Defect detection and classification are crucial in materials science because defects significantly influence material properties. While techniques like transmission electron microscopy (TEM) offer atomic resolution, sample preparation limitations exist. Coherent X-ray diffraction (CXD), particularly Bragg coherent diffraction imaging (BCDI), offers a less restrictive alternative for probing the microstructure of defects, providing 3D information about the local lattice deviations and strain fields around defects. However, analyzing the complex 3D CXDPs and identifying defects remains challenging, often requiring time-consuming data mining. This research proposes a novel approach using a CNN to classify defects directly from the CXDPs, offering a faster, automated solution. Previous works have employed pattern classification and neural networks for defect detection in other imaging modalities. However, applying these methods to the unique challenges posed by 3D CXDPs requires the creation of extensive training datasets representative of real-world defect physics. Advances in computational resources make generating realistic 3D CXDPs for training a CNN feasible, offering a significant advantage over traditional methods. While deep learning has been used in 2D diffraction analysis and in accelerating phase retrieval in CXD, this work focuses on the direct classification of defects from 3D CXDPs.

Existing methods for defect detection in materials science include transmission electron microscopy (TEM), which offers atomic resolution but has sample preparation limitations. Coherent X-ray diffraction (CXD), specifically Bragg coherent diffraction imaging (BCDI), provides a less restrictive alternative capable of 3D imaging of strain fields around defects. However, analyzing these 3D diffraction patterns to identify defects remains challenging and typically involves significant manual data mining. Pattern classification and neural networks have been used successfully in other fields for similar tasks. In diffraction phase microscopy, pattern classification and neural networks have been used for fault detection. Deep learning approaches have also shown promise for optical surface-defect detection and defect segmentation in scanning transmission electron microscopy (STEM). However, the application of these methods to the unique characteristics of 3D CXDPs necessitates large training datasets that accurately capture the variety of defect types and their influence on diffraction patterns. The use of deep learning models to accelerate phase retrieval from CXDPs represents a nascent and promising direction in the field of CXD and BCDI. This paper presents a novel approach using a 3D CNN to directly classify defects in nanocrystals from their 3D CXDPs. This method addresses the limitations of existing techniques and capitalizes on recent computational advances.

The study utilizes a pipeline combining atomistic simulations and a 3D CNN. First, a data set of simulated 3D CXDPs was generated. This involved several steps: 1) Generating nanocrystal geometries based on Wulff and Winterbottom constructions, representing the equilibrium shape of free-standing and substrate-supported crystallites; 2) Introducing dislocations (screw and edge types) into the nanocrystals at various positions (both centered and random), using the MERLIN atomistic simulation code and controlling the Burgers vector (b = [110]); 3) Relaxing the atomistic configurations using LAMMPS, employing different embedded-atom model (EAM) potentials specific to the fcc transition metals (Al, Au, Ag, Pt) under study; 4) Calculating the 3D CXDPs using the PyNX scattering package, leveraging GPU acceleration for efficient computation on 64 x 64 x 64 reciprocal space points; 5) Augmenting the dataset by randomly rotating each CXDP around the scattering vector and varying reciprocal space sampling to prevent overfitting. Two crystal sizes were used: small (40 x 40 x 40 unit cells) and large (80 x 80 x 80 unit cells). Two dislocation introduction strategies were employed: centered dislocations (CD) and random positioned dislocations (RPD). Each dataset comprised approximately 1000 relaxed configurations, with one-third defect-free, one-third with screw dislocations, and one-third with edge dislocations. The 3D CNN architecture consisted of five convolutional layers with ReLU activation functions, followed by two fully connected layers with a final softmax layer for multi-class classification. Dropout (rate = 0.2) was used to mitigate overfitting. The CNN was trained using the Adam optimizer, categorical cross-entropy loss, a learning rate of 10⁻³, and a batch size of 64. The dataset was split into training, validation, and test sets. Model training ceased when validation accuracy plateaued. The CNN's performance was evaluated on a test set of 11,556 CXDPs. Experimental data consisted of 3D CXDPs from Pt nanoparticles measured at two synchrotron beamlines (SixS and P10) at different Bragg reflections. Preprocessing involved centering the CXDP and normalizing the intensity. The trained CNN was then used to predict defect classes from the experimental data.

The 3D CNN achieved a high accuracy of 97.2% on the simulated test dataset, accurately predicting defect-free crystals and distinguishing between screw and edge dislocations. The majority of errors involved misclassifying edge dislocations as screw dislocations. A simpler two-class model (defect-free vs. defective) exhibited even higher accuracy. An occlusion sensitivity test demonstrated that the network primarily used information from the vicinity of the Bragg peak for classification. When applied to experimental data from Pt nanoparticles, the CNN demonstrated excellent performance, correctly classifying all experimental examples. Predictions for mixed dislocations (observed in some experiments) were slightly less accurate (82-94%), likely due to the complex nature of these defects. The choice of the simulated training dataset significantly influenced the CNN’s performance on experimental data. Models trained on datasets with unrelaxed configurations or only a single metal element showed reduced accuracy when predicting mixed dislocations. Including multiple elements in the training data and employing a random dislocation positioning strategy improved the model’s ability to generalize to experimental data with diverse dislocation types and locations. A dataset incorporating a mix of centered and randomly positioned dislocations yielded the best results, allowing the model to accurately predict both centered and off-centered dislocations with high accuracy, showcasing the importance of data diversity. The training data must accurately represent the crystal structure and the displacement fields of the defects. Relaxing the simulated crystal structures is key. Including multiple elements in the dataset enhances the model's generalization ability. Including a mix of centered and randomly positioned dislocations in the training data further improves performance.

The successful application of a 3D CNN to classify defects directly from Bragg coherent X-ray diffraction patterns represents a significant advancement in materials science. The high accuracy achieved on both simulated and experimental data demonstrates the potential of this method to automate defect identification, significantly accelerating data analysis and potentially enabling real-time feedback during experiments. The findings highlight the importance of dataset design, demonstrating the necessity of training data that closely mimics the complexity and variability of real-world samples. The ability to distinguish between screw and edge dislocations, even those close to free surfaces, showcases the robustness and sensitivity of the CNN approach. This methodology could transform how researchers analyze and interpret coherent diffraction imaging data, reducing the need for time-consuming manual analysis and potentially leading to new insights into defect behavior and their influence on material properties.

This study demonstrates the effectiveness of a 3D convolutional neural network for automated defect classification in nanocrystals using Bragg coherent X-ray diffraction patterns. The high accuracy achieved on simulated and experimental data underscores the potential for rapid and accurate defect identification. The importance of diverse and realistic training data was highlighted. Future work could focus on extending this approach to other material systems, including those with more complex defect structures, and integrating this technique into automated data acquisition pipelines for real-time feedback during experiments.

The current model is trained primarily on fcc transition metals. Its generalizability to other crystal structures or material types remains to be tested. The accuracy on mixed dislocations, while good, was slightly lower than that of screw or edge dislocations. The simulations employed the kinematic approximation, which may not be fully accurate for all experimental conditions. Future work should explore the impact of dynamic effects and more sophisticated scattering models.