observed rate. However, the coefficient of surface
ened. Second, the temperature difference across
diffusion required was very high and the tem-
the pores is increased, since the thermal conduc-
perature dependence was large, but this might be
tivity is much higher for ice than for air. For these
reasons the coefficient of diffusion of water vapor
due to changing surface structure as the melting
in snow is much higher than it is in air. This grain-
temperature is approached.
to-grain movement of water vapor was described
It is tempting to account for rapid surface dif-
by Colbeck (1983b) using temperature differences
fusion by assuming a liquid-like or a liquid layer
among the grains, and this theory was further
on the surface of ice, at least at higher tempera-
developed by Gubler (1985) to include the dy-
tures (Dash et al. 1995, Petrenko 1994), but this
namics of a population of grains.
idea must still be put in a convincing, quantita-
A "slab" strength develops simultaneously with
tive form. Gubler (1982) has laid out this problem
the growth of rounded grains, especially when
but left the following concerns: First, he assumed
deposition of the snow layer is accompanied by
the usual reverse curvature for the geometry of
high winds. Ideas from other materials have been
the bond, but there is very little evidence that this
applied to describe the formation of the bonds
is the correct geometry. Second, the viscosity and
that provide that strength. It has long been as-
thickness of the surface layer are critical, but con-
sumed that the bonds, or necks, have a reverse or
troversial. Much remains to be learned about the
concave geometry that causes the migration of
surface of ice before this can be resolved. For
water molecules to the neck by sublimation, sur-
example, the rate is very sensitive to the humidity
face diffusion, surface flow, volume diffusion,
(Hosler et al. 1957), which is not surprising since
plastic flow, and/or grain boundary diffusion.
the structure of an ice surface can change visibly
Kuczynski (1949) pioneered the classical approach
with changes in humidity.
to the physics of sintering. His basic idea was that
Kuroiwa (1962) examined the grain bonds us-
different mechanisms occurred at different charac-
ing Kuczynski's (1949) basic ideas about the pro-
teristic rates and that the dominant mechanism
cesses. He concluded that volume diffusion was
could be determined from the rate. This result is
the dominant process when air filled the pore
often summarized by the equation
space and found that the rate of sintering was
much lower when the air was displaced by kero-
n
x
sene. It is disappointing that Kuroiwa missed an
f (T )
=
(1)
R
apparent conclusion from his own figures, even if
Rm
they were made from thin sections: they show
where x is the radius of the neck, R is the radius of
grain-boundary grooves, not the concave geom-
the grain, f(T) is a function of temperature (T),
etry normally assumed (Fig. 4). Even most of the
and t is time. The constants, m and n, assume
more recent thinking about sintering still as-
different values for different processes and are
sumes this concave geometry (Swinkels and
determined from the appropriate experimental
Ashby 1981), but sintering with grain-boundary
observations of sintering.
grooves has been at least partly described (Zhang
This approach was promoted and extended by
and Schneibel 1995). It is important to realize that,
Kingery (1960), who first applied it to ice. Kingery
since a grain-boundary groove is present, replac-
concluded that the welding together of pieces of
ing air with another fluid will change the dihe-
ice at subfreezing temperatures was due to sur-
dral angle at the groove. It could also change the
face diffusion, an idea that has not received wide
surface structure of ice and its surface energy.
support. By direct observation, he found that the
Thus, we should expect the rate of sintering to
rate of neck growth, when normalized to grain
change, even if the dominant process stays the
size, was proportional to t1/6.9. The rate of sinter-
same.
ing was much more rapid for smaller grains, in
Hobbs and Mason (1964) rejected the approach
accordance with eq 1. Unfortunately, his obser-
of the metallurgists and ceramists, stating that it
vations do not allow a close examination of the
could not be applied to ice. Instead, they believed
geometry of the neck, which could provide some
that sublimation, transfer through the vapor phase,
insight into the processes. Thus, his conclusion
had to be the dominant mechanism, and Ramseier
about the role of surface diffusion was based on
and Keeler (1967) supported this conclusion with
the time-dependence of the experimental results
strength tests of snow with either air or oil in the
and the fact that theory shows that sublimation
pore space. Hobbs and Mason did leave open the
could not happen fast enough to account for the
question of the mechanism(s) during the initial
5
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