4D-STEM and machine learning assisted atomic mapping

Unlike their crystalline counterparts, metallic glasses lack long-range order, giving rise to complex atomic packing motifs, often described in terms of short- and medium-range order networks of distortedicosahedra and other polyhedral clusters. This inherent structural disorder grants them exceptional hardness and corrosion resistance, yet their deformation is dominated by  highly localized shear bands that limit ductility and toughness.

 

Figure 1. Schematic illustration of 4D-STEM–based pair distribution function (STEM-PDF) and strain mapping analysis for nanoscale structural characterization of metallic glasses. A quasi-parallel electron probe is scanned across an electron-transparent metallic glass specimen while a diffraction pattern is recorded at each probe position, forming a four-dimensional dataset (x–y–qₓ–qᵧ). The circular diffraction rings represent isotropic short-range atomic order within the glassy matrix. From each diffraction pattern, local strain information is obtained from the elliptic distortion of the diffraction rings, and atomic pair distribution functions (PDFs) are derived through Fourier transformation of the structure factors. Combining these datasets enables spatially resolved mapping of strain, atomic packing density, and nanoscale structural heterogeneity, providing comprehensive insight into deformation and relaxation mechanisms in metallic glasses.
 

Recent advances in 4D scanning transmission electron microscopy (4D-STEM) and machine learning assisted atomic mapping have opened unprecedented access to the hidden internal landscape of metallic glasses. These state of the art techniques enable direct visualization of nanoscale strain fields, atomic packing fluctuations, and magneto-elastic interactions in deformed glasses. As illustrated in Figure 1,  4D-STEM based pair distribution function (STEM-PDF) and strain mapping provide a powerful platform for correlative analysis of local structure and properties at the nanoscale. By quantitatively linking local atomic configurations with their corresponding structural variations, the approach establishes a comprehensive experimental framework for understanding structureproperty relationships in metallic glasses.

 

Figure 2. Non-negative matrix factorization (NMF)–aided analysis of 4D-STEM pair distribution function (STEM-PDF) data for structural mapping of metallic glasses. (a) Schematic representation of matrix factorization, where the experimental dataset 𝑉 is approximated by the product of the weight matrix 𝑊 and the basis matrix 𝐻. (b) Conceptual diagram of the probabilistic network underlying NMF. (c) Extracted basis PDFs corresponding to distinct structural types, identified as “liquid-like,” “solid-like,” and “noise.” (d) Spatial maps showing the nanoscale distribution of each structural type and their color-mixed representation.  (e, f) Comparison of the spatial fraction of liquid-like and solid-like regions in the as-spun and annealed metallic glass samples, revealing structural densification and a higher proportion of solid-like motifs upon thermal relaxation.
 

To further unravel the nanoscale heterogeneity in metallic glasses, machine learning assisted analysis has been introduced as an extension of the 4D-STEM-PDF approach. Using non-negative matrix factorization (NMF), complex diffraction-derived pair distribution datasets can be decomposed into a small number of characteristic structural motifs without prior knowledge from simulations. As illustrated in Figure 2, the algorithm extracts basis pair distribution functions corresponding to distinct local configurations typically described as liquid-like and solid-like structures and reconstructs their spatial distributions within the amorphous matrix. The resulting structural maps reveal a nanometer scale mosaic of these motifs, whose relative fractions evolve during thermal relaxation, indicating a shift toward denser and more stable short and medium range order. This data driven, correlative framework enables quantitative mapping of structure and properties in metallic glasses, bridging atomic-scale configurations with experimentally observed changes in density, strain, and magnetic response.

 

Figure 3. Visualization of Eshelby-type inclusions in a deformed metallic glass obtained by 4D-STEM strain and atomic density mapping. (a) Vector field representation of the maximum shear strain (τₘₐₓ) showing the orientation and magnitude of local strain. (b) Magnified region marked by the rectangle in (a), compared with maps of volumetric strain (εᵥₒₗ), shear strain component (εₓᵧ), and nearest-neighbor distance derived from the first PDF peak position. (c) Line profiles taken along the dashed line in (b) display periodic variations of deviatoric and volumetric strain, nearest-neighbor distance, and the curl of τₘₐₓ. The correlated oscillations identify a series of Eshelby inclusions surrounded by quadrupolar strain fields, with nano-sized dilated cores embedded in the glassy matrix.
 

Building upon the correlative structural mapping, the 4D-STEM strain and density analysis provides a direct experimental view into the deformation behavior of metallic glasses at the nanoscale. As shown in Figure 3, vector field visualization of the maximum shear strain (τₘₐₓ) reveals alternating quadrupolar strain patterns aligned along the shear band. Quantitative line profiles of the deviatoric and volumetric strain, together with nearest-neighbor distance variations, demonstrate the presence of periodically arranged Eshelby type inclusions with nanometer-sized dilated cores. These inclusions represent localized shear transformation zones where atomic rearrangements concentrate and interact through long-range elastic fields.

This direct observation offers compelling experimental evidence for the long hypothesized microscopic deformation mechanism in metallic glasses and establishes a powerful link between atomic structure, strain localization, and macroscopic plastic flow.

 

Figure 4. Simultaneous visualization of strain, magnetic, and atomic density fields in a deformed metallic glass using Lorentz 4D-STEM. (a) TEM image showing shear bands formed upon deformation. (b) Corresponding strain field map revealing localized shear-induced deformation patterns. (c) Magnetic induction map reconstructed from Lorentz deflection patterns, showing nanoscale magnetic domain rotation and intensity variations correlated with the shear bands. (d) Relative atomic density map derived from local diffraction intensity, indicating densification and dilatation across the shear regions.(e) Correlative visualization of magnetic induction (B) and strain components (ε_com) demonstrating their spatial coupling within the glassy matrix. The observed magnetoelastic contrast highlights the interplay between structural strain and magnetic anisotropy in metallic glasses.

 

Expanding the correlative approach beyond purely structural analysis, Lorentz 4D-STEM enables the simultaneous mapping of strain, magnetic, and density fields in metallic glasses. As shown in Figure 4, shear band networks observed in conventional TEM correspond to pronounced local variations in both the strain and magnetic induction maps. The spatial correlation between strain localization and magnetic contrast reveals a direct coupling between structural and magnetic responses a manifestation of the magnetoelastic effect in amorphous alloys. Regions exhibiting tensile strain tend to show a reduction in magnetic induction, while compressive regions enhance it, reflecting the sensitivity of spin alignment to local atomic packing density.

This simultaneous visualization of structural and magnetic order at the nanometer scale provides a powerful platform to unravel the interplay between mechanical deformation and magnetic functionality in metallic glasses, paving the way toward designing amorphous materials with tunable magnetostrictive and energy dissipative properties.

In our group, we explore this frontier using advanced electron microscopy, Lorentz 4D-STEM, and data-driven analysis to uncover how structure, stress, and magnetism intertwine at the nanoscale in metallic glasses. These efforts aim to transform fundamental understanding into design principles for next-generation structural and functional amorphous materials.

 

 

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