Towards end-to-end structure determination from x-ray diffraction data using deep learning

Abstract

Powder crystallography is the experimental science of determining the structure of molecules provided in crystalline-powder form, by analyzing their x-ray diffraction (XRD) patterns. Since many materials are readily available as crystalline powder, powder crystallography is of growing usefulness to many fields. However, powder crystallography does not have an analytically known solution, and therefore the structural inference typically involves a laborious process of iterative design, structural refinement, and domain knowledge of skilled experts. A key obstacle to fully automating the inference process computationally has been formulating the problem in an end-to-end quantitative form that is suitable for machine learning, while capturing the ambiguities around molecule orientation, symmetries, and reconstruction resolution. Here we present an ML approach for structure determination from powder diffraction data. It works by estimating the electron density in a unit cell using a variational coordinate-based deep neural network. We demonstrate the approach on computed powder x-ray diffraction (PXRD), along with partial chemical composition information, as input. When evaluated on theoretically simulated data for the cubic and trigonal crystal systems, the system achieves up to 93.4% average similarity (as measured by structural similarity index) with the ground truth on unseen materials, both with known and partially-known chemical composition information, showing great promise for successful structure solution even from degraded and incomplete input data. The approach does not presuppose a crystalline structure and the approach are readily extended to other situations such as nanomaterials and textured samples, paving the way to reconstruction of yet unresolved nanostructures.