Introduction

Just over two decades ago, a breakthrough in wet chemical synthesis enabled the growth of metal nanocrystals into selected shapes1,2,3. This breakthrough has launched exciting applications in nanophotonics, sensing, catalysis, optoelectronics and biomedicine, which seek to optimize the properties of nanocrystals by tuning their shape, size and/or facet crystallography4,5,6,7. However, despite over two decades of intense research, key questions regarding the fundamental mechanisms controlling metal nanocrystal growth and morphology remain.

Pivotal to nanocrystal growth and shape control is the modification of the energy of surface facets using surfactants and/or adsorbates (such as ions and metal additives), thereby controlling the rate at which different facets grow and directing the final nanocrystal morphology8,9,10,11. For example, single crystal cuboctahedra gold seeds grown with the cationic surfactant cetyltrimethylammonium bromide (CTAB) can form spheres, single crystal nanorods or nanocuboids, depending on whether they are in the presence of no additive, silver (Ag+) or copper (Cu2+), respectively12,13,14,15,16,17,18. Remarkably, these metal adsorbates are essential to induce symmetry breaking of the initial seed particle13,19 and thereby facilitate the final anisotropic shape.

It is widely recognised that metal additives adsorb to the nanoparticle surface, while surfactants form a layer (or bilayer) surrounding the nanoparticle20. However, these surface models are primarily established based on spectroscopy and/or theoretical calculations, lacking direct experimental evidence of the atomic arrangement at the surface.

To understand growth processes, and more broadly to understand how a nanoparticle interacts with its environment, it is critical to understand the atomic structure at the nanoparticle-metal additive-surfactant interfaces, in concert with the overall nanoparticle size, shape and surfactant chemistry. However, here lies a fundamental problem: nanocrystal facets are typically only a few atoms wide and the metal additives and surfactant components expected at the surface may only be present in trace amounts. The signal they generate is thus extremely weak, particularly in the presence of the adjacent nanoparticle. Measuring the atomic structure – that is, the type, position and relative arrangement of atoms – at the nanoparticle-metal additive-surfactant interface remains extremely challenging20. Methods with both sufficient resolution and sensitivity to detect a monolayer (or sub-monolayer) of ions simultaneously with the nanoparticle surface and the surfactant have been elusive. Hence the atomic structure of the hard–soft interface, that is, the positions of metal additives and surfactant counterions relative to the nanoparticle surface, has not been measured in any nanoparticle and remains unknown. This limits our understanding of the role of metal additives and surfactant counterions on the surface functionality and energetics and hence on nanoparticle growth.

Advanced characterization methods, such as X-ray diffraction21,22, atomic force microscopy (AFM)23,24 and scanning tunnelling microscopy (STM)25, have been used to image the surfactants near to the nanoparticle surface, but have been unable to achieve atomic resolution and/or measure the nanoparticle surface structure ‘hidden’ beneath the surfactant. Spectrometry techniques, such as small-angle neutron scattering, inductively coupled plasma-mass spectrometry, inductively coupled plasma atomic emission spectroscopy and X-ray photoelectron spectroscopy, have excellent chemical sensitivity26,27,28,29,30. However, their spatial resolution is limited to length scales (~10 nm to 10 µm) often larger than the nanocrystal itself, and certainly much larger than the facet or atomic dimensions. This has led to inconsistent reports in their application to detect metal additives on nanoparticle surfaces14,26,27,28,29,31.

Conventional transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) are powerful tools for imaging the atomic structure of nanocrystal surfaces32,33,34,35,36. However, achieving imaging conditions that are simultaneously sensitive to the metal nanocrystal and the surfactant is extremely difficult. Furthermore, the electron scattering processes, and hence image interpretation, at the nanoparticle-metal additive-surfactant interface are severely complicated by the possibility of incomplete surface layers, trace amounts of metal additives and the structural discontinuity presented by the hard (nanoparticle)-soft (surfactant) interface. This means that several hypothetical models of the atomic structure of the nanoparticle-additive-surfactant interface matching the STEM or TEM images cannot be distinguished. These issues are further complicated by the extreme sensitivity to electron beam damage of the delicate surfactants and, to a lesser extent, the metal nanoparticle surfaces37.

While all the above techniques provide vital information, the atomic structure of a nanoparticle-metal additive-surfactant interface remains elusive.

In this work, we develop and apply an approach to determine the atomic structure and measure the interatomic distances at a nanoparticle-metal additive-surfactant interface. We determine STEM imaging conditions that maximise the generation and detection of the extremely weak signals scattered by the different trace atoms at the surface. Specifically, we use electron scattering calculations to identify the electron wavefield that will concentrate scattering from these atoms into a specific angular range which we then detect. This generates directly interpretable images that are preferentially sensitive to the atoms of interest, namely, the nanocrystal surface facet, the metal-adatoms and the surfactant counterion. Furthermore, we select those conditions that keep the electron dose relatively low to minimize damage. We apply these conditions to the gold nanocuboid system (grown in the presence of copper additives and CTAB)12,13,14,15. As noted above, Cu2+ additives are essential to induce symmetry breaking and growth into a nanocuboid, as opposed to a nanocube or nanorod. It is thus important to resolve the location and atomic arrangement of Cu additives and their relationship to the gold surface and surfactant in order to provide insights into the underlying surface energies and mechanisms by which additives induce anisotropic growth of metal nanocrystals. We acquire spatial maps of the angular distribution scattered from gold nanocuboids using a so-called scanning convergent beam electron diffraction or 4D-STEM experimental configuration38. We harness the desired information to generate images sensitive to the interface, from which we generate an initial chemical model. By matching this model against the full angular range of the dataset, we measure the position and interatomic distances between the gold facet, copper adatoms and bromide at the surfactant counterion.

Results

Approximate location and distribution of metal additives and surfactant using conventional methods

We first apply conventional methods to determine the approximate location and distribution of the metal additives and surfactant with low spatial resolution.

In conventional scanning transmission electron microscopy (STEM) imaging experiments, the electron probe is raster scanned across the specimen and at each position of the probe (x,y), the scattered electrons are collected and summed over a fixed angular range using disc or annular detectors to form STEM Bright Field (BF) or Annular Dark Field (ADF) images, respectively. At the same time, X-rays emitted by the specimen can be detected with an X-ray spectrometer to deliver a map of chemical elements versus probe position (x,y) (Fig. 1).

Fig. 1: Overview of STEM experiments in characterizing copper additives and CTAB surfactants on a gold nanocuboid surface.
Fig. 1: Overview of STEM experiments in characterizing copper additives and CTAB surfactants on a gold nanocuboid surface.
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A focused electron probe is scanned across the nanocuboid surface, and at each probe position electron signals are collected by various detectors. A EDX maps provide the location of additives (Cu) and surfactant counterion (Br) at nanometre resolution. B Conventional STEM integrates the diffraction pattern using a disc or annular detector. Top: <100> zone axis STEM-HAADF image of surfactant attached to the {100} facets; Bottom: Atomic resolution <110> zone axis STEM-BF image of surfactant attached to the edge where two {100} facets meet. Red-boxed images on the right are the magnified, rotated images of the red box annotation in the images on the left. C 4D-STEM collects the diffraction pattern at each probe position with a pixel array detector. Electron scattering simulations identify conditions for direct imaging of the nanocuboid-metal additive-surfactant interface. Under these conditions, a collection of diffraction patterns is acquired and a direct image of the nanocuboid-metal additive-surfactant interface is generated from which the atomic arrangement and distances will be measured.

We used energy dispersive X-ray spectroscopy (EDX) to obtain nanometre resolution chemical information regarding the distribution of copper additives and surfactants on the gold nanocuboid. We deliberately use a low spatial resolution of ~1 nm to keep the radiation dose, and hence damage, relatively low (Fig. 1A). EDX reveals Cu on all the surfaces of the Au nanocuboid, although the distribution is not always even (Fig. 1A and Supplementary Note 1). Trace amounts of bromide near the surface are also detected, but we emphasize that this signal is just marginally above the noise in the EDX spectra (bromide is expected because it is the counterion of the cetyltrimethylammonium (CTA+) surfactant). In the vertically averaged EDX intensity across the nanocuboid in Supplementary Fig. S2, it is evident that the Cu and Br atoms are located somewhere within a ~2 nm wide region at the nanocuboid-metal additive-surfactant interface. However, the resolution of this experiment does not permit a more precise assessment of the location. Obtaining EDX data at higher spatial resolution would require significantly higher electron dose and with this comes ambiguity arising from beam damage, including the degradation of surfactants, reconstruction of surface structure and alloying of Au and Cu, which are discussed in detail in Supplementary Note 2.

Having identified Cu additives and Br from the CTAB surfactant in the vicinity of the surface, we consider the location of the organic tail group (CTA+) of CTAB. The qualitative distribution of surfactant is identified using conventional STEM-HAADF at 80 kV and 300 kV (Fig. 1B top, and Supplementary Notes 3, 14). The surfactant is distributed at a similar density on all facets and in these projected images extends about 1.5 nm from the nanoparticle {100} facets and about 1 nm from the corner facets. The projected surfactant length in these images is smaller than the 2–4 nm chain length of CTAB determined by neutron scattering30 and STEM electron energy loss spectroscopy39 and recently by liquid-cell TEM40. This may be because the carbon chains have collapsed and/or condensed while preparing the TEM sample, or because the surfactants are not aligned exactly perpendicular to the Au surfaces, and so appear shorter in projection40.

The individual surfactants can just be resolved by examining the nanoparticle in the <110> orientation in STEM-BF (Fig. 1B bottom). In this projection, the surfactants attached to the thin end of the wedge (where two {100} facets meet) can be isolated. The surfactants are measured to be ~1.84 nm long, closer to the length of the CTAB molecule. As noted above, the cetyl chain may be curved, making the surfactant appear shorter in projection.

In principle, the conventional STEM techniques above can be applied at atomic resolution and may show atomic layers at the surface with different intensity. However, there are too many parameters influencing the intensity to correlate it with a unique structural model, as noted above and discussed in detail in Supplementary Note 4. New imaging modalities at doses lower than that needed for spectroscopic imaging must be developed to determine unambiguously the atomic model of the gold nanocuboid-adatom-surfactant surface.

Identifying conditions to image the position of Cu and Br surface adatoms relative to Au

In conventional STEM, the integration of the scattered signal over a large angular range reduces the information about the material transferred to the final image. Recently, the advent of relatively fast, pixel array detectors has made it possible to record the full angular distribution of scattered electrons (kx,ky) at each probe position (x,y), so-called 4D-STEM (Fig. 1C).

From the above preliminary conventional experiments, we know that there are copper atoms, bromide ions and the electrostatically attracted CTA+ surfactant in the vicinity of the surface of the Au nanocuboid. Though we cannot identify exactly where they are from those experiments, we can make a few reasonable starting assumptions. Firstly, from chemical considerations, we expect the copper atoms to be on the Au nanoparticle surface or alloyed within the particle. Secondly, based on the molecular dynamics calculations that suggest that bromide ions are present as the counterion of the surfactant (CTAB)41, we might expect the bromide ions to adsorb at the nanoparticle surface, resulting in a negatively charged surface which the ammonium group of the CTA+ surfactant would associate with. We now consider whether we can identify exact locations of these atoms using the additional information embedded in 4D-STEM datasets and thereby reconstruct an atomic model of the nanocuboid-adatom-counterion interface.

The approach we take is generalised in the guidelines and flow chart provided in Supplementary Note 5. Having identified the target atom species above (step 1 in the flow chart), we undertake multi-slice simulations42 of the electron scattering processes43 (step 2) to identify experimental conditions for distinguishing copper and bromine from gold at atomic resolution, while minimising electron dose (as detailed in Supplementary Note 5). Specifically, we plot scattered intensity versus angle for each atom species and identify those scattering angles that reveal significantly different scattering behaviours between copper, bromine and gold atoms (step 3). There are several sets of conditions that can achieve this – we select that set with a relatively small incident probe convergence angle (9 mrad), and hence electron dose (compared with typical atomic-resolution STEM). We note that these differences in scattering behaviour persist across a wide range of possible specimen thicknesses, removing potential ambiguities in image interpretation associated with different atomic layer thicknesses, including incomplete surface layers. This approach can be applied more generally to other metal nanoparticle systems with different additives and/or surfactant counterions, following the guidelines in Supplementary Note 16. As examples, we illustrate this with other surfactant species in a Au nanoparticle system (Supplementary Note 16).

To show the effectiveness of these conditions to provide sensitivity to the presence of Cu on the nanoparticle surface when they are implemented in 4D-STEM, we calculate and compare the 4D-STEM dataset generated by two different idealized nanocuboid surface structures. Figure 2 compares diffraction patterns across the interface for two model structures: one for pure Au (Fig. 2A) and the other where the two outer layers are instead Cu columns (Fig. 2B) (the latter as suggested by conventional STEM in Supplementary Figs. S8, S9). For each model, a series of diffraction patterns was simulated, with a 9 mrad probe scanning across the nanocuboid, from bulk into vacuum, in the direction perpendicular to a {100} surface facet.

Fig. 2: Simulation of convergent beam electron diffraction patterns with a 9 mrad convergence angle (corresponding to a 1.3 Å diameter probe) moving across a gold nanocuboid into vacuum (position 1–7).
Fig. 2: Simulation of convergent beam electron diffraction patterns with a 9 mrad convergence angle (corresponding to a 1.3 Å diameter probe) moving across a gold nanocuboid into vacuum (position 1–7).
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A Pure gold nanocuboid. B Equivalent simulation with the last two layers replaced by Cu atoms. Model thickness is the average size of gold nanocuboids, 25 nm. The probe step size is 2.04 Å so that the probe positions coincide with the atomic column positions. Central discs are masked for better observation of the intensity distribution beyond the central disc (unmasked raw diffraction patterns are shown in Supplementary Fig. S11). The coloured intensity scale, common to all diffraction patterns, ranges from 0 to 0.005% of the maximal vacuum probe intensity. Blue boxes indicate the features that are sensitive to copper atoms but are insensitive to the vacuum interface. Yellow boxes indicate the features arising from the nanocuboid-vacuum interface. The interface breaks the mirror symmetry in the direction perpendicular to the surface, indicated by the differences in reference to the dashed yellow line.

For both nanocuboid models, the location of the nanocuboid-vacuum interface is evident in the loss of a vertical mirror plane in the diffraction pattern (most evident at position 5 in Fig. 2) parallel to the {100} face. At this discontinuity of the electron-specimen potential field, there is stronger scattering in the <100> direction compared with the <\(\bar{1}00\)> direction, particularly just outside the central disc, as previously observed in scanning diffraction experiments44,45. We will call this the “discontinuity signal”. Importantly, this asymmetric “flare” just beyond the central disc only exists in the direction perpendicular to the edge (regions marked by yellow boxes), enabling its differentiation from effects arising from surface atomic structure or composition.

When the probe is positioned within the pure Au nanocuboid, the STEM diffraction patterns are essentially identical to those of a pure Au crystal lattice (position 1–4, Fig. 2A). When the outermost two layers of the Au nanocuboid are replaced by Cu atoms and the probe is atop the Cu columns, the scattered intensity just beyond the central disc is significantly stronger than for pure Au (Fig. 2B), consistent with the predictions in Supplementary Note 5. This suggests a mechanism by which Cu may be distinguished from Au (or surfactant/vacuum) at the nanocuboid surface. In particular, if a detector selects and integrates the region of the diffraction pattern that is sensitive to copper (blue boxes in Fig. 2) but specifically excludes the region that is also sensitive to the structural discontinuity at the nanocuboid-vacuum interface (yellow boxes in Fig. 2), copper columns would appear much brighter than Au columns in the reconstructed image, independent of the presence of this interface. Importantly, simulations at different thicknesses (Supplementary Figs. S12, S13) indicate that this difference in intensity holds for a wide range of thicknesses, including the full range of possible thicknesses of these nanostructures and their surface layers, with no contrast reversal.

Similarly, analogous calculations show that bromine preferentially scatters electrons into the same detection range, distinguishing them from the Au columns in a similar way (Supplementary Fig. S14). This effect is less pronounced than for Cu but still greater than for Au, so that under these tailored, special imaging conditions Au atomic columns will have least intensity, Br columns will have higher intensity and Cu columns will have the highest intensity, enabling the three atomic species to be distinguished (Supplementary Fig. S15). We will call images taken under these special conditions “Cu–Br-sensitive images” (specifically, taken with 9 mrad probe convergence angle and 9–15 mrad detector angle).

While many different types of images can be reconstructed from the 4D-STEM dataset (e.g. ptychographic, differential phase contrast and centre of mass), the proposed image reconstruction is tailored specifically to the problem at hand, generating images that can be interpreted in terms of Au, Cu and Br atoms by direct inspection. This is only possible because of our a priori knowledge that these are the only elements present on or within the nanoparticle but it nevertheless provides an unequivocal approach for generating an image of the location of these elements in the nanoparticle. This tailored image reconstruction approach is not limited to this specific nanoparticle system. Given a different nanoparticle system with different target species, we can apply the same general recipe to reconstruct directly interpretable images of the nanoparticle’s species-specific, hard–soft interface (Supplementary Note 16).

Qualitative atomic model using Cu–Br sensitive imaging conditions

Using these parameters, 4D-STEM datasets were collected by a fast pixel array detector46. The position-averaged diffraction pattern (PACBED) shows that the nanocuboid is oriented near to the <100> zone axis (Fig. 3A). The total electron dose using these parameters for the 4D-STEM dataset (3.6 × 105 e/Å2 as calibrated in Fig. S16), is in the dose region where the Au–Cu additive arrangement does not change and the CTA+ surfactant layers remain largely preserved (namely, <9.9 × 105 e/Å2, as measured in Supplementary Note 2). Furthermore, the resultant image of the Au–Cu–Br structure plus continuous CTA+ surfactant layer is consistent with that imaged at a much lower dose (1.1 × 104 e/Å2 or 2 orders of magnitude less than the damage threshold) using conventional annular detectors (Supplementary Fig. S17), giving a further check that the structure in Fig. 3 has not been induced under the electron beam. This electron dose in 4D-STEM is also 4 orders of magnitude lower than that used for the EDX experiments for the detection of surface adatoms in Fig. 1A (1.7 × 109 e/Å2). Several images were reconstructed from this dataset using different parts of the angular distribution of intensity, guided by the multi-slice calculations above.

Fig. 3: Experimental 4D-STEM dataset collected by scanning a 9 mrad probe across a gold nanocuboid surface.
Fig. 3: Experimental 4D-STEM dataset collected by scanning a 9 mrad probe across a gold nanocuboid surface.
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A PACBED pattern. B Cu–Br-sensitive detector determined by multi-slice simulations. Images are reconstructed by integrating segments labelled by C A + B, and D C + D. E, F Image reconstructed by integrating the whole 9–15 mrad annular range. G Schematic surface model derived from the reconstructed images (yellow atoms – Au, blue atoms – Cu(i), Cu(ii), red atoms – Br). The leftmost dashed line is midway between the outermost Au atoms and the Cu(i) layer, while the other line demarcates the boundary between the Br and Cu(ii) layer. The relative rotation of real space and diffraction pattern is calibrated in Supplementary Note 7. Reconstructed images are scan-artefact corrected and filtered as detailed in Supplementary Note 8. Arrows in (C, F) indicate surface adatoms: Cu and Br.

The first reconstructed image (Fig. 3C) is generated by integrating the regions of the diffraction pattern identified above as preferentially sensitive to the presence of copper and bromine while simultaneously excluding any complicating signal arising from the discontinuity at the nanocuboid-adatom-counterion interface (green regions, A + B in Fig. 3B). In this way we can be confident that the highest intensity signal evident at the surface in the reconstructed image (Fig. 3C) is due to the presence of copper and the next highest intensity is due to bromine, with neither complicated by the discontinuity signal. The second reconstructed image (Fig. 3D) is generated by integrating the complementary regions, C + D, which includes the discontinuity signal. The difference in image intensity distribution between the two images can in part be attributed to the slight nanoparticle mistilt about the <100> direction, which causes a slight intensity asymmetry between segments A and B (but not in C and D, due to the mistilt direction) as shown in the PACBED pattern in Fig. 3A. (This also causes a corresponding reduction in resolution in Fig. 3C). We have investigated the effects of mistilt on image contrast (Supplementary Note 7) and found that, even in the presence of mistilt, Cu and Br can still be reliably identified (Supplementary Fig. S18).

To improve the signal-to-noise ratio and the resolution, a third image is reconstructed that uses all of the signals that are preferentially sensitive to copper and bromine, not just half of them (Fig. 3E, F). While the additional 2 detector quadrants (Fig. 3D by integrating C, D in Fig. 3B) will include some discontinuity signal, a comparison of the two Cu-Br-sensitive images with and without this signal shows a consistent form of the intensity distribution and location of the maxima, suggesting the copper and bromine signal dominates over the discontinuity signal (Fig. 3C, D, F). This is consistent with the full PACBED pattern in Fig. 3A, which only shows a very slight asymmetry between the intensity in quadrant C and D. (Note, we do not expect the discontinuity signal to be as strong as in the calculations in Fig. 2 because of the presence of the surfactant at the real interface, as opposed to the vacuum used in the idealised calculations).

In the Cu–Br-sensitive image in Fig. 3F, from left to right across the nanocuboid, we observe low intensity atomic contrast in the bulk of the gold nanocuboid, a high intensity signal at the surface (red arrow), plus a monolayer of mid-intensity maxima at a nominal distance from the surface that is significantly larger than the gold lattice spacing (blue arrow). The superior resolution of the image using the full annulus also suggests the copper distribution comprises a complete monolayer followed by a half-occupied sublayer. We formulate an initial model by ascribing these intensity maxima to Au, Cu and Br (from left to right, Fig. 3G). At this stage, this model is the most plausible, informed by the aforementioned conventional EDX and STEM experiments in Fig. 1 and the Cu–Br-sensitive 4D-STEM experiments in Fig. 3F, plus the molecular dynamics calculations previously reported41.

Note that additional images can be reconstructed from the 4D-STEM dataset which also reveal similar intensity features, such as by using non-negative matrix factorization and ptychography (Supplementary Note 10). However, unlike our direct Cu–Br-sensitive images, these reconstructed images are not interpretable without iterative calculations. While these are reassuring, they are not generated with any prior understanding of the origin of these features, unlike the directly interpretable Cu–Br-sensitive image in Fig. 3C, and therefore they are not used here to infer an atomic model. Our approach also differs from differential phase contrast (DPC), which measures electric fields using the difference between opposite segments. Instead, we sum signals from detector regions aligned parallel to the nanoparticle surface, thereby minimising contributions from surface-induced electric-field effects.

We also considered other mechanisms (other than different atomic species) that might cause bright surface contrast, for example the relaxation of surface atoms or an increase in thermal vibrations of surface atoms or atomic-scale roughness on the Au nanocuboid surface, but these were found to be unlikely (Supplementary Notes 11, 15).

Quantitative atomic structure with interatomic distances

The above provided a qualitative structural model for the nanocuboid-adatom-counterion (Au–Cu–Br) interface (Fig. 3G). To further validate and improve the model, we use the known structure of the interior of the Au nanocuboid as a reference to quantify various experimental parameters, which enables the measurement of the nanocuboid thickness profile and the interatomic distances of the nanocuboid-adatom-counterion structural model.

We first measure the thickness variation approaching the nanocuboid surface. Averaged experimental diffraction patterns from gold columns are compared to simulated diffraction patterns at different thicknesses by a template matching method (Supplementary Fig. S25). Through the thickness determination of all gold atomic columns from bulk towards the surface, we reconstruct the thickness profile of the nanocuboid (Fig. 4A).

Fig. 4: Refinement of the gold nanocuboid surface model.
Fig. 4: Refinement of the gold nanocuboid surface model.
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A Reconstructed nanocuboid thickness plot close to the nanocuboid surface. Colour bar represents thickness from 8 to 20 nm. Validation of the final model: comparison of experimental (B) and simulated (C) images with vertically integrated intensity profiles in (D) based on the atomic structure in (E) for 4 different annular ranges for the detector. E Final, quantitative atomic structure of the Au–Cu–Br interface with measured interatomic distances (as projected in <100> direction) (Au - yellow, Cu - blue, Br - red): Au–Cu(i) = 1.81 Å, Cu(i)-Cu(ii) = 1.13 Å, Cu(ii)-Br = 2.56 Å. Note the organic CTA+ surfactant is shown for illustrative purposes but has not been quantified in this work.

Knowledge of this thickness profile removes significant variables and uncertainties from image simulations and opens the possibility of quantitative measurement of the interatomic distances in our hitherto qualitative structural model of the Au–Cu–Br interface (Fig. 3G). To do this, we simulate the 4D-STEM data for this thickness-refined structural model and quantitatively compare it with the experimental dataset across different angular ranges. We adjust and refine the positions of surface Cu and Br layers to obtain a match (Fig. 4B–D). In this process, the large variety of different detector angular ranges is important to constrain the solution by ensuring the number of unknowns is much smaller than the knowns (Supplementary Note 12). This leads to refined atomic distances in projection of 1.81 Å from the last Au layer to the first copper Cu(i) layer, 1.13 Å from the first Cu(i) monolayer to the second copper Cu(ii) sublayer and 2.56 Å from the Cu(ii) sublayer to the Br- counterion layer. As a reference, the distance between Au layers are 2.04 Å. The resultant structure model is shown in Fig. 4E.

The degree of validity of this quantitative model and interatomic distances is displayed in the comparison of simulated and experimental data in Fig. 4B–D. The contrast at the nanocuboid surface observed in all four sets of images exhibits close agreement between the simulated and experimental data, despite the image streaking caused by scan noise and specimen movement (due to the relatively slow acquisition time for this first-generation pixel array detector). Moreover, the intensity profiles accurately match the simulation results, in terms of peak positions and relative peak intensities, indicating that the final quantitative structure model, including the projected interatomic distances, reliably represents the structure of the nanocuboid-adatom-counterion interface.

To better understand our experimental findings, density functional theory (DFT) calculations were performed to model the Cu-Au interface in the presence of a CTAB surfactant (N⁺(CH3)3(CH2CH2CH3) is used as the model in DFT to reduce the computational cost) (Supplementary Note 13). The optimized DFT structure revealed the experimental surface model to be a stable configuration and, more importantly, the interlayer distances between gold atoms and Cu adatoms and the Br- ions that closely match the experimental values (Fig. 4E and Supplementary Table S1). Additionally, our DFT results suggest that achieving complete Br- coverage on the Cu(ii) layer is challenging due to the interplay of steric hindrance and long-range charge interactions. Consequently, the experimentally observed projected Br- layer is likely a partially passivated configuration, with Br- ions adopting a mix of bridging and dangling binding modes. This is consistent with the variations in image intensity at Br- atomic positions in the experimental measurements (discussed in Supplementary Note 14).

Discussion

This work demonstrates an approach to determine the atomic structure at the hard–soft interface of a metal nanoparticle, grown in the presence of metal adatoms and surfactants, which has hitherto been elusive. The approach starts by using conventional methods to measure the surface profile and composition at low resolution. Using this preliminary information plus dynamical electron scattering calculations, we purpose-design an atomic resolution imaging mode that can be interpreted directly in terms of metal additives, counterions and gold atoms, while minimizing uncertainties from thickness variation, mistilt, partially occupied atomic layers and/or nanocuboid-metal additive-surfactant interfaces. Furthermore, it does this at an undamaging electron dose. From these purpose-designed images, we identify the location of metal additives, in this case copper, and the surfactant counterion (bromine) on the surface without ambiguity and generate a qualitative atomic model for the nanocuboid-metal additive-surfactant interface. We then validate and quantify this model using the full 4D-STEM data, which heavily constrains the solution (Fig. 4 and Supplementary Note 15). This approach allows for the unambiguous determination of the Au–Cu–Br surface atomic structure, including determination of the nanoparticle thickness profile and, critically, measurement of the projected interatomic distances between Au, Cu and Br at the interface. Importantly, this quantitative atomic structure provides the basis for a quantitative understanding of how the Cu and Br might modify the Au surface energy.

Notably, underpotential deposition (UPD) studies on Au(100) have proposed a pseudomorphic (\(1\times 1\)) Cu adlayer in sulfuric acid media and an (\({{{\rm{n}}}}\times 2\)) structure in chloride-containing solutions47. In contrast, our TEM-measured atomic model in a realistic CTAB environment reveals a bilayer: a fully coherent Cu (\(1\times 1\)) layer directly on Au(100), capped by a (\(\sqrt{2}\times \sqrt{2}\)) Cu layer. The Cu layer exhibits compressed interatomic spacings of 1.81 Å and 1.13 Å, indicative of a compressively strained surface. These dedicated additive layers are stabilised by halide counterions from the surfactant, which reshape the Au surface chemistry and promote anisotropic growth. We also observe that Cu additives can easily diffuse and alloy with the topmost Au layers upon surfactant loss.

Such Au–Cu–Br–CTA hard–soft interface features have been inaccessible to prior surface imaging methods, which are obscured by the organic overlayer or lack spatial resolution at the atomic-scale48,49. Importantly, rather than simple halide adsorption on Au, the metal-additive layer reorganises surfactant binding via a Cu–Br complex, increasing the halide-Au separation to ~5.5 Å, substantially larger than the ~2.5 Å predicted by theoretical calculations in the absence of Cu additives41. Together, these results show that cooperative additive-surfactant interactions govern surface modification far more than UPD or surfactant adsorption considered in isolation.

DFT calculations agree reasonably well with this experimentally measured structure and interatomic distances. Furthermore, it provides insights into the two primary configurations of the binding of bromide to the Cu(ii) atom, namely, in a dangling and bridging mode. This also accounts for some variations in image intensity at the bromide site. This provides direct evidence for nanoparticle growth mechanisms which propose control of nanoparticle growth via underpotential deposition of metal additives47,50. It is the complex nature of this surface which leads to symmetry breaking and the formation of the single-crystal nanocuboid products.

The nanocuboid surfaces appear to be encapsulated by the organic CTA+ surfactant layers, including the facets at cuboctahedra corners (Supplementary Note 14) (noting the caveat that we are looking at the surface in projection). While the distribution of the organic surfactant appears largely continuous, the Cu additive and the Br- counterion distribution is more heterogeneous. There are ad hoc regions a few atoms in projected length with reduced or no Cu and/or Br. Furthermore, surface variations of one or two Au atomic layers are observed in some places on the Au nanocuboid facets, causing some atomic-scale surface roughness.

If we are to understand how metal additives and surfactants control the energy of tiny nanoparticle facets and, in turn, control their growth and chemical activity, we need to know the atomic structure of the nanoparticle-additive-surfactant interface. That is, we need to know whether and where the metal additives and surfactant counterions are positioned relative to the nanoparticle surface. Moreover, we need to know this precisely. Different atomic configurations and interatomic distances will generate very different surface energetics, atomic mobility and chemical reactivity. We need ways to measure this but these hard–soft interfaces present an extreme measurement challenge, comprising just one to three atomic layers of heavy and light atoms sandwiched between a heavy metal nanoparticle and a thick organic surfactant overlayer. Here we have presented a systematic 4D-STEM imaging approach to measure this class of complex hard–soft interface by mining the full diffraction pattern for the components preferentially sensitive to the atom species of interest (workflow in Supplementary Fig. S33). Relative to conventional STEM, 4D-STEM (such as ptychography, DPC) and STEM-EDX methods, this approach can deliver higher interface sensitivity at reduced dose, enabling directly interpretable images of the nanoparticle-additive-counterion interface. We provide a recipe, workflow and further example simulations in Supplementary Note 16 to provide practical guidelines for selecting contrast windows to image hard–soft interfaces in other metal nanoparticle systems with other, additives, and ligand/halide chemistries, underscoring the general applicability of the approach beyond the Au–Cu–Br–CTA system considered here.

Applying this approach, we have demonstrated the measurement of a hard–soft interface in Au nanocuboids grown in Cu-additives and CTAB. Specifically, this provided concurrent identification and positioning of Au surface atoms, Cu adatoms, Br anions and the CTA+ counterion layer at sub-Ångström precision, including interatomic distances and registry to specific Au facets. This revealed an unanticipated interface structure and interatomic distances, in contrast to previous underpotential deposition studies of Au {100} surfaces in other media47. This includes:

  1. (1)

    a Cu bilayer on Au comprising a coherent (\(1\times 1\)) layer capped by a (\(\sqrt{2}\times \sqrt{2}\)) layer.

  2. (2)

    compressive surface strain with projected Au–Cu–Cu spacings of ~1.81 Å and ~1.13 Å.

  3. (3)

    Cu–Br co-localization that reorganizes surfactant binding into Cu–Br–CTA motifs, displacing the halide plane to ~5.5 Å from the Au surface (cf. ~2.5 Å in Cu-free models41).

  4. (4)

    heterogeneity in inorganic additives and counterions coverage and homogeneity in organic surfactants coverage on {100} side facets.

These coordinates, distances, and correlations provide the quantitative inputs essential for facet-specific surface-energy calculations. Without these, arguments about the influence of metal additives and surfactants on surface energies and hence crystal growth and shape control are purely speculative. When coupled with kinetic models, this precise atomic-structure and interatomic distances can provide critical information, currently missing, towards explanations of anisotropic growth and enable predictions for catalytic activity and surface stability.

Methods

Chemicals

Gold (III) chloride trihydrate (HAuCl4·3H2O) (≥99.9%), copper (II) chloride (CuCl2) (≥99.999%), sodium borohydride (NaBH4) (≥99.9%), and L-ascorbic acid (≥99.9%) were purchased from Sigma-Aldrich. Hexadecyltrimethylammonium bromide (CTAB) (98%) was purchased from Ajax Finechem. Ultrapure water (milli-Q, R > 18.2 MΩ·cm) was used for the preparation of all solutions. All glassware used for the syntheses were cleaned using aqua regia prior to use.

Gold nanocuboid synthesis

Seeds

Aqueous solutions of CTAB (1.875 mL, 0.2 M), HAuCl4 (0.025 mL, 0.05 M) and milli-Q water (2.83 mL) were mixed thoroughly. Aqueous NaBH4 solution (0.3 mL, 0.01 M) was then rapidly added into the solution with vigorous stirring, and stirred for an additional 10 min. The resulting seed solution was kept at 28 ± 1 °C for 40 min prior to use. The seed solution was diluted 10 times with milli-Q water, immediately prior to the further use for growth of gold nanocuboid.

Growth

Aqueous solutions of CTAB (1 mL, 0.2 M) and HAuCl4 (0.1 mL, 0.05 M) were mixed with milli-Q water (11.38 mL). The resultant solution was thoroughly stirred and left for at least 5 min to ensure homogenisation. Aqueous ascorbic acid solution (1.5 mL, 0.1 M) was then added, mixed thoroughly, and after 5 minutes, aqueous CuCl2 (27 μL, 0.01 M) was added, and mixed thoroughly. After 1 minute, the diluted seed solution was added and mixed thoroughly. The nanocuboids were then grown for 48 hours, at 28 ± 1 °C. The nanocuboids were purified via centrifugation and redispersion to give a final concentration of CTAB of 0.001 M.

TEM experiments

The ultrathin carbon coated Cu TEM grids were plasma cleaned in H2/O2 for 30 s before use. A sample of the cleaned nanocuboids was immediately dropped onto the TEM grid and left for 5 min. The grid was placed into ultra-pure ethanol for 20 min to remove excess CTAB. Plasma cleaning was avoided to retain the pristine CTAB attached to the nanoparticles. For imaging the organic CTA+ surfactant, graphene coated TEM grids were used. For EDX experiments, SiN TEM grids were used.

Electron microscopy was carried out at the Monash Centre for Electron Microscopy (MCEM) on a FEI Titan3 80–300 kV FEGTEM and a Thermo Fisher Scientific Spectra φ FEGTEM equipped with both probe and imaging spherical aberration correctors for (S)TEM. Conventional STEM experiments were carried out at 300 kV with a 15 mrad probe-forming aperture and 4D-STEM experiments with a 9 mrad probe-forming aperture. 4D-STEM datasets were recorded with a hybrid pixel array detector (electron microscopy pixel array detector, or EMPAD) at 1 kHz framing rate.

CBED simulations

Images and diffraction patterns were calculated using a GPU-enhanced frozen-phonon multi-slice code (μSTEM)43, including multiple elastic scattering and multiple thermal diffuse scattering. Simulation parameters were matched as closely as possible to the measured experimental setup, namely a probe convergence angle of 9.35 mrad, defocus of 0.4 nm, and a specimen tilt of 1.3 mrad away from the [001] zone axis. 30 unique phonon configurations were incoherently assumed to ensure convergence of the frozen-phonon calculations.

DFT calculations

All DFT calculations were carried out using the QUICKSTEP module within the CP2K software package51,52. Gas-phase geometries were fully optimized at 0 K using the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA) density functional53. The Goedecker-Teter-Hutter (GTH) pseudopotentials were employed in combination with the double-ζ valence-polarized (DZVP-MOLOPT-SR-GTH) basis set. Convergence criteria were set to an energy threshold of 10⁻⁶ Hartree and an atomic force threshold of 4.5 × 10⁻⁴ Hartree/Bohr54,55. Gamma point sampling was used for the k space sampling. To model the extended system, a 20 Å vacuum layer was introduced perpendicular to the Au(100) facet to prevent interactions between neighbouring cells along this direction. Periodic boundary conditions (PBC) were applied in the remaining two directions.