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Experimental Powder X-ray Diffraction Crystal Structure Determination with RealPXRD-Solver

Qi Li, Mingyu Guo, Rui Jiao, Jing Gao, Fanjie Xu, Haonan Xue, Weixiong Zhang, Wenbing Huang, Junchi Yan, Linfeng Zhang, Cheng Wang, Zhuang Yan, Guolin Ke, Weinan E, Zhiyong Tang, Shifeng Jin, Lin Yao

Abstract

Determining crystal structures from experimental powder X-ray diffraction data remains challenging because peak overlap, preferred orientation, and impurity phases obscure atomic arrangements. We present RealPXRD-Solver, a generative model trained on 6,250,238 theoretical structures with experiment-mimicking augmentations and a universal encoder of d-spacing--intensity fingerprints, enabling both lattice-conditioned and lattice-free inference. RealPXRD-Solver reaches a 98.3% Top-20 match rate on a 10,000-structure theoretical benchmark and achieves Top-1/Top-20 accuracies of 77.9%/91.9% on CNRS and 78.8%/92.9% on RRUFF experimental datasets, and it solved 39 previously unreported Powder Diffraction File entries.

Experimental Powder X-ray Diffraction Crystal Structure Determination with RealPXRD-Solver

Abstract

Determining crystal structures from experimental powder X-ray diffraction data remains challenging because peak overlap, preferred orientation, and impurity phases obscure atomic arrangements. We present RealPXRD-Solver, a generative model trained on 6,250,238 theoretical structures with experiment-mimicking augmentations and a universal encoder of d-spacing--intensity fingerprints, enabling both lattice-conditioned and lattice-free inference. RealPXRD-Solver reaches a 98.3% Top-20 match rate on a 10,000-structure theoretical benchmark and achieves Top-1/Top-20 accuracies of 77.9%/91.9% on CNRS and 78.8%/92.9% on RRUFF experimental datasets, and it solved 39 previously unreported Powder Diffraction File entries.
Paper Structure (26 sections, 9 equations, 10 figures, 5 tables)

This paper contains 26 sections, 9 equations, 10 figures, 5 tables.

Table of Contents

  1. Design of RealPXRD-Solver for experimental data
  2. RealPXRD-Solver achieves high accuracy on a large-scale theoretical benchmark
  3. Robustness against diverse experimental perturbations
  4. Performance on quantitative experimental benchmarks
  5. Overcoming inherent limitations of powder X-ray diffraction
  6. Automated solution of unreported structures from the PDF database
  7. Conclusion
  8. Acknowledgments

Figures (10)

  • Figure 1: Design of RealPXRD-Solver for experimental PXRD data.(a) Experimental variability in PXRD patterns of LiFePO4. Patterns measured under different conditions (background noise level, peak width/FWHM, $2\theta$ range, and step size) nevertheless collapse to a consistent d–I (interplanar spacing–intensity) fingerprint, highlighting its invariance to measurement settings and sample quality. (b) Schematic of the full RealPXRD-Solver workflow. Simulated (training) and preprocessed experimental (inference) diffraction profiles are both converted to d–I lists and encoded by a universal XRD encoder into latent diffraction features. Conditioned on the chemical formula (and, when available, unit-cell parameters), a flow-based generative module proposes candidate crystal structures, which are subsequently ranked and refined by automated Rietveld analysis (e.g., GSAS-II).
  • Figure 2: Dataset diversity and theoretical benchmark performance of RealPXRD-Solver.(a) Distribution of crystal systems and space groups in the full theoretical corpus (6,250,238 unique entries). (b) Elemental occurrence heat map across the same corpus. (c) Distribution of primitive-cell atom counts, highlighting the long-tail extension beyond 25 atoms. (d) Cumulative Top-$k$ match rates (Top-1 and Top-20) and mean structural RMSE (root-mean-square error) on the 10,000-structure test set, with and without lattice parameters conditioning.
  • Figure 3: Robustness to experimental perturbations. Multi-panel examples from the PDF database, showing input patterns (top), fitted vs. observed profiles (middle), and generated/refined structures (bottom). (a) High-background noise: Ca2CuFeO3S (RMSE = 0.019). (b) Preferred orientation: Ag2SnHgSe4 (RMSE = 0.056). (c) Impurity phases: CsNdNb2O7 (RMSE = 0.114). All structures are displayed in primitive cells, with atoms color-coded by element. (d) Cross-model comparison on the CNRS subset of the opXRD experimental PXRD database. Scatter plot of Top-1 versus Top-20 structure match rates on 126 CNRS patterns for RealPXRD-Solver and previously reported generative PXRD-solving models.
  • Figure 4: Overcoming challenging scenarios in PXRD structure determination. Examples from the PDF and CNRS datasets, comparing predicted and observed primitive structures. (a) Distinguishing neighboring elements: Ca3CoMnO6, correct Co/Mn assignment (RMSE=0.025). (b) Locating light atoms: MnPO4·H2O (RMSE=0.100). (c, d) Solving Large unit cells: (c) Sc2W3O12 (68 atoms, RMSE=0.066). (d) NbBi4BrO8 (56 atoms, RMSE=0.189).
  • Figure 5: Automated solution of unreported PDF entries. For each coordinate-less entry, the pipeline output is shown: the input pattern (top; derived from the preprocessed d-I list), the final generated and refined crystal structure (inset; atoms color-coded by element), and the Rietveld fit (bottom; observed, calculated, and difference profiles). Solved structures and reliability factors (Rwp) are: (a) Al8Co1Cu3Pr1, Rwp=3.78%, (b) As4Cu12Fe1S13, Rwp=4.03%, (c) Cu2Hg1Si1Te4, Rwp=11.46%. Full CIFs in Extended Data 1.
  • ...and 5 more figures