Geology Reference
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coefficient for cobalt (
D
Co
) changes with temperature
and composition in basalt and andesite melts. The data
are presented in the form of an Arrhenius plot, in
which they lie on straight lines. Thus one can express
the temperature dependence of
D
in terms of an equa-
tion similar to Equation 3.5:
T
/K
1500
1000
-20
Diffusion of
Co in melts
10
-10
-25
Basalt
Fig. 3.6(b)
DD
ERT
−
/
-30
=
0
e
(3.12)
a
Andesite
or in log form:
Diffusion of
Ni in olivine
10
-15
-35
E
RT
D
1
ln
D
=− ⋅ +
a
ln
(3.13)
Along z-axis
of crystal
0
-40
These equations are identical to Equations 3.5 and 3.7,
except that the pre-exponential factor is written
D
0
.
Thus, although we think of diffusion as a physical
phenomenon, it resembles a chemical reaction in being
governed by an activation energy
E
a
. Like a person
caught up in a dense crowd, the diffusing atom or ion
must jostle and squeeze its way through the voids of
the melt (Chapter 9), and pushing through from one
structural site to the next presents an energy hurdle
which only the more energetic ('hotter') atoms can
surmount.
Measured diffusion coefficients differ from one
element to another (Co as opposed to Cr, for example)
for diffusion in the same material at the same temper-
ature. Figure 3.6b shows that the diffusion coefficient
for one element in a melt will also vary with the com-
position of the melt (Box 9.2).
Along y-axis
-45
10
-20
0.5
0.6
0.7 .8
0.9
1.0
10
3
/K
-1
T
Figure 3.7
Comparison of volume diffusion rates in silicate
melts and olivine crystals. (Source: Data from Henderson
1982).
is that the crystals have more closely packed, ordered
atomic structures than melts (Box 8.3), and diffusion
through them is much slower (lower
D
). Figure 3.7
contrasts the diffusion behaviour of similar metals in
melts and in olivine crystals (in which the diffusion
coefficients are lower by a factor of about 10
5
). Notice
that diffusion in olivine takes place more readily along
the crystallographic
z
-axis than along the
y
-axis.
Crystallographic direction is an important factor in
diffusion through
anisotropic
crystals, reflecting the
internal architecture of the crystals (Chapter 8).
Solid-state diffusion
From the point of view of diffusion, a crystalline solid
differs from a melt in several important respects.
Atoms diffusing through a silicate melt encounter a
continuous,
isotropic
medium (
D
is independent of
direction) that is a relatively disordered structure. Most
crystalline solids, on the other hand, are polycrystal-
line aggregates that offer two routes for diffusion:
within and between crystals.
Grain-boundary (inter-crystalline) diffusion
Grain-boundary diffusion exploits the structural dis-
continuity between neighbouring crystals as a channel
for diffusion. This is much more difficult to quantify
because the rate of diffusion depends upon:
(a) the grain size of the rock: in a fine-grained rock,
the total area of grain boundaries is larger in rela-
tion to the total volume of the rock, and diffusion
will be easier;
(b) the microscopic characteristics of the grain bound-
aries, e.g. the presence or absence of water.
Volume (intra-crystalline) diffusion
Volume diffusion through the three-dimensional vol-
ume of the constituent crystals is similar in general
terms to diffusion through a melt. The main difference
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