Geoscience Reference
In-Depth Information
and the proportional coefficient is the electrical
conductivity,
I
an insulator in which all electrons are strongly
bound to the atomic nuclei. In these materials,
all electrons belong to the filled bands and they
become mobile only when an electron is removed
from the filled valence band to the empty con-
duction band by thermal activation (Figure 5.1).
The creation of these mobile electrons and holes
can be described by
=
σE
. Therefore one has
σ
=|
q
|
nμ
(5.1)
where
q
is the charge of the particle that car-
ries the current,
n
is the number density of the
particle and
μ
υ/E
is the mobility where
υ
is
the drift velocity of the particle. When there are
multiple charged species that carry the electric
current, Equation (5.1) should be modified to
σ
=
e
h
•
⇔
+
perfect crystal
(5.2)
=
where
e
is electron (with excess negative charge)
and
h
•
is hole (with positive effective charge).
From the law of mass action and the requirement
of charge neutrality by these two defects, one
has [
e
]
i
|
q
i
|
n
i
μ
i
(each quantity with a suffix
i
refers
to a quantity for the
i
-th species) and the electri-
cal conductivity is dominated by the motion of
charged species that has the highest
2
RT
where [
x
] denotes the
concentration of a species x. Using this relation,
and considering that the density of state of elec-
trons follows the Fermi statistics, the electrical
conductivity can be given by (e.g., Ziman, 1960;
Kittel, 1986),
exp
E
g
[
h
•
]
n
i
μ
i
.
In metals, the number of charge carriers is fixed
|
q
i
|
=
∝
−
(
number of free electrons), and the temperature
dependence of electrical conductivity comes only
from that of mobility. The mobility of free elec-
trons is controlled by the scattering by phonons
and weakly dependent on temperature,
μ
∝
=
1
T
(
T
:
temperature) (e.g., Kittel, 1986). Most of minerals
are semi-conductors or insulators where mobile
charged particles are present only by thermal acti-
vation and their concentrations are highly sensi-
tive to the amount of impurities as well as temper-
ature. In addition, the mobility of charge carriers
in minerals is often highly sensitive to tempera-
ture. Therefore the electrical conductivity inmin-
erals is not only sensitive to temperature but also
sensitive to parameters that control the activities
of impurities including water and oxygen fugac-
ity. Consequently, there is a potential to infer the
distribution of these chemical factors (as well as
temperatures) from the study of electrical conduc-
tivity that are otherwise difficult to infer. In the
following, we will first review the fundamentals
of mechanisms of electrical conduction in min-
erals, and review some experimental issues, and
then summarize the results of laboratory studies
and their interpretation and applications.
2
e
2
2
πkT
h
2
3
/
2
(
m
e
m
h
)
3
/
4
σ
=
·
·
(
μ
e
+
μ
h
)
exp
E
g
2
RT
×
−
(5.3)
conduction band
V
M
′′
E
g
H
M
′
Fe
•
acceptor level
valence band
Fig. 5.1
Energy band structure of a typical mineral.
E
g
is the band gap. There are several impurity states in the
band gap that provide extrinsic electronic conduction
including ferric iron at M-site,
Fe
M
, vacancy at M-site,
V
M
, and a singly charged hydrogen-related defect at
M-site,
H
M
.
5.2.2 Electrical conductivity and impurities
(a) Intrinsic conductivity
A typical silicate or
oxide mineral free from transition metals such
as MgO (periclase) or Mg
2
SiO
4
(forsterite)
is
