Extraction of a structural short-range order descriptor from nanobeam electron diffraction patterns using a transfer learning approach

Amorphous solids exhibit structural short-range order despite lacking long-range crystalline order, with this structural descriptor found to be important for determining mechanical properties. Nanobeam electron diffraction offers a potential route for experimental characterization of structural short-range order, yet efforts to date have been primarily qualitative in nature. In this work, machine learning approaches based on transfer learning are used to enable quantitative analysis of nanobeam electron diffraction data from amorphous solids. A ResNet-18 model is trained on virtual diffraction patterns taken from different locations within simulated metallic glasses and amorphous grain boundary complexions in the Cu-Zr alloy system that were created with hybrid molecular dynamics and Monte Carlo simulations. The disorder parameter is found to be a superior target structural descriptor compared to traditional Voronoi indices for this task. The model achieves a low validation mean absolute error across diffraction patterns corresponding to different interaction volumes, demonstrating excellent performance and potential transferability. Testing was performed using other simulated nanobeam electron diffraction data as well as experimental nanobeam electron diffraction patterns, showing that the model can reliably capture spatial variations in local structural state. As a whole, this framework is able to overcome the challenges in the quantitative experimental characterization of structural short-range order, enabling improved characterization of amorphous solids and the exploration of structure-property relationships.

💡 Research Summary

This paper presents a novel workflow that quantitatively links nanobeam electron diffraction (NBED) patterns to the local structural short‑range order (SSRO) of amorphous solids, using transfer learning with a deep convolutional neural network. The authors focus on the Cu‑Zr alloy system, generating extensive atomistic models of metallic glasses and amorphous grain‑boundary complexions via hybrid molecular dynamics/Monte Carlo simulations. These models provide a continuous spectrum of disorder, from crystalline grain interiors to fully amorphous interfacial regions.

From each simulated structure, four types of interaction volumes are defined—single‑layer atomic clusters, two‑layer clusters, cylindrical, and ellipsoidal regions—to mimic the varying probe sizes encountered in real NBED experiments. Virtual diffraction patterns are computed with LAMMPS’s compute saed command, producing image data that resemble the 4‑dimensional STEM scans used experimentally. For every diffraction pattern, a ground‑truth “disorder parameter” χ is calculated based on bond‑orientational order. χ ranges from 0 (perfect crystal) to 1 (completely disordered liquid) and therefore serves as a continuous, physically meaningful descriptor of SSRO. The authors also compute traditional Voronoi indices for comparison, but demonstrate that these discrete topological descriptors are less predictive of the diffraction features.

A ResNet‑18 architecture pre‑trained on ImageNet is fine‑tuned on the synthetic diffraction‑χ pairs. Training proceeds for 400 epochs using the Adam optimizer, a learning‑rate schedule that halves the rate on plateau, and a mean absolute error (MAE) loss function. Validation results show an MAE well below 0.03 across all interaction volumes, indicating that the network can reliably infer χ from diffraction images regardless of probe size or local composition. When Voronoi indices are used as targets, the MAE rises substantially, confirming that χ is a superior structural label for this regression task.

To assess transferability, the trained model is applied to (i) simulated NBED data that were not part of the training set, and (ii) experimental NBED patterns extracted from the literature. In both cases the network predicts spatially varying χ values that correlate with known structural features: higher disorder near amorphous grain‑boundary interiors and lower disorder in adjacent crystalline grains. Importantly, the model remains robust when experimental parameters such as beam diameter and sample thickness change, suggesting practical applicability to real‑world NBED measurements.

The study thus bridges the gap between atomistic simulations and experimental electron microscopy, providing a quantitative metric for SSRO that can be mapped with nanometer resolution. By demonstrating that a deep learning model can decode complex diffraction patterns into a physically interpretable disorder parameter, the work opens pathways for systematic exploration of structure‑property relationships in amorphous alloys, glasses, and amorphous‑crystalline composites. Future directions include extending the approach to other alloy systems, integrating it into real‑time NBED acquisition pipelines, and using the χ maps to guide alloy design for improved mechanical performance, toughness, and radiation tolerance.