Machine Learning Tackles the Challenge of Powder X-ray Diffraction Indexing for All Crystal Systems

The indexing of powder X-ray diffraction (PXRD) in ab initio unknown structure determinations is a critical yet challenging step in crystallography, particularly for low-symmetry systems (e.g., monoclinic, triclinic) and/or large unit cell systems (V > 1000 ų). In this work, a machine learning-based indexing method is presented, which achieves high-precision, end-to-end prediction of crystal symmetry and unit cell parameters from powder diffraction peaks for all crystal systems. The trained models (denoted as AIdex) achieve a top-5 accuracy of ∼97% in extinction group (symmetry class) identification, and a mean absolute percentage error (MAPE) <5% for indexing, demonstrating significant improvements in both accuracy and time consumed compared to traditional algorithms (TREOR/ITO/DICVOL). AIdex also shows high capacity for experimental applications, maintaining a success rate of ∼90% even under extreme conditions involving zero-shift error (±0.6°) and uncertainty noise (±0.15°). Applied to practical PXRD data, AIdex gives predicted unit cell parameters close to the experimentally refined ones (MAPE < 5%), serving as ideal initial inputs for further Pawley refinements. This leads to a new paradigm for rapid indexing in ab initio unknown structure determination, facilitating the advancement of crystallographic analysis toward automation and intelligent methodologies.