Geoscience Reference
In-Depth Information
The ice crystal lattice is an open structure, where molecules are more sparsely packed
than in the liquid phase of water, and therefore ice is much less dense than liquid water. At
the freezing point, the densities of liquid and solid phases are 999.84 and 916.7 kg m
−
3
,
respectively, and therefore the density decreases by 8.3 % at freezing. This amount of
density decrease at the phase change from liquid to solid is exceptional,
1
and actually
water shows the largest decrease among all substances in the Earth
s nature. Freshwater
ice behaves as normal solid media with density decreasing with temperature. The thermal
expansion coef
'
10
−
4
C
−
1
at 0
10
−
4
C
−
1
at
cient is from 1.59
×
°
°
C to 1.43
×
°
−
30
°
C
(volume expansion). The density of pure ice is 920.8 kg m
−
3
at
−
30
°
C.
Example 3
. Ice density from the crystal lattice (Pounder 1965). The density of ice can be
evaluated as the mass/volume ratio of one mole of ice. The mass is obtained from the atomic
weights of hydrogen and oxygen as 18.02 g, and the volume is obtained from the geometry
of the crystal lattice, which has been determined by X-ray diffraction (see the right side of
Fig.
3.1
b). The geometric measures shown are at 0
.
1
°
C. The length of one side (d) and width
p
d
(a) of the hexagon are related as
a ¼
, and consequently the area of the hexagon is
A ¼
2
p
a
2
¼ 0
:
1772 nm
2
. The vertical separation between these double layers of oxygen
atoms is r + r
′
′
). This
unit volume has six oxygen atoms, but each is shared between three hexagons. Thus the unit
prism contains the mass of 6/3 = 2 oxygen atoms or two water molecules, and the volume of
one mole is consequently
= 0.2760 nm + 0.0923 nm = 0.3683 nm. The prism volume is A(r + r
) = 19.65 cm
3
, N
A
being Avogadros number. The ice
½
N
A
A(r + r
′
C becomes then 917.0 kgm
−
3
(the direct measurement has given 916.7 kgm
−
3
).
The best method to determine the bulk density of ice is the direct way: measure the
mass of a geometrically regular sample. The presence of pores in the ice gives biased
estimates when the method of submersion of a sample in a liquid is employed.
density at 0
°
Example 3.2
. Ice density is a fundamental property of
fl
floating ice. According to the
Archimedes law, the freeboard hf
f
is given by
q
w
q
i
q
w
h
f
¼
h
Thus for solid ice, the freeboard is 8.3 % of the thickness of the ice sheet, and an ice
block of 1 m
3
volume can support the
floating of a mass of 83 kg. The freeboard is 8.3 %
of the total thickness. If the gas content of freshwater ice is 1 %, the freeboard would be
9.2 % of the ice thickness. The saying that 1/9 (11.1 %) of an iceberg is visible relates to
icebergs
fl
floating on seawater, which has higher density than fresh water; with
ρ
w
= 1,025 kg m
−
3
, the freeboard would be 10.5 %, and adding 1 % gas content brings the
freeboard to 11.4 %.
fl
1
Bismuth, gallium and germanium, for example, become less dense in the liquid
-
solid phase
change. But the change is by far not so large than in water.
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