Geoscience Reference
In-Depth Information
oxidation-reduction reaction or closed. In most
of the laboratory experiments, the system is open
(i.e., equilibriumwith the surroundings), whereas
in the Earth the systemmay be closed (see Karato,
1973). However, this effect is relatively small.
Figure 5.6 compares electrical conductivity of
hydrogen-free samples at
X
Fe
=
10
2
10
1
F/Q/M
10
-0
F/Q/M
10
-1
Fe/FeO
10
-2
F/Q/M
Fe
0
.
1for
f
O
2
corresponding to the QFM (quartz-fayalite-
magnetite) buffer. When compared at the same
Fe content and oxygen fugacity, electrical con-
ductivity of different minerals shown here is not
much different. This means that the electrical
conductivity in iron-bearing minerals is primarily
a function of temperature and iron content.
The influence of iron content on the electri-
cal conductivity of (nearly) hydrogen-free olivine
was studied by Cemi c
et al
. (1980). A similar
study was conducted on pyrope-almandine gar-
net by Romano
et al
. (2006). These results are
summarized in Figure 5.7. In these studies, the
water content of the samples was not measured,
but judging from the reported activation energy,
we assume that the conduction is mainly due to
electron holes created by ferric iron. The influ-
ence of iron content may be interpreted in terms
of the variation in the pre-exponential term or in
the activation energy. If we assume its effect is
=
Fe/FeO
10
-3
Fe
+
Mg
10
-4
Olivine (with various buffers)
Garnet (10 GPa)
Garnet (19 GPa)
Ringwoodite (20 GPa)
10
-5
10
-6
10
-7
20
40
60
80
100
Mg # (=100*Mg/(Mg+Fe))
Fig. 5.7
Dependence of electrical conductivity in
hydrogen-free samples on iron content (olivine: (Cemi c
et al
., 1980), pyrope garnet (Romano
et al
., 2006),
ringwoodite (Yoshino & Katsura, 2009) (note: for
pyrope and olivine, hydrogen content was not
measured but based on the activation energy, we infer
that the conduction is due to iron-related defects),
orthopyroxene (Dai & Karato, 2009a), wadsleyite (Dai
& Karato, 2009c).
expressed by the following form,
σ
∝
exp(
βX
Fe
)
(5.18)
we get
β
≈
9 for most of minerals where
X
Fe
=
1-Mg#
/
100)
3
(Figure 5.7). A similar ef-
fect is also found for hydrogen-related conduction.
Such a relation can be interpreted by an ioniza-
tion energy model of activation energy in which
the activation energy is inversely proportional
to the dielectric constant (the dielectric constant
in minerals increases with iron content (Cygan
& Lasaga, 1986; Shannon
et al
., 1991; e.g., Kit-
tel, 1986) or a model where activation energy is
proportional to the melting temperature (melting
temperature decreases with iron content). The ef-
fect of iron is not large in the mantle where the
chemical composition is nearly homogeneous.
For example, a variation in iron content of 0.02
(i.e., a change in Mg# of 2) results in the change in
Fe
(
=
10
-2
Fe
+
Mg
10
-3
10
-4
10
-5
Olivine
Orthopyroxene
Garnet
Wadsleyite
10
-6
10
-7
10
-8
8
9
10
11
12
13
10
4
/ T (K
-1
)
Fig. 5.6
A comparison of electrical conductivities in
various dry (hydrogen-free) samples at Fe
/
(Fe
+
Mg)
=
0.1 at fO
2
∼
QFM. Data source: olivine (Constable
et al
., 1992), pyrope garnet (Dai & Karato, 2009b).
3
Mg#=100[Mg/(Mg+Fe)] where Mg and Fe are the molar
fraction of Mg and Fe respectively.
