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has large uncertainties, and the magnitude of
influence of water under these conditions is
essentially unconstrained by these low-pressure
studies (see Figure 4.13). Because most plastic
deformation in the Earth occurs below
Mei and Kohlstedt (2000)
Karato and Jung (2003)
10
5
20 km,
the applicability of these studies is highly
limited. A more complete analysis was made by
Karato and Jung (2003) based on the data from the
pressure range spanning from 0.1 to 2.0GPa by
which the two key parameters (
r
and
V
wet
)were
well constrained (Figures 4.13 and 4.14).
So far, sufficiently detailed studies on the influ-
ence of water on plastic deformation have been
made only for olivine. But even from less detailed
studies, one can see a general trend that the water
weakening effect is stronger for more SiO
2
-rich
minerals (Karato, 2008). For instance,
r
∼
olivine
10
3
V
wet
=
30 cm
3
/mol
/m
/mo
10
1
10
−
1
V
wet
=
0
10
−
3
1600 K
T
=
10
−
5
∼
1for
10
0
2
4
6
8
olivine but
r
∼
2 for garnet (Katayama & Karato,
pressure, GPa
2008a) and
r
3 for clinopyroxene (in the disloca-
tion creep regime (Chen
et al
., 2006b)). Therefore
the rheological contrast among these minerals
changes with water fugacity (water content).
∼
Fig. 4.13
Pressure versus creep strength relationship in
a water-saturated system (modified from Karato,
2010b). Creep strength (stress) under water-saturated
conditions initially decreases with pressure because of
the increase in the water content in olivine, but
eventually increases with pressure at higher pressures.
In the pressure range used by Mei and Kohlstedt,
(2000a,b) the latter effect is not visible and the
extrapolation of such data to higher pressures cannot
be done with any confidence (errors in the creep
strength (viscosity) at
4.4.4 Effect of crystal structure and bonding
In the Earth and planetary interiors, the nature
of chemical bonding and crystal structures un-
dergoes many changes due to the variation in
pressure (and temperature). Therefore it is impor-
tant to understand how these changes may affect
rheological properties. Ashby and Brown (1982)
and Frost and Ashby (1982) conducted extensive
studies to classify plastic properties of solids.
In many cases, materials with the same crys-
tal structure and bonding form an isomechanical
group where when plastic properties are com-
pared at the same normalized conditions, all the
data converge to a well-defined master curve. For
instance, when strain-rate is normalized by the
Debye frequency,
5,6
ν
D
, temperature by melting
10
6
).
The pressure range used by Karato and Jung (2003)
covers both regions and the key parameters were well
constrained and the results can be extrapolated to
higher pressures. Reproduced with permission of
Elsevier.
∼
400 km is a factor of
∼
enough. Consequently, Mei and Kohlstedt
(2000a,b) tried to determine only one parameter,
r
, for olivine (because the value of
r
provides a
clue as to the atomistic processes of deformation)
assuming a range of
V
wet
. But the influence of
V
wet
on the inferred
r
for a plausible range of
V
wet
(0-30 cm
3
/mol) is too large to make any useful
conclusions as to the microscopic mechanisms
of deformation (an error in
r
is
5
Normalization of strain-rate is not essential because
Debye frequency changes only modestly among differ-
ent materials.
6
Ashby and Brown (1982) used
D
(
T
m
)
/b
2
(
D
(
T
m
): dif-
fusion coefficient at melting temperature), but, this
normalization is not practical for our purpose because
D
(
T
m
) is unknown for many materials.
0.3-0.4). Besides,
with an unconstrained
V
wet
, extrapolation of
these results to the depth deeper than
±
∼
20 km
