Geoscience Reference
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γ
SL
γ
SL
dihedral
angle
melt
θ
solid
solid
γ
SS
(a)
q
< 60
°
(b)
q
> 60
°
1
olivine
+
MORB (A
=
2.3)
KLB1(A
=
1.7)
Yoshino
et al
. (2005)
1.8
contact face
X
C
wetted face
X
C
=
0
1.6
=
1
1.4
1.2
A
=
1
1
2
20
°
1-
ϕ =
A
φ
40
°
60
°
3
2.5
2
0.1
1
⌠
⌡
X
C
dS
contiguity
ϕ =
4
π
R
2
θ =
80
°
von Bargen & Waff (1986)
(c) a solid grain
0.001
0.01
0.1
Melt fraction
φ
(d)
Fig. 3.1
Equilibrium geometry of melt under hydrostatic stress. At relatively small melt fractions, (a) an
interconnected network of grain-edge melt tubules develops with dihedral angles of
60
◦
, and (b) isolated melt
θ<
60
◦
. (Insert) Cross-section of a melt tubule perpendicular to the grain edge, showing the
equilibrium dihedral angle
pockets develop with
θ>
θ
that is given by 2 cos(
θ/
2)
=
γ
SS
/γ
SL
so that the solid-solid and solid-liquid interfacial
tensions,
)isdefinedbytheratioofthe
grain-to-grain contact area relative to the total surface area of each grain. It plays an essential role in determining
the mechanical properties of granular aggregates. (d) Wetness (
γ
SS
and
γ
SL
, are balanced at triple junctions. (c) The contiguity (
ϕ
=
−
ϕ
φ
1
) versus melt fraction (
) measured for
partially molten peridotites (symbols), and theoretically predicted for various
using the model of von Bargen and
Waff (1986) (thick lines). Modified from Yoshino
et al
. (2005). Reproduced with permission of the American
Geophysical Union.
θ
parameter
A
increases with decreasing dihedral
angle. Equation (3.1) provides a simple and useful
empirical relationship between
shape of the melt phase from tubule to sheet (Faul
et al
., 1994; Hirth & Kohlstedt, 1995). The good
agreement between the predicted and measured
contiguities (Figure 3.1d) indicates that the effect
of faceting is small. However, because of the
limited resolution of microscopic observations,
and because of the difficulty in distinguishing
tubes from sheets in two-dimensional (2D) cross-
sections, the effect of faceting is still subject
to debate. Recent progress in X-ray synchrotron
ϕ
φ
and
,which
is used in later sections with A
=
2.3 (olivine
+
20
◦
).
The standardmodel of von Bargen&Waff (1986)
neglects crystallographic anisotropy, and hence
neglects faceting. Several researchers have sug-
gested that faceting at the mineral-melt interface
enhances grain boundary wetting by changing the
MORB, or
θ
=
