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conductivity of a factor of
20%. However, the
difference in the iron content is large between the
crust and mantle (
X
Fe
≈
∼
hydrogen (water) content (Figure 5.8) as
f
O
2
f
0
O
2
q
H
·
exp
H
∗
H
RT
0.3-0.5), that results in
σ
H
=
A
H
·
C
r
W
·
−
(5.19)
a factor of
10 or more difference in conductivity.
Xu
et al
. (2000) reported results on the experi-
mental studies to determine the pressure effects
on electrical conductivity of iron-bearing olivine
with little hydrogen (again the water content of
the samples was not measured but judging from
the reported activation energy, we infer that the
conduction is due to electron holes created by
ferric iron). They showed a weak pressure effect
(conductivity is reduced by pressure, but only
by a factor of
∼
1.0 and
H
∗
H
=
with
r
100 kJ/mol,
and in case the oxygen fugacity dependence is
=
0.6
−
70
−
10
0
1273 K
1173 K
1073 K
973 K
873 K
10
-1
2 by a change in pressure of
10GPa). Expressed in terms of activation volume,
V
∗
=
∼
10
-2
0.6 cc/mol. Dai and Karato (2009b)
reported the pressure effects on conductivity in
dry pyrope where conduction is likely due to fer-
ric iron (or electron hole). The observed pressure
effect is similarly modest: pressure reduces con-
ductivity by a factor of
0.6
±
10
-3
10
-4
∼
10 by 12GPa. Again in
terms of activation volume, the results implies
V*
10
-5
=
2.5
±
0
.
5 cc/mol.
10
-3
10
-2
10
-1
10
0
10
1
Water content (wt%)
(a)
5.4.2 Conduction due to hydrogen-related
impurities
The possibility of enhanced conduction by proton
was first proposed by Karato (1990) motivated by
the reported high diffusion coefficient of hydrogen
(Mackwell & Kohlstedt, 1990). This hypothesis
was first examined by Wang
et al
. (1999) for
diopside. However, because natural samples were
used in their study, it is not clear if the differ-
ent conductivity is due to the different hydrogen
content or the concentration of some other impu-
rities. The first definitive test of this model was
made by Huang
et al
. (2005) for wadsleyite and
ringwoodite, and later for olivine (Wang
et al
.,
2006), for pyrope garnet (Dai & Karato, 2009b),
for orthopyroxene (Dai & Karato, 2009a; Yang
et al
., 2012), and clinopyroxene and plagioclase
(Yang
et al
., 2011, 2012). These results show that,
when hydrogen content is high (typically higher
than
10
-1
Wet-1273 K
Wet-1173 K
Wet-1073 K
Wet-973 K
Wet-873 K
10
-2
10
-3
10
-4
Dry-1273 K
Dry-1173 K
Dry-1073 K
Dry-973 K
Dry-873 K
10
-5
10
-6
10
-7
10
-10
10
-8
10
-6
10
-4
10
-2
10
0
10
2
10
4
f
O
2
(Pa)
(b)
Fig. 5.8
(a) Influence of water content on the electrical
conductivity of wadsleyite, (b) influence of oxygen
fugacity on the electrical conductivity of hydrogen-rich
and hydrogen-poor wadsleyite (after Dai & Karato,
2009c) (results at P
10
−
3
wt % water), electrical conductivity
is higher than those values expected from ferric
iron-related conduction and the activation energy
is smaller, and the conductivity increases with
∼
15 GPa). Reproduced with
permission of Elsevier.
=
