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acceptor level is created above the edge of the
valence band (Figure 5.12c). The presence of such
an impurity level enhances electrical conductiv-
ity exactly in the same way as ferric iron enhances
conductivity. (Wang
et al
., 2012b) showed that the
impurity level created by the addition of charged
hydrogen-related defect can explain the observed
conductivity of hydrous olivine with a reason-
able assumption of the mobility of electrons (or
holes). We conclude that in addition to the direct
contribution to conductivity through the migra-
tion of free proton (
H
•
), dissolution of hydrogen
enhances electronic conduction through the cre-
ation of an impurity level in the band gap. These
two mechanisms may have different conductivity
anisotropy.
Dependence of hydrogen-assisted conductivity
on iron content has not been determined. How-
ever, if we use the results of dependence of hydro-
gen solubility on iron content (e.g., Zhao
et al
.,
2004), then we can predict that the electrical con-
ductivity at a given water fugacity will increase
with iron content due to the increase in hydro-
gen solubility. In addition, a comparison of the
results by Dai and Karato (2009a) and Yang
et al
.
(2012) on orthopyroxene with the same hydro-
gen content but different iron content shows that
the electrical conductivity of hydrogen-bearing
orthopyroxene increases with iron content at the
same hydrogen content. This suggests that iron
increases the mobility of hydrogen (or electron
hole created by hydrogen defect).
of partial melting on electrical conductivity in
the asthenosphere and concluded that a large
melt fraction (a few percent) is needed to en-
hance conductivity appreciably. Gaillard
et al
.
(2008) provided a new data set on carbonatite
melt showing high conductivity, and Yoshino
et al
. (2010) measured the electrical conductivity
of olivine
carbonatite melts
with equilibrium melt geometry. These recent
studies showed that if more than
+
basaltic, olivine
+
1% of these
melts are present then the conductivity will be
enhanced to be
∼
10
−
1
S/m or higher (Figure 5.13)
(a similar result was obtained by Ni
et al
., 2011)
for a hydrous basaltic melt). Although these stud-
ies showed somewhat larger effect of partial melt
than those by Shankland and Ander (1983); Shank-
land and Waff (1977),
∼
1% of melt occurs only
at the vicinity of mid-ocean ridges. In the as-
thenosphere far from mid-ocean ridges the melt
fraction is
∼
0.1% or less (e.g., Plank & Langmuir,
1992; Hirschmann, 2010) and therefore the influ-
ence of partial melting is likely not large in the
asthenosphere away from the oceanic ridges.
It is emphasized that in estimating the volume
fraction of melt, one needs to distinguish the
∼
100
carbonatite
basalt 1600K
basalt 1500K
10
5.4.3 Influence of partial melting
1
Melts in general have higher electrical conductiv-
ity than minerals. This is essentially due to the
high diffusion coefficients of charged species in
melts (e.g., Hofmann, 1980). Consequently, the
presence of partial melt will contribute to high
electrical conductivity.
The importance of partial melt on electrical
conductivity depends on (1) the conductivity ra-
tio between the melt and the mineral, (2) the
volume fraction of melt and (3) the melt geome-
try (dihedral angle). Shankland and Ander (1983);
Shankland and Waff (1977) analyzed the influence
0.1
Conductivity anomaly
0.01
0.001
0.01
Melt fraction
0.1
1
Fig. 5.13
Influence of partial melting on the electrical
conductivity of upper mantle rocks (Yoshino
et al
.,
2010). Reproduced with permission of Elsevier.
