applied the analysis of x-ray intensity angular correlation function to dilute ensembles of identical spinel crystals. Firstly, we show that the angular correlation from measured diffraction patterns with many crystals per shot converges to the correlation for single crystal. Secondly, we determined the diffraction pattern from single crystal from diffraction patterns of many crystals. Finally, we discussed the full 3D reciprocal space retrieval and its potential application in solving structure with dilute powder diffraction data, where the intensity fluctuation could be observed on each ring.