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In-Depth Information
ringwoodite
10
4
Grain size (
μ
m)
10
−
2
10
−
1
1
10
10
3
2.5
0.4
diffusion creep
(superplasticity)
10
2
0.5
10
2
704 (S)
704 (L)
1740
0.6
1
(
s
/
μ
~10
−
2
)
10
−
1
0.7
1.5
710
10
−
2
900
temperature, K
1000
dislocation creep
800
850
950
0.8
1
10
1
10
2
10
3
L/b
10
4
10
5
Fig. 4.21
Influence of temperature on the grain-size of
wadsleyite (ringwoodite) formed by transformation
from olivine in a slab (after Riedel & Karato, 1997).
Reproduced with permission of Elsevier.
Fig. 4.20
The deformation mechanism map for
ringwoodite (after Karato
et al
., 1998). T: temperature,
Tm: melting temperature, L: grain-size, b: the length of
the Burgers vector,
σ
: stress,
μ
: shear modulus. The
experiments were conducted at
σ/μ
≈
order of 1
m. Using the critical grain-size for the
transition to diffusion creep of
μ
10
−
2
. In Earth's
1mm and the ini-
tial grain-size of several mm, I conclude that the
viscosity reduction will be
∼
10
−
3
and the grain-size for the
mechanism change will scale as
L/L
o
=
10
−
5
interior,
σ/μ
≈
−
m
where
n
is the stress exponent and
m
is the grain-size
exponent. Therefore at lower stresses in Earth, the
transition grain-size will be larger. Results similar to
these were obtained by Kawazoe
et al
. (2010).
Reproduced with permission of Nature.
n
−
(
σ/σ
o
)
−
∼
6-9 orders of magni-
10
6
-10
9
,
η
:vis-
cosity,
L
: grain-size). In contrast, a warm slab
will not weaken because the grain-size after a
phase transformation will be large. This causes
a regional variation in the slab strength, and
provides a possible explanation for the observed
paradoxical correlation between the slab deforma-
tion and slab temperatures (Karato
et al
., 2001)
(Figure 4.22).
(
L/L
o
)
2
,
L/L
o
)
3
tude (
η/η
o
=
=
the western Pacific are deformed in the transi-
tion zone. A possible explanation of this puzzling
observation is the weakening caused by the grain-
size reduction after a phase transformation in
a slab. When a subducted slab penetrates into
the transition zone, a series of phase transitions
will occur that will modify the grain-size. Riedel
and Karato (1997) studied the influence of tem-
perature on the size of newly formed grains in
a slab. They found that the grain-size after a
phase transformation depends strongly on the
temperature and the grain-size is small when
the transformation occurs at low temperatures
(Figure 4.21). When a cold slab subducts, then
the grain-size reduction is significant and the
small grain-size will persists (because of slow
grain-growth), leading to substantial weakening
(Riedel & Karato, 1997; Karato
et al
., 2001). For
instance, the grain-size after the phase transfor-
mation in a cold slab is estimated to be on the
4.6.4 The lower mantle
(a) What is the deformation mechanism in the
lower mantle, and how does viscosity change
with depth in the lower mantle?
Very little ex-
perimental data are available for the rheological
properties of the lower mantle minerals. Quan-
titative deformation experiments under lower
mantle conditions have not been performed
at the time of this writing (February 2012).
Low-temperature deformation experiments at
unknown strain-rate were performed at lower
mantle pressures (e.g., Merkel
et al
., 2003,
2006, 2007; Cordier
et al
., 2004; Miyagi
et al
.,
2011). But, the relevance of these results to
deformation in the lower mantle is questionable,
