Atomic imaging of the edge structure and growth of a two-dimensional hexagonal ice

Abstract

The formation and growth of water-ice layers on surfaces and of low-dimensional ice under confinement are frequent occurrences1,2,3,4. This is exemplified by the extensive reporting of two-dimensional (2D) ice on metals5,6,7,8,9,10,11, insulating surfaces12,13,14,15,16, graphite and graphene17,18 and under strong confinement14,19,20,21,22. Although structured water adlayers and 2D ice have been imaged, capturing the metastable or intermediate edge structures involved in the 2D ice growth, which could reveal the underlying growth mechanisms, is extremely challenging, owing to the fragility and short lifetime of those edge structures. Here we show that noncontact atomic-force microscopy with a CO-terminated tip (used previously to image interfacial water with minimal perturbation)12, enables real-space imaging of the edge structures of 2D bilayer hexagonal ice grown on a Au(111) surface. We find that armchair-type edges coexist with the zigzag edges usually observed in 2D hexagonal crystals, and freeze these samples during growth to identify the intermediate edge structures. Combined with simulations, these experiments enable us to reconstruct the growth processes that, in the case of the zigzag edge, involve the addition of water molecules to the existing edge and a collective bridging mechanism. Armchair edge growth, by contrast, involves local seeding and edge reconstruction and thus contrasts with conventional views regarding the growth of bilayer hexagonal ices and 2D hexagonal matter in general.

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Fig. 1: Experimental setup and STM and AFM images of 2D bilayer ice.
Fig. 2: Detailed AFM characterization of the 2D bilayer ice and the corresponding structural model.
Fig. 3: Proposed growing process for zigzag and armchair edges.
Fig. 4: Molecular-dynamics simulation of the growth of the zigzag and armchair edges.

Data availability

The source data are available from the corresponding authors upon reasonable request.

Code availability

The custom code and mathematical algorithms that support the findings of this study are available from the corresponding authors upon reasonable request.

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Acknowledgements

We thank J.-J. Wang for discussions. This work was supported by the National Key R&D Program under grant numbers 2016YFA0300901, 2017YFA0205003 and 2015CB856801, the National Natural Science Foundation of China under grant numbers 11888101, 11634001, 21725302 and 11525520, the Strategic Priority Research Program of the Chinese Academy of Sciences under grant number XDB28000000, and the Beijing Municipal Science & Technology Commission. J.S.F. and X.C.Z were supported by US National Science Foundation (CHE-1665324). We are grateful for the computational resources provided by the TianHe-1A and TianHe II supercomputers, by the High-performance Computing Platform of Peking University supercomputing facility, and by the UNL Holland Computing Center.

Author information

Y.J. and E.-G.W. designed and supervised the project. R.M. and Y.T. performed the STM/AFM measurements with J.G. and J.P.; D.C., J.C., X.-Z.L. and L.-M.X. performed ab initio DFT calculations. C.Z., J.S.F. and X.C.Z. carried out the classical molecular-dynamics simulations. D.C. carried out the theoretical simulations of the AFM images. R.M., D.C., C.Z., Y.T., J.C., X.-Z.L., X.C.Z., L.-M.X., E.-G.W., and Y.J. analysed the data. Y.J., R.M., D.C., L.-M.X., C.Z. and X.C.Z. wrote the manuscript with the input of all other authors. The manuscript reflects the contributions of all authors.

Correspondence to Xiao Cheng Zeng or Li-Mei Xu or En-Ge Wang or Ying Jiang.

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The authors declare no competing interests.

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Peer review information Nature thanks Miquel Salmeron and Yoshiaki Sugimoto for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Experimental evidence for the bilayer nature of 2D ice.

a, d, STM images of a bilayer ice island (a) and cluster (b). Set point, 100 mV and 10 pA. be, AFM images of the same ice island (b) and cluster (e). b was acquired at the constant-current mode with set point 100 mV and 50 pA. e was recorded at a constant height of 280 pm, referenced to the set point of 100 mV and 50 pA on the Au(111) substrate. c, Height-distribution diagram within the red dashed rectangular area in a. The red arrow denotes the bottom layer of the bilayer ice, proving the bilayer nature of the 2D ice. f, Height profile across the red line shown in d, giving two different steps with heights of about 150 pm and about 250 pm, consistent with the results of the 2D ice island. g, False-colour STM image of a 2D ice island grown on a Au(111) surface, where the honeycomb structure of the 2D ice and the herringbone reconstruction of the Au(111) surface are distinguishable. The atomically resolved STM images of the Au(111) lattice are superimposed within the face-centred cubic (fcc) and hexagonal close-packed (hcp) regions, showing good registry between the 2D ice and the Au substrate. The set points are 100 mV and 10 pA and 5 mV and 6 nA for the ice island and the Au(111) lattice, respectively. The white dashed grids correspond to the 1 × 1 lattice of Au(111) within the fcc and hcp regions. The inset at the upper-right corner is a composite 2D-FFT image of the Au(111) and 2D-ice lattice, and shows the corresponding 1 × 1 and \(\sqrt{3}\times \sqrt{3}\) periodicities.

Extended Data Fig. 2 Interruption of the armchair edges by defects and kinks.

ae, Constant-height AFM images of edge areas that contain short reconstructed armchair edges. The tip height is zoffset = −10 pm, referenced to the STM set point 100 mV and 50 pA on the water molecules of the second layer of bilayer ice. The red and green lines represent the armchair and zigzag edges, respectively. The red, green and yellow arrows point to three types of kinks at the armchair edges. Type-1 (red) and type-2 (yellow) kinks correspond to the cases where the armchair edges are terminated at the hexagons and pentagons, respectively. The local seeding growth model requires individual nucleation centres to facilitate the growth of the armchair edges, naturally leading to these step-like structures. f, Schematic showing the formation of type-3 (green arrows) kink defects, consisting of 647-type member rings. These defects are formed owing to the position of the heptagons at the armchair edges, which leads to two different structure series. The green shaded areas represent 5657-member-ring series, and the unshaded areas represent the 5756-type member ring series. The joint of the two different series results in a type-3 defect, which could further develop into a trapped 7-type member ring in the second-outermost layer, as indicated by a red circle in e.

Extended Data Fig. 3 The mechanism of submolecular-resolution AFM imaging.

a, b, Experimental AFM frequency-shift (∆f) images obtained at tip heights and oscillation amplitudes of 70 pm and 40 pm (a) and 0 pm and 100 pm (b). c, Δf curves (oscillation amplitude, 40 pm) above a vertical water molecule (vertical), a flat molecule (flat) and the hollow site of hexagonal ice lattice (denoted as background, bkgd) as a function of the tip height. z1 and z2 denote the tip heights of the two ∆f images in a and b, respectively. de, Simulated ∆f images at different tip heights z (given above each image) obtained with quadrupole (\({d}_{{z}^{2}}\), q = −0.25e; d) and neutral (q = 0; e) tips. f, Top view of the 2D bilayer ice structure (top layer) on the Au(111) substrate. The bottom ice layer is hidden to highlight the structure of the top layer. The green and red dashed parallelograms in df denote the sub-lattices of the vertical and flat water molecules, respectively. g, Calculated electrostatic potential map of the bilayer ice on the Au(111) in a plane 7.24 Å above the highest atom in the Au substrate. h, Simulated total potential map of the bilayer ice on Au(111) in a plane, corresponding to the position of the CO-tip apex at a tip height of 12.5 Å. ik, Vertical force above the flat (Fz–f) and vertical (Fz–v) water molecule as a function of tip height. i, Experimental Fz obtained by integrating the experimental ∆f(z) in c according to ref. 42. Before the integration, ∆f(z) was smoothed using a moving average filter with a span of 5. jk, Simulated Fz computed with \({d}_{{z}^{2}}\) (j) and neutral (k) tips. l, Simulated lateral deflection of the quadrupole probe particle in the x direction (Xq–d) as a function of the tip height. Xq–d–v and Xq–d–f correspond to Xq–d above the vertical water molecule and the flat water molecule, respectively. Tip-height references are the same as those in Fig. 2. In g and h, H and O atoms in the top-layer ice are denoted as white and red spheres, respectively. The image sizes in a, b and dh are 1.25 nm × 1.25 nm. See Methods for details.

Extended Data Fig. 4 DFT-calculated formation energies of different edges of the 2D ice.

ae,Top view of the top layer of bulk (a), zigzag (ZZ)-edged (b, c), and armchair (AC)-edged (d, e) 2D ices on a Au(111) substrate. The three different zigzag and armchair edge type are denoted in a by solid and dashed poly lines, respectively. The fixed edges during the structural relaxation are marked in orange. The bottom ice layer is hidden, to highlight the structure of the top layer. Image sizes: 6.52 nm × 2.17 nm (a), 2.00 nm × 2.61 nm (bc), and 1.73 nm × 2.61 nm (de). Lateral size of the supercell used in the DFT calculations: 2.00 nm × 3.46 nm (bc) and 1.73 nm × 3.50 nm (de). f, The relative formation energy (ΔEf) of the different edge types. See Methods for details.

Extended Data Fig. 5 Insight into the stability of the zigzag and armchair edges.

a, b, Decomposed DFT-calculated relative formation energies of the 2D bilayer ice with different edge types (ZZ1 and AC1, a; ZZ2 and AC2, b). The relative formation energies of different edges are referenced to that of the corresponding unreconstructed 6666-type edge. The cyan, blue and red bars represent the relative energy of the interaction between the Au(111) substrate and the bilayer ice, the isolated bilayer ice, and the Au-supported bilayer ice, respectively. c, The average O–O distance43 (dOO) and H-bonding angle43 (O–H…O angle) of the outermost rings of different armchair edges. d, Experimental length distribution diagram of 5656- and 5756-type armchair edges for ten ice islands, n = 122. Inset, Statistics on the total length of corresponding edges. See Methods for details.

Extended Data Fig. 6 Tip-induced growth of the pentagon structure at the zigzag edge.

a, b, AFM images of the same area during the consecutive scanning showing the formation of the pentagon structure. Tip height, zoffset = −10 pm, referenced to the STM set point of 100 mV and 50 pA on the water molecule of the bilayer ice. cd, The corresponding snapshots in the molecular-dynamics simulations. The dangling-like water molecule corresponds to the molecule attached to the top layer (see the black arrows in a and c), and the water molecule located at the middle of the bilayer ice has an apparently shorter bond (grey arrows in a and c). As highlighted by the red dashed circles in a and b, during close imaging at a very small tip height, a complete pentagon structure at the zigzag edge can be formed, induced by the perturbation of the tip.

Extended Data Fig. 7 Molecular-dynamics simulation of 2D ice formation and armchair edge stability.

a, Top (upper) and side views (lower) of a snapshot show 1,394 water molecules deposited on a Au(111) surface at 120 K. The bottom layer of water molecules is shown in blue and the top layer in red. Au atoms of the Au surface are shown in black. No good registry between the 2D ice and the Au substrate is found, probably due to the weak interaction between them. Although 5656-type armchair edges appear, the 5756-type and 6666-type armchair edges are absent, because of the coincident number of the water molecules added and the limited length of the edges. b, Transverse density profile of the 2D bilayer ice. The intensity of the lower peak is slightly larger than that of the higher one, indicating that the growth of bilayer ice starts from the bottom layer. c, Snapshot of a bilayer ice ribbon (20.76 nm in length) on a Au(111) surface after relaxation for 20 ns, originally with two armchair edges of 5656-type (upper) and 6666-type (lower). Some 5656-type structures spontaneously convert to 5756-type structures (highlighted by blue ellipses) during the simulation, indicating that the 5756-type edge should be thermodynamically more stable than the 5656-type edge. d, Snapshot at t = 1 μs after 63 water molecules were introduced to 6666-type armchair edges. Most of 6666-type structures change to 5756-type or 5656-type structures, suggesting that the growth of armchair edges is governed by the 5756-to-5656 conversion in the absence of a 6666-type edge.

Extended Data Fig. 8 Nucleation of the 2D ice on the Au surface.

a, Top (upper) and side views (lower) of consecutive snapshots show 8, 10, 11, 14, 41, 43, 100 and 256 water molecules deposited on a Au(111) surface at 120 K. The 2D bilayer ice structure was gradually formed through single-layer and double-layer liquid clusters. b, Top (upper) and side views (lower) of snapshots at times t = 0 and 23.5 ps after the deposited water molecule (green ball) arrived at the Au surface. c, Top (upper) and side views (lower) of snapshots at times t = 0 and 787 ps after the deposited water molecule (green ball) arrived on the surface of bilayer ice. The bottom layer of water molecules is shown in blue and the top layer in red, and the Au atoms of the Au surface are shown in black. The water molecule landing on the Au or ice-island surface moves around until it finds its way to attach to the edge of the ice, without creating any new nucleation centres.

Extended Data Fig. 9 Stability of various intermediate structures at the zigzag and armchair edges obtained by molecular-dynamics simulations.

a, b, Molecular-dynamics simulations snapshots of various intermediate structures during the growth of the zigzag (a) and armchair (b) edges. One water molecule was introduced to the simulation cell every 100 ns. The representative water molecules with low coordination at the edges are marked by numbers. c, The calculated interacting energy (ΔEb) for the different intermediate structures shown in a and b. ΔEb is defined as the interacting energy between a specific water molecule and the remaining water molecules together with the Au atoms in substrate after optimization. The maximum energy values are indicated in red. See Methods for details.

Extended Data Fig. 10 The influence of water spacing on the stability of different edges.

a, b, The DFT-calculated edge-formation energies as a function of water spacing (dw) for free-standing 2D ice with different proton ordering (AC1 and AC2, see Extended Data Fig. 4a for detailed definitions). The 2D ice with minimum energy has a water spacing of 2.706 Å. The relative stability of the different armchair edges remains unchanged with water spacing from 2.706 Å to 2.884 Å; the 5756-type armchair edge is the most stable edge. The abscissa reflects the cell size in the direction parallel to the edge, which is crucial, owing to the periodic boundary conditions in the calculation. dw corresponds to the nearest water–water spacing along the direction parallel to the edge. Ef represents the edge formation energy, similar to that defined in Methods section ‘DFT-calculated formation energies of different edges of the 2D ice’. All atoms in the ice edge were fully relaxed and the structures of the different ice edges are similar as those in Extended Data Fig. 4. c, The relative formation energy (ΔEf) of different edges calculated by classical force field, which follows 5656 > 6666 > 5756 for all cases, regardless of the water spacing and the commensurability with the substrate.

Supplementary information

Video 1:

Formation of a second pentagon at the zigzag edge. The video was generated by molecular-dynamics simulations at 120 K. The red and blue spheres represent top-layer and bottom-layer water molecules of a preexisting bilayer ice grain, while the green spheres represent newly deposited water molecules. And the black dots represent the Au atoms of the Au(111) surface. Newly deposited water molecules tend to form separate pentagon structures with a periodicity of 2aice (aice: lattice constant of the 2D ice).

Video 2:

Formation of 565 structure at the zigzag edge. The video was generated by molecular dynamics simulations at 120 K. The red and blue spheres represent top-layer and bottom-layer water molecules of a preexisting bilayer ice grain, while the green spheres represent newly deposited water molecules. And the black dots represent the Au atoms of the Au(111) surface. A periodic but unconnected pentagon array is formed at the zigzag edge. The subsequent incoming water molecules attempt to bridge two adjacent pentagons to form a 565 structure.

Video 3:

Formation of 566 structure at the zigzag edge. The video was generated by molecular dynamics simulations at 120 K. The red and blue spheres represent top-layer and bottom-layer water molecules of a preexisting bilayer ice grain, while the green spheres represent newly deposited water molecules. And the black dots represent the Au atoms of the Au(111) surface. The subsequent incoming water molecules tend to join a pentagon of 565 structure to form a 566 structure, instead of further bridging other pentagons.

Video 4:

Formation of 5666 structure at the zigzag edge. The video was generated by molecular dynamics simulations at 120 K. The red and blue spheres represent top-layer and bottom-layer water molecules of a preexisting bilayer ice grain, while the green spheres represent newly deposited water molecules. And the black dots represent the Au atoms of the Au(111) surface. Starting from a 566 structure, the incoming water molecule bridges the gap between the 566 structure and an adjacent pentagon to form the 5666 structure.

Video 5:

Formation of 575/656 structure at the armchair edge. The video was generated by molecular dynamics simulations at 120 K. The red and blue spheres represent top-layer and bottom-layer water molecules of a preexisting bilayer ice grain, while the green spheres represent newly deposited water molecules. And the black dots represent the Au atoms of the Au(111) surface. Adding two water molecules to the 5756-type armchair edge converts the 575 structure in the bottom layer to 656 structure, while the 575 structure in the top layer keeps unchanged, resulting in a composite 575/656 structure.

Video 6:

Formation of 656 structure at the armchair edge. The video was generated by molecular dynamics simulations at 120 K. The red and blue spheres represent top-layer and bottom-layer water molecules of a preexisting bilayer ice grain, while the green spheres represent newly deposited water molecules. And the black dots represent the Au atoms of the Au(111) surface. Adding two water molecules to the 575/656 structure converts the 575 structure in the top layer to 656 structure, leading to the formation of 656-step structure at the armchair edge.

Video 7:

Expansion of the 656 structure to form the 5656-type armchair edge. The video was generated by molecular dynamics simulations at 120 K. The red and blue spheres represent top-layer and bottom-layer water molecules of a preexisting bilayer ice grain, while the green spheres represent newly deposited water molecules. And the black dots represent the Au atoms of the Au(111) surface. The 656-step serves as the nucleation center to expand towards the right side, leading to the formation of 5656-type armchair edge. It suggests that the growth of the armchair edge follows a local seeding mechanism.

Video 8:

Adding one water molecule to the 5656-type armchair edge. The video was generated by molecular dynamics simulations at 120 K. The red and blue spheres represent top-layer and bottom-layer water molecules of a preexisting bilayer ice grain, while the green spheres represent newly deposited water molecules. And the black dots represent the Au atoms of the Au(111) surface. The addition of one water molecule into the 5656-edge results in a highly mobile unpaired-molecule structure.

Video 9:

Formation of the 5756-type armchair edge. The video was generated by molecular dynamics simulations at 120 K. The red and blue spheres represent top-layer and bottom-layer water molecules of a preexisting bilayer ice grain, while the green spheres represent newly deposited water molecules. And the black dots represent the Au atoms of the Au(111) surface. Two unpaired water molecules can coalesce into a more stable heptagon structure at ~0.2 ns, completing the 5656-5756 conversion.

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Ma, R., Cao, D., Zhu, C. et al. Atomic imaging of the edge structure and growth of a two-dimensional hexagonal ice. Nature 577, 60–63 (2020). https://doi.org/10.1038/s41586-019-1853-4

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