Geoscience Reference
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(a)
(b)
(d)
σ
1
a
200
µ
m
20
°
b
σ
3
(c)
10
µ
m
10
µ
m
Fig. 3.2
Experimental results of stress-induced melt redistribution (a, b, c) around each grain and (d) over distances
much greater than the grain scale. The vertical bar on the left side of (a) and (b) roughly shows the grain size.
(a) Melt preferred orientation under uniaxial compression (Daines & Kohlstedt, 1997). (b) Melt alignment under
simple shear (Zimmerman
et al
., 1999). (c) Enhanced grain boundary wetting under pure shear observed by shear
wave splitting (Takei, 2010). Reproduced with permission of Mineralogical Society of America. (d) Shear-induced
melt segregation into melt-rich bands, as reported in Holtzman
et al
. (2003a,b). Bottom image is a magnification of
a melt-rich band that looks dark in the top image. Reprinted with permission from AAAS.
scale disequilibrium geometries, produced exper-
imentally, are mostly anisotropic, and they can-
not be fully described by the single scalar variable
of contiguity (
and transport properties of partially molten
mantle. Stevenson (1989) theoretically predicted
the spontaneous segregation of melt into bands
during pure shear, and showed that the decrease
in matrix viscosity with increasing melt fraction
plays an essential role in band formation. Spiegel-
man (2003) extended this model to simple shear.
These models predict that the bands develop at
45
◦
to the shear plane (the bands are parallel to the
σ
1
direction), and they cannot explain the experi-
mentally observed lower angles. Katz
et al
. (2006)
explained the development of low-angle bands in
terms of nonlinear (power law) viscosity. In these
models of Stevenson (1989), Spiegelman (2003),
and Katz
et al
. (2006), a possible deviation of the
grain-scale melt geometry from the equilibrium
geometry is not taken into account. Recently,
Takei and Holtzman (2009c) presented a new
model in which the stress-induced anisotropy
on the grain scale is taken into account, and
they showed that an anisotropy in the matrix
). In Section 3.4, I present a general
formulation of the contiguity model that can be
applied to these anisotropic geometries.
In the partially molten rock samples deformed
in simple shear, Holtzman
et al
. (2003a,b)
observed spontaneous segregation of melt into
bands (Figure 3.2d). This demonstrates the
redistribution of melt over distances much
greater than the grain scale. The bands develop
at small strains (
ϕ
<
1) and persist at low angles
20
◦
) to the shear plane. The width and
spacing of the bands decrease with increasing
stress. When stress is removed, the melt-rich
bands spontaneously diffuse out to minimize the
total interfacial energy (Parsons
et al
., 2008).
A lot of attention has been paid to the
formation of melt-rich bands, because such
bands can significantly change the mechanical
15
◦
−
(
∼
