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compared to the study of seismic wave velocities
and elasticity. However, the sensitivity of these
two properties to various parameters is different
and the use of these observables is complemen-
tary. For instance, seismic wave velocities are
highly sensitive to the major element chemistry
and crystal structure (see Chapters 6 and 7,
this volume) but relatively insensitive to water
content. In contrast, electrical conductivity is
highly sensitive to water content and relatively
insensitive to other factors as we will show in this
chapter. Therefore in order to infer the water dis-
tribution, electrical conductivity plays a primary
role (see also Karato, 2011). The approaches using
these two observables are complementary and by
using both of them, one can get a detailed knowl-
edge of composition and evolution of the Earth.
Hydrogen (water) has important influence on
rheological properties (e.g., Karato & Jung, 2003;
Mei & Kohlstedt, 2000) and melting relationship
(e.g., Kushiro et al ., 1968; Inoue, 1994) that con-
trol the dynamics and evolution of the Earth and
other terrestrial planets (see also Chapters 1, 4,
12 and 13, this volume). In some regions of the
mantle such as the highly depleted lithosphere,
there is essentially no water (less than a few
wt ppm) whereas in certain regions
an important advancement in our understanding
of water distribution in the current Earth's man-
tle. Consequently, a large number of papers have
been published on this topic after 1990.
However, the measurements and the inter-
pretation of experimental results on electrical
conductivity are not straightforward, particularly
those on samples with hydrogen (water), and
there have been some confusions in the commu-
nity. As a result, somewhat different results have
been published and largely different models were
proposed on the distribution of hydrogen from
electrical conductivity. For example, Huang et al .
(2005) and Karato (2011) proposed a relatively
high water content (
1.0wt%)inthe
transition zone, whereas Yoshino et al . (2008a)
and Yoshino (2010) proposed a dry (water-free)
transition zone. Therefore it seems important
to review the basic physics of electrical con-
ductivity, including the technical issues on the
experimental methods, to evaluate the validity
of different results and models.
In this chapter, we will first review the ba-
sic physics of electrical conductivity and point
defects in minerals and discuss some issues on
the experimental studies and their interpreta-
tion. Then important experimental results will
be summarized and the microscopic mechanisms
of electrical conduction in minerals will be re-
viewed. Finally, the results will be applied to
infer the physical and chemical state of Earth
and planetary (mostly the Moon) interiors from
electrical conductivity.
0.1
1wt%of
water is inferred to be present (Stolper & New-
man, 1994). Therefore the range of water content
in Earth's mantle spans more than four orders
of magnitude. However, these estimates are from
petrological studies and the spatial distribution of
water is poorly constrained. Consequently, if one
can infer the water content with an uncertainty of
a factor of
2, this will be a major improvement
of our understanding of water distribution and
hence the dynamics and evolution of Earth (and
other planets) 1 . According to a model by (Karato,
1990), the electrical conductivity is proportional
to the water content (minor revision is needed
for some minerals as we will discuss later), so
if one can infer electrical conductivity within a
factor of
5.2 Microscopic Physics of Electrical
Conductivity
5.2.1 Some fundamentals
When an electric field is applied, electrical cur-
rent flows in materials due to the motion of
charged particles (electrons and/or ions). There-
fore the electrical conductivity is proportional
to the number density of charged particles and
their mobility. In most cases there is a linear
relationship between the electrical current (I)
and the applied electric field E (the Ohm's law),
2 and if the influence of other factors
is small or properly corrected, then one can make
1 The uncertainties in the geochemical estimate of water
content are similar (e.g., Hirschmann (1006)).
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