old grains. Direct observations of bond growth
D δ
Γ= b b .
rate and geometry are needed during their growth.
(7)
Ds δs
They found, for example, for a dihedral angle of
DISCUSSION AND CONCLUSIONS
150, that the time to reach 50% of the final neck
shape decreased as log (Γ) increased. Thus, for each
There is a fundamental difference between wet
order-of-magnitude increase in grain-boundary
and dry snow since liquid water causes major
diffusivity, there is an increase of a factor of two
reconfigurations of both grains and bonds. Within
to five in the rate of sintering due to the removal
the wet and dry snow categories there are also
of material from the grain boundary and deposi-
two important divisions: wet snow at low and
tion of that material on the free surfaces.
high liquid contents and dry snow at low and
While this theory ignores sublimation, crystal-
high growth rates. Wet snow is cohesionless and
lographic differences, and the role of the macro-
slushy at high liquid contents because the grain
scopic temperature gradient in determining the
boundaries are unstable against pressure melt-
rate of sintering, at least it includes the role of the
ing. However, wet snow is well-bonded at low
dihedral angle and grain-boundary diffusion. Per-
liquid contents where ice-bonded clusters form.
haps its greatest limitations are the assumptions
A transitional form of snow, meltfreeze grains,
of a constant dihedral angle and an adiabatic en-
can be either wet or dry. These amorphous,
vironment.
multicrystalline particles arise from meltfreeze
cycles. They are solid within and well-bonded to
Faceted grains
their neighbors.
Faceted grains grow rapidly due to high tem-
Rapidly growing grains in dry snow lack bond-
perature gradients and low densities. They have
ing because they consume the existing grains, they
long been of interest because they are associated
are large, and they grow rapidly. However, strong
with low strength and avalanche release. In 1973,
bonds form among rounded grains, and they grow
de Quervain proposed that grains situated at spe-
slowly. Their growth processes and geometry have
cific sites would preferentially grow more rap-
probably been misunderstood, even though this
idly. This includes "end grains" that are not
is the most studied case of sintering in snow. The
connected at their lower end and thus point down-
bonds are usually described as necks with a con-
ward into the upward-moving stream of vapor
cave geometry as in most studies of sintering of
being driven by the temperature gradient (Fig.
other materials. However, this geometry would
11). Without being connected at their lower ends,
not seem possible for a crystalline material be-
they grow rapidly, especially if there is a large
cause the equilibrium form of the crystal requires
distance between the end grain and the grain be-
the presence of a grain-boundary groove at the
low it. Furthermore, because they are not con-
crystalline boundary.
nected at the bottom, they fail to form a bond
In the past it has been assumed that the reverse
there. This is one reason why, during a major
geometry causes the migration of water molecules
recrystallization, where the rounded grains are
to the neck by one of many possible processes; the
replaced by faceted grains, the bond density of
dominant mechanisms were identified by the ob-
the new grains is low compared with that of the
served dependence on time. Kingery (1960) first
applied this approach to ice; he concluded that
the bonding was due to surface diffusion. How-
Cold
ever, the coefficient of surface diffusion required
was very high, and although this might be ex-
plained by a highly mobile surface layer, this idea
remains to be convincingly demonstrated.
Kuroiwa (1962) concluded that volume diffu-
Figure 11. End grain
sion was the dominant process, but Hobbs and
pointing downwards
Mason (1964) believed that sublimation, transfer
into the upward-moving
through the vapor phase, had to be the dominant
stream of vapor as sug-
mechanism. The vapor transfer mechanism has
gested by de Quervain
since received wide support and was supported
(1973).
by the strength tests of Ramseier and Keeler (1967).
Warm
9
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