Geoscience Reference
In-Depth Information
determined, it shows a negative correlation, i.e.,
q
H
<
0 Dai and Karato (2009c).
These studies essentially support the hypoth-
esis of (Karato, 1990) that hydrogen enhances
electrical conductivity, but in details, these ob-
servations do not agree with some aspects of the
simple model by (Karato, 1990). First the activa-
tion energy of electrical conductivity due to hy-
drogen is considerably smaller (
O
O
H
O
H
O
O
HH
O
M-site
O
O
H
′
+
H
·
(2H)
X
70-100 kJ/mol)
than the activation energy of hydrogen diffu-
sion (
∼
(a)
130-150 kJ/mol) (e.g., Du Frane & Tybur-
czy, 2012; Hae
et al
., 2006; Kohlstedt & Mack-
well, 1998), second the dependence of electrical
conductivity on the water content is not always
as expected from the simple model, and third the
electrical conductivity in hydrogen-bearing min-
erals depends on oxygen fugacity although the
original model predicts no dependence on oxygen
fugacity.
Such deviations from the simple model can be
explained by a hybrid model of hydrogen disso-
lution (Karato, 2006). In this model, we consider
that the hydrogen atoms dissolved in minerals
are present as several different species and the
concentrations of hydrogen in various species
are controlled by the thermodynamic equilibrium
(and by the charge balance). For example, when a
majority of hydrogen atoms goes to the M-site as a
neutral defect, (2
H
)
M
, that defect can be ionized as
∼
H
·
H
′
Δ
E
2
Δ
E
1
(2H)
X
(b)
Fig. 5.9
A model of hydrogen-related defects in a
nominally anhydrous mineral. (a) A majority of
hydrogen-related defects in mantle minerals is a
neutral defect such as (2
H
)
M
(two protons at M-site
vacancy). However, some fraction of these neutral
defects are ionized to form charged defects by a
reaction (2
H
)
M
⇔
H
M
+
H
•
(
H
M
: one hydrogen
trapped at M-site vacancy,
H
•
: ''free'' proton). (b) The
energy levels of hydrogen-related defects. At
equilibrium the concentrations of these charged
defects are controlled by the thermo-chemical
equilibrium of the above reaction as well as the
conditions of charge balance. The presence of these
three defects was inferred for wadsleyite (Nishihara
et al
., 2008). Even if the concentrations of these defects
are smaller than that of a neutral defect, the minority
charged defects could control electrical conductivity if
the product of mobility and concentration is high.
E
1,2
is the energy difference between different defects
relative to the neutral defect (2
H
)
M
.
H
M
+
H
•
(2
H
)
M
⇔
(5.20)
where
H
M
is a M-site vacancy that contains one
proton (Figure 5.9) and
H
•
is ''free'' proton. In
most cases the concentrations of
H
M
and
H
•
are
less than that of (2
H
)
M
. However if the mobility
of
H
M
or
H
•
is larger than that of (2
H
)
M
,then
contributions from these minority defects can
be important. There are a few observations that
are consistent with this hybrid model. First,
(Nishihara
et al
., 2008) found that several infrared
absorption peaks of wadsleyite correspond to
different hydrogen-defects ((2
H
)
M
,
H
M
,
H
•
).
Second is the dependence of conductivity on the
water content. When ionization of a neutral defect
occurs as shown by Equation (5.21), then the con-
centrations of charged defects can be calculated
as a function of water fugacity using the law of
mass action and appropriate charge balance rela-
tionship. It can be shown that the concentration
of
H
•
depends on the water fugacity (and hence
the total water content (we use
C
W
∝
f
H
2
O
,for
olivine and wadsleyite)) as Karato (2006),
2[
V
M
]
[
H
•
]
f
1
/
2
H
2
O
f
−
1
/
12
for [
Fe
•
M
]
∝
=
(5.21a)
O
2
