Geology Reference
In-Depth Information
high‐pressure allotropic forms and known as ices II-XIV
(only up to ice IX are shown in Figure 4.4).
Even at the coldest possible temperature on Earth, say
−70 °C, it needs a huge pressure for the next type, i.e., ice II,
to exist. Pounder [1965, p. 10] stated: “Except at tempera-
tures much lower than those occurring naturally on Earth,
none of these ices (i.e., other than Ih) can exist at pressures
of less than 2000 atm. Since the thickest of ice sheet in the
world—in Antarctica—is less than 4000 m thick, corre-
sponding to a maximum pressure at the base of the ice of
about 350 atm, it is clear that none of these artificial ices
can normally exist on the earth.” Hence, only characteris-
tics of Ih are of general interest for terrestrial ice.
At the atomic and molecular level, oxygen and hydro-
gen atoms inside the Ih lattice are arranged following
the Bernal‐Flower rules [ Bernal and Flower, 1933]. Each
water molecule has one oxygen atom and two hydrogen
atoms similar to a normal molecule in its liquid state, but
the hydrogen atoms are also shared by the neighboring
oxygen atoms within the ice lattice Each oxygen atom is
surrounded by four other oxygen atoms in a tetrahedral
arrangement and by two hydrogen atoms to form a water
molecule. Each of the dipolar water molecules is oriented
so that its two hydrogen atoms face two of the four neigh-
boring oxygen atoms that surround in the tetrahedral
coordination. The orientation of adjacent molecules is
such that only one hydrogen atom lies between each pair
of oxygen atoms. Under ordinary conditions any of the
large number of possible configurations is equally proba-
ble, each corresponding to a certain distribution of hydro-
gen atoms with respect to oxygen atoms.
c or optic axis, <0001>
a 1
a 2
a 3
Basal plane
(0001)
Figure 4.5 Hexagonal crystal with four crystallographic axes
consisting of three equatorial axes: a 1 , a 2 , and a 3 and one c axis
or optic axis, <0001>, normal to the basal plane, (0001).
basal plane, perpendicular to the c axis. All a axes are of
equal length and lie in one plane with 120° angles between
them, as presented earlier in Figure 4.3.
The Miller indices for planes and directions are defined
in terms of four digits for hexagonal crystals instead
of three digits used for cubic crystals. The four digits of
Miller indices of a plane are enclosed in parentheses, such
as (0001) for the basal face. The indices for general direc-
tions (as opp o sed to planes) are enclosed in brackets, for
example, (1010) is the notation for the diagonal axes in
the basal plane. A particular direction is given in terms of
four digits enclosed by the arrows, such as <0001> for the
c axis normal to (0001) plane. In addition to the top and
bottom basal faces, the hexagonal prism is also defined
in  terms of six primary pris m ati c faces [r eferred to in
M il ler indices a s planes (0110), 1100), (1010), (0110),
(1100), and (1010)]. Moreover, there are si x secondary
pr ismatic faces r ef erred to as planes (1120), (1210),
(2110), (1120), (1210), and (2110). The order of the
planes in these two index systems (between the brackets)
is going clockwise. More information on the numbers that
these indices represent in terms of the axes and planes
of  the hexagonal crystals can be found in Reed‐Hill and
Abbaschian [1992] or Campbell [2008].
4.2.2. Miller Indices for Hexagonal Ice
Since the crystalline structure of ice depends on the
environmental conditions and the type of water bodies
(including its salt content), it is important to know the
structural aspects of natural ice, particularly the texture
in terms of major planes and directions of ice. The crys-
tals may be thought of as consisting of sheets lying on
top of each other. In this respect, the Miller system of
designating indices for crystallographic orientations of
major planes and directions of any type of crystal, includ-
ing hexagonal ice [see Hobbs, 1974], is very useful. The
details of the procedures used for defining the planes and
directions in cubic and hexagonal crystals in terms of sev-
eral simple integers can be found in textbooks on metal-
lurgy, for example, Reed‐Hill and Abbaschian [1992]. Only
a brief introduction is given here for hexagonal crystals.
The hexagonal characteristics of ordinary ice (Ih) can
be visualized in the form of a hexagonal prism consisting
of two top and bottom basal faces and six primary pris-
matic faces as shown in Figure  4.5. The prism is also
defined by four axes: one c axis and three a axes in the
4.2.3. Growth Direction of Ice Crystals
Once nucleated, a hexagonal ice crystal can grow in any
direction, but the rate of growth depends on the tempera-
ture of the supercooled water surrounding the crystal
and the ability of each face to form greater extents of
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