Surface Transition on Ice Induced by the Formation of a Grain Boundary
Citation: Pedersen C, Mihranyan A, Strmme M (
Surface Transition on Ice Induced by the Formation of a Grain Boundary
Christian Pedersen 0
Albert Mihranyan 0
Maria Strmme 0
Richard Haverkamp, Massey University, New Zealand
0 Department of Engineering Sciences, Uppsala University , Uppsala , Sweden
Interfaces between individual ice crystals, usually referred to as grain boundaries, play an important part in many processes in nature. Grain boundary properties are, for example, governing the sintering processes in snow and ice which transform a snowpack into a glacier. In the case of snow sintering, it has been assumed that there are no variations in surface roughness and surface melting, when considering the ice-air interface of an individual crystal. In contrast to that assumption, the present work suggests that there is an increased probability of molecular surface disorder in the vicinity of a grain boundary. The conclusion is based on the first detailed visualization of the formation of an ice grain boundary. The visualization is enabled by studying ice crystals growing into contact, at temperatures between 220uC and 215uC and pressures of 12 Torr, using Environmental Scanning Electron Microscopy. It is observed that the formation of a grain boundary induces a surface transition on the facets in contact. The transition does not propagate across facet edges. The surface transition is interpreted as the spreading of crystal dislocations away from the grain boundary. The observation constitutes a qualitatively new finding, and can potentially increase the understanding of specific processes in nature where ice grain boundaries are involved.
Funding: The work was financially supported by the Swedish Science Council (VR), the Carl Trygger Research Foundation (CTS 09:248) and faculty funding from
Uppsala University. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
The importance of water on earth, and in the atmosphere, has
made it one of the most investigated molecules. Ice crystals are
involved in the production of thunderstorms , affect the
destruction of ozone in the stratosphere  and constitute the
snow that falls to the ground. Interfaces between individual ice
crystals are referred to as grain boundaries, and grain boundaries
are involved in many processes in nature  (throughout this
paper, the term grain boundary does not include the ice-air
interface). The properties of ice grain boundaries are unknown
to a large extent, much due to the difficulty in investigating a grain
boundary at thermodynamic equilibrium [3,4]. It is for example
uncertain to what extent grain boundaries affect the structure of
ice surfaces in their vicinity .
The thermodynamically stable form of ice at ambient temperature
and pressure is ice Ih, which has a hexagonal crystal structure .
Hexagonal prism growth is the basic growth morphology of ice Ih, and
the growth of simple ice prisms has therefore undergone much
investigation . Ice crystals growing into contact has been
investigated previously , but the process of two ice prisms growing into
contact with each other has not been visualized in detail prior to this
work (i.e. growth from vapor). Such an experiment would provide basic
information on how facets are affected by an adjacent grain boundary.
This paper explores the possibility of visualizing two ice prisms
growing into contact, using Environmental Scanning Electron
Microscopy (ESEM). ESEM is a technique that operates at higher
pressure than does regular SEM, and its principal of detection takes
advantage of a signal amplification from secondary electrons
produced by electron-gas interactions . The gas used in the
present work was pure water vapor. Ice crystallisation was controlled
by careful adjustments of chamber pressure and sample stage
temperature. The experiments were conducted by initially lowering
pressure and temperature to a condition at which ice sublimation
occurs (0.20.5 Torr, and between 215uC and 220uC) to remove
ice from the sample, and subsequently raising the pressure stepwise
until crystal growth was observed. Ice crystal growth was studied on
two types of surfaces: the stainless steel surface of an ESEM sample
stage, and the surface of a polyvinyl alcohol cryogel.
On the stainless steel surface, the average distance between
nucleation sites was relatively short, which prohibited studying the
growth of individual crystals; every crystal was in contact with another
crystal already as the first image was recorded, as shown in Figure 1.
The observation of relatively short distance between nucleation sites is
in analogy with previous ESEM experiments, where the formation of
ice was investigated on other solid surfaces [2,12].
When ice crystal growth was investigated on the surface of a
polyvinyl alcohol cryogel, nucleation occurred at much fewer sites
as compared to the stainless steel surface, which enabled
monitoring the growth of individual ice crystals. The crystals
generally grew with hexagonal prism morphology, with sharp facet
edges and smooth facets, until they came into contact with another
crystal. It was observed that the transition of a facet structure from
smooth to wavy could be catalysed by a contact with an adjacent
crystal, as shown in Figure 2. An extended version and discussion
of Figure 2 is presented in Supporting Information S1. The facet
transition exemplified in Figure 2 was only observed on facets
directly after they had come into contact with another growing
crystal (see also Figure S5 and discussion in Supporting Information
S1). For the largest facets observed (facet edges within the range
200300 mm), the transition from smooth to wavy of the entire
facet occurred faster than the time interval between image
acquisitions (i.e. 3040 s), as shown in Figure S3. The transition
did not propagate across facet edges to adjacent facets, as shown in
The results clearly show that it was the contact between crystals
and not, e.g., a certain temperature which initiated the transition,
since the transition only was observed on facets directly after they
had come into contact with another crystal (see observations made
at different temperatures; Figure S1 and Figure S2). In addition, it
is unlikely that the observed transition should be induced by heat
flow between the two crystals in contact (i.e. slightly different
surface temperatures before contact); the transition always halted
at a facet edge, whereas heat is expected to flow through the
crystal in three dimensions and not halt at facet edges. It could also
be mentioned, in this context, that the observed transitions can not
be the result of a pressure forcing the crystals together, since the
crystals investigated in this work have grown into contact (contact
load is known as a factor that accelerates ice sintering [13,14]).
Images of ice crystals growing into contact has been presented
prior to this work, in investigations of epitaxial ice crystal growth
on covellite substrates, studied with light microscopy [8,10]. In
those studies, ice crystals were growing on a single-crystalline
substrate with their basal facets parallel to the substrate. The
Figure 2. Crystals of hexagonal ice (ice Ih) growing on the surface of a polyvinyl alcohol cryogel. The Figure shows that facets which
come into contact with another crystal undergo a surface transition. For clarity, facets of interest are named in the 108 s picture. At 184 s, facets A2
and B1 has grown into contact and undergone a surface transition. At 218 s, facet B2 has undergone a surface transition. At 257 s, facets A1 and B3
have grown into contact with other crystals and undergone surface transitions (facet B3 is in contact with the crystal in the lower right corner). The
chamber pressure of water vapor is 1.2 Torr. The temperature of the sample stage is 220uC, and the crystal surface temperature is estimated to
between 216.2uC and 217.4uC (see Methods section). The scale bar is 100 mm. An extended version of this image series is given in the Supporting
studies showed that contact between two ice crystals facilitates
incorporation of molecules into the crystal structure, by the
formation of new molecular layers at the grain boundary which
spread laterally away from the grain boundary. Consequently, the
contact was observed to accelerate growth and transform smooth
basal facets into slopes or stair-case like structures (so-called
Hopper development [10,15]). The present results, however,
clearly show that contact between crystals transforms facets into
wavy structures (i.e. not slopes or staircase-like structures), which
means that new molecular layers are not predominantly initiated at
the grain boundary (see Figure 2). The present work differs from
the previous studies in a number of ways. The present work is an
electron microscopy study performed at low pressure, and the
magnification and resolution are considerably higher as compared
to the previous studies performed with light microscopy.
Furthermore, in the present study, the crystal lattices of two
crystals in contact are randomly oriented relative to each other
(the basal facets were parallel to each other in the previous studies).
When two randomly oriented crystals are in contact, the grain
boundary can be viewed as an array of dislocations , and it is
known that the presence of one dislocation facilitates the formation
of additional dislocations . The surface transition observed in
the present study is therefore interpreted as the spreading of crystal
dislocations away from a grain boundary during ice growth.
It is difficult to comment on the dislocation density of the
transforming facets. One possibility is that the distances between
the waves on the wavy surface structure are connected to the
distances between dislocation layers. Another possibility is that the
dislocation density is very high, and that the surface close to the
boundary can be compared to a melted condition. The theory of
dislocation-mediated melting has indeed suggested that continuous
melting transitions can occur as an avalanche of dislocations,
propagating away from the original dislocation . Such an
avalanche is brought about by a lowering of the energy of
creation of additional dislocations, in the presence of the original
dislocation. Grain boundaries are arrays of crystal dislocations,
and they can in this work be viewed as the original dislocations.
To the best of our knowledge, no theoretical model has been
presented which describe the spreading of crystal dislocations
away from a grain boundary. It is also beyond the scope of the
present work to create such a model; the purpose of this report is
the rapid communication of a qualitatively new finding. The
finding will potentially improve the understanding of processes in
nature where ice grain boundaries are involved; one example is the
sintering of snow. In the case of snow sintering, it is unknown
whether or not the surface structure varies over the ice-air surface
of an individual grain . Todays theoretical snow sintering
models assume that there are no variations in surface roughness
and surface melting, when considering the surface of a single grain
. However, the results presented here show an example of ice
crystals in contact where the ice-air surface structure varies
strongly over each individual grain; a grain boundary-induced
surface transition is observed, which does not propagate across
facet edges. The results therefore suggest that it is possible that the
probability of molecular surface disorder is increased in the
vicinity of a grain boundary. At present, we do not know how
generalizable the results are, e.g. if similar grain boundary-induced
transitions can occur at conditions found in nature. We do not
know how far the surface transition would spread if the crystal
surface was slightly curved before transition (instead of a smooth
facet), and we do not know if similar transitions can occur at
ambient pressure. Unfortunately, those conditions can not be
investigated with the present experimental setup. Nevertheless, the
observed transitions are caused by the contact between two crystals,
i.e. two crystal lattices which mismatch at the grain boundary,
and the mismatch is the same regardless of surrounding pressure.
It should also be kept in mind that prism growth is the basic
growth morphology of ice Ih, and all understanding of more
complex growth morphologies (e.g. the crystal morphologies found
in a snowpack) is based on the understanding of simple prism
growth. To summarize the interpretation of the results, they
suggest the possibility that there is an increased probability of
molecular surface disorder in the vicinity of a grain boundary.
When exemplifying the impact the observations might have on
the understanding of phenomena in nature, it should be recalled
that the grain boundary-induced transition is connected to an
increased crystal growth rate (Figure S4). One of the major mass
transfer mechanisms in snow sintering is vapor transport [5,18
20], and vapor transport can - a bit simplified - be summarized in
three steps: (i) evaporation at the ice surface far away from the
grain boundary, (ii) water vapor diffusion towards the grain
boundary and (iii) condensation of water vapor close to the grain
boundary. It has been argued that the latest sintering models
underestimate the influence of vapor transport , and it is
therefore possible that the present findings implicate that the
models can be improved; an increased probability of molecular
surface disorder close to a grain boundary would facilitate water
attachment in the vicinity of the grain boundary, and thereby
accelerate the vapor transport . In particular, the present results
could be valuable for the understanding of the early stages of dry
snow sintering, since those stages show the strongest resemblance
to the presently investigated system (e.g. temperature, grain
In summary, this work shows that the formation of an ice grain
boundary can be visualized in detail using ESEM. Experiments
are shown where the formation of a grain boundary induces a
surface transition on facets which grow into contact, and the
transition does not propagate across facet edges. The surface
transition is interpreted as the spreading of crystal dislocations
away from the grain boundary. The fact that an ice grain
boundary can induce a surface transition which does not propagate
across facet edges constitutes a novel qualitative finding. The
results suggest the possibility that there is an increased probability
of molecular surface disorder in the vicinity of a grain boundary.
Previous studies of ice grain boundaries have mostly been attempts
to investigate grain boundaries at thermodynamic equilibrium; this
work shows that information on ice grain boundary properties also
can be gained by studying the formation of a grain boundary
during ice growth.
Cryogels of polyvinyl alcohol, PVA, were produced by
dissolving 6 wt% PVA (Mw 89,00098,000) in water, and the
solution was subjected to 7 freeze-thaw cycles (each cycle
contained approximately 20 hours at 220uC followed by 4 hours
at room temperature). Images of ice crystals were recorded using a
Philips ESEM-FEG XL30, operating in wet mode. The
environmental gas used was pure water vapor. PVA cryogels, 12 mm
thick and containing water, were placed on a sample stage (a
Peltier cooler stage with a stainless steel surface), and the pressure
was first lowered and then raised to replace air with water vapor.
The pressure was thereafter lowered to 0.20.5 Torr while
simultaneously lowering the temperature of the sample stage to
between 215uC and 220uC. The lowering of temperature and
pressure caused ablation of water from the surface layer of the
cryogel. The pressure was subsequently re-raised stepwise by
letting in water vapor, 0.1 Torr/step, until the growth of ice
crystals was observed. Ice crystal growth was studied within the
pressure range 0.91.6 Torr, and images of individual ice crystals
could be recorded with roughly 30 s intervals. The process of two
crystals growing into contact with each other was investigated
more than 100 times, at sample stage temperatures between
215uC and 220uC.
After investigating crystal growth, the pressure was lowered
stepwise, 0.1 Torr/step, in order to study at which pressure crystal
growth converted to ablation. The result was then used to estimate
the crystal surface temperature [21,22]. For the images exhibited
in Figures 2 and S1, which were recorded with a sample stage
temperature of 220uC, the crystal surface temperature is
estimated to between 216.2uC and 217.4uC, based on the fact
that crystal growth converted to ablation when the pressure was
decreased from 1.1 to 1.0 Torr (Figure S1).
Supporting material text.
Figure S1 Crystals of hexagonal ice (ice Ih) growing on
the surface of a polyvinyl alcohol cryogel. The temperature
of the sample stage is 220uC and the pressure of the sample
chamber is given in the pictures. Crystal growth converts to
ablation as the pressure is lowered from 1.1 to 1.0 Torr, and the
temperature of the crystal surface can therefore be estimated to
between 216.2uC and 217.4uC. The scale bar is 50 mm.
Figure S2 An example of grain boundary-induced
surface transition, observed at a sample stage
temperature of 2156C. The crystal surface temperature is estimated to
between 213.6uC and 214.5uC. The water vapor density is
1.6 Torr. The scale bar in (d) is 100 mm.
Figure S3 An example of a facet which grew to have
edges longer than 200 mm before it came into contact
with another crystal. In Figure S3b the facet appears perfectly
smooth. In Figure S3c, the upper part of the facet has come into
contact with another crystal, and the whole facet has undergone a
surface transition. The sample stage temperature was 218.5uC,
and the temperature of the crystal surface is estimated to between
217.3uC and 218.5uC.
Figure S4 Increase in the linear growth rate of the
facets which undergo grain boundary-induced surface
transition. The figure shows two crystals that grow into contact,
referred to as the left and the right crystal. For the left crystal, facets
are named F1 and F2 while facet edges are named x and y, as
shown in (a). Contact between the crystals is first observed in (l),
and the contact results in a surface transition of facet F2. The x/y
ratio of facet F1 is constant before the two crystals come into
contact, but changes after contact is reached. The change in x/y
ratio can be attributed to an increasing linear growth rate of facet
F2. The water vapor density was 0.9 Torr. The temperature of the
sample stage was 220uC, and the temperature of the crystal
surface is estimated to between 218.4uC and 219.7uC. The scale
bar in (p) is 50 mm.
Figure S5 An example of a facet which develops an
irregularity without contact with another crystal. Such
irregularities generally disappeared relatively fast, as exemplified in
this figure: the right facet appears perfectly smooth in (ab),
exhibits an irregularity in (cd) and appears perfectly smooth in (e
f ). The water vapor density was 0.9 Torr. The temperature of the
sample stage was 220uC, and the temperature of the crystal
surface is estimated to between 218.4uC and 219.7uC. The scale
bar in (f ) is 50 mm.
Conceived and designed the experiments: CP AM. Performed the
experiments: CP AM. Analyzed the data: CP AM MS. Contributed
reagents/materials/analysis tools: MS. Wrote the paper: CP AM MS.
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