Geoscience Reference
In-Depth Information
where
k
is the Boltzmann constant,
R
is the gas
constant (
R
2000
1500
1000 (K)
10
0
N
A
k
,
N
A
: the Avogadro number),
h
is the Planck constant,
m
e
,
h
is the effective mass
of electron or hole respectively,
μ
e
,
h
is the mo-
bility of electron or hole, and
E
g
is the band gap
(Figure 5.1). These thermally activated electrons
or holes behave like free electrons. In most cases,
the mobility of electrons (or holes) is controlled
by phonon scattering and decreases with tempera-
ture as
μ
e
,
h
∝
=
10
−
1
10
−
2
10
−
3
1
T
(Kittel, 1986) (the slight difference
between free electrons in metals and electrons
and hole non-metallic solids is expressed by the
effective mass).
Because the band gap is large for most minerals
(several hundreds of kJ/mol) (Nitsan and Shank-
land, 1976), the contribution from this intrinsic
conduction mechanism is small. For instance for
Mg
2
SiO
4
(forsterite) the electrical conductivity
at 1500K is
10
−
4
10
−
5
10
−
6
4
6
8
10
12
14
10000/T (K)
10
−
4
S/m (Schock
et al
., 1989). In
comparison, the electrical conductivity of iron-
bearing olivine is
Fig. 5.2
A comparison of the results on electrical
conductivity measurements on olivine. Results for
''pure'' Mg
2
SiO
4
, San Carlos olivine (without
hydrogen), San Carlos olivine with hydrogen
(0.01wt%) are compared (forsterite: Schock
et al
.,
1989), San Carlos olivine (Constable, 2006), wet olivine
(Wang
et al
., 2006)). Results on single crystals are
averaged to compare with results for polycrystals.
∼
10
−
3
S/m for hydrogen-free
conditions (Constable
et al
., 1992), and it is
∼
∼
10
−
1
S/m for hydrogen-rich olivine at the same
temperature (Wang
et al
., 2006). Therefore, the
electrical conductivity in typical minerals is usu-
ally due to some ''impurities'' such as ferric iron
and hydrogen (Figure 5.2).
The electrical conductivity in iron-bearingmin-
erals can still be ''intrinsic,'' i.e., conductivity
could occur by the formation of a pair of elec-
trons and holes through Reaction (5.2). However,
if this were the dominant mechanism of con-
duction, then the electrical conductivity would
be independent of oxygen fugacity. Laboratory
observations on hydrogen-free but iron-bearing
minerals often show a positive dependence of
electrical conductivity on oxygen fugacity (e.g.,
Schock
et al
., 1989), showing that the intrinsic
conduction is not important in most cases.
In the following we will review two impor-
tant mechanisms of the electrical conductivity
in minerals where impurities play an essential
role. When the electrical conductivity is con-
trolled by impurities, the electrical conductivity
increases with the impurity content. However,
the relation between the conductivity and impu-
rity content is not always linear. The best-known
impurity conduction is the electrical conduc-
tion in impurity-doped semi-conductors such as
boron-doped Si. In these cases, the charge bal-
ance is maintained by the ionization of impurity
atoms themselves and if the concentration of
impurities is hi
gh
, electrical conductivity is pro-
portional to
√
N
(
N
: impurity content) (Kittel,
1986). We will discuss a similar case in hydrogen
conduction. In the following we will review the
relationship between electrical conductivity and
thermo-chemical parameters.
(b) Conductivity due to iron
Outer electrons (in
the d-orbit) of Fe (iron) are only weakly bound to
the nucleus. Consequently, it is easy to remove an
electron from Fe ion to change the valence state
from ferrous (
Fe
2
+
) to ferric (
Fe
3
+
). Ferric iron is an
''impurity'' in most of minerals where normally
ferrous iron occupies the site for doubly charged
