Neural Network Models Towards Space Group Determination Using Dynamically Simulated EBSD and TKD Patterns

Accurate determination of crystallographic space groups is a cornerstone in materials science, enabling the elucidation of material properties and guiding the design of novel materials. This study introduces a novel approach that leverages neural network models and high-throughput simulation to predict space groups from Electron Backscattered Diffraction (EBSD) or Transmission Kikuchi Diffraction (TKD) patterns. By employing advanced machine learning techniques and simulated datasets, this method may help overcome traditional limitations by offering a robust, high-throughput tool for automated crystallographic analysis without the prerequisite of prior material phase knowledge. EBSD and TKD are SEM modalities that have established applications for determining characteristics of materials such as orientation and crystal structure [1-3]. Furthermore, the relatively fast scanning speeds in an SEM may allow EBSD to eventually facilitate automated high-throughput materials characterization. For this application, Hough indexing and spherical indexing are some potential high-throughput EBSD analysis techniques. However, one shortcoming of these methods is the necessity of identifying candidate phases beforehand using prior knowledge of the material sample. There are methods for EBSD crystal symmetry classification that are accurate and do not require prior knowledge, but they are often time-consuming and may require manual inspection [4, 5]. Recently, neural networks have been employed to predict Bravais lattices using an EBSD pattern as input, with strong performance for novel samples and fast inference times [6]. While attempts have been made to train models to predict space groups as well, models developed have not been rigorously shown to generalize to novel materials and have only exhibited high accuracies when tested on patterns from the same materials as in the training data [7]. A possible reason for this is the low materials diversity in the training data, such that training models on larger datasets with a more diverse set of materials may increase accuracy. This study attempts to develop neural network models that can predict the space group of novel crystal structures, i.e., those that are outside the training dataset, by using a large, simulated dataset of EBSD patterns. A schematic of the workflow in this study is shown in Figure 1. This study focuses on 6 space groups (221, 223, 225, 227, 229, 230) from the 4/m,3¯⁠,2/m point group because of their ready availability of experimental EBSD patterns in the literature to potentially use as testing data [7]. However, to decouple error from experimental conditions from error from crystal structure differences, the test dataset used in this study consisted of dynamically simulated patterns of 17 materials in the experimental dataset, matching the experimental settings and sample-detector geometry. To obtain a training dataset, crystal structures are queried from the Materials Project database [8] from the 6 space groups, for which dynamically simulated EBSD patterns are created using the EMsoft software [9]. These simulations also matched the experimental settings and sample-detector geometry of the experimental testing data. The crystal structures were chosen by selecting an arbitrary unit cell volume cutoff for each space group and simulating all the structures in the space group with a unit cell volume below that cutoff. This was done to maximize the material diversity of the training dataset, keep the distribution of unit cell volumes of the training materials close to that of the test dataset (at the cost of some overfitting), and keep the computational requirements manageable as simulating materials with large unit cell volumes is known to be time-consuming. A total of 5131 cubic materials were simulated for training, and the simulated training patterns were then split into a 5-fold cross-validation dataset, such that each fold contained an entirely distinct set of materials different from the other folds. A neural network with the ResNet18 architecture was trained on the 5-fold cross-validation dataset and obtained a validation accuracy of 91% averaged over the 5 folds, shown in Figure 2. The class-balanced test accuracy on the small set of 17 materials obtained was 75%. Thus, our findings suggest that EBSD patterns in theory contain generalizable space group information that can be learned by a neural network, but that there may be some variance in performance depending on the material. Previous studies have used Grad-CAM to identify areas of significance in an EBSD pattern for the neural network’s decision-making when classifying space groups [7]. To corroborate with previous findings, Grad-CAM was also used to highlight areas of importance in each image in the test dataset for the neural network’s decision-making. Regions given high significance were often either zone axes or areas next to zone axes, which is partially in agreement with previous studies. An example of a simulated image with its Grad-CAM heatmap is shown in Figure 3. Some simplifications of the simulations include setting a constant Debye-Waller factor of 0.005 nm2 for all atoms and setting a constant pattern center for all materials and orientations; it was assumed that the space group information in the images would still be preserved through these approximations. Nevertheless, the current findings suggest that neural network models have the potential to determine space groups from EBSD and TKD patterns across a range of materials. This ability is a step toward more efficient material characterization processes that can operate without extensive prior knowledge of the samples. Future efforts will focus on adapting the models to experimental data as well as expanding the models to accommodate all 230 space groups and to better handle the variability of unit cell volumes. By enhancing both the speed and accuracy of these models, we hope to support the practical needs of high-throughput environments like nanoparticle libraries. Overall, our results suggest that such comprehensive, AI-driven EBSD/TKD pattern characterization may be possible, streamlining the identification and analysis of new materials [10]. Workflow for predicting crystal space groups using a neural network, starting from querying the Materials Project database, to dynamical EMsoft simulations of EBSD/TKD patterns, and ending with training and testing the classification model. Confusion matrix displaying the neural network’s classification accuracy for six space groups, with true labels on the y-axis and predicted labels on the x-axis. a) Simulated EBSD pattern of Ge. b) Grad-CAM heatmap showing regions of importance for the neural network’s decision-making. As indicated in the color bar, red regions indicate higher significance while blue indicates lower significance.