Machine learning (ML) is a type of artificial intelligence that has been applied to a wide range of applications. Starting with a set of data, a machine learning program can readily find patterns that might otherwise prove difficult to identify. In this study scientists created a custom machine learning program to analyze the three-dimensional mappings of lattice strain and orientation in slightly deformed samples of 304L stainless steel. The sub-micron 3D resolution maps of lattice distortions were measured using differential-aperture X-ray structural microscopy (DAXM), performed at beamline 34-ID-E of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science user facility at DOE’s Argonne National Laboratory.
The X-ray measurements centered on a single crystallite in polycrystalline 304L, and subsequent analysis revealed that the crystal lattice rotation field followed a multimodal distribution, while its deviatoric elastic strain exhibited a single-mode distribution. The research findings demonstrate that DAXM and other 3D imaging techniques can be integrated with machine learning analysis to determine the self-organized dislocation structures within deformed crystals, providing new insights into the mechanisms governing the plastic deformation of metals.
A dislocation is a linear misalignment of atoms in a crystalline lattice. As a metal's crystalline structure begins to yield under loading, pre-existing dislocations move and multiply. Under increasing load, these dislocations collectively interact to form distinct, organized patterns known as cells. Gaining new insights into the collective dislocation interactions is critical since they greatly influence the strength of metals.
In this study both optical and TEM imaging techniques were used to characterize the polycrystalline structure of the 304L stainless steel samples (Fig. 1a) and highlight dislocation structures inside single crystals (Figs. 1b, c). However, because TEM is usually performed on thin foils, it provides only limited information of bulk dislocation arrangements. High-energy X-ray measurements do not suffer this limitation and are thus vital to fully characterizing the 3D nature of dislocation structures.
The DAXM technique involved scanning a platinum wire through a polychromatic x-ray beam in a series of six steps. This scanning procedure manipulated the x-ray beam contour, providing depth profiling within a single grain to a resolution of 0.5 micrometer. The resulting high-resolution data set allowed the researchers to assemble 3D maps of lattice orientations and rotations, as well as deviatoric elastic strain.
Stresses within a material are the internal forces that oppose an applied external load. Strain, on the other hand, is a material's deformation in response to stress. All the examined samples exhibited a two percent tensile strain. Deviatoric strain is the shape-changing component of a material's total deformation, without any hydrostatic (volume-changing) effects. Determining deviatoric strain is crucial for analyzing plastic deformation and ultimate yield strength. From the DAXM measurements the deviatoric strain tensor was delineated over a large portion of a grain within a 304L sample.
The lattice rotations measured by DAXM formed several clusters, or modes. Such a multimodal data set is often treated as a Cauchy distribution. Statistically a Cauchy distribution more accurately represents elastic field data arising from crystalline dislocations than does the famous bell-shaped Gaussian distribution. This is due to the physical nature of elastic fields.
To interpret the complex lattice rotations measured by DAXM, the researchers crafted and applied an unsupervised Cauchy mixture machine (CMM) learning model. Unsupervised means that human direction is not needed to pre-define or classify the data. Instead, inherent patterns in the data are uncovered by applying the algorithms of the learning model without any guidance.
The pair of histograms in Fig. 2 were plotted by applying the unsupervised CMM learning model to the DAXM data. The histograms depict the diagonal and off-diagonal components of deviatoric strain within a single metallic grain, with each color-coded component fitted to a Cauchy distribution. Figs. 3a-c display the magnitude of the dislocation density tensor projected over the individual lattice rotation components within a single grain, as identified by CMM. Fig. 3d combines the three rotation components to reveal the subgrains, with boundaries enhanced by the dislocation tensor (black color).
The experimental results demonstrate the capability of synchrotron x-ray techniques to generate high-resolution tomographic maps of lattice distortions, while concurrently showcasing the ability of machine learning to analyze microdiffraction data to identify complex strain fields and patterns of dislocations. Future investigations could examine larger domains and strain levels than those observed here, as well as the evolution of sample strain over time. – Philip Koth
See: K. SharafEldin1, B.D. Miller2, W. Liu3, J. Tischler3, B. Anglin2, A. El-Azab1, “Informed unsupervised machine learning analysis of dislocation microstructure from high-resolution differential aperture X-ray structural microscopy data,” Acta Mat. 303, 121624 (2026) 10.1016/j.actamat.2025.121624
Author affiliations: 1Purdue University; 2Naval Nuclear Laboratory; 3Argonne National Laboratory
The authors are grateful for the support from the Naval Nuclear Laboratory, operated by Fluor Marine Propulsion, LLC for the US Naval Reactors Program. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science user facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No DE-AC02–06CH11357. The final writing and revision of the manuscript were supported by the U.S. Department of Energy, Office of Fusion Energy Sciences, through award number DE-SC0024585 at Purdue University.
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