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Physical Chemistry Chemical Physics c2cp23438f
Q1Non-hexagonal ice at hexagonal surfaces: the role oflattice mismatch
Stephen J. Cox, Shawn M. Kathmann, John A. Purton,Michael J. Gillan and Angelos Michaelides
Grand canonical Monte Carlo has been employed to studythe role of lattice mismatch in ice nucleation.
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Q1 Non-hexagonal ice at hexagonal surfaces: the role of lattice mismatchw
Stephen J. Cox,a Shawn M. Kathmann,b John A. Purton,c Michael J. Gilland andAngelos Michaelidesa
Received 31st October 2011, Accepted 16th April 2012
DOI: 10.1039/c2cp23438f
It has long been known that ice nucleation usually proceeds
heterogeneously on the surface of a foreign body. However, little
is known at the microscopic level about which properties of a
material determine its effectiveness at nucleating ice. This work
focuses on the long standing, conceptually simple, view on the
role of a good crystallographic match between bulk ice and the
underlying substrate. We use grand canonical Monte Carlo to
generate the first overlayer of water at the surface and find that
the traditional view of heterogeneous nucleation does not ade-
quately account for the array of structures that water may form
at the surface. We find that, in order to describe the structures
formed, a good match between the substrate and the nearest
neighbour oxygen–oxygen distance is a better descriptor than a
good match to the bulk ice lattice constant.
The formation of ice is one of the most common everyday
phenomena, yet the underlying physical processes that deter-
mine its nucleation rate are poorly understood. In the absence
of impurities, water can be held in a supercooled state down to
approximately �40 1C but by far the more prevalent form of
freezing, at temperatures closer to the melting point, is that
facilitated by a surface. This process, termed heterogeneous
nucleation, is a crucial process in atmospheric science where,
for example, it has been found to play an important role in
cirrus and mixed-phase cloud formation,1–3 with consequences
regarding the radiative budget of the Earth’s atmosphere4,5
and the hydrological cycle.6–9 Understanding the microscopic
detail of heterogeneous ice nucleation is also of biological
relevance10–12 and has implications for the airline and food
industries, as well as providing potential insight into clathrate
hydrate formation.13
There are numerous textbook arguments (e.g. insolubility,
size or defects) for a substrate to be an effective ice nucleation
agent (IN) but an important one, which lead to AgI being used
as a cloud seeding agent,14 is a good crystallographic match
with bulk hexagonal ice.15,16 The crystallographic match can
be quantified by the disregistry (or ‘‘mismatch’’), defined in a
simplified manner as
d � a0;S � a0;i
a0;ið1Þ
where a0,S is the lattice constant of the substrate and a0,i is the
bulk lattice constant of ice Ih. The original theory, developed
within the context of classical nucleation theory by Turnball
and Vonnegut,16 envisages a situation where the growing
crystal can be pictured as consisting of regions of good fit
(strained slightly to fit the underlying lattice) bounded by line
dislocations.17 Furthermore, through the interpretation of
early experimental data (in particular from low energy electron
diffraction experiments), the concept of an ice-like bilayer
forming at pristine metal surfaces was developed in which
the water molecules occupy 2/3 of adsorption sites (2/3
monolayer coverage).18
This theory is often used as an explanation for the excellent
ice nucleating abilities for many materials, including kaoli-
nite,15 AgI16 and long chain aliphatic alcohols.19 However, in
certain specific cases, it has been questioned what role, if any,
the lattice mismatch plays in ice nucleation.20–22 Indeed,
density functional theory (DFT) calculations on idealised ice
bilayers at different metal surfaces23 have shown that through
relaxation normal to the surface, the water molecules manage
to maintain near constant hydrogen bonding energy, in con-
tradiction to the traditional theory (Fig. 1B). Also, recent
experimental evidence, especially from scanning tunneling
microscopy, has revealed a number of complex structures of
water on the first overlayer of metal surfaces, inconsistent with
the bilayer model.24–27
Here, through the use of grand canonical Monte Carlo
(GCMC) and simple intermolecular potentials, we shall probe
the effect of the lattice constant of the substrate on the
structure of the first water overlayer formed. It should be
noted that of the four basic modes of heterogeneous ice
nucleation,15 we are most closely simulating the deposition
mode, in which water is adsorbed directly from the vapour
phase onto the surface where it forms the ice phase. Although
there have been previous theoretical works that have used
model surfaces to study the structure of interfacial water (e.g.
ref. 28–31), none has explicitly tackled the effect of changing
the lattice parameter of the substrate alone on the structures
that form in the first water overlayer. What we will see is that,
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a Thomas Young Centre, London Centre for Nanotechnology andDepartment of Chemistry, University College London, LondonWC1E 6BT, U.K.
bChemical and Materials Sciences Division, Pacific NorthwestNational Laboratory, Richland, Washington 99352, United States
c STFC, Daresbury Laboratory, Warrington WA4 4AD, U.K.d Thomas Young Centre, London Centre for Nanotechnology andDepartment of Physics and Astronomy, University College London,London WC1E 6BT, U.K.
w Electronic supplementary information (ESI) available. See DOI: 10.1039/c2cp23438f
This journal is c the Owner Societies 2012 Phys. Chem. Chem. Phys., 2012, ]]], 1–6 | 1
PCCP Dynamic Article Links
Cite this: DOI: 10.1039/c2cp23438f
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in contrast to the traditional theory, the first water overlayer
consists of a significant fraction of non-hexagonal arrange-
ments, with smaller lattice constants favouring smaller sized
rings and fully hexagonal overlayers only observed on sub-
strates with expanded lattice constants. We will argue that, as
most molecules in the contact layer are of a similar height, the
nearest neighbour oxygen–oxygen distance r0,i becomes more
relevant than the bulk ice lattice constant a0,i in describing the
structures observed (see Fig. 1), consistent with recent experi-
mental observations on close packed metal surfaces.24,32
We wish to obtain a qualitative overview of the influence of
the lattice constant alone on the structures that form in the
first water overlayer. DFT, whilst proven to be a useful
method for investigating interfacial water (e.g.
ref. 24,27,32–34), would be inappropriate for such a study
not only because of the restriction in system size that could be
used (we are using surfaces with areas on the order of 50 � 50
A2 and sampling millions of configurations), but also because
we would be unable to freely vary the lattice parameter of the
surface without changing other properties of the surface. To
this end, we shall use intermolecular potentials to model the
interaction between the water and the surface. Even though
the use of simple potentials cannot describe the ‘chemistry’
present at real surfaces, this is to our advantage in that we can
effectively decouple the lattice parameter from other proper-
ties of the surface. However, to be as careful as we can to
ensure our observed trends are general and not just applicable
to one type of model, we have used two types of water–surface
potential and two standard water models. Details of these tests
can be found in the ESI,w along with tests using Møller–Plesset
perturbation theory on small clusters formed during these
simulations. It must be stressed that this work is not aiming
to model water layers at real surfaces, but to probe an often-
used, long-standing theory that only concerns the geometrical
distribution of adsorption sites, which has so far proved
inadequate in a number of cases.24–27
The first type of surface employed consists of four layers of
points each in a hexagonally closed packed arrangement,
interacting with the oxygen atoms of the water molecules
through a Lennard-Jones interaction. The adsorption sites
are located at the HCP and FCC sites of this surface, giving
rise to a honeycomb arrangement of potential energy minima
for the water monomer – we shall refer to this surface as the
‘‘honeycomb’’ surface. The second surface used is an explicitly
defined external potential acting on the oxygen atoms of the
water molecules. The adsorption sites on this surface are in a
hexagonally close packed arrangement – this surface is re-
ferred to as the ‘‘HCP’’ surface. On both surfaces, the mono-
mer adsorption energy was chosen to be comparable to, but
slightly stronger than, the TIP4P dimer binding energy
(�26.09 kJ mol�1)35 and similar to the optB88-vdW func-
tional36,37 value on Ag(111)38 (�27.112 kJ mol�1).39 Full
details of both these surfaces can be found in the ESI.wThe simulations presented here all used the TIP4P model, a
rigid simple point charge model, to represent the water–water
interaction.40 The TIP4P water model has been shown to
reproduce the phase diagram of water qualitatively well,41
even though it predicts a melting temperature of ice Ih to be
Tm = 232 K. Furthermore, TIP4P has been shown to repro-
duce the intermolecular vibrational density of states of ice Ih
obtained by inelastic neutron scattering reasonably well.42 As
mentioned previously, in order to see how dependent the
results are on the choice of water force field used, the simula-
tions have also been performed with the SPC/E water model,43
with good agreement between the two models (see ESIw).GCMC simulations were performed on six different slab
geometries for the two types of surfaces at 215 K corres-
ponding to a supercooling of 17 K (the SPC/E calculations
were performed at 198 K to achieve the same supercooling),
each with different lattice constant, using the simulation
package DL_MONTE.44 The surface areas varied between
slabs (ranging from 47.51 � 41.14 A2 to 55.41 � 47.99 A2) but
the cell volume was kept constant between simulations, ensur-
ing there was a vacuum of at least 42.65 A between periodic
images in the z-direction. Full periodic boundary conditions
were employed and electrostatic interactions were treated
using the three-dimensional Ewald method45 and short range
interactions were calculated by employing a spherical cut-off
of 17 A. A GCMC step could be either a molecule translation,
rotation, insertion or deletion and these were attempted with a
ratio of 33 : 33 : 17 : 17. The surface was fixed throughout.
Simulations were run until a single overlayer of water was
obtained. After the GCMC simulations, final structures were
annealed at 15 K and water molecules whose oxygen atom was
greater than 3.5 A above the surface were removed. The
structures were then annealed for a further 5 � 106 MC steps
at 15 K.
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Fig. 1 Schematic of the first water overlayer at a surface. (A) Part of
a single isolated ice bilayer shown from the side (left) and top (right).
The bulk ice lattice constant a0,i and nearest neighbour oxygen–oxygen
distance r0,i are labelled. (B) Ice bilayer at the surface according to the
traditional theory. On the left, the ice bilayer has strained to fit the
lattice of the surface, which has a lattice constant a0,S slightly larger
than bulk ice. On the right, the bilayer is allowed to relax normal to the
surface. (C) Along with relaxation normal to the surface, we can also
envisage a scenario where changes in morphology in the plane of the
surface are favourable.
2 | Phys. Chem. Chem. Phys., 2012, ]]], 1–6 This journal is c the Owner Societies 2012
GCMC is a powerful technique most often used as a method
for calculating adsorption isotherms. However, here we are
using it to efficiently sample configuration space when gener-
ating the single water overlayers.46 The GCMC simulations
generated an array of structures in the first overlayer on the
different surfaces, with coverages on the HCP surfaces (d =
�0.07 to 0.10) increasing approximately linearly from B0.61
monolayer coverage to B0.78 monolayer coverage. This is in
contrast to the traditional theory in which 2/3 monolayer
coverage is predicted. Fig. 2 presents snapshots of water layers
obtained for selected values of d on both the honeycomb and
HCP surfaces. One trend is immediately clear; as the mismatch
is increased, more open ring-like structures are favoured,
whereas as d is decreased, we begin to see more closely packedarrangements. However, perhaps the most striking feature of
these pictures is that on the d = 0.00 surfaces, there is still a
significant proportion of non-hexagonal structures present,
with the only fully hexagonal overlayers being formed on the
honeycomb surface for d Z 0.07.
Presented with these results, it is interesting to ask why we
see such an array of structures in the different overlayers and
why it is only on larger d that we see hexagons starting to
become more favourable. To address these questions, it is
informative to look at the radial distribution functions
(RDFs) and the energies of different overlayers, which are
given in Fig. 3 (the corresponding plots for the honeycomb
surface are included in ESIw). From the RDFs, we can see that
the position of the first peak is quite insensitive with regard to
the underlying substrate, lying at approximately 2.75 A. The
significance of this can be understood by revisiting the defini-
tion of the disregistry, d (eqn (1)) and looking more closely at
the ‘ice bilayer’ model.
In bulk ice Ih, the oxygen atoms lie in layers perpendicular
to the c-axis, each layer being built up of puckered hexagonal
rings (a single ice ‘bilayer’), arranged in ABABAB. . . stacks. A
schematic of a single ice bilayer is shown on the left of Fig. 1.
The lattice constant, a0,i corresponds to the distance between
two nearest coplanar oxygen atoms and not the distance
between two nearest hydrogen bonded water molecules (la-
belled r0,i in Fig. 1). From the RDFs it appears that the water
is able to relinquish long range order in favour of maintaining
a constant nearest neighbour distance. It should be stressed
that this ‘‘constant’’ nearest neighbour distance refers to the
position of the first peak and that this peak exhibits a finite
width (ranging from just under 2.6 A to approximately 3.2 A).
In addition, rather than forming an ice bilayer at the surface, a
flat monolayer forms (see Fig. S5 in ESIw). With these last two
points in mind, simple geometry is enough to explain why we
see such a significant proportion of pentagons at the d = 0.00
surface; the distance between adjacent sites of potential energy
minima r0,S is not large enough to accommodate a fully
hexagonal overlayer with a favourable r0,i. As the surface is
stretched, r0,S becomes larger allowing easier formation of
hexagons at the surface. When the surface is compressed,
however, one way that the water molecules can arrange
themselves such that they keep a favourable r0,i and bind near
the adsorption sites is to adopt structures with smaller O–O–O
angles.
The energy profiles in Fig. 3 are useful in explaining these
observations further, where we have separated the different
contributions to the total energy (water–water and water–sur-
face interactions)47 for the different overlayers. The first thing
to note is that there is surprisingly little variation in the total,
water–water and water–surface interactions as the lattice
constant of the substrate is changed (the scale on each panel
is 4 (kJ mol�1)/H2O E 41 meV/H2O). There is a slight
stabilisation in the total energy on the expanded substrates,
due to an increase in binding to the surface. More importantly,
there is very little change in water–water energy, indicating
that water is able to relinquish long range order without
incurring a severe energy penalty. This tells us that on surfaces
where the water–water and water–surface interactions are
comparable, the cost of forming an overlayer that is commen-
surate with the substrate (with r0,S o r0,i) outweighs the gain
in binding to the surface. Therefore, provided the water
molecules can still bind near to the favoured adsorption sites,
the water molecules will alter their O–O–O angles in order to
maintain a favourable nearest–neighbour distance.
With these results, we are now in a position to compare to
the traditional theory of heterogeneous nucleation,16 where it
is assumed that for d sufficiently small, the growing crystal willstrain to fit the substrate lattice. What is unaccounted for in
this formalism (and what is observed in these simulations),
however, is the ability of the first overlayer to change topol-
ogy; firstly, the water molecules bind as a flat layer to increase
their binding to the surface and secondly, they distort their
O–O–O angles so as to maximise their nearest–neighbour
water–water interactions. To make a semi-quantitative com-
parison to the traditional theory, we can try to estimate the
stability of the traditional ice bilayers relative to the structures
found through GCMC. In order to do this, we took a single ice
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Fig. 2 Snapshots for selected values of d. The top row shows the
honeycomb surface and the bottom row shows the HCP surface. The
value of d (disregistry, as defined in eqn (1)) is shown in the top left
corner. We can see that on both d= 0.00 surfaces there is a significant
proportion of non-hexagonal arrangements of water molecules, the
effect being more pronounced on the HCP surface. As d is increased
hexagons become more favoured and conversely, as d is decreased, wesee an increase of more compact structures. For clarity, only a section
of the entire simulation cell is shown and the atoms have been depicted
to be the same size.
This journal is c the Owner Societies 2012 Phys. Chem. Chem. Phys., 2012, ]]], 1–6 | 3
bilayer (consisting of 24 molecules) from a bulk ice Ih struc-
ture and geometry optimised for various sizes of the lattice
constant using the GROMACS simulation package.48 We
performed two types of geometry optimisations; one set where
we constrain the positions of the water molecules such that the
c/a ratio is constant and another set where we allow the
heights of the water molecules to vary, only constraining the
layer to maintain hexagonal symmetry.49 The results from this
analysis are shown in Fig. 4, where we can see that the
structures generated by GCMC are more stable by approxi-
mately 2–3 kJ mol�1 per H2O relative to the most stable
bilayer (the total adsorption energy is shown in the bottom
panel). From inspection of the contribution to the total energy
arising from water–water interactions (middle panel) we can
see that, on the whole, the hydrogen bonding network is
slightly destabilised compared to the bilayer in which the
height of the water molecules is allowed to relax. In fact, for
d o 0.03, the conventional ice bilayer has a more stable
hydrogen bonding network than the GCMC overlayers.
Where the GCMC overlayers gain their overall stabilisation,
however, is by binding in a flat layer to the surface; the
increase in water–surface interaction offsets the very small
energy penalty in forming a flat hydrogen bonded network
relative to a buckled one.
Although we have only used simple potentials to describe
the water–surface interaction, we note here that this conclu-
sion is consistent with a recent DFT study50 in which ‘‘H-
down’’ and ‘‘H-up’’ bilayers were studied at Cu(110) and
Ru(0001): the H-up bilayers tend to have a corrugation
comparable to that of bulk ice and stronger hydrogen bonding
than the H-down bilayers, whereas the latter form flatter
overlayers with a weaker hydrogen bonding network, but have
an increased binding to the surface. We include a more
comprehensive comparison, along with a detailed assessment
of the water-surface interaction, in the ESI.wIn this work we have investigated the role of lattice mis-
match alone on the structure of the first water overlayer
through the use of GCMC and model hexagonal surfaces.
We find that, in direct contrast to the traditional theory, the
first overlayer alters its topology away from that of the
traditional bilayer model in order to maximise its interaction
with the surface and in doing so, suffers little energy cost
regarding its water–water interactions. We explain this ob-
servation by the fact that once the water molecules relax along
the surface normal, there is very little energy associated with
changing the O–O–O angles and that independent of the
underlying substrate lattice constant, the water molecules
maintain a near constant O–O nearest neighbour distance
(although our results do not preclude the existence of short
O–O distances due to other driving forces, for example, charge
transfer to the surface). Our results also suggest that, unless
there is an inherent corrugation of the adsorption sites on the
surface, one should not expect to observe fully hexagonal
overlayers for substrates that have a mismatch close to zero,
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Fig. 3 Left: radial distribution functions for different d (HCP surface). Note that the position of the nearest–neighbour peak is essentially
invariant as the substrate lattice constant is changed, located at approximately 2.75 A. Right: contributions to the total energy as d varies. There isa slight stabilisation in the total energy (bottom) as d is increased, which arises from an increased binding to the surface (top). This trend is seen as
r0,S is closer to r0,i for expanded d, meaning more water molecules can bind close to preferred adsorption sites with a favourable nearest–neighbourdistance. The water–water interaction (middle) is very flat, indicating that varying the O–O–O angle is a facile process.
Fig. 4 Comparison to the traditional theory of heterogeneous ice
nucleation. The bottom panel shows the total energy of the different
types of overlayer at the HCP surface, the middle panel shows the
water–water energy and the top panel shows the interaction energy of
the water with the surface. ‘‘Fully constrained’’ is a bilayer whose c/a
ratio was kept constant, whereas ‘‘xy-constrained’’ is a bilayer in
which the relative heights of the water molecules was allowed to
change whilst keeping the lateral coordinates of the water molecules
fixed. We can see that by all water molecules binding closely to the
surface, the structures generated by GCMC are stabilised relative to
the bilayer models.
4 | Phys. Chem. Chem. Phys., 2012, ]]], 1–6 This journal is c the Owner Societies 2012
consistent with recent experimental findings.32 Not only does
this work confirm the findings that the lattice match alone is
insufficient to make a material an efficient IN,20,21,28,51,52 but is
also suggests that a good lattice match in the conventional
sense (eqn (1)) may possibly be detrimental to ice nucleation,
as large molecular rearrangement in the first water overlayer
may be required to form an ice nucleus.53 Indeed, if the first
water overlayer bears little resemblance to an ice bilayer, it is
not entirely obvious what role it plays in heterogeneous ice
nucleation. Future work to try and understand this phenom-
enon will focus on details of the water surface interaction (e.g.
binding energy and corrugation), as well as on defects at the
surface, as it is likely that they either give rise to electric fields
(computed from either classical point charges or ab initio via
the nuclear plus the electronic charge density) that enhance the
ordering of interfacial water molecules,54 or allow the facile
reconstruction of the first water overlayer.
Acknowledgements
The authors are grateful to Dr Gregory Schenter for many
useful discussions and Dr Peter Feibelman for his comments
on the manuscript. This research used resources of the Na-
tional Energy Research Scientific Computing Center, which is
supported by the Office of Science of the U.S. Department of
Energy under Contract No. DE-AC02-05CH11231. We are
grateful to the London Centre for Nanotechnology and UCL
Research Computing for computational resources. via our
membership of the UK’s HPC Materials Chemistry Consor-
tium, which is funded by EPSRC (EP/F067496), this work
made use of the facilities of HECToR, the UK’s national high-
performance computing service, which is provided by UoE
HPCx Ltd. at the University of Edinburgh, Cray Inc., and
NAG Ltd., and funded by the Office of Science and Technol-
ogy through EPSRC’s High End Computing Programme.
A.M. is supported by the ERC.
References
1 P. DeMott, D. Rogers and S. Kreidenweis, J. Geophys. Res., 1997,102, 19575.
2 D. Rogers, P. DeMott, S. Kreidenweis and Y. Chen, Geophys. Res.Lett., 1998, 25, 1383.
3 R. W. Saunders, O. Moehler, M. Schnaiter, S. Benz, R. Wagner,H. Saathoff, P. J. Connolly, R. Burgess, B. J. Murray,M. Gallagher, R. Wills and J. M. C. Plane, Atmos. Chem. Phys.,2010, 10, 1227.
4 Y.-S. Choi and C.-H. Ho, Geophys. Res. Lett., 2006, 33, L21811.5 J. Lee, P. Yang, A. E. Dessler, B.-C. Gao and S. Platnick,J. Atmos. Sci., 2009, 66, 3721.
6 M. B. Baker, Science, 1997, 276, 1072.7 J. Verlinde, J. Y. Harrington, G. M. McFarquhar, V. T. Yannuzzi,A. Avramov, S. Greenberg, N. Johnson, G. Zhang, M. R. Poellot,J. H. Mather, D. D. Turner, E. W. Eloranta, B. D. Zak,A. J. Prenni, J. S. Daniel, G. L. Kok, D. C. Tobin, R. Holz,K. Sassen, D. Spangenberg, P. Minnis, T. P. Tooman, M. D. Ivey,S. J. Richardson, C. P. Bahrmann, M. Shupe, P. J. DeMott,A. J. Heymsfield and R. Schofield, Bull. Am. Meteorol. Soc.,2007, 88, 205.
8 G. M. McFarquhar, G. Zhang, M. R. Poellot, G. L. Kok,R. McCoy, T. Tooman, A. Fridlind and A. J. Heymsfield,J. Geophys. Res., 2007, 112, D24201.
9 B. J. Murray, T. W. Wilson, S. Dobbie, Z. Cui, S. M. R. K. Al-Jumur, O. Moehler, M. Schnaiter, R. Wagner, S. Benz,M. Niemand, H. Saathoff, V. Ebert, S. Wagner and B. Kaercher,Nat. Geosci., 2010, 3, 233.
10 K. A. Sharp, Proc. Natl. Acad. Sci. U. S. A., 2011, 108, 7281.11 Y. Liou, A. Tocilj, P. Davies and Z. Jia, Nature, 2000, 406, 322.12 B. C. Christner, C. E. Morris, C. M. Foreman, R. Cai and
D. C. Sands, Science, 2008, 319, 1214.13 E. D. Sloan and C. A. Koh, Clathrate Hydrates of Natural Gases,
CRC Press, Boca Raton, Florida, USA, 3rd edn, 2008.14 B. Vonegut, J. Appl. Phys., 1947, 18, 593.15 H. R. Pruppacher and J. D. Klett, Microphysics of Clouds and
Precipitation - Second Revised and Enlarged Edition with an Intro-duction to Cloud Chemistry and Cloud Electricity, Kluwer Aca-demic Publishers, Dordrecht, The Netherlands, 1997.
16 D. Turnball and B. Vonnegut, Ind. Eng. Chem., 1952, 44, 1292.17 In the original theory, Turnball and Vonnegut define two regimes:
a low disregistry regime (d o 0.2), where the crystal growscoherently with the substrate and a high disregistry regime, wherethe crystal grows incoherently with the substrate. All resultspresented here fall into the low disregistry regime. It should benoted, however, that the differences from the original theory foundin this work give this decomposition into two regimes littlemeaning.
18 D. Doering and T. Madey, Surf. Sci., 1982, 123, 305.19 R. Popovitz-Biro, J. L. Wang, J. Majewski, E. Shavit,
L. Leiserowitz and M. Lahav, J. Am. Chem. Soc., 1994, 116, 1179.20 X. L. Hu and A. Michaelides, Surf. Sci., 2007, 601, 5378.21 T. Croteau, A. K. Bertram and G. N. Patey, J. Phys. Chem. A,
2008, 112, 10708.22 P. J. Feibelman, Phys. Chem. Chem. Phys., 2008, 10, 4688.23 A. Michaelides, A. Alavi and D. A. King, Phys. Rev. B: Condens.
Matter Mater. Phys., 2004, 69, 113404.24 S. Nie, P. J. Feibelman, N. C. Bartelt and K. Thuermer, Phys. Rev.
Lett., 2010, 105, 026102.25 S. Standop, A. Redinger, M. Morgenstern, T. Michely and
C. Busse, Phys. Rev. B: Condens. Matter Mater. Phys., 2010,82, 161412.
26 M. Gallagher, A. Omer, G. R. Darling and A. Hodgson, FaradayDiscuss., 2009, 141, 231.
27 J. Carrasco, A. Michaelides, M. Forster, S. Haq, R. Raval andA. Hodgson, Nat. Mater., 2009, 8, 427.
28 D. R. Nutt and A. J. Stone, Langmuir, 2004, 20, 8715.29 H. Witek and V. Buch, J. Chem. Phys., 1999, 110, 3168.30 T. Lankau and I. Cooper, J. Phys. Chem. A, 2001, 105, 4084.31 H. Henschel, T. Kraemer and T. Lankau, Langmuir, 2006,
22, 10942.32 F. McBride, G. R. Darling, K. Pussi and A. Hodgson, Phys. Rev.
Lett., 2011, 106, 226101.33 M. Forster, R. Raval, A. Hodgson, J. Carrasco and
A. Michaelides, Phys. Rev. Lett., 2011, 106.34 A. Michaelides and K. Morgenstern, Nat. Mater., 2007, 6, 597.35 D. J. Wales and M. P. Hodges, Chem. Phys. Lett., 1998, 286, 65.36 J. Klimes, D. R. Bowler and A. Michaelides, J. Phys.: Condens.
Matter, 2010, 22, 022201.37 J. Klimes, D. R. Bowler and A. Michaelides, Phys. Rev. B:
Condens. Matter Mater. Phys., 2011, 83, 195131.38 Although we have taken values for the binding and barrier height
from DFT using the optB88-vdW functional, this is only to give abinding energy that is comparable to, but stronger than, theTIP4P-dimer binding energy and a reasonable barrier height. Wedo not expect our simulations, nor indeed are we attempting, tomimic water on Ag(111).
39 J. Carrasco, J. Klimes and A. Michaelides, unpublished Q2.40 W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey
and M. L. Klein, J. Chem. Phys., 1983, 79, 926.41 E. Sanz, C. Vega, J. L. F. Abascal and L. G. MacDowell, Phys.
Rev. Lett., 2004, 92, 255701.42 S. Dong and J. Li, Phys. B, 2000, 276–278, 469.43 H. J. C. Berendsen, J. R. Grigera and T. P. Straatsma, J. Phys.
Chem., 1987, 91, 6269.44 J. Purton, DL_MONTE: Monte Carlo Simulation Package, www.
ccp5.ac.uk, 2011.45 M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids,
Oxford, Clarendon Press, 1989.46 Although GCMC provides an efficient manner by which to explore
configuration space, there is no guarantee that it will generate thelowest energy structures. In fact, it should also be noted that theperiodicity imposed by the boundary conditions may play a role in
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preventing the lowest energy structures being found. However,byusing large simulation cells (between 288 and 400 adsorption sites),we reduce this finite size effect as much as possible within ourcomputational resources.
47 In general, such energy decompositions are arbitrary since it isassumed that the hydrogen bonding within the overlayer does notchange upon approaching the surface. When using forcefields, thisassumption is correct but in general this is not the case. For a moredetailed discussion on this type of energy decomposition see, forexample, ref. 23.
48 B. Hess, C. Kutzner, D. van der Spoel and E. Lindahl, J. Chem.Theory Comput., 2008, 4, 435.
49 The total adsorption energy of the bilayers at the HCP surface byassuming that all water molecules lie directly above the adsorptionsites and that the low-lying water molecules are at the optimalheight. As we know the functional form of the water surfaceinteraction, calculating the energy of the high-lying water mole-cules is trivial.
50 J. Carrasco, B. Santra, J. Klimes and A. Michaelides, Phys. Rev.Lett., 2011, 106.
51 X. L. Hu and A. Michaelides, Surf. Sci., 2008, 602, 960.52 V. Sadtchenko, G. Ewing, D. Nutt and A. Stone, Langmuir, 2002,
18, 4632.53 K. Thurmer and N. C. Bartelt, Phys. Rev. Lett., 2008, 100, 186101.54 J. Y. Yan and G. N. Patey, J. Phys. Chem. Lett., 2011, 2, 2555.
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