Learning Crystal Structure from Powder X-Ray Diffraction Data Using Invariants*

We present a framework-independent machine learning (ML) method to determine unit cell parameters and classify Bravais lattices from powder X-Ray diffraction (XRD) data. Traditional powder indexing algorithms encounter errors when dealing with noisy experimental data. This causes complications in the accuracy of peak identification, subsequent crystal structure determination, and is one of the main bottlenecks in materials discovery. ML methods offer the potential to surpass time-consuming conventional techniques through their ability to learn from diverse datasets.

Previous ML studies have performed worse on lower symmetry crystal systems for both symmetry classification and unit cell parameter regression. Additionally, ambiguity in the definition of unit cell representation can lead to discrepancies in results. We thus develop an unambiguous reciprocal space lattice representation using invariants. Each lattice can be represented by a spherical harmonic projection. The bispectrum is then the scalars and pseudoscalars from the tensor product of the projection with itself. We first learn the bispectrum from XRD data using ML and then show that the bispectrum can be inverted to obtain the lattice vectors. We train and test our models on established crystallographic databases and assess their performance on experimental crystal structures. This presents a new avenue for XRD crystal structure determination through developing an invertible convention free representation.