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et al
., 2011). Karato (2011a) discussed the fact that
at pressures around
be included in addition to the temperature
dependence. This means that one needs to use at
least three parameters to characterize the rheo-
logical structure of super-Earths: mean viscosity,
temperature dependence of viscosity (viscosity
near the surface), and pressure dependence of
viscosity (deep mantle viscosity). In addition,
when one evaluates whether plate tectonics
occurs on these planets or not, one should also
consider the dependence of lithosphere thickness
on planetary size.
1TPa, several processes
will make materials weaker and that a model of
constant
V
∗
is not valid under these conditions.
At such a pressure range, deviations from the
conventional formulation such as Equation
(4.9) occurs including (1) transition in diffusion
mechanisms,
∼
(2) transition to a weaker phase
→
(B1
B2), (3) dissociation of a post-perovskite
phase and (4) transition to metallic state. All
of these processes reduce viscosity. Therefore
viscosity in the deep interior of a super-Earth is
likely lower than that of the lower mantle of the
Earth (Figure 4.25).
In modeling the dynamics of super-Earths,
pressure dependence of viscosity needs
4.8 Summary and Perspectives
Plastic deformation (rheological properties) of
minerals and rocks plays a crucial role in con-
trolling the dynamics and evolution of terrestrial
planets. However because of the presence of
multiple mechanisms of deformation, sensitivity
to many parameters and also because of nonlinear
rheological behavior (in most cases), reliable
quantitative studies of rheological properties is
difficult. I summarized some basics of rheological
properties that will guide a reader to make a good
judgment when he/she applies laboratory data or
results of computational studies to understand
the dynamics of the Earth and the planets.
High-resolution mechanical data obtained at
low pressures (
<
0.5GPa) on synthetic samples
with controlled water content and grain-size con-
tributed to understand the microscopic processes
of deformation (see Kohlstedt, 2009 for a re-
view). However, the applicability of these results
is limited to less than
to
I
II
III
∼
20 km depth in Earth.
Experimental results applicable to Earth's inte-
riors below
(~0.1 TPa)
(~0.5 TPa)
Depth (pressure)
(~1 TPa)
20 km can be obtained only from
experiments at pressures above
∼
Fig. 4.25
A schematic diagram showing the depth
variation of viscosity in the mantle of super-Earth
where the maximum pressure reaches
1GPa or higher.
The existing experimental data and seismologi-
cal observations strongly suggest that power-law
dislocation creep and diffusion creep are the domi-
nant mechanisms of deformation in most regions
of Earth's (and planetary) interior. Rheological
properties of minerals and rocks are highly sen-
sitive to temperature, pressure, water (hydrogen)
content and grain-size. Characterizing the influ-
ence of these parameters on rheological properties
∼
1TPa(from
Karato, 2011a). Under these high-pressure conditions, a
commonly held view of higher viscosity at higher
pressure will not work. Several processes including (i) a
change in diffusion mechanism, (ii) a change to a more
compact crystal structure (B1
∼
B2, decomposition of
post-perovskite) and (iii) transition to metals will
weaken the material. Reproduced with permission of
Elsevier.
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