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because deformation mechanisms are likely
high-stress mechanism such as the Peierls
mechanism that is irrelevant for most of the
hot mantle.
Based on the absence of seismic anisotropy,
Karato
et al
. (1995b) proposed that the majority of
the lower mantle deforms by grain-size sensitive
creep such as diffusion creep although disloca-
tion creep dominates in some regions of the D''
layer. Given this notion, some useful conclusions
can be obtained on the rheological properties
from the measurements of diffusion coefficients.
(Yamazaki & Karato, 2001) conducted such a
study and concluded that the depth variation
in viscosity is modest because both activation
energy and volume of lower mantle minerals (per-
ovskite and (Mg,Fe)O) are small. This provided a
simple explanation of the inferred modest varia-
tion in viscosity in the lower mantle (Figure 4.23).
They also noted that (Mg,Fe)O is likely weaker
than perovskite, and consequently, strain soften-
ing and resultant shear localization likely occur
in the lower mantle. If shear localization occurs,
then much of deformation in the lower mantle is
in narrow regions and a large portion of the lower
mantle is isolated from the large-scale material
circulation. Recently, Xu
et al
. (2011) determined
the diffusion coefficients of Si and Mg in MgSiO
3
perovskite. They used theoretical models of dif-
fusion creep and dislocation creep to discuss the
deformation mechanisms. They found that the
contribution from diffusion creep is comparable
to that of dislocation creep in the lower mantle.
However, a model of dislocation creep is not well
established and the conclusions based on a model
has large uncertainties.
A possible role of spin transition on diffu-
sion and rheological properties was discussed
by Wentzcovitch
et al
. (2009). Using the elastic
strain energy model of activation energy (Keyes,
1963), they suggest that the spin transition may
enhance plastic deformation. However, such a
conclusion is highly speculative because the elas-
tic strain energy model is a crude model for the
activation energy for diffusion and the appropri-
ate elastic constants to be used in this model is
not well known.
When deformation occurs by diffusion creep,
then viscosity depends strongly on grain-size.
However, the grain-size in the lower mantle is
poorly constrained. There is no sample from
the lower mantle except for small inclusions
in diamond (e.g., Harte, 2010). Yamazaki and
Karato (2001) estimated the average grain-size
from the comparison of the diffusion coeffi-
cients with geodynamically inferred viscosity.
Yamazaki
et al
. (1996) showed slow grain-growth
kinetics. Solomatov
et al
. (2002) investigated
the grain-growth kinetics through numerical
modeling and concluded substantially faster
Fig. 4.23
The viscosity-depth profiles
for the lower mantle calculated from
diffusion coefficients (from Yamazaki &
Karato, 2001). (a) dT/ dz
24
3
10%
30%
Perovskite
=
0
.
3K/kmand
22
(b) dT/ dz
0
.
6K/km. In both cases, the
pressure dependence of viscosity was
calculated by the elastic strain energy
model where the activation free energy
is assumed to be proportional to the
strain energy. The experimental results
on the activation volume are consistent
with the strain energy model.
Reproduced with permission of
Mineralogical Society of America.
=
Perovskite
3%
10%
30%
20
MgO
MgO
18
1000
2000
3000
Depth (km)
1000
2000
3000
(a)
(b)
