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Examples were shown for B1 (NaCl structure)
(Ashby & Brown, 1982) and garnet (Karato
et al
.,
1995a) (see Figure 4.15a,b). (Karato, 1989c) ex-
tended such a study to oxides and silicates and
noted that there is a large variation in plastic prop-
erties among oxides and silicates even after the
normalization ((Ashby and Brown, 1982) treated
oxides as a single group). In particular, this study
showed that a transition to a dense structure does
not necessarily lead to a high resistance to plas-
tic deformation. (Karato, 2011a) extended such
an analysis to include the influence of transition
to the metallic state and the influence of the
B1
olivine
10
3
T
=
1473 K
•
10
−
4
s
−
1
=
10
2
r
=
1.20
+
/
−
0.05
B2 transition (Figure 4.15c).
Such an analysis shows that unlike elastic-
ity where a phase transformation to a denser
structure leads to a higher elastic constant
with a minor correction for the influence of
coordination (the Birch's law - Liebermann,
1982), density does not play an important role
in high-temperature plasticity. The Birch's law
of correspondent state does not work for plastic
properties. In many cases, a change in crystal
structure has only a modest effect. An increase in
melting temperature, therefore, will increase the
effective viscosity modestly. Also, if a transition
to metallic state occurs in the deep mantle
of super-Earths (
→
10
10
−
1
10
2
1
10
fH
2
O, GPa
(a)
9000
8000
7000
6000
T
=
1473 K
•
=
10
−
4
s
−
1
5000
4000
1TPa), then a substantial
reduction in effective viscosity will occur.
∼
V*
w
=
24
+
/
−
2 cm
3
/mol
3000
2000
0
0.5
1
1.5
2
2.5
4.4.5 Influence of partial melting
Pressure, GPa
(b)
Figure 4.16 summarizes the experimental obser-
vations on the influence of partial melting
on plastic deformation of olivine aggregates
(Kohlstedt, 2002). Deformation experiments
were performed both for the diffusion creep
and dislocation creep regimes. The influence of
partial melting is stronger in the diffusion creep
regime than in the dislocation creep regime.
This is due to the fact that in the diffusion
creep regime, fast diffusion in the melt as well
as stress concentration enhances deformation
whereas in the dislocation creep regime only
stress concentration enhances deformation.
They proposed an empirical formula to explain
Fig. 4.14
Analysis of the influence of water on creep
strength in olivine under water-saturated conditions
(after Karato & Jung, 2003). (a) the determination of the
water content exponent
r
. (b) the determination of the
activation volume
V
wet
(shown as
V
w
). Reproduced
with permission of Taylor & Francis.
temperature,
T
m
, and stress by shear modulus,
μ
,
then most of the data fall into a master curve,
F
T
ε
(
T
,
P
,
σ
)
ν
D
σ
μ
(
P
)
=
T
m
(P)
,
(4.18)
