Geology Reference
In-Depth Information
when one ion tends to diffuse much more slowly than the other, the diffusion
coefficient for the molecular species is essentially equal to that for the slower ion.
An attempt has been made to calculate the diffusion coefficient from assumed
atomic interaction potentials and Eyring rate process theory (Miyamoto and
Takeda
1983
). In spite of assuming fixed atom positions and thus neglecting the
important relaxations that can be expected as the diffusing atom passes, rough
agreement with observed values in olivine was obtained, encouraging the sug-
gestion that diffusion coefficients too low to be measured, as for example, in
pyroxenes, could be estimated in this way.
3.5.5 Polycrystal Diffusion and High Diffusivity
So far we have considered diffusion in a 3D homogeneous body. When the body is
a polyphase composite, the average or bulk diffusivity will depend on the diffu-
sivities in the individual phases, on their volume fractions and on their shape and
connectivity (Crank
1975
, Chap. 12). Also in polycrystalline bodies there are
potentially important high-diffusivity or short-circuit paths which are in effect
heterogeneities of relatively small volume fraction but high diffusivity. These
paths may be interfaces (phase or grain boundaries or free surface) or linear
regions (pipes, including dislocations and liquid-filled triple-grain junctions, which
can be viewed as distinct narrow regions with a certain effective thickness or
diameter d and a characteristic diffusion coefficient D
sc
much higher than the
diffusion coefficient D
V
in the volume of the grains.
When the diffusion distance is much greater than the spacing of interfaces or
pipes, the apparent or bulk diffusion coefficient D will be
D
¼
D
V
1
x
ð
Þþ
D
SC
ð
3
:
41
Þ
1
þ
D
SC
D
V
D
V
x
for x
1
(Le Claire
1976
) where x is the mole ratio of the amount of the diffusing species in
the high-diffusivity regions to that in the remaining volume (this ratio may be very
different from the volume fraction of the high-diffusivity region in the case of a
chemically different species on account of segregation). If d is the spacing of the
interfaces or pipes, then x is of the order of d
=
d for interfaces and d
=ð
2
for pipes.
Thus, since d is likely to be *1 nm or somewhat less for grain boundaries or
dislocations, for example, d for NiO was found to be 0.7 nm (Atkinson and Taylor
1981
), we have x
10
6
for a grain size of 1 mm or a dislocation spacing of 1 lm;
similarly, x
10
6
for triple-grain junctions if d * 1 lm and d * 1 mm. In these
cases, we need D
SC
=
D
V
10
6
in order that the short-circuit diffusion and volume
diffusion give equal contributions to the bulk diffusion; such a ratio D
SC
=
D
V
is
