Article
Methods
STM and AFM experiments
All the experiments were performed with a combined noncontact
AFM/STM system (Createc) at 5 K using a qPlus sensor equipped with
a tungsten tip (parameters: spring constant, k 0 ≈ 1,800 N m−1; resonance
frequency, f 0 = 26.7 kHz; quality factor, Q ≈ 45,000). Ultrapure H 2 O
(deuterium-depleted, ≤1 ppm; Sigma Aldrich) was used and further
purified under vacuum by 3–5 freeze-and-pump cycles to remove
remaining gas impurities. Then H 2 O molecules were dosed in situ onto
a clean Au(111) surface held at 120 K through a dosing tube. The as-
grown sample was first checked by STM at 77 K, and then quickly cooled
down to 5 K for further STM and AFM measurements. Throughout the
experiments, bias voltage refers to the sample voltage with respect
to the tip. The STM topographic images and AFM frequency-shift (Δf)
images were obtained with the CO-terminated tips in constant-current
and constant-height modes, respectively. The CO tip was obtained by
positioning the tip over a CO molecule on the Au(111) surface at a set
point of 100 mV and 30 pA, followed by increasing the bias voltage to
300 mV. The oscillation amplitude of experimental AFM imaging is
100 pm if not specifically mentioned.
DFT calculations
DFT calculations were performed using the Vienna Ab initio Simu-
lation Package (VASP version 5.3)^31 ,^32. Projector-augmented wave
pseudopotentials were used with a cutoff energy of 550 eV for the
expansion of the electronic wave functions^33. Van der Waals correc-
tions for dispersion forces were considered using the ‘optB86b-vdW’
functional^34 ,^35. In the DFT calculations, the system consisted of the
hexagonal 2D bilayer ice on top of a Au(111) substrate modelled by a
four-layer slab. The lattice constant for Au was set to be 4.078 Å and
the bottom three-layer Au substrate was fixed in the DFT calculations.
Monkhorst–Pack k-point meshes of spacing denser than 2π × 0.058 Å−1
were used and the thickness of the vacuum slab was larger than 13 Å.
The geometry optimizations were performed with a force criterion
of 0.01 eV Å−1.
Simulations of AFM images
The Δf images were simulated with a molecular-mechanics model based
on methods described previously^28 ,^36. We used the following param-
eters for the probe-particle–tip model: effective lateral stiffness,
k = 0.75 N m−1; atomic radius, Rc = 1.661 Å. A quadrupole-like (dz 2 ) charge
distribution at the tip apex was used to simulate the CO tip^12 with
q = −0.25e. dz 2 represents the atomic-orbital function used to simulate
the spatial distribution of charge density at the tip apex, d is the atomic
orbit, z is the orientation of the orbit, e is the elementary charge and q
is the magnitude of the quadrupole charge at the tip apex. The elec-
trostatic potentials of the ice on Au(111) used in the AFM simulations
were obtained from DFT calculations. The Lennard-Jones parameters
for O and H atoms in the AFM simulation were: rH = 1.487 Å,
εH = 0.680 meV, rO = 1.661 Å and εO = 9.106 meV.
Molecular-dynamics simulations
We performed large-scale molecular-dynamics simulations and used
the monoatomic model for water–water interactions^37 , which consists
of short-ranged two-body and three-body non-bonding potentials
without explicitly including hydrogen atoms^37 ,^38. The 12-6 Lennard-Jones
potential was used for the interaction between water and the Au atoms
of the Au(111) surface. The Lennard-Jones parameters were determined
to be εAu−wat = 1.553 kJ mol−1 and σAu−wat = 3.2 Å to match the experimentally
measured contact angles for a water droplet on the Au(111) surface^39.
A cutoff of 10 Å was used for the Lennard-Jones potential. The velocity
Verlet algorithm was used to integrate the equations of the motion
with a time step of 2 fs. Periodic boundary conditions were applied
in all three directions of the simulation box. All molecular-dynamics
simulations were carried out using the Large-scale Atomic/Molecular
Massively Parallel Simulator (LAMMPS) package^40.
We performed deposition simulations of water vapour on the Au(111)
surface at 120 K. The deposition was initiated on a bare Au sheet with an
area of 155.72 Å × 159.832 Å consisting of three atomic layers. The simula-
tions were performed in a constant-volume and constant-temperature
(NVT) ensemble. The temperature was controlled by a Langevin ther-
mostat with a relaxation time of 1 ps. The Au sheet was kept rigid during
the molecular-dynamics simulations, and the water molecules—initially
located 20–25 Å above the Au surface—were given initial velocities with
a random magnitude from 5.0 to 10.0 Å ps−1 in the direction towards the
Au surface. First, we introduced one water molecule to the simulation
cell every 0.3 ns. Next, more detailed molecular-dynamics simulations
were performed to explore the growth behaviour of the bilayer ice at
the zigzag and armchair edges, after the larger-sized bilayer ice grains
were formed. For these more detailed simulations, one water molecule
was introduced to the simulation cell every 100 ns at either the zig-
zag edge or the armchair edge. The water molecules were placed at a
random initial location with a distance of 3 Å from the nearest water
molecule at the edge.The mechanism of submolecular-resolution AFM imaging
In refs.^7 ,^27 , the electrostatic forces of the individual water clusters give
rise to dark features at the position of H atoms at large tip heights.
However, for 2D bilayer ice at large tip heights, the long-range attractive
van der Waals background of the extended water network (Extended
Data Fig. 3c, green line) smears out the dark contrast of the H atoms
(Extended Data Fig. 3a, z 1 in Extended Data Fig. 3c). Instead, we found
that the O–H directionality imaging of the 2D ice can be achieved
at smaller tip heights (z 2 in Extended Data Fig. 3c), where the Pauli
repulsive forces start to set in, such that the total force signals of the
water molecules are separated out from the van der Waals background
(Extended Data Fig. 3b). Such an imaging mechanism relies on the deli-
cate interplay between the higher-order electrostatic forces and Pauli
repulsion forces. The contribution from the electrostatic force of H and
O atoms (Extended Data Fig. 3g) can spatially modulate the Δf contrast
of the Pauli repulsions, leading to the apparent O–H directionality.
To confirm the role of the higher-order electrostatic force in the AFM
images, we performed systematic AFM image simulations for the 2D
bilayer ice using quadrupole (dz 2 ) (Extended Data Fig. 3d) and neutral
(Extended Data Fig. 3e) tip apexes at different tip heights. The O atoms
of the flat water molecules are about 1–2 pm higher than those of the
vertical water molecules. At a large tip height, the vertical water mol-
ecules exhibit brighter contrast than the flat water molecules with the
dz 2 tip (Extended Data Fig. 3d, left), and the brighter features corre-
spond to the flat molecules for neutral tip (Extended Data Fig. 3e, left).
When the tip height was set to an intermediate value at which the
higher-order electrostatic and Pauli repulsion forces are comparable,
the O–H directionality of the water molecule is evident in the simulated
AFM images with the dz 2 tip (Extended Data Fig. 3d, middle). However,
such submolecular features are much less obvious when using the
neutral tip (Extended Data Fig. 3e, middle). Therefore, the inclusion
of the higher-order electrostatic force (dz 2 tip) is essential to reproduce
the experimental AFM contrasts (Extended Data Fig. 3b). At a smaller
tip height, where the AFM signals are dominated by the Pauli repulsion^12 ,
the simulated AFM images show the same honeycomb structure of the
2D ice for both the neutral and dz 2 tips (Extended Data Fig. 3d, e, right).
To further justify the importance of the dz 2 tip in reproducing the
experimental results, we compare the experimental and simulated
force curves in Extended Data Fig. 3i–k. We note that the dip in the
experimental force curve (Fz) of the flat water molecules is deeper than
that of the vertical water molecules (Extended Data Fig. 3i), which can-
not be explained by the simple picture based on the height difference
of the flat and vertical water molecules. Instead, such a difference can
be attributed to the fact that the negatively charged tip apex gains a