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Weertman, 1968, 1999), then the creep rate at
high-temperature has nothing to do with the
Peierls stress. In order to infer the dominant slip
systems, one needs to evaluate the strain-rate for
each slip system that is controlled by the in-
terplay of several processes including dislocation
glide and climb. Cordier
et al
. (2012) presented
a more sophisticated analysis of deformation of
MgOwhere they calculated the effective viscosity
at geological strain-rates under the lower mantle
conditions from the dislocation velocity using a
model of dislocation glide over the Peierls bar-
rier. However, in order to calculate the creep
strength from dislocation glide velocity and com-
pare the creep strength for another mechanism
(recovery-controlled creep), they used unconven-
tional models. For example, they argued that
the effective viscosity cannot be defined for a
recovery-controlled regime (''athermal regime'' in
their terminology) because the flow stress is in-
dependent of strain-rate (and temperature). Such
a notion is not supported by the experimental
observations nor by the theoretical models as dis-
cussed in this chapter (Equation (4.9); see also
Frost & Ashby, 1982; Weertman, 1968, 1999;
Karato, 2008; Poirier, 1985). Consequently, the
validity of their conclusions is highly question-
able.
In these studies, it is essential to demonstrate
the validity of the method one uses by comparing
the results on some materials for which detailed
experimental studies are available. For example, if
one wants to predict the dominant slip system of
post-perovskite through computational studies,
one should apply such a method to a material for
which the dominant slip systems are well known
(e.g., olivine at low pressures). Unfortunately, this
important step is often ignored.
The more promising and important role of the-
ory is to provide some guide to interpret and
extrapolate experimental data. For example, there
is an important issue of the interpretation of
X-ray diffraction to determine the stress. One
needs a theory to apply this technique to deter-
mine stress acting on a sample (e.g., Karato, 2009).
Also, the development of lattice-preferred orien-
tation (LPO) during deformation is an important
topic but conducting deformation experiments
with a broad range of deformation geometry is
difficult. Theoretical modeling of LPO develop-
ment plays an important role in this area (e.g.,
Kaminski
et al
., 2004). Shear localization is an
important process to control the strength of the
lithosphere. However, experimental studies on
shear localization are limited partly by the limita-
tion of a sample size. Theoretical considerations
will help guide experimental studies on shear
localization.
4.6 Some Applications
In this section, I will illustrate how the knowledge
on rheological properties of minerals and rocks
and the models of temperature, water distribu-
tion may be integrated to understand rheological
properties and dynamics of the Earth's interior.
4.6.1 Is the lower crust weak?
Deformation of the continental lower crust
makes important contributions to the tectonics
of the continents including rifting and deforma-
tion associated with continental collisions. An
important question that has been asked is either
the lower crust and the upper mantle are well
coupled or not. If the lower crust is significantly
weaker than the upper mantle, then the crust
and mantle will be decoupled mechanically. The
rheological properties of the continental lower
crust can be estimated by the analyses of some
geophysical observations including post-seismic
crustal deformation, topography and gravity and
the results suggest a large regional variation (e.g.,
B urgmann & Dresen, 2008).
The dominant minerals of the continental
lower crust include ortho- and clinopyroxenes,
plagioclase and garnet (these minerals make
a mafic rock such as gabbro) and they have
substantially higher FeO and SiO
2
content than
the upper mantle (Rudnick & Fountain, 1995).
Experimental data on these minerals or rocks are
limited but the results on diabase (basaltic rock),
plagioclase and clinopyroxene show that under
