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the anisotropy in electrical conductivity in an
aggregate with nonrandom crystallographic ori-
entations.
mm (Av e Lallemant
et al
., 1980), we conclude
that the influence of grain-size is not important
in most of the Earth's mantle. Yang and Heidel-
bach (2012) also obtained the same conclusion for
clinopyroxene.
(b) Influence of element partitioning
In a multi-
phase aggregate, various elements are distributed
among coexisting minerals. The concentration
ratios of these elements are controlled by ther-
mochemical equilibrium, and these ratios are
referred to as partition coefficients. Particularly
important is the partition coefficients of hydro-
gen. Experimental studies on hydrogen partition-
ing have been conducted (e.g., Hauri
et al
., 2006)
and these results are needed to develop a model
of conductivity-depth profile. Because the solu-
bility of an element depends on the physical and
chemical conditions, the partition coefficients are
dependent on the physical and chemical condi-
tions and not the constants (Karato, 2008a). For
instance, the partition coefficient of hydrogen be-
tween olivine and orthopyroxene changes with
the total water content (i.e., the water fugacity)
by more than a factor of 10 in the upper mantle
(Dai & Karato, 2009a). In evaluating the influence
of hydrogen partitioning, such an effect needs to
be taken into account.
(d) Influence of fluid phases
Fluids in general
have high ionic conductivity and therefore if
fluids are present they enhance the electrical con-
ductivity of a rock. Both aqueous fluids (in the
crust) and silicate or carbonatite melts are often
invoked to explain high electrical conductivity.
The degree to which the presence of fluids af-
fects the electrical conductivity depends on (i)
the conductivity ratio of the fluid and mineral;
(ii) the volume fraction of the fluid; and (iii) the
geometry of the fluids (dihedral angle if the fluid
geometry is controlled by the interfacial tension).
The influence of partial melt on electrical con-
ductivity was discussed by Shankland and Waff
(1977), but new experimental observations sug-
gest that some modifications are needed (e.g.,
Gaillard
et al
., 2008; Yoshino
et al
., 2010). We
will provide a review on the importance of flu-
ids including partial melting incorporating new
laboratory and geophysical observations.
Similar to the influence of a fluid phase, the
influence of graphite is sometimes proposed (e.g.,
Duba & Shankland, 1982). Graphite has a very
high (and anisotropic) conductivity and therefore
even a small amount of carbon can enhance con-
ductivity if carbon assumes a connected phase.
Yoshino and Noritake (2011) studied this issue
for the quartz-carbon system and found that car-
bon does not assume a connected geometry and
its influence on electrical conductivity is small.
The geometry of carbon in an aggregate is con-
trolled by the interfacial tension and therefore
depends on minerals. Similar studies on mantle
minerals have not been conducted.
(c) Influence of grain-boundaries
Grain-bounda-
ries are present in any polycrystalline aggregates.
Grain-boundaries may enhance or may reduce
electrical conduction. When electronic conduc-
tion dominates, grain-boundaries act as barriers
for the electric current. When ionic conduction
plays an important role, grain-boundaries may
enhance conduction if grain-boundary diffusion
is enhanced. Roberts and Tyburczy (1991) and ten
Grotenhuis
et al
. (2004) studied the influence of
grain-size on the electrical conductivity in olivine
aggregates. ten Grotenhuis
et al
. (2004) found
a clear evidence for the contribution of grain-
boundary diffusion for their fine-grained synthetic
forsterite samples (
1-5
μ
m). However, a com-
parison to single crystal data by Schock
et al
.
(1989) shows that the grain-boundary effect is not
important for grain-size larger than
∼
5.3 Issues on the Experimental Studies
The measurements of electrical conductivity are
relatively simple compared to the measurements
of rheological properties (e.g., Karato, 2008a and
0.1mm. Be-
cause a typical grain-size in the mantle is several
∼
