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cannot explain the marked anisotropy of water
weakening effects reported by Mackwell et al .
(1985) because the diffusion coefficient under
water-rich conditions is nearly isotropic (Costa
and Chakraborty, 2008). Katayama and Karato
(2008b) reported that plastic deformation of
olivine in the Peierls mechanism is enhanced
by water and concluded that the Peierls stress is
reduced by the addition of water.
Based on these observations, I conclude that
the enhanced deformation in olivine is due to at
least two factors: (1) enhanced diffusion and (2)
reduced dislocation energy such as the Peierls po-
tential. The reduction of the Peierls potential is
likely anisotropic, and it also increases the jog and
kink density. Such a model explains the observed
anisotropic enhancement of creep and resultant
fabric transitions in olivine (Karato et al ., 2008)
and also predicts that the influence of water is
stronger for dislocation creep than for diffusion
creep. In both cases, because the amount of hy-
drogen dissolved in minerals is proportional to
some power of water fugacity, the strain-rate un-
der hydrous conditions can be written as (Karato,
1989a),
quartz
3.0
Present study
r/n = 0.47
Kronenberg & Tullis
[1984] r/n = 0.50
2.5
r/n = 0.28
2.0
2.0
2.5
3.0
Log f H 2 O (MPa)
3.5
4.0
(a)
olivine
10 3
T
=
1523 K
s = 64 MPa
d
=
15
μ
m
a H 2 O
1
10 4
r dif = 0.69
(V = 0 m 3 /mol)
( V = 20 × 10 6 m 3 /mol)
(V = 38 × 10 6 m 3 /mol)
exp
r dif = 0.98
E wet +
PV wet
RT
10 5
f r H 2 O ( P , T )
ε wet
·
(4.17)
r dif
=
1.25
10 1
10 2
10 3
where f H 2 O is the fugacity of water. It
should be noted that both the water fugac-
ity term, f r H 2 O ( P , T ), and the exponential term,
f H 2 O (MPa)
exp
RT , depend strongly on pressure
(and temperature) but changes with pressure dif-
ferently. Consequently the determination of two
parameters, r and V wet , is a key to obtain a for-
mula from which one can estimate the influence
of water under a broad range of conditions.
However, if one uses a high-resolution but
low-pressure apparatus such as the gas-medium
apparatus, one cannot determine any of these
parameters uniquely. The reason is as follows.
The contributions of these two terms (the fugac-
ity term and the exponential term) are similar
in magnitude under low-pressure conditions (see
Figure 4.13). But with a small pressure range,
one cannot determine two parameters precisely
(b)
E wet +
PV wet
Fig. 4.12 Influence of water fugacity on the creep
strength of (a) quartz (Post et al ., 1996) and (b) olivine
(Mei & Kohlstedt, 2000b). Stress needed for
deformation (creep strength) decreases with water
fugacity. In these experiments, water fugacity was
changed by changing the confining pressure.
oxygen (Hier-Majumder et al ., 2005 reported the
enhanced Mg-Fe diffusion by hydrogen). The
magnitude of enhancement is roughly same
as the amount of enhancement in strain-rate.
Therefore, enhancement of diffusion is clearly
a cause of weakening (e.g., Kohlstedt, 2006).
However, the enhancement of diffusion alone
 
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