Geology Reference
In-Depth Information
A perfect crystal resists this very effectively, because
a whole layer of bonds must be broken simultaneously,
requiring a colossal input of energy. The presence of an
edge dislocation, however, changes this picture
dramatically. When the shear stress is applied, the
dashed row of bonds immediately to the right of the
dislocation (already stretched in the unstressed crys-
tal) becomes more stretched than other bonds, and will
be the first to rupture. This will happen when the dis-
tance from row
a
to row
b
becomes less than the
stretched bond length
b-c
. These bonds will at this
point flip to link rows
a
and
b
instead. Row
a
is now
part of a complete layer, and the dislocation has
migrated to row
c.
If the stress is maintained, this pro-
cess will be repeated until the dislocation has migrated
to the edge of the crystal. The result is the net move-
ment of the upper half of the crystal over the bottom
half (Figure 8.8b), in a manner that requires
only one
row of bonds to be broken
at one time. The stress required
is orders of magnitude less than that needed to deform
a perfect crystal. Edge dislocations therefore explain
why the shear strength (and tensile strength) of crys-
talline materials is less than theoretically expected.
A square centimetre of any crystal intersects 10
8
-10
12
edge dislocations. The exact number depends upon the
crystal's deformation history. Deformation - 'working'
in the metallurgist's jargon - causes dislocations to
multiply and initially makes the crystal more ductile.
Most minerals are considerably more brittle than
metals. At high temperatures and pressures, however,
dislocation creep
can become an important mechanism of
rock and mineral deformation. Its effect is to make
silicate rocks behave in a ductile (plastic) manner if
subjected to stress over long periods of time. It thereby
becomes possible for solid mantle rocks to
convect
(circulate in response to temperature-induced density
gradients), the phenomenon upon which terrestrial heat
flow and plate tectonics largely depend. If all crystals
were perfect, the Earth would be a very different planet.
Exercises
8.1
Predict the degree of Si − O polymerization of the
following minerals:
edenite NaCa
2
Mg
5
(alSi
7
O
22
)(Oh)
2
hedenbergite CaFeSi
2
O
6
paragonite
Naal
2
(alSi
3
O
10
)(Oh)
2
Leucite
K(alSi
2
O
6
)
acmite
NaFeSi
2
O
6
8.2
Express the first analysis in Table 8.5 (Exercise 8.3)
below in terms of element percentages.
Table 8.5
Analyses for Exercise 8.3
Garnet*
Epidote
‡§
Pyroxene
¶
Feldspar
||
X
3
Y
2
Z
3
O
12
X
3
Y
2
Z
3
O
12
(Oh)
M
2
Z
2
O
6
X
4
Z
8
O
32
SiO
2
38.49
39.28
46.92
52.73
al
2
O
3
18.07
31.12
3.49
29.72
tiO
2
0.55
†
-
1.19
-
Fe
2
O
3
5.67
4.15
0.95
0.84
FeO
3.76
0.42
20.31
-
MnO
0.64
0.01
1.13
-
MgO
0.76
0.01
7.30
-
CaO
31.59
23.44
17.35
12.23
Na
2
O
-
-
1.24
4.19
K
2
O
-
-
-
0.13
h
2
O
+
-
1.87
§
-
-
total
99 63
.
100 30
.
99 84
.
99 84
.
* In the garnet structure, all divalent ions reside in the 8-fold
('X') site.
†
RMM
of TiO
2
= 79.9. (Others given in Table 8.4.)
‡
Calculate to 13 oxygens (12 + one OH group).
§
The
total
water content of an analysis consists of:
(a) Internal structural 'water' (actually present as OH
but measured as H
2
O). This is generally assumed to
be released only at temperatures above 110 °C.
Denoted H
2
O
+
.
(b) Adsorbed water (moisture adhering to the surface of the
powdered sample grains). Assumed to be released at
temperatures below 110 °C. (Denoted 'H
2
O−').
Further reading
Cox, K.G., Price, N.B. and Harte B. (1988)
The Practical Study
of Crystals, Minerals and Rocks
. London: McGraw-Hill.
Klein, C. and Philpotts, A.R. (2013)
Earth Materials -
Introduction to Mineralogy and Petrology.
Cambridge:
Canbridge University Press.
Krauskopf, K.B. and Bird, D.K. (1995)
Introduction to
Geochemistry
, 3rd edition. New York: McGraw Hill.
White, W.M. (2013)
Geochemistry
. Chichester: Wiley-Blackwell.
¶
Fill the Z site with sufficient Al to make 2.0000 (cf. Table 8.4).
The remaining Al goes in M. In a pyroxene formula it is difficult
to distinguish between M1 and M2 (Box 8.5), because Mg, Fe
2+
and Mn enter both sites. Here they are considered together as
two 'M' sites.
||
Si, Al and Fe
3+
reside in the Z-site.
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