The determination of crystal structure is crucial for understanding material properties. Powder X-ray diffraction (XRD) is the standard technique, but current indexing methods require significant human intervention and expertise, hindering high-throughput analysis. The increasing volume of data generated by in situ XRD techniques further exacerbates this challenge. This paper proposes to address this limitation by developing a generalized deep learning (DL) model capable of classifying crystal systems and space groups from XRD patterns. Existing automated classifiers suffer from accuracy limitations and reliance on human intervention. DL models, with their ability to learn complex patterns from large datasets, offer a potential solution. While some prior work has explored DL for XRD data analysis, these models often lack generalizability, performing poorly on experimental data or limited subsets of materials. This research aims to develop a robust and generalized DL model capable of classifying a wide array of inorganic crystalline materials, addressing the challenges of noise, peak shifts, and variations in experimental conditions.

Previous research has explored machine learning and deep learning methods for diffraction data analysis, including pattern decomposition, cluster analysis, crystal structure classification, structure-property relationships, and phase mapping. However, existing models often suffer from limitations in accuracy, generalizability, and reliance on synthetic data. For instance, Park et al. used a convolutional neural network (CNN) trained on simulated data, but its generalizability was limited. Similarly, Vecsei et al. trained a DNN and CNN, achieving better results on synthetic data than on the RUFF experimental dataset. Other studies focused on classifying smaller subsets of crystal symmetry classes or specific material datasets. The need remains for a robust model capable of classifying dynamic and/or unseen real XRD data from diverse materials.

The study employs three main strategies to develop a generalized and robust deep learning model. First, an augmented synthetic dataset is generated to mimic real experimental XRD data, incorporating variations in noise, peak shifts, and instrumental parameters. This dataset is built from 171,076 distinct crystallographic information files retrieved and processed from the Inorganic Crystal Structure Database (ICSD). Seven synthetic datasets were created with varying Caglioti parameters and noise implementations. These were combined to create three training datasets: baseline (171k data points), mixed (171k from datasets 1-4), and large (1.2 million from all seven datasets). Second, model architectures are designed to reflect scientific classification strategies based on Bragg's Law. Three architectures are explored: a standard convolutional neural network (SCNN), a multi-layer perceptron (MLP), and a no-pooling convolutional network (NPCNN). Third, a domain adaptation technique is used to improve the model's ability to handle experimental data. This involves incorporating a subset of the RUFF experimental dataset into the training process. The models were trained using PyTorch and the UnifelM deep learning library. Performance is evaluated using three datasets: the RUFF dataset (experimental), the Materials Project (MP) dataset (inorganic crystals with enhanced electromagnetic properties), and a Lattice Augmentation dataset (synthetic cubic crystals with varied lattice constants). Model performance is assessed using accuracy, F1 score, and confusion matrices. The impact of model architecture on classification strategy is analyzed by examining properties of convolutional, pooling, and dense layers, such as receptive field, permutation invariance, and translational equivalence.

The study demonstrates that the quality of training data significantly impacts model performance. The augmented synthetic datasets, particularly the mixed and large datasets, significantly improved the model's generalizability compared to a model trained solely on a baseline synthetic dataset.The inclusion of experimental data through domain adaptation further enhanced performance, especially the NPCNN model which outperformed other architectures. The NPCNN, lacking pooling layers, showed superior performance on the RUFF dataset (74% accuracy for 7-way crystal system classification and 28% accuracy for 230-way space group classification) due to its ability to preserve local information crucial for interpreting peak relationships in XRD patterns. The MLP model showed strong performance on the MP dataset, highlighting its robustness to different material distributions. The Lattice Augmentation dataset demonstrated the models’ capacity to classify based on relative peak intensities and distances, consistent with Bragg's Law. Despite high overall accuracy, the analysis revealed a bias towards overrepresented space groups in the training data, necessitating future work to address class imbalance. This bias is analyzed using F1 scores which showed consistent results with accuracy. A scatterplot analysis revealed a correlation between accuracy on the MP dataset and class count in the training data, highlighting the impact of class imbalance on model performance. The study further analyzed the impact of model architecture on classification strategies, showing the importance of local peak relationships for accurate classification in XRD analysis.

The results highlight the importance of data quality and architecture in developing effective DL models for XRD analysis. The use of augmented synthetic data, incorporating variations in experimental conditions, and domain adaptation using real experimental data significantly improves model generalization. The superior performance of the NPCNN architecture demonstrates the value of preserving local peak information for accurate interpretation of XRD patterns. The observed bias towards overrepresented classes in the training data underscores the need for techniques to address class imbalance, such as data augmentation or weighted loss functions. The ability of the models to accurately classify materials with limited data points in the MP dataset shows promise for application in material discovery and design. The findings suggest that DL models can effectively automate the analysis of large XRD datasets, enabling high-throughput materials characterization.

This work presents a novel generalized deep learning model for automated classification of crystal systems and space groups from XRD data. The use of augmented synthetic training data, domain adaptation, and an optimized NPCNN architecture yielded state-of-the-art performance. Future work should focus on addressing class imbalance in training datasets and developing models agnostic to the beam source. The methodology presented here is readily adaptable to other spectroscopy techniques.

The study's reliance on a primarily synthetic training dataset, while augmented to improve realism, may limit the model's performance on highly unusual or unconventional materials not adequately represented in the training data. The observed bias towards overrepresented space groups highlights a limitation that future work should address through class balancing techniques. While the model showed robust performance across various evaluation datasets, the generalizability to all possible materials and experimental conditions remains to be fully tested.