Scanning electron microscopy and
molecular dynamics of ice surfaces:
What is the origin of trans-prismatic strands?
1. Introduction
Will
1,2
Pfalzgraff ,
and Martina
2
Roeselova
1University of Puget Sound, Tacoma, WA
2Institute of Organic Chemistry and Biochemistry, Prague, Czech Republic.
*nesh@pugetsound.edu
3. Insights from MD
Climatologically significant optical properties of atmospheric ice crystals depend not only on crystal
habit but also on mesoscopic (μm-level) surface properties1. Variable-pressure scanning electron
microscopy (VPSEM) observations of growing and ablating hexagonal ice crystals have revealed
mesoscopic surface features associated with low supersaturation and ablation, called trans-prismatic
strands2 (Figs. 1-3). Using a combination of VPSEM experiments and molecular dynamics (MD)
simulations of the ice-vapor interface, we explore possible factors influencing these features.
Fig. 1. Facets observed in
VPSEM-grown ice
crystals, designated here as
basal (0001), prismatic
(1010), and pyramidal
(1011) (from ref. 2).
Steven
1
Neshyba *,
Fig. 2. Evidence of ledge
growth instability on
prismatic facets.
1. Thermodynamics. Previous MD simulations of ice slabs at 250K with basal surfaces exposed to vacuum7
exhibited a sublimation rate equivalent to Pvap ≈ 230 Pa (Fig. 7). To explore whether thermodynamic
stability (using equilibrium vapor pressure as a proxy for chemical potential) influences mesoscopic
structuring, we carried out sublimation studies of prismatic and pyramidal facets. Simulations over 200 ns
revealed sublimation rates identical to that of basal surfaces, to two significant figures. Conclusions: The
chemical potential of facet surfaces is probably washed out by the QLL at 250K. Moreover, since all
surfaces are likely to be QLL-covered at this temperature, we infer that thermodynamic considerations do
not influence structure at the mesoscopic level.
2. Sublayer nucleation dynamics. We observed growth in our VPSEM experiments as fast as 1 μm/s, which corresponds to ~10-6 layers/ns; observed mesoscopic structures
appear to develop on an even slower time scale (seconds). To investigate whether such structuring could be influenced by layer nucleation, we carried out MD simulations at
250K of the prismatic and pyramidal slabs modified such that a second QLL was inserted under the existing one, producing a “doubled QLL” (Fig. 8). It was found that
doubled-QLLs re-freeze after ~5 ns (0.2 layers/ns) (Fig. 9), with prismatic slightly faster. Conclusion: Sublayer nucleation occurs on a time scale that is fast enough to
influence observed mesoscopic structuring. If such is the case, it follows that differences between prismatic and pyramidal freezing rates may play a significant role in
influencing mesoscopic structure.
(a)
Fig. 3. Mesoscopic trans-prismatic strands associated with growth (A; C-F) and ablation (B; G-I) (from ref. 2).
2. Methods
(b) ~10 ps
(c) ~5 ns
(d)
Fig. 8. Doubled-QLL MD experiment for a prismatic facet. (a) 2880-molecule
prismatic slab with fully developed upper and lower QLLs. (b) Displaced upper QLL
replaces the underlying ice layer. (c) Layers coalesced into a doubled-QLL a few
picoseconds later. (d) QLL restoration after 5 ns.
Fig. 9. Potential energy curves of doubled-QLL simulations, for
2880-molecule prismatic and pyramidal slabs. Multiple runs
correspond to slightly different initial configurations of the
doubled-QLL. Green curves indicate the mean +/- 1 standard
deviation of potential energies of unperturbed slabs.
3. Surface diffusion dynamics. Mesoscopic structure seen on prismatic facets of VPSEM-grown ice exhibits strong directional preference. Under conditions near the frost point,
surface growth appears to be morphologicaly unstable (see Figs. 2 & 3). To investigate whether such preference could be influenced by surface diffusion, we used MD to
evaluate the root-mean-square displacement of surface molecules (Figs. 10 & 11). Diffusion of molecules on the prismatic facet is found to be anisotropic (Dx>Dz), i.e.,
trans-prismatic diffusion is faster than basal-to-basal diffusion. Analogous behavior is observed for diffusion of molecules on the pyramidal facet (Dx>Dz’), although the
anisotropy is smaller. Conclusion: Anisotropic diffusivity is a plausible cause of the geometrical and dynamical asymmetry observed of trans-prismatic strands in VPSEM
experiments, perhaps via a mechanism analogous to the morphological instability of terrace edges in step flow8,9.
1. VPSEM. The chamber of a Hitachi S-3400N variablepressure scanning electron microscope equipped with a
backscatter detector was humidified with a liquid or ice
reservoir, resulting in ice crystal formation on a cold stage
(Fig. 4). Growth and ablation were controlled by adjusting
the temperature of the cold stage (nominal Tmin = -50°C).
2. MD. Slabs consisting of 2880 rigid water molecules,
interacting via the NE6 intermolecular potential3 at T=250K
(~40°C below the NE6 melting temperature4), were
allowed to evolve classically using Gromacs5 molecular
dynamics software. The prismatic slab, created using a
proton-disordering algorithm6, measured 5.4, 4.7, and 3.7
nm (in the x-, y-, and z-directions). The simulation box was
extended in the y-direction to simulate exposure of the
prismatic surface to vacuum. The pyramidal slab was
structured similarly, but rotated 28° along the x-axis, with
rectangular periodic boundary conditions adjusted
accordingly (Fig. 5). The resulting slab measured 5.4, 4.1,
and 4.2 nm (in the x-, y’-, and z’-directions). The
simulation box was extended in the y’-direction to simulate
exposure of the pyramidal surface to vacuum. Fig. 6 shows
densities of oxygen atoms normal to exposed facets of each
slab. Degradation of peaks at the extremes indicates
quasiliquid layer (QLL) formation.
Fig. 7. Three unit cells of a
1280-molecule slab in
which upper and lower basal
surfaces are exposed to
vacuum, a few picoseconds
after a sublimation event
(from ref. 7).
Fig. 4. Hitachi S-3400NVPSEM
chamber with Peltier cooler.
Fig. 5. Coordinate
systems for prismatic
and pyramidal slabs.
Fig. 6. Oxygen atom densities as a function of distance along the
surface normal of 2880-molecule prismatic and pyramidal slabs. Each
outer layer of the prismatic slab is designated quasiliquid (QLL); each
1½ outer layer of the pyramidal slab is designated QLL.
Fig. 10. MD simulation showing displacement of QLL
molecules in the z’ (basal-to-basal) direction of a
pyramidal slab after 10 ns simulated time.
Acknowledgements
This research was supported by the Czech Science Foundation (grant no.
P208/10/1724), the Ministry of Education of the Czech Republic (grant no.
ME09064), and the University of Puget Sound. We thank Babak Minofar and
Morteza Khabiri for technical assistance related to MD, and Al Vallecorsa for
technical assistance related to VPSEM. We would especially like to acknowledge
Victoria Buch for her generosity in various respects: in providing computer code that
generated proton-disordered ice configurations, and in listening carefully and sharing
her insights during many fruitful discussions about liquid water and ice.
Fig. 11. MD-derived mean-squared
displacement of QLL molecules in
prismatic and pyramidal slabs, assuming
ice:QLL ratios of 10:2 for the prismatic
slab and 9:3 for the pyramidal slab (see
Fig. 6). Diffusion coefficients are onedimensional, in units 10-5 cm2/s.
Coordinates are as specified in Fig. 5.
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