Geoscience Reference
In-Depth Information
H
∗
=
PV
∗
with a constant
V
∗
) is no longer
valid, and generally
V
∗
decreases with pressure
(Poirier and Liebermann, 1984; Karato, 2011a).
Because of this nonlinear effect, the effective vis-
cosity at very high-pressures will not be as high
as one would expect from Equation (4.9) with a
constant
V
∗
. Possible implications of this effect
will be discussed later in relation to the rheologi-
cal properties of the deep interiors of planets such
as super-Earths.
E
∗
+
olivine
10
2
V*
=
25
17
20
T
=
1573 K
15
10
−
5
s
−
1
10
10
1
10
−
1
4
8
12
16
Pressure, GPa
Fig. 4.11
Influence of pressure on the creep strength of
olivine (from Kawazoe
et al
., 2009). Different stresses
at the same pressure correspond to the stress estimate
using different diffracting lattice planes. V
∗
is
activation volume (in cm
3
/mol). Reproduced with
permission of Elsevier.
4.4.3 Effect of water
David Griggs and his coworkers discovered that
the creep strength of silicates such as quartz and
olivine decreases strongly with water content
(Griggs, 1967; Blacic, 1972). This early notion
was confirmed by the later studies using im-
proved experimental techniques (Kronenberg &
Tullis, 1984; Post
et al
., 1996; Chopra & Pater-
son, 1984; Karato
et al
., 1986; Mei & Kohlstedt,
2000a; Karato & Jung, 2003). These studies also
showed that a finite amount of hydrogen is dis-
solved in these minerals and that the degree to
which materials weaken depends on the amount
of dissolved hydrogen. Figure 4.12 shows some
examples of experimental observations on water
weakening effects.
The precise atomistic mechanisms by which
dissolved hydrogen may weaken minerals are
not well understood. However, based on the
theoretical models described in the previous
section, one can imagine a few possibilities.
(1) Dissolved water may enhance diffusion that
in turn enhances diffusion-controlled creep
(diffusion creep, dislocation creep controlled
by dislocation climb). (2) Dissolved water may
increase the concentration of jogs along the dislo-
cation that enhances dislocation climb and hence
deformation. (3) Dissolved water may increase
the concentration of kinks (see Figure 4.3b) and
hence enhances dislocation glide.
Using olivine for which the most detailed
studies have been performed, I will review some
observations. Costa and Chakraborty (2008)
reported that the addition of water (hydrogen)
to olivine enhances diffusion of silicon and
obtained under the conditions down to the depth
of
∼
300 km in the mantle, so there is no need for
large extrapolation in terms of pressure to esti-
mate the creep strength in the deep upper mantle.
Extrapolation in strain-rate is still needed but
the uncertainties in this extrapolation are small
because the stress exponent is well constrained
(
n
3-4). When the relationship (9) is used, we
obtain
V
∗
=
=
15-20 cm
3
/mol.
Diffusion coefficients are easier to measure at
high pressures than creep strength. Consequently,
a relatively large number of data are available
on diffusion coefficients measured at high pres-
sures than those on creep strength. For instance,
the diffusion coefficient of silicon (and oxygen) in
MgSiO
3
perovskite (Yamazaki
et al
., 2000) and the
diffusion coefficient of magnesium and oxygen in
MgO (Van Orman
et al
., 2003) were measured
at lower mantle pressures. Similarly, Shimojuku
et al
. (2004, 2009) measured the silicon and oxy-
gen diffusion coefficient in wadsleyite and applied
these results to high-temperature creep in wads-
leyite.
In Equation (4.9), the activation volume
V
∗
is
assumed to be independent of pressure. This is a
good approximation at low pressures (
P/K
0
<
0.1,
K
0
: zero-pressure bulk modulus (
K
0
=
120GPa for
olivine)). However at pressures comparable to or
larger than
K
0
, such a linear approximation (i.e.,
