Recent advancements in X-ray technology have dramatically increased the volume and quality of powder diffraction data, enabling high-throughput measurements. This leads to the acquisition of terabytes of data per experiment, making data analysis the primary bottleneck. Traditional methods like Rietveld refinement, while providing valuable physicochemical information (lattice parameters, crystallite size, phase composition), struggle to keep pace with these data rates. Deep learning, particularly convolutional neural networks (CNNs), offer a scalable solution for handling big data. Previous studies have used CNNs for crystal structure prediction and phase identification, but applications to quantitative parameter extraction from powder diffraction data remain limited. This study presents PQ-Net, a regression CNN designed to address this challenge by rapidly and accurately extracting physicochemical information from powder diffraction patterns.

The authors review existing literature on deep learning applications in materials science and X-ray diffraction analysis. They highlight the use of CNNs in medical imaging and tomography and their increasing relevance in materials characterization. They discuss previous works focusing on CNNs for crystal structure prediction, space group classification, and phase identification but emphasize the lack of regression models for quantitative parameter extraction from diffraction data. The Rietveld method is presented as a commonly used but computationally intensive alternative. The authors point out that most existing research concentrates on classification (phase presence/absence), unlike their proposed regression-based approach focusing on quantitative parameter extraction.

The authors detail the architecture of PQ-Net, a regression CNN designed for single- and multi-phase systems. The single-phase network comprises a pattern block (three convolutional layers and max-pooling), a phase block (five convolutional and max-pooling layers), and a parameter block (fully connected layers). The parameter block outputs scale factors, crystallite sizes, and lattice parameters. For multi-phase systems, the network extends the architecture to include separate phase blocks for each phase. Deep ensembles were used to improve robustness and provide uncertainty quantification by training multiple networks with different initial weights and averaging the outputs. The training process utilizes simulated diffraction patterns generated using TOPAS software, employing mean absolute error (MAE) as the loss function and Adam optimizer. The effect of dataset size on accuracy was investigated. Simulated and experimental XRD-CT datasets of increasing complexity were used to evaluate PQ-Net's performance, comparing its results against Rietveld analysis.

PQ-Net demonstrated accurate predictions of scale factors, lattice parameters, and crystallite sizes for both simulated and experimental data. For a single-phase simulated dataset, errors were below 5% for scale factors, below 1 nm for crystallite size, and below 10⁻³ Å for lattice parameters. In the multi-phase simulated data, PQ-Net accurately generated phase distribution maps, crystallite size maps, and lattice parameter maps. Analysis of an experimental XRD-CT dataset (approximately 20,000 patterns) of a five-phase Ni-Pd/CeO₂-ZrO₂/Al₂O₃ catalyst yielded accurate scale factor maps consistent with Rietveld results. PQ-Net captured chemical gradients, resolving heterogeneities in crystallite size and lattice parameters of CeO₂-ZrO₂ phases, matching Rietveld analysis. The deep ensemble approach provided uncertainty estimates. Processing of the 20,000 patterns took approximately 10 seconds with PQ-Net, compared to approximately 4.4 hours for Rietveld analysis of a smaller subset (9,000 patterns). The Rwp values from PQ-Net were within 2% of the Rietveld results.

The results demonstrate PQ-Net's ability to accurately extract physicochemical information from XRD patterns, handling both simulated and experimental data, including complex multi-phase systems. Its speed advantage is substantial, making real-time analysis feasible for in situ/operando experiments. While not intended to replace Rietveld refinement, PQ-Net can be used for rapid initial analysis, with Rietveld refinement applied for fine-tuning if needed. The deep ensemble approach enhances the model's robustness and provides quantitative uncertainty measures, crucial for reliable interpretation. The ability to pre-generate diffraction libraries for model pre-training allows real-time data analysis during experiments, allowing for adaptive experimental control.

PQ-Net is a robust and efficient tool for quantitative analysis of powder diffraction data. Its speed significantly exceeds traditional methods, opening possibilities for real-time analysis during dynamic experiments. Further development could incorporate automated phase identification to eliminate the need for prior chemical knowledge and explore applications to other scattering techniques.

PQ-Net's accuracy relies on the quality of the training data and requires prior knowledge of the sample's chemical composition. The model's performance might degrade in cases of significant background noise or the presence of unexpected phases. Future work should address these limitations by incorporating automated phase identification and improved noise handling.