Organizations: Guangzhou Municipal Key Laboratory of Materials Informatics, Advanced Materials Thrust, Sustainable Energy and Environment Thrust, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, 511453, China · Materials Genome Institute, Shanghai University, Shanghai 200444, China · Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China, Hefei, Anhui 230026, China · Material Characterization and Preparation Facility, Hong Kong University of Science and Technology (Guangzhou), Guangzhou 511400, China
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 the whole-pattern expectation--maximization (WPEM) algorithm, 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 (PbSO4 and Tb2BaCoO5), where it yields lower Rp/Rwp than widely used packages (FullProf and TOPAS) under matched refinement conditions. We further demonstrate generality across realistic experimental scenarios, including phase-resolved decomposition in multiphase materials, quantitative recovery of mixture compositions, separation of crystalline peaks from amorphous backgrounds in semicrystalline systems, high-throughput operando lattice tracking, automated refinement of compositionally disordered solid solutions, and quantitative phase-resolved analysis of complex archaeological samples 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 & tables
Figure 1: From AI-generated hypotheses to physically admissible refined structures. Given a batch of experimental diffraction patterns, the AI phase/structure identification model Xqueryer [ 8 ] 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 PRDNet [ 5 ] 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 ( PbSOX4 and TbX2BaCoOX5 ) 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 β , α and α′ contributions and the corresponding phase fractions estimated from integrated intensities. e Quantitative composition analysis of NaCl – LiX2COX3 powder mixtures showing agreement between inferred and nominal mass ratios.
Figure 3: High-throughput PXRD workflows enabled by WPEM. a In situ tracking of lattice-parameter evolution in Li(Ni0.8Co0.1Mn0.1)O2 during electrochemical cycling. b Automated solid-solution refinement of a Ru-substituted Mn oxide using a 3×3 supercell model (CCDC 2530452).
Figure 4: Deciphering an ancient Egyptian make-up sample. a, Synchrotron PXRD profile (points) and WPEM fit (line) collected with λ=0.96270A˚ . b–f, Phase-resolved component patterns recovered by WPEM for CaSOX4⋅2HX2O (gypsum), PbX2ClX2COX3 (phosgenite), PbCOX3 (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. The Egyptian portrait was generated by ChatGPT-5o and does not infringe any third-party copyrights.
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.
Powder X-ray diffraction (PXRD) is the routine probe of crystalline matter, yet its analysis is the rate-limiting step as laboratories automate acquisition. Deep-learning analyzers excel on simulated patterns and degrade on measured ones. This simulation-to-real gap is structural, not additive: synthetic denoising gives no measurable lift on real spectra, whereas correcting a small peak-position drift more than doubles median retrieval correlation. Real-spectrum fine-tuning, peak-aligned reranking, and recalibration narrow what remains and restore the coverage synthetic anchors lose. Xtalyst integrates these in an agent-orchestrated system spanning phase identification, refinement, and calibrated property prediction. On a frozen held-out partition (n=534) each module measured on both splits reproduces its development finding -- including the synthetic-anchor under-coverage, whose magnitude differs between the two pools -- while held-out refinement converges and preserves symmetry without reaching profile-quality fits, and on a diffractometer its wet-dry recommend-rescan-reanalyze loop flips a blinded silicon standard to a gated PASS and changes which minor phase is resolved on a multi-metal alloy.
Shaoguang Wang, Weiyu Guo, Ben Fei +3
The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China. · The Chinese University of Hong Kong, Hong Kong SAR, China. · Suzhou National Laboratory, Suzhou, China. +2
Determining crystal structures from powder X-ray diffraction (PXRD) would enable routine characterization of newly synthesized materials, including those absent from reference databases. Generative models offer a promising approach, but existing evaluations remain fragmented and largely assume single-phase samples with known composition. To fill this gap, we introduce PXRD-Bench, a unified benchmark that extends evaluation to unknown per-element atom counts and recovery of both structures in two-phase mixtures. It provides approximately 4.1 million training structures with simulated PXRD, tests generalization to unseen compositions and structural prototypes, and evaluates recovery from experimental PXRD after excluding structurally matching training entries. To provide a strong reference baseline, we also introduce Bragglite, a PXRD-to-structure model developed through a systematic study of PXRD modeling choices. It achieves a 44.2% Top-1 match rate on experimental RRUFF patterns with known composition, 24.6% above the strongest prior baseline. Further analysis yields several key findings: some models fail to benefit from experimental PXRD, while generalization to unseen structural prototypes and recovery from two-phase mixtures remain challenging. Together, our benchmark, systematic studies, and Bragglite clarify the capabilities and limitations of current PXRD-to-structure models.
Dongyeop Woo, Nofit Segal, Nayoung Kim +3
Korea Advanced Institute of Science & Technology (kaist.edu) · Massachusetts Institute of Technology (mit.edu)
Determining the crystal structure of a material from its powder X-ray diffraction (PXRD) pattern is a central challenge in materials science. PXRD is an accessible and widely used characterization technique, yet recovering the atomic structure from diffraction data requires solving an underdetermined inverse problem due to the loss of phase information. Generative modeling can provide a prior over atomic structure and learn the mapping from PXRD patterns to crystal structures via simulated structure-spectrum pairs. We present XRDiff, a diffusion model that recovers crystal structures from PXRD given either the stoichiometry or, in a more challenging setting, the elemental constituents and total number of atoms in the unit cell. We evaluate on datasets where each stoichiometry has multiple polymorphs and all polymorphs of a given composition are held out together, ensuring that high performance reflects genuine use of the diffraction signal. XRDiff achieves strong structure recovery rates on simulated benchmarks, indicating that the model learns a spectrum-to-structure mapping precise enough to differentiate between polymorphs. To address generalization to experimental data, we compare a full-spectrum encoding against an encoding based on peak descriptors. The peak-based encoding generalizes substantially better, outperforming even a model trained on full spectra with augmentations fitted to the experimental noise distribution. These results demonstrate that representations robust to the noise and artifacts present in real-world PXRD offer a practical and scalable path toward closing the simulation-to-experiment gap, enabling zero-shot crystal structure solution from experimental PXRD with full or partial chemical composition input.
Nofit Segal, Mingda Li, Benjamin Kurt Miller +1
Department of Materials Science and Engineering, MIT, Cambridge, MA, USA. · Department of Nuclear Science and Engineering, MIT, Cambridge, MA, USA. · FAIR, Meta, San Francisco, CA, USA.