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# Reversible superdense ordering of lithium between two graphene sheets

## Abstract

Many carbon allotropes can act as host materials for reversible lithium uptake1,2, thereby laying the foundations for existing and future electrochemical energy storage. However, insight into how lithium is arranged within these hosts is difficult to obtain from a working system. For example, the use of in situ transmission electron microscopy3,4,5 to probe light elements (especially lithium)6,7 is severely hampered by their low scattering cross-section for impinging electrons and their susceptibility to knock-on damage8. Here we study the reversible intercalation of lithium into bilayer graphene by in situ low-voltage transmission electron microscopy, using both spherical and chromatic aberration correction9 to enhance contrast and resolution to the required levels. The microscopy is supported by electron energy-loss spectroscopy and density functional theory calculations. On their remote insertion from an electrochemical cell covering one end of the long but narrow bilayer, we observe lithium atoms to assume multi-layered close-packed order between the two carbon sheets. The lithium storage capacity associated with this superdense phase far exceeds that expected from formation of LiC6, which is the densest configuration known under normal conditions for lithium intercalation within bulk graphitic carbon10. Our findings thus point to the possible existence of distinct storage arrangements of ions in two-dimensional layered materials as compared to their bulk parent compounds.

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## Data availability

The data that support the findings of this study are available from the corresponding authors on request.

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## Acknowledgements

We acknowledge financial support from the Baden-Württemberg Stiftung gGmbH (project CT 5) and from the European Union Graphene Flagship. We are grateful to FEI/ThermoFisher Scientific for providing drawings and specifications of the NanoEx-i/v holder. F.B., J.B. and U.K. acknowledge funding from the German Research Foundation (DFG) and the Ministry of Science, Research and the Arts (MWK) of the federal state of Baden-Württemberg, Germany, in the frame of the SALVE project. A.V.K. thanks the Academy of Finland for support under project number 286279 and the DFG under project KR 4866/1-1. The theoretical study of Li diffusion (A.V.K.) was supported by the Russian Science Foundation (project identifier, 17-72-20223). We thank K. v. Klitzing for discussions and support and J. Popovic for useful comments on the manuscript. We acknowledge CSC Finland and PRACE (HLRS, Stuttgart, Germany) for generous grants of CPU time.

### Reviewer information

Nature thanks I. Honma and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

J.H.S. and U.K. composed the project. M.K. and S.F. fabricated samples and performed electrochemical measurements. F.B. performed the TEM and EELS experiments. M.G. and A.V.K. did the DFT calculations. J.B. helped with TEM and EELS experiments and did TEM imaging simulations. U.K. supervised the TEM work. D.S. contributed to the electrochemical design of the experiment. M.K. and J.H.S. wrote the manuscript and all authors contributed to it.

### Competing interests

The authors declare no competing interests.

Correspondence to Ute Kaiser or Jurgen H. Smet.

## Extended data figures and tables

### Extended Data Fig. 1 Atomic resolution SALVE TEM images of lithium.

a, Original TEM image (acquired between Fig. 2b, c). b, Same as a, but with graphene signals filtered out. c, Magnified view of area shown boxed in b. d, Slightly Gauss-filtered version of c. e, Same as d, but with red and blue circles indicating single Li atoms and symmetric positions without Li atoms, respectively. The latter show that the contrasts are not delocalization artefacts. f, Line profiles of the imaging contrast, centred on two neighbouring, individual Li atoms (left panel) and on the negative atomic contrast of a missing C atom in one graphene sheet, artificially inserted by the filtering procedure (right panel). The red arrows and red dashed lines indicate the signal intensity of the respective atomic species. g, Fourier-filtered version (bilayer graphene lattice removed) of a TEM image acquired during lithiation at t = 266 s (bottom image), between Fig. 2b, c. The top row shows two zoom-ins centred on locations where the line profiles in f have been extracted. h, Temporal evolution of the C vacancy in one of the two graphene sheets from which the line profile in g has been extracted at t = 266 s. Each row corresponds to data from a single time: left, magnified sections of our TEM images as acquired; right, the same sections after the removal of the graphene lattice by Fourier filtering. Scale bars, 1 nm.

### Extended Data Fig. 2 80 kV SALVE TEM image simulations.

a, b, Atomistic model of a hexagonal close-packed Li wedge (red), with five additional single Li atom rows at its left edge as well as with single-atom vacancies, between two graphene sheets (cyan). Shown are a three-dimensional representation (a, top), a side view (a, bottom), and a top view of its thin front without C lattices (b). ce, 80 kV dose-limited (applied dose 2 × 106 e nm−2) TEM image simulations. c, Embedded in graphene. d, Fourier-filtered image with graphene removed. e, Unfiltered image simulated without graphene. In d and e, the yellow arrows mark single Li atoms and the white arrows point to a vacancy in the Li lattice. f, g, Image simulation of wedges of two different close-packed Li systems (cubic and hexagonal shown at left and right, respectively). f, Atomistic model used for the simulations, showing side and top views. The thickness gradually increases by one layer from left (one layer) to right (six layers). g, Image simulations for two different values of defocus, seen along [111] for cubic close-packed Li and along [0001] for hexagonal close-packed Li. The von Hann-filtered Fourier transforms on the right (diffractograms) are calculated for 4 layers at +6 nm overfocus. For the simulation the corresponding experimentally measured electron dose was applied.

### Extended Data Fig. 3 Fourier filtering.

Filtering mask for removing the graphene lattice and the moiré effects. a, Portion of the signal cut out by the applied mask. b, Remaining Fourier transform. The streaking (indicated by yellow arrows) results from the edges of the real image and was not Fourier-filtered to avoid masking too-large portions of Fourier space.

### Extended Data Fig. 4 Thickness determination of crystalline Li.

a, Main panel, Fourier-filtered TEM image. Dashed lines demarcate major edges enclosing regions of the Li phase with approximately constant thickness. Two-coloured lines demarcate grain boundaries. Fourier transforms from two selected regions of different thickness (yellow boxes) are shown on the right. Signals from the Li phase in the Fourier transforms for both regions lying within one grain are identical. bd, Magnified views of selected areas of the TEM image (white boxes) in a. e, f, Relative thickness determination from contrast quantification. e, Fourier-filtered TEM image (graphene lattice removed), identical to the main panel in a. Dashed lines demarcate major edges enclosing regions of the Li phase with approximately constant thickness. Arrowheads point outwards from thicker areas. f, Area-normalized intensity histograms acquired from the shaded regions in e that are labelled i, ii and iii. The full-widths at half-maximum (FWHMs) are indicated by white double-headed arrows.

### Extended Data Fig. 5 Electron energy-loss spectroscopy.

a, Low-loss EEL spectra of pristine (blue) and lithiated (yellow) bilayer graphene, with the close-packed Li phase present in the latter case. b, Calculated ELNES (electron energy loss near-edge structure; Methods) of the Li-K edge for bilayer graphene containing 1, 2 and 3 Li layers compared to the experimental ELNES. The spectrometer broadening is taken into account by convoluting the result with a Gaussian function. Two different broadenings have been considered (left and right panels). The spectrometer broadening is given as the FWHM of the respective Gaussian function.

### Extended Data Fig. 6 Atomic configurations and energetics of a single layer of Li atoms between two graphene sheets.

a, b, Structural evolution of a finite single-layer cluster of Li atoms between two graphene sheets with different stacking: AA-stacking (a) and AB-stacking (b). Left and right structures are before and after relaxation (that is, energy minimization); top and bottom are top and side views, respectively. The relaxation gives rise to the formation of a system with a geometry close to the C6LiC6 configuration. Note that the configurations correspond to a local, not global, energy minimum. c, d, The periodic C6LiC6 configuration with Li atoms arranged in a commensurate $$\left(\sqrt{3}\times \sqrt{3}\right){\rm{R}}3{0}^{\circ }$$ superstructure between graphene sheets for AA stacking (c) and AB stacking (d). dLi-Li refers to the separation of Li atoms. Double-headed arrows indicate the spacing between graphene sheets. e, f, Electron density difference between the combined system and its isolated parts. Red colour corresponds to a decrease in the electron density, blue to an increase. Charge transfer between Li and graphene (with an average value of 0.85 electrons per Li atom) is clearly observable.

### Extended Data Fig. 7 Atomic configurations and energetics of Li bilayers between two graphene sheets.

a, The geometric arrangement of the atoms of a finite bilayer cluster of Li atoms encapsulated between two graphene sheets after energy minimization for two different rotation angles θ between the Li and C lattices. The original configuration of the cluster was the perfect h.c.p. lattice. The structure is largely preserved during the relaxation. The distance between the Li atoms is denoted as dLi-Li. A very weak dependence on the angle between graphene and h.c.p. lattice is found, as shown in the table at right. b, Atomic configurations and energetics of the infinite commensurate Li bilayer h.c.p./graphene structure and the dependence of the energy on the orientation angle θ between surfaces. Very weak dependence on the angle between graphene and the h.c.p. Li lattice is found. A small amount of strain introduced into the system to make the graphene and Li lattices commensurate affects the results by no more than 0.01 eV, as evident from the tables presenting Ef for different θ.

### Extended Data Fig. 8 Atomic configurations and energetics of Li multilayers between two graphene sheets.

a, b, Atomic configurations and energetics of the infinite commensurate Li trilayer with h.c.p. structure between two graphene sheets for AA stacking (a) and AB stacking (b). c, Main panel, charge transfer from Li to graphene as a function of the number of close-packed Li layers NLi between two graphene sheets. The corresponding atomic configurations are shown above the plot. The blue values are obtained as ΔqLi = q0 − qLi, where qLi is the charge of Li after intercalation and q0 is the charge of the isolated Li atom. Since the charge transfer is relevant for outermost Li layers only, we also plot the full charge transfer renormalized by the number of Li atoms in these outermost Li layers without considering the other Li layers (purple). d, e, Energy difference between different possible close-packed configurations (stacking orders), calculated for three layers of Li between two graphene sheets (d) and four layers of Li between two graphene sheets (e). To illustrate the stacking order, below each top view we include a side view of atoms within the red rectangle. The energy differences with respect to each f.c.c. case are stated below the side views.

### Extended Data Fig. 9 Registry of graphene layers.

a, b, Successive SALVE TEM images at different defocus values before lithiation (a) and after delithiation (b). The red lines are guides for the eye. We do not observe a change in registry of the two graphene sheets when comparing TEM images of the graphene lattice before lithiation and after delithiation. The registry can be checked at sites where one of the two graphene sheets features a moderately big hole. The stacking is AB without any sign of change throughout the experiment.

### Extended Data Fig. 10 Lateral diffusion of a Li atom inside the close-packed Li system confined between two graphene sheets.

a, b, Schematic atomistic configuration (top and side view). The red sphere represents the extra interstitial Li atom. c, Schematic of the diffusion process. d, The actual initial/final positions of atoms. The yellow and blue transparent triangles in c and d mark the initial and final configurations of the interstitial atom with regard to the nearest Li atoms in the undistorted (c) and the optimized (d) structures. The red and blue arrows connect the initial and final positions of the diffusing atoms.

## Supplementary information

### Video 1

TEM image sequence TEM image sequence showing the propagation front of a Li crystal forming inside bilayer graphene during lithiation

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• #### DOI

https://doi.org/10.1038/s41586-018-0754-2