Dara: Automated multiple-hypothesis phase identification and refinement from powder X-ray diffraction

TL;DR

Dara tackles the inherent ambiguity in interpreting multiphase powder XRD by combining an exhaustive tree-search for phase combinations with a peak-matching heuristic and a robust BGMN-based Rietveld refinement. The framework generates and ranks multiple plausible phase hypotheses, groups similar solutions for interpretability, and reports unmatched peaks to guide further characterization. Benchmarking against commercial software and human experts shows Dara can match or exceed automated and human performance on realistic precursor and solid-state reaction datasets, while providing rapid, scalable analysis suitable for autonomous laboratories. This work positions automated XRD analysis as a feasible component of self-driving materials discovery pipelines, enabling reliable, multi-hypothesis interpretation of complex diffraction data.

Abstract

Powder X-ray diffraction (XRD) is a foundational technique for characterizing crystalline materials. However, the reliable interpretation of XRD patterns, particularly in multiphase systems, remains a manual and expertise-demanding task. As a characterization method that only provides structural information, multiple reference phases can often be fit to a single pattern, leading to potential misinterpretation when alternative solutions are overlooked. To ease humans' efforts and address the challenge, we introduce Dara (Data-driven Automated Rietveld Analysis), a framework designed to automate the robust identification and refinement of multiple phases from powder XRD data. Dara performs an exhaustive tree search over all plausible phase combinations within a given chemical space and validates each hypothesis using a robust Rietveld refinement routine (BGMN). Key features include structural database filtering, automatic clustering of isostructural phases during tree expansion, peak-matching-based scoring to identify promising phases for refinement. When ambiguity exists, Dara generates multiple hypothesis which can then be decided between by human experts or with further characteriztion tools. By enhancing the reliability and accuracy of phase identification, Dara enables scalable analysis of realistic complex XRD patterns and provides a foundation for integration into multimodal characterization workflows, moving toward fully self-driving materials discovery.

Figures (6)

• Figure 1: Overview schematic of XRD phase analysis performed with Dara. (a) The preprocessing workflow filters reference phases, which are a set of crystalline material structures, from structure databases such as the Crystallography Open Database (COD) Grazulis2012Grazulis2009. First, all phases within the chemical system of the input XRD pattern are selected. Then, duplicate phases are removed based on the formula and space group. High-energy phases are further filtered out using thermodynamic data from the Materials Project. The resulting phases are used as the reference phases in the downstream search routine. (b) A search tree is constructed with each node representing a phase combination, and directed edges representing the addition of one phase to the previous node’s phases. The color of each node represents the weighted profile residual ($R_{wp}$) values. Darker colors represent lower $R_{wp}$ (indicating a better fit). (c) A peak matching algorithm to quickly filter phases that can fit well to any of the remaining unmatched peaks to prune unlikely phases and save computation time. (d) Identified phases are then passed to a Rietveld refinement engine, such as BGMN. The black crosses are the experimental pattern. The orange line represents the calculated pattern output by Rietveld refinement. (e) Multiple results are extracted from the search tree and presented to the user. The results are ranked by R-values and grouped based on their compositions and structures for easier interpretation. Results with excessively high R-values are removed.
• Figure 2: Preparation of the precursor mixture dataset and benchmarking results. (a) Schematic illustration of the procedure for generating the precursor mixture dataset. Ten commercial precursors are randomly selected and mixed at varying ratios between 10 wt% and 90 wt%, resulting in 10 binary and 10 ternary precursor mixtures. XRD patterns are collected using a benchtop diffractometer under two scanning programs (2 minutes and 8 minutes) to produce datasets of different measurement qualities. (b) Comparison of correctly indexed patterns by Jade and Dara. Correct means the analysis method successfully identifies all the precursor phases without any spurious phases. Blue bars indicate patterns scanned using the 2-minute (low-quality) program, while pink bars represent the 8-minute (medium-quality) scans. The top of each bar shows the number of correct predictions compared to the total number of patterns for that scan type. (c) Relationship between the $R_{wp}$ values from Rietveld refinement using groundtruth phases and Dara’s top result (represents the solution of lowest $R_{wp}$ that Dara can find). The ground-truth phases are the precursor phases added during sample preparation. Blue and pink dots correspond to 2-minute and 8-minute scans, respectively. (d) Dara's runtime per pattern as a function of the number of reference phases in the database. Blue and pink dots represent 2-minute and 8-minute scans, respectively. Dashed horizontal lines mark 2 and 8 minutes on the time axis, corresponding to the measurement time to obtain these patterns in the diffractometer. The time is measured on a workstation with Intel(R) Core(TM) i9-10920X CPU @ 3.50GHz.
• Figure 3: Preparation of the solid-state reaction dataset and benchmarking results. (a) Schematic illustration of the workflow for preparing the reaction dataset and approximating ground truth solutions through human expert evaluation. (b) Number of XRD patterns that have all peaks indexed in the analyses conducted by human experts, Dara, and Jade. (c) Comparison of the absolute lattice volume shifts after Rietveld refinement between the phases with the highest FoM scores (pink bars) and other phases with lower scores (blue bars) within each phase group found by Dara. A phase group refers to a set of phases that yield similar XRD patterns and are therefore expected to provide a comparable fit to the experimental peaks. The x-axis represents the absolute value of lattice volume shift (in %), and the y-axis shows the normalized frequency (with the sum of frequency set to 1). Pink bars on top indicate the volume shifts of the most appropriate phases selected by Dara in each phase group, based on a figure of merit (FoM) that incorporates both the quality factor $(1 - \rho)$ and lattice shift $(\Delta U)$. Blue bars represent all other phases with lower FoM, which Dara did not choose to continue the search but considers as alternative phases to the FoM-selected phases in the result. The median for each histogram is shown as a dashed line in the plot. (d) Correlation between the $R_{wp}$ values from human-expert Rietveld refinement and Dara’s best-fit solution (i.e., the one yielding the lowest $R_{wp}$ identified by Dara).
• Figure 4: Example of multiple phase solutions identified by Dara for an experimental solid-state reaction sample. The raw XRD pattern and its corresponding chemical system are supplied to Dara. After searching, four solutions are found to fit the pattern similarly well, all of which contain three phases. The calculated patterns for each phase are displayed in the corresponding boxes in the plot. Phases 1 and 2 are shared across all the solutions, which are groups of NaAlSiO4 with Nepheline structure (11 phases) and LiCoO2-LiAlO2 solid solutions (35 phases), respectively. Phase 3, however, includes four possible phases that differ greatly in structure/composition: SiO2 (ICSD #155249), Co11O16/Co2SiO4 structure family (7 phases), Al2CoO4 structure family (25 phases), and NaCo3O4 (ICSD #163993), indicating that further compositional characterization may be necessary. The common peak at around 36.5° is marked with an orange triangle in the plot.
• Figure 5: Screenshots of the Dara web interface. (a) Analysis job submission page, where users input the pattern, elements that can exist in the pattern, and diffractometer information. (b) Overview page for viewing the status of and accessing each analysis job. (c) Result detail page with a summary of the job's outcome, including analysis parameters, the best result's $R_{wp}$, and the most probable phases. (d) Result detail page with all solutions and phases found by Dara. (e) Interactive plot to visualize the refinement produced by Dara.