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CuAu, a hexagonal two-dimensional metal

Growth of two-dimensional metal structures has eluded materials scientists since the discovery of the atomically thin graphene and other covalently bound 2D structures. Here we report a two-atom-thick hexagonal copper-gold alloy, grown through thermal evaporation on freestanding graphene and hexagonal boron nitride. Islands with sizes up to tens of nanometers were grown, but there should be no fundamental limit to their size. The structures are imaged at atomic resolution with scanning transmission electron microscopy and further characterized with spectroscopic techniques. Electron irradiation in the microscope provides sufficient energy for the crumpling of the 2D structure---atoms are released from their lattice sites with the gold atoms eventually forming face-centered cubic nanoclusters on top of 2D regions during observation. The presence of copper in the alloy enhances sticking of gold to the substrate, which has clear implications for creating atomically thin electrodes for applications utilizing 2D materials. Its practically infinite surface-to-bulk ratio also makes the 2D CuAu particularly interesting for catalysis applications.

The discovery of graphene in 2004 [1] was quickly followed by an effort to expand this new class of two-dimensional materials, with several notable successes. For example, monolayers of elemental 2D materials [2,3,4,5,6,7,8,9,10,11], hexagonal boron nitride (hBN) [12], transition-metal mono-and dichalcogenides [13,14], as well as a number of other materials [15] have been reported. The interest in 2D materials can be traced back to the extraordinary properties of graphene [1,16,17,18], the changes in materials' properties when the dimensionality is reduced [19], and the possibility for creating heterostructures with atomically thin materials without the need of epitaxy due to the weak van der Waals interaction between most 2D materials [20]. So far, the discovered 2D materials share covalent intralayer bonding, although some of the structures have a metallic character. While 2D structures consisting of metallic bonding have been sculpted within other structures by removing the non-metallic atoms or thinning a bulk structure [21,22], typically through electron irradiation, no 2D structures with metallic bonding have until now been grown on weakly interacting substrates.
Metallic bonds are nearly isotropic and thus lack the spatial preferences typical for covalent bonds. This leads to the close packed crystal structures typical for metals. Very small gold clusters provide a curious counter-example: when they contain less than 14 atoms, they tend to have flat structures. With increasing number of atoms, however, gold also turns threedimensional [23]. This preference, together with weak bonding with other elements, means that covering surfaces with thin layers of gold presents a challenge for example when creating electric contacts on surfaces through lithography. This is typically solved using an adhesive layer, for example of chromium, between gold and the substrate.
Gold forms alloys with a number of other metals, including copper. The CuAu system is well known in bulk form and displays a variety of structures depending on stoichiometry and temperature [24]. Its stoichiometric phase forms a tetragonal (elongated face centered cubic) L1 0 phase. Cu as well as Au and its bimetallic alloys have recently garnered increasing interest for applications, e.g. in catalysis and plasmonics. While Cu has been recognized as a viable catalyst for some time [25,26], for CuAu and Au this has not been the case. In fact, bulk Au is virtually inert. However, as the size of the structures is reduced in some dimensions down to the nanometer regime, Au displays increased catalytic activity-most notably for CO oxidation at sub-ambient temperatures [27,28]. Recent efforts to reduce the dimensionality of Au even led to sub-nanometer thick Au nano-sheets, grown with a confining agent to non-uniform crystallinity, exhibiting pronounced catalytic performance [29]. For bimetallic CuAu alloy nanoparticles only few studies on its catalytic reactivity have been reported so far. They have however indicated that it could be used in fine-tuning reactivities observed in Au nanoparticles [30,31].
Generally, two-dimensional materials with their high surface-to-bulk ratio represent a promising route to reduce the cost of catalysts. The size and shape of Au nanoparticles can also impact the photonic response, used for example in photoacoustic imaging [32], which is tunable with a bias voltage for particle thicknesses under some nm [33]. The plasmonic response of low Cu-content CuAu nanocrystals was also already used in photothermal therapy [30], and tunable plasmon responses are predicted also for other atomically thin noble metals [34].
Here we report for the first time the growth of a two-dimensional structure with metallic bonds on weakly interacting substrates. The growth of the stoichiometric CuAu alloy is carried out through thermal evaporation of gold at 1080 • C directly onto free-standing graphene and hBN membranes that contain copper from the growth of the substrate material itself. In situ cleaning of the samples and their atomic-resolution after-growth imaging were carried out with the Nion UltraSTEM 100 microscope in Vienna at 60 kV and 80 kV with the high-angle annular dark field (HAADF) detector. Additional energy-dispersive X-ray spectroscopy (EDX) was carried out to confirm the elemental composition of the material. The discovered structure consists of a hexagonal two-atom-thick lattice, matching the atomic arrangement in the (111) plane of face centered cubic (fcc) lattice, where all gold atoms are in the first layer and all copper atoms in the second one. Under continuous electron irradiation in the microscope, gold atoms are released and migrate on top of the structure, initiating the formation of fcc gold nanoclusters, demonstrating the weak coupling of the gold atoms with the substrate and their preference for a close-packed structure.

Experimental
Commercially available graphene and hBN monolayers, grown by chemical vapour deposition on copper substrates, were deposited on perforated SiN transmission electron microscopy grids. Such prepared freestanding 2D materials with an abundance of Cu left over from the sample growth served as substrates for the subsequent experiments. After preparation, the substrates were transferred into a ultra-high vacuum (UHV) setup (base pressure 10 −9 mbar) in Vienna [35] connecting through a vacuum transfer system several independent experimental setups, including a customized [36] Nion UltraSTEM 100 [37] aberration-corrected scanning transmission electron microscopy (STEM) instrument and a Knudsen cell thermal evaporator.
Graphene substrates were first imaged and subsequently cleaned in the microscope column with a high-power laser [38] to obtain large areas of contamination-free monolayer graphene substrate. Spectroscopic pre-characterisation was carried out in situ with electron energy-loss spectroscopy (EELS) confirming abundand copper (see Supplementary Information Fig. S1).
Au was deposited onto the substrates in UHV at 1080 • C. The resulting structures were imaged at atomic resolution via STEM. On the contrary, hBN substrates were not cleaned prior to deposition, resulting in smaller (∼ 5 nm) metallic islands after Au deposition due to hydrocarbon contamination on the substrate, reducing the mobility of Au and acting as nucleation site [39].
A typical STEM HAADF image recorded at 60 kV of the metallic islands on graphene can be seen in Fig. 1a. The HAADF intensity is proportional to the atomic number of the scatterer [40] and the thickness of the imaged location of the sample. Large areas of the graphene substrate appear dark with a uniform contrast, due to the lack of hydrocarbon contamination or metal clusters. On more active sites, such as grain boundaries (gb) or folds, contamination and brighter nanostructures can be seen. Smaller clusters (white triangle) display increasing intensity with size, indicating spherical structures (nanoclusters) for which the thickness increases with the size of the particle. Other structures consisting of metal atoms based on their intensity are much larger in size and display uniform intensity (yellow triangle). In Fig 1b such a larger structure is shown at higher magnification, which reveals an ordered flat arrangement of atoms with overall uniform intensity and only some thicker regions at the edges. The Fourier transforms (FT) of the structure (red box) and the underlying graphene substrate (blue box) are compared in Fig. 1c,d. The FT of the grown two-dimensional structure (Fig. 1c) reveals a hexagonal symmetry, typical for two-dimensional materials and in contrast to the previously reported AuC structure [41]. Comparing it to the graphene substrate (Fig. 1d) shows a different lattice constant (ca. 0.268 nm as compared to 0.246 nm) and orientation. This suggests that it is not epitaxial with graphene, typical for a weakly bound material [42]. Increasing the magnification further (inset of Fig. 1b) reveals that the structure consist of two different elements, reflected in the different scattering intensity, in a one-to-one stoichiometry and confirms their hexagonal arrangement, as already seen in the FT.
The small size and electron-irradiation sensitivity of the structures as well as the overlap of gold O 2,3 and copper M 2,3 EELS peaks prevented direct in situ characterization after the growth (see Supplementary Information Fig. S1). Instead, we carried out further characterization through EDX spectroscopy with an image-side corrected FEI Titan 80-300 transmission electron microscope in the STEM mode. For this, we first characterized a hBN substrate with a number of relatively small grown islands via STEM ( Fig. 2a-b), and subsequently transferred the sample through air to the other microscope. The atomic resolution STEM images revealed both types of structures (larger flat ones marked with the yellow triangle as well as the smaller three-dimensional ones, white triangle). A similar sample area was then found in the other microscope, and several point spectra and a spectral map were recorded at 80 kV. The results of the 3 × 3 pixel spectral map for the cluster marked in Fig. 2c are shown in Fig. 2d-g. The only significant peaks in the EDX spectra recorded on top of the cluster (in addition to carbon) were from Au and Cu, for which the peak intensities are shown in the maps in Fig. 2e and f, respectively (white marks the pixel with the highest intensity and other pixels are shown in gray scale reflecting the corresponding measured intensity). Clearly, the structures with uniform contrast contain only copper and gold, and those elements are limited exactly to the locations of these structures (the three-dimensional clusters contain mostly gold, but also pure copper and gold-copper clusters are found on the samples). The image recorded after the spectrum map ( Fig. 2g) reveals that the electron-beam exposure has crumpled the originally flat structure into a three-dimensional nanocluster. This is a common feature for all observed structures, and will be discussed further below.

Structure
Atomic resolution images revealed a metallic two-component hexagonal structure that according to spectroscopic analysis consists of copper and gold atoms that appear to be in a stoichiometric configuration. To confirm that such a structure is indeed possible, we turn to density functional theory (DFT). The atomic structure, as relaxed by the simulations, is shown in Fig. 3a. The in-plane lattice constant is found to be 0.268 nm, in excellent agreement with the experimental estimate of 0.268(2) nm. The calculated inter-layer distance between the copper and gold planes is 0.224 nm. Fig. 3b compares an image simulation (left, simulated using PyQSTEM [43,44] with parameters corresponding to the experiments) to an experimental image (right) showing again excellent agreement. This structure is reminiscent of the bulk tetragonal L1 0 phase cut along the (102) lattice plane and including adjacent layers of gold and copper (see Supplementary Information Fig. S2), with the important difference that in order to obtain the perfect hexagonal arrangement of the atoms, a c/a = 1/ √ 2 is required, instead of the for bulk measured ca. 0.93 [24]. This ratio, when applied to the bulk structure would lead to an interplane distance of 0.056 nm between the Cu and Au planes. In the actual 2D structure the distance between these planes is hence nearly four times larger to compensate for the much shorter c as compared to bulk. Based on electronic band structure calculations (see Supplementary Information Fig. S3), the 2D structure has a similar metallic character as bulk metals, and is not magnetic. Finite temperature molecular dynamics simulations (1 fs time step, 300 K, 50 Cu and 50 Au atoms) reveal that the 2D CuAu structure is stable against thermal fluctuations.
However, there exists a buckled configuration that is energetically close to the flat ground state configuration (see Supplementary Information Fig. S4). Thus, upon structural disturbances, 2D CuAu can have a tendency for buckling out of plane. This instability is observed experimentally during electron irradiation, as described below.

Crumpling
Electron beam-driven structural changes are common during transmission electron microscopy, especially in thin structures, such as 2D materials [45]. In small gold clusters imaged at higher acceleration voltages (200 kV) electron irradiation has been shown to lead to continuous phase changes [46]. Also the 2D CuAu structures are prone to electron beam damage despite the low transferred energies, but in a unique way (a typical experiment is shown in the Supplementary Information Fig. S5). This is likely due to the tendency for buckling that can make the structure locally unstable upon electron impacts. Indeed, already the lowest electron doses required for atomic resolution imaging tend to lead to changes at the edges of the structures where a clear reduction of area is visible while the thickness increases due to local crumpling. At the same time, small vacancy-type defects appear inside the structure, growing to larger defects with increasing electron irradiation dose.
To understand how the crumpling proceeds, we recorded atomically resolved images ( Fig.   4a-c) of the process for a monolayer region adjacent to an already formed thicker cluster. During the STEM image acquisition (16.5 seconds per image), a third layer of atoms is appearing on top of the initially two-atom-thick structure (Fig. 4b). The additional layer completes within the acquisition of the image, and a few atoms have already started to create a fourth atomic layer on top of the structure in Fig. 4c. The layer-by-layer growth follows the hexagonal close packed structure, which for a one-component material would correspond to α − β − γ stacking in the [111] lattice direction of the fcc structure, as illustrated in Fig. 4d-f. In agreement with the experiment, DFT calculations show that gold adlayers on CuAu are favourable over small three-dimensional gold clusters (see Supplementary Information Fig. S6). However, as is clear from other experimental images (see Supplementary Information Fig. S5), eventually the crumpling leads to more three-dimensional shapes and finally to the formation of nanoclusters.

Conclusions
We have demonstrated the first two-dimensional material with metallic bonding. The material was grown via thermal evaporation of gold on free-standing graphene and hBN samples containing left-over copper from their own growth process, creating thus van der Waals heterostructures with each of the substrate materials. It consists of separate layers of copper and gold atoms, which each have a trigonal intralayer symmetry, separated by 0.224 nm to form a hexagonal structure with an in-plane lattice constant of 0.268(2) nm. The lattice is similar to two adjacent (102) atomic planes of the bulk L1 0 CuAu crystal, with the significant difference that for the hexagonal structure a c/a ratio of exactly 1/ √ 2 is required instead of the bulk value of ca. 0.93 and the distance between the copper and gold layers is significantly larger. In the twodimensional structure the spins are paired and no magnetism is predicted. Due to its metallic nature and atomic thinness it could be a beneficial electrode material for applications utilizing 2D materials and their heterostructures. Because the 2D structures anchor at contamination sites on the substrate, such structures could also be patterned via electron-beam-induced deposition [39]. Catalytic and electro-optical performances of Au and CuAu make the exploration of such properties for this resource-conserving and straightforwardly produced novel material intriguing.

Sample Preparation
Commercially available graphene (Graphenea Inc.) and hBN monolayers (Graphene Laboratories Inc.), grown by chemical vapour deposition on copper substrates, deposited on perforated SiN transmission electron microscopy grids were used as substrates for the growth. Graphene substrates were cleaned in the column of the STEM with a high-powered laser (6 W) to obtain large clean areas. Connected in the same UHV-setup, Au was deposited (Knudsen Cell thermal evaporator at 1080 • C) onto the substrates, with abundand Cu left from the growth substrate.

Microscopy and Spectroscopy
Scanning transmission electron microscopy high-angle annular dark field images were acquired with a Nion UltraSTEM 100 in Vienna (annular range 80-300 mrad, convergence semiangle 30 mrad). Electron energy loss spectroscopy measurements were carried out in the same microscope with a Gatan PEELS 666 spectrometer, retrofitted with an Andor iXon 897 electronmultiplying charge-coupled device camera. Energy-dispersive X-ray spectroscopy measurements were carried out at an image-side corrected FEI Titan 80-300 transmission electron mi-croscope equipped with an EDAX spectrometer.

Simulations
DFT simulations were performed using the Vienna Ab initio Software Package (VASP) [47,48], adopting the strongly constrained and appropriately normed (SCAN) functional [49,50] with an energy cut-off of 500 eV. Structural optimization was carried out for the unit cell containing two atoms. Finite temperature molecular dynamics simulations and comparison of 2D and 3D adstructures were carried out for a 2D CuAu structure with 50 Cu and 50 Au atoms (with additional 12 Au atoms in the latter case). STEM image simulations were carried out using PyQSTEM [43,44].

Data availability
All data needed to evaluate the conclusions in the paper are present in the paper or the Supplementary Information. All original microscopy images, spectra and computational structure files are available through [51].   Figure 1: STEM HAADF images of CuAu on a graphene substrate. a, Overview of graphene substrate with nanostructures of different sizes and shapes that appear on or close to grain boundaries (gb) or folded-over graphene. The larger structures (marked by yellow triangles) display characteristic, uniform low intensities, indicating a flat structure with a comparably low thickness. Other structures (marked by white arrows) display size-and shape-dependent intensities indicating their three-dimensional nature. b, Higher magnification overview image shows that the uniform structures are crystalline. The inset (with overlay) reveals that they consist of two different kinds of atoms arranged into a hexagonal lattice. c,d, Fourier transforms taken from within the red (flat nanostructure) and blue (graphene) squares, respectively. The differing orientations of the two structures are clearly visible through the overlaid hexagons. All images were recorded at 60 kV. . c, Two adjacent (102) planes for the structure of (a) corresponding to trigonal arrangements of Au in the first plane (yellow atoms) and Cu in the second one (orange atoms), and the atoms from those two planes shown together from the same perspective. The height difference between the Au and Cu planes as calculated from the structure is h ≈ 0.056 nm, which is nearly four times shorter than what is obtained computationally for the actual 2D structure (0.224 nm). The flat structure is more stable with a lattice constant of a = 0.268 nm and an interlayer distance of ∆z = 0.224 nm. By applying compressive strain, the structure is driven towards a phase transition: at a = 0.26 nm, the Au atoms buckle out of the plane (∆β = 0.079 nm); larger compressive strains further enhance the buckling (see the table included in the figure). Conversely, the Cu layer remains flat upon compression. We relate this different behaviour to the different lattice constants of the Au and Cu free-standing monolayers (0.269 nm and 0.244 nm, respectively, as calculated by DFT). On the one hand, the small energy difference of ∆E = 80 meV between the buckled structure and the ground-state determine a dynamical instability at finite temperatures, as discussed in the main text. On the other hand, the flat structure is stable upon tensile strain, and it continuously decreases the interlayer distance up to stabilizing a quite flat monolayer of both Cu and Au atoms (∆E = 1.25 eV).  Figure 5: Electron irradiation effects on monolayer CuAu. Electron irradiation causes the material to crumple (0 − 39 s)-regions on the rim vanish from the interaction with the electron beam while at the same time brighter clusters appear on the 2D metal. Further irradiation (48 − 100 s) creates holes in the 2D material and enlarges them, while the clusters grow. In severely damaged 2D regions the crumpling process can be highly dynamic (182 − 301 s & 726 s) with sections disappearing during and between scans. Moving to another location on the 2D structure (497 s), reveals a mostly intact crystal. Defects in the crystal can also be healed (497 − 540 s), most likely from mobile Au and Cu from the crumpling process. Ultimately, the whole 2D structure transforms (1729 s) into a set of 3D nanoclusters. All images were recorded at 80 kV.