AI-Driven Structure Refinement of X-ray Diffraction

TL;DR

WPEM, a physics-constrained whole-pattern decomposition and refinement workflow that turns Bragg's law into an explicit constraint within a batch expectation--maximization framework, closes the gap between AI-generated hypotheses and diffraction-admissible structure refinement on challenging XRD data.

Abstract

Artificial intelligence can rapidly propose candidate phases and structures from X-ray diffraction (XRD), but these hypotheses often fail in downstream refinement because peak intensities cannot be stably assigned under severe overlap and diffraction consistency is enforced only weakly. Here we introduce WPEM, a physics-constrained whole-pattern decomposition and refinement workflow that turns Bragg's law into an explicit constraint within a batch expectation--maximization framework. WPEM models the full profile as a probabilistic mixture density and iteratively infers component-resolved intensities while keeping peak centres Bragg-consistent, producing a continuous, physically admissible intensity representation that remains stable in heavily overlapped regions and in the presence of mixed radiation or multiple phases. We benchmark WPEM on standard reference patterns (\ce{PbSO4} and \ce{Tb2BaCoO5}), where it yields lower $R_{\mathrm{p}}$/$R_{\mathrm{wp}}$ than widely used packages (FullProf and TOPAS) under matched refinement conditions. We further demonstrate generality across realistic experimental scenarios, including phase-resolved decomposition of a multiphase Ti--15Nb thin film, quantitative recovery of \ce{NaCl}--\ce{Li2CO3} mixture compositions, separation of crystalline peaks from amorphous halos in semicrystalline polymers, high-throughput operando lattice tracking in layered cathodes, automated refinement of a compositionally disordered Ru--Mn oxide solid solution (CCDC 2530452), and quantitative phase-resolved deciphering of an ancient Egyptian make-up sample from synchrotron powder XRD. By providing Bragg-consistent, uncertainty-aware intensity partitioning as a refinement-ready interface, WPEM closes the gap between AI-generated hypotheses and diffraction-admissible structure refinement on challenging XRD data.

Figures (5)

• Figure 1: From AI-generated hypotheses to physically admissible refined structures. Given a batch of experimental diffraction patterns, the AI phase/structure identification model Xqueryercao2025xqueryer proposes an initial structural hypothesis from the raw PXRD data. The subsequent EM--Bragg refinement performs Bragg-law-constrained whole-pattern decomposition to enforce diffraction consistency and yield a physically grounded refined structure. Finally, the property-prediction model PRDNetcao2025beyond estimates key materials properties (e.g., formation energy, band gap and elastic moduli) to support downstream screening and optimization.
• Figure 2: Benchmarking and quantitative decomposition.a,b Whole-pattern decomposition of reference data (PbSO4 and Tb2BaCoO5) and comparison of agreement factors against FullProf and TOPAS. c Summary of profile factors for WPEM, FullProf and TOPAS (FPA). d Decomposition of a multiphase Ti--15Nb thin film into $\beta$,$\alpha$ and $\alpha'$ contributions and the corresponding phase fractions estimated from integrated intensities. e Quantitative composition analysis of NaCl--Li2CO3 powder mixtures showing agreement between inferred and nominal mass ratios.
• Figure 3: High-throughput PXRD workflows enabled by WPEM.a Operando/in situ tracking of lattice-parameter evolution in $\mathrm{Li_{x}Ni_{y}O_2}$ during electrochemical cycling. b Automated solid-solution refinement for Ru-substituted Mn oxide using a $3\times3$ supercell model (CCDC 2530452).
• Figure 4: Deciphering an ancient Egyptian make-up sample.a, Synchrotron PXRD profile (points) and WPEM fit (line) collected with $\lambda = 0.96270\,\text{\AA}$. b--f, Phase-resolved component patterns recovered by WPEM for CaSO4.2H2O (gypsum), Pb2Cl2CO3 (phosgenite), PbCO3 (cerussite), PbS (galena) and PbOHCl (laurionite), respectively. The decomposition quantitatively separates strongly overlapped reflections in this complex multiphase mixture, enabling phase-level interpretation directly from the full profile.
• Figure 5: Quantitative analysis of semicrystalline diffraction.a Decomposition of the PE form I pattern into four crystalline peaks and three amorphous halos. b Decomposition of the PE form II pattern into three crystalline peaks and three amorphous halos. c Decomposition of the PB-I diffraction profile into form I, form II and amorphous-halo contributions.