Abstract
Ice surfaces are closely relevant to many physical and chemical properties, such as melting, freezing, friction, gas uptake and atmospheric reaction1,2,3,4,5,6,7,8. Despite extensive experimental and theoretical investigations9,10,11,12,13,14,15,16,17, the exact atomic structures of ice interfaces remain elusive owing to the vulnerable hydrogen-bonding network and the complicated premelting process. Here we realize atomic-resolution imaging of the basal (0001) surface structure of hexagonal water ice (ice Ih) by using qPlus-based cryogenic atomic force microscopy with a carbon monoxide-functionalized tip. We find that the crystalline ice-Ih surface consists of mixed Ih- and cubic (Ic)-stacking nanodomains, forming \(\sqrt{19}\times \sqrt{19}\) periodic superstructures. Density functional theory reveals that this reconstructed surface is stabilized over the ideal ice surface mainly by minimizing the electrostatic repulsion between dangling OH bonds. Moreover, we observe that the ice surface gradually becomes disordered with increasing temperature (above 120 Kelvin), indicating the onset of the premelting process. The surface premelting occurs from the defective boundaries between the Ih and Ic domains and can be promoted by the formation of a planar local structure. These results put an end to the longstanding debate on ice surface structures and shed light on the molecular origin of ice premelting, which may lead to a paradigm shift in the understanding of ice physics and chemistry.
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Data availability
The tabulated data used to create the figures and the Extended Data figures, as well as the molecular-dynamics trajectories, have been deposited at Zenodo (https://doi.org/10.5281/zenodo.10827371)60. All other data needed to evaluate the conclusions in the paper are present in the paper or Supplementary Information.
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Acknowledgements
We thank C. Wang and X. Zeng for discussions and the computational resources provided by the TianHe-1A, TianHe II supercomputer, High-performance Computing Platform of Peking University. This work was supported by the National Key R&D Program under grant 2021YFA1400500; the National Natural Science Foundation of China under grants 11888101, 92361302, 11935002, 12250001, U22A20260 and 12204039; the Strategic Priority Research Program of Chinese Academy of Sciences under grant XDB28000000; the Key R&D Program of Guangdong Province under grant 2020B010189001; the China Postdoctoral Science Foundation under grants BX20230021 and 2023T160011. D.P. acknowledges support from the Hong Kong Research Grants Council (GRF-16306621) and National Natural Science Foundation of China through the Excellent Young Scientists Fund 22022310. Y.J. acknowledges support from the New Cornerstone Science Foundation through the New Cornerstone Investigator Program and the XPLORER PRIZE.
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Y.J. and E.-G.W. designed and supervised the project. J.H. and Y.T. performed the AFM measurements with X.L. and D.G. T.L., Y.S., B.T. and L.-M.X. performed ab initio DFT calculations, molecular-dynamics simulations and AFM simulations. Y.J., E.-G.W., L.-M.X., D.P., J.C., J.G., J.H., Y.T., T.L., X.L., Y.S., D.G., Z.Y., J.-D.G., B.T. and D.C. analysed the data. Y.J., J.H., Y.T., T.L., L.-M.X. and E.-G.W. wrote the paper with input from all other authors. The paper reflects the contributions of all authors.
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Extended data figures and tables
Extended Data Fig. 1 Height-dependent experimental and simulated ∆f images with quadrupole/neutral tips.
a-e, Experimental (upper) and simulated ∆f images with quadrupole (dz2, q = −0.1 e, middle) and neutral (q = 0 e, lower) tips. Simulated images acquired by the quadrupole tip agree better with the experimental results. At a larger tip height, the H-up water molecules are visualized as individual depressions both by quadrupole and neutral tips (middle and lower panels in a), due to long-range vdW attraction from the higher O atoms (~13 pm). However, the electrostatic force between the quadrupole tip and H atoms can enlarge the attractive interaction, leading to much larger force contrast. When the tip height is further decreased, the H-up water molecules evolve into bright protrusions due to the Pauli repulsion. Meanwhile, because of the electrostatic repulsion, O-up water molecules also show bright feature with the quadrupole tip, indicated by red dashed circles in upper and middle panels in c. In contrast, the O-up water molecules are revealed as dark features by the neutral tip, indicated by the red dashed circle in the lower panel in c. Tip heights are given above each image. f-h, Experimental (f, oscillation amplitude, 40 pm) and simulated (g,h, oscillation amplitude, 200 pm) frequency-shift (∆f) versus distance curves above an H-up water molecule (red line) and an O-up water molecule (black line). The experimental (f) and simulated (g, the quadrupole tip) curves show qualitatively similar behavior, where the turning point of the H-up water molecule occurs at a larger tip height and its minimum ∆f is deeper than that of the O-up water molecule. The curve acquired by the neutral tip (h) shows the opposite behavior, where the minimum ∆f of the O-up water molecule is deeper. Such a difference arises from the attractive (repulsive) force between the positively (negatively) charged H (O) and the negatively charged CO tip.
Extended Data Fig. 2 Intra-bilayer stacking disorder existing only on the surface.
a, b, The snapshots of MD simulations of intra-bilayer stacking disorder on the topmost surface. The hexagonal surface bilayer was grown on an Ih substrate after an equilibration period of 2500 ns. To see more clearly, we extracted two 12 nm × 12 nm images from the original calculated image. Typical “55-8-55” line defects between the Ic and Ih domains at the surface are denoted by blue dashed lines. It should be mentioned that the mW potential does not explicitly include the individual H atoms. O atoms in the topmost bilayer and the bulk are denoted as red and light blue spheres, respectively. c, The evolution of the second topmost bilayer after the deposition of a new surface bilayer. Water molecules with cubic and hexagonal ice order are identified using CHILL +61 and the cubicity is defined as the ratio of the number of Ic-stacking water molecules to the total number of molecules in both Ic and Ih-stacking patterns within the second topmost bilayer. Upon deposition of a new bilayer and subsequent equilibration at 180 K, there is a gradual decrease in the area of Ic-stacking nanodomains that existed in the previously deposited bilayer (now the second topmost bilayer) with time (Supplementary Video 1). Consequently, this clearly indicates that the intra-bilayer stacking disorder only exists on the surface.
Extended Data Fig. 3 The long-range order of superstructures.
a, The constant-frequency-shift AFM image of the overall ice surface, acquired at the set point of −100 mHz. Two zoom-in areas within different terraces are spaced 170 nm apart, indicated by letters b and c. b, c, Constant-height AFM images corresponding to the insets in a, depicting perfect superstructures with the same orientation. Superstructures exhibit long-range order and could extend across entire terraces. The orange and yellow triangles represent tetrahedron structures in different stacking types.
Extended Data Fig. 4 Detailed AFM characterization of the \(\sqrt{{\bf{19}}}\times \sqrt{{\bf{19}}}\) and \({\bf{2}}\sqrt{{\bf{19}}}\times \sqrt{{\bf{19}}}\) superstructures.
a-d, Zoom-in constant-height AFM images and the simulations of the pinwheel-like structure in the \(\sqrt{19}\times \sqrt{19}\) phase at tip heights of 0 pm/24.60 Å, −190 pm/23.50 Å, −240 pm/22.60 Å and −270 pm/22.30 Å, respectively. e, Top view of the schematic \(\sqrt{19}\times \sqrt{19}\) phase. All single-tetrahedron structures have the same stacking type, showing only the “55-8-57” boundary. f-i, Zoom-in constant-height AFM images and the simulations of the pinwheel-like structure in the \(2\sqrt{19}\times \sqrt{19}\) phase at tip heights of 0 pm/24.60 Å, −240 pm/23.50 Å, −290 pm/22.50 Å and −330 pm/22.10 Å, respectively. j, Top view of the schematic \(2\sqrt{19}\times \sqrt{19}\) phase. The single-tetrahedron structures with the same stacking type are in a stripe pattern, showing three types of boundaries (“57-8-57”, “55-8-55”, and “55-8-57”). The orange and yellow triangles represent tetrahedron structures with different stacking types. H and O atoms of the upper-lying and lower-lying water molecules in the topmost bilayer are denoted as white, red and dark blue spheres, respectively. Bilayers below the surface are shown in light blue.
Extended Data Fig. 5 Distribution of SOH in experimental superstructures.
a, The statistics of SOH in two superstructures in experiments. Although the experimentally obtained superstructures don’t exhibit complete proton ordering due to the presence of residual entropy, we can divide the surface area into units that are equivalent to the unit cell in \(\sqrt{19}\times \sqrt{19}\) phase for statistical analysis. The small SOHs for superstructures in experiments (SOH ≤ 5) represent the homogeneous distribution of dangling OH bonds at the surface, with a dominant value of ~3. b, c, Typical surface structures of SOH = 1/12 + 2/3 + 1 + 1/12 + 1 + 1/6 = 3 (calculated \(\sqrt{19}\times \sqrt{19}\) phase) and SOH = 1/2 + 1/2 + 1/2 + 1 + 1/2 = 3 (experimental). The contribution value of 1 in SOH is assigned to both of the two nearest-neighboring dangling OH bonds that are located within the unit cell. For dangling OH bonds located at the boundary or corner, the contribution to SOH is determined based on the proportion of their portion belonging to the unit cell. Pairs of nearest-neighbor dangling OH bonds are denoted by green circles. The orange and yellow triangles represent tetrahedron structures in different stacking types. H and O atoms of the upper-lying and lower-lying water molecules in the topmost bilayer are denoted as white, red and dark blue spheres, respectively. Bilayers below the surface are shown in light blue.
Extended Data Fig. 6 Calculated ideal 1 × 1 surfaces and superstructures with different SOH.
a, b, Ideal 1 × 1 phase with SOH = 8 and SOH = 15, respectively. c, d, \(\sqrt{19}\times \sqrt{19}\) phase with SOH = 2 and SOH = 9, respectively. e, f, \(2\sqrt{19}\times \sqrt{19}\) phase with SOH = 2 and SOH = 9, respectively. The black lines indicate the areas used to determine the total number of nearest-neighbor dangling OH pairs. SOH describes the total number of nearest-neighbor dangling OH pairs within an area equivalent to the unit cell of \(\sqrt{19}\times \sqrt{19}\) phase. For \(2\sqrt{19}\times \sqrt{19}\) phase, since its unit cell area is twice as large as that of \(\sqrt{19}\times \sqrt{19}\) phase, the obtained SOH should be divided by 2. The orange and yellow triangles represent tetrahedron structures in different stacking types. H and O atoms of the lower-lying water molecules in the topmost bilayer are denoted as white, and dark blue spheres, respectively. O atoms of H-up and O-up water molecules are denoted as red and yellow spheres, respectively. Bilayers below the surface are shown in light blue.
Extended Data Fig. 7 Surface energies of different ice surface phases as a function of order parameter SOH.
Surface energy per unit area versus order parameter SOH is derived by DFT-based energetic calculations. The zero energy is set to be the minimum surface energy of the ideal 1 × 1 surface, corresponding to SOH = 8. All observed trends and curves are consistent with those presented in Fig. 3. A linear correlation between surface energy and SOH is evident, and the superstructures with homogeneous arrangements of dangling OH bonds (SOH ≤ 5) tend to be more stable than the ideal 1 × 1 surface. For \(\sqrt{19}\times \sqrt{19}\) and 1 × 1 phases, data points at each SOH value represent the averaged formation energy calculated for eight surface structures with different H-bonding configurations and error bars represent their standard deviation. For the \(2\sqrt{19}\times \sqrt{19}\) phase, only three surface structures at each SOH were calculated. The dashed vertical line and shaded blue area represent the average SOH = 2.6 and the standard deviation for superstructures obtained in experiment, respectively. The Ih substrate remains consistent in all phases, with a SOH value of 11.
Extended Data Fig. 8 The structure of PLS under a more disordered local environment than that in Fig. 4c–e.
a,b, Constant-height experimental AFM images and simulations of the PLS at the intersection of multiple Ic and Ih domains. c, Top and side views of the PLS. The H-bonding network in the second topmost bilayer undergoes slight adjustments depending on the local environment of the surface PLS. Tip heights for a: −140 pm, 23.30 Å and b: −190 pm, 22.90 Å. The interstitial water molecule is indicated by the red arrow. O atoms of PLS are denoted as yellow spheres in the schematic models. H and O atoms of the upper-lying and lower-lying water molecules in the topmost bilayer are denoted as white, red and dark blue spheres, respectively. Bilayers below the surface are shown in light blue.
Extended Data Fig. 9 Temperature-dependent surface morphology and high-resolution AFM images of ice surfaces.
a-c, Constant-frequency-shift (upper) and corresponding constant-height (lower) AFM images of ice films grown at 121 K, 125 K and 152 K, respectively. As the temperature increases, the surface experiences a growing level of disorder due to the pre-melting process. The appearance of a deep valley in the surface morphology at 152 K arises from the desorption of water molecules in vacuum. The PLSs, the peripheries of Ic/Ih domains and the surface disorder area are indicated by red arrows, orange/yellow lines and white dashed lines, respectively. Constant-frequency-shift images were acquired at the set point of −100 mHz, −200 mHz and −100 mHz, respectively, all with 200-pm oscillation amplitude.
Extended Data Fig. 10 The oxygen-oxygen radial distribution function (RDF) of two superstructures and the ideal 1 × 1 surfaces.
a, The RDF graph containing both experimental and theoretical data. gOO(r) defines the probability of finding an O atom at a distance r from another O atom within the upper part of the topmost bilayer. The green curve is statistically derived from the AFM image of superstructures, with binomial smoothing. The black, red and blue curves are obtained by averaging all surface structures with different SOH in simulation (64 structures for both ideal 1×1 phase and \(\sqrt{19}\times \sqrt{19}\) phase, 29 structures for \(2\sqrt{19}\times \sqrt{19}\) phase), using a bin size of 0.2 Å. The simulation results have good agreement with the experiment values. The calculated truncation distance of 5.5 Å effectively distinguishes the first nearest neighbors of the undercoordinated water molecules within the upper part of the topmost bilayer, consistent with the definition of SOH. b, The top view of schematic \(\sqrt{19}\times \sqrt{19}\) phase. In the superstructures, the nearest-neighbor peak (ranging from 3.8 to 5.4 Å) exhibits significant broadening compared to that of the ideal surface (ranging from 3.9 to 4.5 Å). Such a difference arises from the nearest-neighbor water molecules within the five, seven and eight-membered rings at the defective boundaries, indicated by black (average distance: 4.1 Å) and green (average distance: 4.9 Å) lines in b. Compared to the ideal surface, the next nearest-neighbor peak is also broader and gets closer to the nearest-neighbor peak in superstructures, typically resulting from the next nearest-neighbor water pairs (average distance: 6.55 Å) crossing the defective boundaries, indicated by purple lines in b.
Supplementary information
Supplementary Information
The file contains Supplementary Figs. 1–12, Tables 1 and 2, and References 1–12.
Supplementary Video 1
The transformation from Ic stacking into Ih stacking after the deposition of a new surface bilayer. The video was generated by molecular-dynamics simulations with a coarse-grained monoatomic model of water potential at 180 K. Structural visualizations were carried out by ovito. O atoms in the topmost bilayer and all underlying bilayers are denoted as light blue and dark blue spheres, respectively. After growing a new ice bilayer (hidden for clarity), the Ic-stacking layer originally located on the ice-Ih surface is gradually transformed into Ih stacking, because the hexagonal ice is thermodynamically more stable than the cubic ice.
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Hong, J., Tian, Y., Liang, T. et al. Imaging surface structure and premelting of ice Ih with atomic resolution. Nature 630, 375–380 (2024). https://doi.org/10.1038/s41586-024-07427-8
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DOI: https://doi.org/10.1038/s41586-024-07427-8
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