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is used to interpret the results for each
mechanism. This equation contains two param-
eters characterizing the chemical environment,
i.e., f O 2 and C w . This corresponds to the thermo-
dynamic properties of the system that depend
on two factors, f O 2 and f H 2 O (at a fixed oxide
activity). Note that the activation enthalpy, H ,
is for a fixed water (hydrogen) content. This
choice is made because most of experimental
studies are made at a fixed water content, and
also the water content in most of Earth's interior
is ''fixed'' (i.e., no diffusional exchange of water
(closed system behavior)).
Electrical conductivity for dry (water-free)
samples can also be described by this equation
by using r
and the conductivity increases with oxygen
fugacity as (Figure 5.5)
f O 2
f O 2
q Fe
exp
H Fe
RT
σ Fe =
A Fe ·
·
(5.17)
with q Fe
is
the oxygen fugacity exponent
(
0.20 (Schock et al ., 1989; Dai & Karato,
2009c) and H Fe
0.10
is
the activation enthalpy
(
150 kJ/mol). The activation enthalpy
depends on either the system is open to the
100
-2.5
0. In a more general case, both
hydrogen-independent and hydrogen-dependent
mechanisms of conduction operate, and in these
cases, contributions from each must be added.
For example, when iron-related and hydrogen-
related conduction occurs simultaneously, one
should use
=
-3.0
-3.5
[100]
[010]
[001]
f O 2
f O 2
q Fe
exp
f O 2
f O 2
q H
H Fe
RT
-4.0
σ
= A Fe ·
·
+ A H ·
-8
-6
-4
-2
0
2
log 10 fO2 (Pa)
exp
.
H H
RT
C r w ·
·
(5.16)
(a)
-3.5
[001]
In the following, we will review the major
observations using selected well-executed exper-
imental results.
-4.0
[100]
-4.5
5.4.1 Electronic conduction due
to iron-related impurities
[010]
Schock et al . (1989) conducted a detailed study
of electrical conductivity of iron-bearing, dry
(hydrogen-free) olivine where they reported not
only the dependence of conductivity on oxygen
fugacity but also they measured the Seebeck
coefficient to demonstrate that charge carrier
has positive charge in iron-bearing, hydrogen-free
olivine. Together with point defect analysis
(e.g., Schock & Duba, 1985; Karato, 1973), these
studies showed that the electrical conduction
in iron-bearing minerals such as olivine is due
mostly to electron holes created by ferric iron,
-5.0
-8
-6
-4
-2
0
2
4
log 10 fO2 (Pa)
(b)
Fig. 5.5 Electrical conductivity of dry (hydrogen-free)
olivine as a function of oxygen fugacity (after Schock
et al ., 1989). Electrical conductivity in iron-bearing
olivine increases with oxygen fugacity, whereas
electrical conductivity of ''pure'' forsterite (Mg 2 SiO 4 )
shows a more complex oxygen fugacity dependence.
Results at 0.1 MPa and T
=
1473 K.
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