Understanding the microstructure of polycrystalline solids, including grain size, morphology, and crystallographic orientation, is vital for connecting processing, microstructure, and material properties. This knowledge is key to predicting component behavior and designing advanced materials. Electron backscatter diffraction (EBSD) is a widely used diffraction-based technique for crystallographic characterization. EBSD accurately maps phases and grains by analyzing diffraction patterns generated by the atomic lattice. However, its dependence on electron microscopy limits throughput, field of view, and sample size. This makes EBSD inefficient for large, heterogeneous samples or extensive materials libraries, particularly hindering additive manufacturing (AM) research where complex microstructures vary significantly across builds and batches. Optical microscopy offers a faster, larger-field-of-view alternative. However, direct atomic lattice resolution is impossible with visible light. Optical orientation mapping requires analyzing optical signals encoding crystallographic orientation. Existing techniques measure orientation-dependent changes in light intensity and polarization or reconstruct the topography of etch pits. Directional reflectance microscopy (DRM) falls into the latter category, measuring light reflection as a function of illumination direction. Preferential dissolution during chemical etching creates topographical surface features linked to crystallographic orientation, causing anisotropic reflectance. Computational methods analyze DRM data to map grain orientation. This approach has been limited to pure crystalline solids, using material-specific, physics-based models. Extending high-throughput optical orientation imaging to engineering alloys is challenging due to their complex microstructures and difficult-to-decode optical signals. This research introduces an optical method for grain orientation mapping in metal alloys using convolutional neural networks (CNNs) to infer crystal orientation from DRM optical signals. The model, named EulerNet, predicts orientation as Euler angles, circumventing limitations of physics-based approaches by autonomously learning relationships between reflectance and orientation, handling complex patterns, and offering flexibility for application to diverse alloys and microstructures. The effectiveness of EulerNet is demonstrated using Inconel 718 specimens produced by directed energy deposition (DED).

The paper reviews existing techniques for crystallographic characterization, highlighting the limitations of EBSD in terms of throughput and sample size. It discusses the principles of optical microscopy for orientation mapping, specifically mentioning techniques based on orientation-dependent changes in light intensity and polarization, and those that rely on reconstructing the topography of etch pits. The use of directional reflectance microscopy (DRM) is described, emphasizing its potential for high-throughput analysis but its current limitations in application to complex engineering alloys. The authors highlight the challenge of developing accurate physics-based models for interpreting the optical signals generated by these complex alloys, motivating their machine learning approach.

Ten Inconel 718 specimens (24 mm × 24 mm × 12–18 mm) were produced using directed energy deposition (DED) with varying process parameters (laser power, speed, layer height, powder feed rate) to create diverse microstructures. Post-deposition, a standard heat treatment created intermetallic δ (Ni3Nb) precipitates. Chemical etching selectively dissolved the γ matrix, leaving the corrosion-resistant δ platelets to protrude from the surface, creating the anisotropic reflectance for DRM measurements. DRM measurements were conducted using a setup consisting of a stereomicroscope, a monochrome CMOS camera, and a moving white LED light source. Reflectance intensity was measured as a function of illumination angle (θ, φ). Peaks in reflectance intensity correspond to angles at which δ platelets reflect light directly into the microscope. The orientation of these platelets is linked to the γ matrix grain orientation. A convolutional neural network (CNN), EulerNet, was trained to predict crystal orientation (Euler angles) from the DRM data. The input was a 6 × 72 array of reflectance intensities. The CNN architecture included two convolutional and max-pooling layers for feature extraction (low-level features like edges and blobs, followed by high-level features representing reflectance peak characteristics) and two fully connected regression layers for predicting Euler angles. EBSD measurements provided the ground truth for training. Model performance was evaluated using ten-fold cross-validation. Disorientation angles between predicted and EBSD orientations were calculated at grain centers (to minimize misregistration effects) and analyzed, along with the orientation dependence of the prediction error. An anomaly detection model based on principal component analysis (PCA) was used to identify outliers in new datasets to ensure data reliability.

EulerNet accurately predicted crystal orientation from DRM data, achieving a median disorientation angle of 6.7° ± 0.8° across all cross-validation splits. This value is likely an overestimate due to the challenges in registering DRM and EBSD datasets. Orientation-dependent error analysis showed slightly lower errors along the out-of-plane direction, possibly due to easier alignment during specimen mounting. The model performed reliably across specimens with varying microstructures resulting from different DED parameters. An anomaly detection method using PCA effectively identified specimens with lack-of-fusion defects or underdeveloped δ precipitates, highlighting the importance of data quality control. The trained EulerNet model is publicly available, facilitating broader use and collaborative improvements. The key figures illustrate the successful application of the methodology: Figure 3 shows visually similar orientation maps generated by EulerNet and EBSD for a specimen not used in training. Figure 4 displays the architecture of the CNN model, EulerNet. Figure 5 presents the distribution of disorientation angles and its orientation dependence, demonstrating the accuracy and relative uniformity of the model's predictions. Figure 6 demonstrates the effectiveness of the anomaly detection method in highlighting defects and regions with insufficient δ phase precipitates.

This research addresses the need for high-throughput crystal orientation mapping by successfully integrating DRM and machine learning. EulerNet provides a reliable method for orientation mapping in complex metal alloys, significantly improving upon the throughput limitations of EBSD. The data-driven approach makes the method adaptable to various alloys and manufacturing processes. The accuracy, while not matching EBSD's precision, is sufficient for many applications, particularly in AM, where large-scale microstructure characterization is crucial. The incorporation of an anomaly detection model ensures data quality and reliability, improving the trustworthiness of the results. The publicly available model and data promote community collaboration and further advancements in the field.

This study demonstrates a novel machine learning approach for high-throughput crystal orientation mapping using directional reflectance microscopy. The developed EulerNet model provides accurate and reliable predictions of grain orientation in Inconel 718, overcoming limitations of traditional EBSD techniques. The method's data-driven nature and ease of adaptation make it valuable for various materials and applications, particularly in additive manufacturing. Future research could focus on improving model accuracy through advanced network architectures or refined data pre-processing, and extending the method to other alloy systems.

The accuracy of the method is influenced by factors such as the precision of the DRM apparatus, the quality of specimen preparation, and the accuracy of the EBSD-DRM data registration. The reported error of 6.7° is likely an overestimate due to registration challenges. The anomaly detection method relies on the training data's representativeness and might not capture all types of anomalies. While the PCA-based anomaly detection is effective, the interpretation of the z-score still requires expert judgment.