Ab initio structure solutions from nanocrystalline powder diffraction data via diffusion models.

A major challenge in materials science is the determination of the structure of nanometre-sized objects. Here we present an approach that uses a generative machine learning model based on diffusion processes that are trained on 45,229 known structures. The model factors measured the diffraction pattern as well as the relevant statistical priors on the unit cell of atomic cluster structures. Conditioned only on the chemical formula and the information-scarce finite-sized broadened powder diffraction pattern, we find that our model, PXRDnet, can successfully solve the simulated nanocrystals as small as 10 Å across 200 materials of varying symmetries and complexities, including structures from all seven crystal systems. We show that our model can successfully and verifiably determine structural candidates four out of five times, with an average error among these candidates being only 7% (as measured by the post-Rietveld refinement R-factor). Furthermore, PXRDnet is capable of solving structures from noisy diffraction patterns gathered in real-world experiments. We suggest that data-driven approaches, bootstrapped from theoretical simulation, will ultimately provide a path towards determining the structure of previously unsolved nanomaterials.