Geology Reference
In-Depth Information
5.4 Coble Creep
If the grain boundaries act as the transfer paths as well as being the sources and
sinks for diffusion creep in a polycrystalline material, with the diffusion rate-
controlling, the mechanism is referred to as Coble creep (Coble
1963
). The Coble
creep law can be obtained from (
5.7
) in a similar way to the Nabarro-Herring law
(
5.9
), with V
d
3
and l
d but now with the cross-sectional area of the order dd
where d is the effective width of the grain boundary for grain boundary diffusion,
so that lV
=
A
t
d
3
=
d. Then with c
¼
1
=
V
m
,(
5.7
) becomes
e
¼
C
CO
V
m
D
GB
d
RT
r
1
r
3
d
3
ð
5
:
11
Þ
where D
GB
is the grain boundary diffusion coefficient and C
CO
is a numerical
constant differing somewhat from C
NH
in (
5.9
) because of the different geometry
of the transfer path, C
CO
being about three times greater that C
NH
:
Values of C
CO
of around 45 have been calculated by Coble (
1963
) and by Raj and Ashby (
1971
)
for particular assumed geometries meeting compatibility requirements.
As an illustrative example for comparison with the previous Nabarro-Herring
example, again taking V
m
¼
10
4
m
3
;
T
¼
1200 K and r
1
r
3
¼
10 MPa and
assuming d
¼
1nm
;
a value of D
GB
¼
10
12
m
2
s
1
would give e
10
3
s
1
for
d
¼
1lm and e
10
15
s
1
for d
¼
1mm
:
Thus laboratory experiment on fine-
grained materials will tend to emphasize Coble creep even where Nabarro-Herring
creep might be more favoured with coarser grain sizes geologically.
Since both the material transfer and the relative grain movements associated with
the two types of diffusion creep are additive, the total creep rate can be obtained by
summing (
5.9
) and (
5.11
) in cases where both are contributing significantly. For the
contributions of Nabarro-Herring and Coble creep to be similar, D
GB
has to be about
three orders of magnitude greater than D
V
in the case of 1 lm grain size, or six orders
of magnitude greater in the case of 1 mm grain size, if d is of the order of 1 nm.
Diffusion measurements (
Sect. 3.5.5
) indicate that a ratio of six orders of magnitude
between D
GB
and D
V
is realistic but the ratio will depend on temperature, dimin-
ishing at higher temperatures because of lower activation energies for grain boundary
diffusion. It has been noted that the cation diffusion is often rate controlling in grain
boundary diffusion and hence in Coble creep, in contrast to the control by the anions
in Nabarro-Herring creep (Gordon
1973
,
1975
).
5.5 Fluid-Transfer Diffusion Creep
If material is transferred from sources to sinks by diffusion through a fluid phase
existing in intergranular cavities or cracks, and if the transfer process is rate
controlling, the creep relation should be of the same form as for Coble creep,
