Researchers at Lawrence Berkeley National Laboratory have developed a 4D-STEM workflow that can isolate and solve atomic structures from individual nanocrystals buried inside dense, tangled clusters, a task that existing electron microscopy techniques could not reliably perform. Published in the Proceedings of the National Academy of Sciences, the method applies software-defined “virtual apertures” to four-dimensional scanning transmission electron microscopy data, picking out coherently diffracting domains from agglomerated UiO-66 metal-organic framework nanocrystals and resolving them at sub-angstrom precision through ab initio phasing. The advance matters because the nanocrystals used in batteries, drug delivery, and sensor design rarely sit in isolation; they clump together, and until now that crowding made their internal structures effectively invisible.
Why Crowded Nanocrystals Defeated Earlier Methods
A technique called micro-electron diffraction, or MicroED, had already proven it could solve ab initio structures from specimens too small for conventional X-ray diffraction. That capability opened the door to studying nanoscale materials that could never be grown into the large crystals X-ray labs require, and it has been especially powerful for fragile organic compounds that do not survive long exposures. But MicroED works by flooding a selected area with the electron beam, then physically inserting an aperture inside the microscope column to try to capture diffraction from a single target crystal. When multiple crystals sit within that aperture, diffraction patterns blur together and produce results that are difficult or impossible to interpret, particularly when the grains are misoriented or partially overlapping.
“Yet even MicroED has its limitations,” said first author Ambarneil Saha, a postdoctoral fellow at Berkeley Lab’s National Center for Electron Microscopy, in a statement released by the laboratory. Saha explained that MicroED effectively bathes everything in the beam, so researchers cannot isolate the signal from the target crystal when several nanocrystals lie within the illuminated region. That limitation is not merely academic. Real-world nanomaterial samples, whether synthesized for catalysis or harvested from biological tissue, almost always consist of particles packed tightly together or embedded in complex matrices. A method that demands a lone, well-separated crystal effectively locks out the majority of samples scientists actually need to study, leaving crucial questions about defects, interfaces, and local chemistry unanswered.
How Virtual Apertures Crack the Crowding Problem
The new workflow sidesteps the physical aperture entirely. In 4D-STEM, also known as scanning nanobeam electron diffraction, a focused probe rasters across the sample pixel by pixel, recording a full two-dimensional diffraction pattern at every position in a two-dimensional grid. The result is a four-dimensional dataset: two spatial coordinates plus two reciprocal-space coordinates for each scan point. Because each probe position is logged, the team can go back after the experiment and computationally define “virtual apertures” that select only those scan positions where a single coherent domain produced clean Bragg diffraction. Earlier conference work from LBNL-affiliated authors had described this concept of ex post facto apertures, but the new PNAS paper demonstrates the approach working end-to-end on a real, agglomerated UiO-66 sample to deliver a fully solved crystal structure.
The distinction between a physical and a virtual aperture is not just a matter of convenience. A physical aperture is fixed in size and position before data collection begins, so if the operator misjudges where one crystal ends and another starts, the data are contaminated from the outset and cannot be untangled. Virtual apertures, applied after the fact, let researchers iterate: they can test different spatial masks, verify which scan pixels belong to the same diffracting grain, and discard overlapping regions that show mixed diffraction. The PNAS study shows that this post-hoc selection, combined with ab initio phasing, yields sub-angstrom solutions from UiO-66 MOF nanocrystals that would have been unsolvable by conventional MicroED, and it highlights how flexible masking can be tuned to follow irregular grain boundaries rather than simple circular apertures.
From Raw Diffraction Movies to Solved Structures
Turning 4D-STEM data into an atomic model involves several computational steps beyond drawing virtual apertures. First, the diffraction patterns at selected scan positions must be corrected for distortions and then summed to boost signal-to-noise while preserving sharp Bragg peaks from the chosen nanocrystal. The resulting composite diffraction dataset is then indexed to determine the crystal’s orientation and unit cell parameters, much as in conventional crystallography. With that information in hand, the researchers can perform ab initio phasing, using algorithms that reconstruct the electron density directly from the measured intensities without requiring a prior structural model. In the UiO-66 demonstration, this pipeline recovered the expected zirconium-based framework and organic linkers, validating that the virtual aperture did indeed isolate a single coherent domain.
The authors emphasize that this 4D-STEM approach is not merely a workaround for a single tricky sample but a general strategy for crowded nanocrystal ensembles. In their PNAS report, they note that selective data extraction from complex diffraction fields should translate to other classes of materials, including beam-sensitive organics and heterogeneous catalysts. Because the probe scans over tens of thousands of positions, a single dataset can contain information from many different grains and orientations, enabling multiple structures to be solved from one acquisition. That efficiency could be especially valuable for screening libraries of metal-organic frameworks or pharmaceutical polymorphs, where each nanocrystal might adopt a slightly different configuration.
Algorithmic Sorting for Bigger, Messier Datasets
Manually drawing virtual apertures works when a handful of grains are visible, but many real samples contain dozens or hundreds of overlapping domains. Scaling the approach requires automation that can recognize patterns in the data without exhaustive human supervision. A related preprint describes unsupervised clustering tailored for efficient processing of 4D-STEM and even five-dimensional STEM datasets, in which probe tilt adds an extra degree of freedom. These algorithms compress the massive data volumes and perform spatially coherent segmentation, grouping scan positions that share similar diffraction signatures into clusters that likely correspond to individual crystals or domains.
Such clustering is a critical bridge between proof-of-principle demonstrations and routine use in busy materials labs. By automatically labeling regions with consistent diffraction, the software can propose candidate virtual apertures that the microscopist then refines, dramatically cutting down on manual trial and error. At the same time, clustering can flag rare or unusual patterns that might indicate defects, secondary phases, or transient intermediates in a reaction. As 4D-STEM cameras and fast detectors continue to improve, generating ever-larger datasets, these algorithmic tools will be essential to keep analysis times manageable and to ensure that subtle structural variations are not lost in the noise.
Disentangling Overlaps in Thick and Heterogeneous Samples
Even with precise spatial segmentation, some samples pose an additional challenge: structures overlapping along the beam direction through the full thickness of the foil. In these cases, diffraction from different depths superimposes at each scan position, complicating the identification of a single coherent domain. Separate peer-reviewed work in Ultramicroscopy addresses this problem by combining diffraction-vector analysis with clustering to separate components that overlap in projection. By tracking how specific reciprocal-space vectors vary across the scan and grouping them into consistent families, the method can tease apart multiple crystalline or semi-crystalline contributions that occupy the same lateral coordinates.
This kind of component separation is especially relevant for complex heterostructures, catalysts with support particles, or biological specimens where inorganic labels sit within thicker tissue. When combined with the Berkeley Lab team’s virtual-aperture strategy, diffraction-vector–based decomposition could enable a multi-layered view: first, disentangle overlapping phases in reciprocal space, then carve out spatially coherent domains for ab initio structure solution. Together, these techniques point toward a future in which even thick, heterogeneous samples yield interpretable structural information at the nanometer scale, rather than forcing researchers to rely on idealized, ultra-thin specimens.
What This Means for Nanomaterials Research
The ability to pull clean, single-crystal diffraction from crowded ensembles has immediate implications for fields that depend on nanostructured materials. In battery research, for example, active particles often undergo phase transformations and develop strain gradients during cycling, phenomena that are difficult to capture in isolated crystals. Applying 4D-STEM with virtual apertures could allow researchers to solve the structures of individual particles within an electrode cross-section, revealing how local chemistry and defects correlate with performance and degradation. Similarly, in catalysis, active sites frequently reside in small domains at interfaces or within porous hosts, environments where traditional crystallography struggles but scanning diffraction can thrive.
More broadly, the Berkeley Lab team’s work demonstrates that clever data acquisition and analysis strategies can extend the reach of existing microscopes without requiring exotic new hardware. By reimagining the role of apertures as software-defined masks that can be iteratively refined, they have turned a long-standing limitation of electron diffraction into an opportunity. As unsupervised clustering, diffraction-vector decomposition, and other computational tools mature, it is likely that workflows inspired by this study will become standard for characterizing crowded nanocrystal systems. For now, the demonstration that atomic structures can be solved from nanocrystals once deemed unsalvageable marks a significant step toward making real-world, messy samples as structurally accessible as the pristine crystals that have long dominated crystallography.
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*This article was researched with the help of AI, with human editors creating the final content.
