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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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