Geology Reference
In-Depth Information
the grains (Bender et al.
1980
; Dobson et al.
2007
; Johnson
1977
; Kingery et al.
1979
; Seah and Hondros
1973
; Unertl et al.
1977
). The enrichment ratio may also
vary with the nature of the boundary (Balluffi
1979
).
In contrast to the highly localized nature of equilibrium segregation in grain
boundaries, systems that are not in equilibrium may show gradients in chemical
composition that extend much further into the grains, even tens or hundreds of
microns (Westbrook
1969
). Such gradients can generally be viewed as frozen-in
transients in systems that are in course of adjustment to changing conditions, most
commonly involving the precipitation of excess solute as the solid solubility
decreases during cooling (Kingery
1974
); presumably the precipitation occurs in
the grain boundaries because of easier nucleation there (Clemm and Fisher
1955
).
The process has been modeled by Cai (
1991
) and Xu (
1987
).
Minor phases present in the boundary regions between the major phases can be
of special importance in the experimental deformation of rocks. These accessory
phases may be of igneous origin, be formed during metamorphism or weathering,
or represent cements in sedimentary rocks. They commonly give rise to a fluid
phase at elevated temperatures, either because of dehydration of hydrous phases or
because of partial melting related to a relatively low solidus in the system of
phases present. Interest attaches to the role of such fluid phases in grain boundaries
both from the point of view of interpreting high temperature experimental
observations and for possible application to natural systems such as migmatites or
low velocity regions in the lithosphere.
The influence of a small amount of melt on the flow properties of a rock
depends on the distribution of the melt, which in turn is related to its amount and to
the relative solid-solid and solid-liquid interfacial energies, c
SS
and c
SL
.Ifa
simple grain boundary intersects a pocket of melt and thermodynamic equilibrium
is established, the grain-melt interfaces will take on spherical curvatures and the
dihedral angle h where these interfaces meet the grain boundary (Fig.
1.1
)is
governed, in the absence of anisotropy, by the following considerations (Bulau
et al.
1979
; Raj
1981
; Raj and Lange
1981
; Smith
1948
,
1952
; Wray
1976
):
1. When c
SL
c
SS
=
2
;
the dihedral angle h
¼
0
:
The melt will then tend to pene-
trate the total grain boundary area and so have a maximum direct mechanical
effect. However, taking into account also the maximization of the interfacial
curvature, complete wetting of the grain boundaries at equilibrium for a fixed
grain size will not occur unless the relative volume of melt exceeds about 21 %,
depending on the exact grain shapes (Wray
1976
); below this fraction, the melt
will tend to concentrate in the 3-grain and 4-grain junctions and to be not
interconnected. The case h
¼
0 is only to be expected where there is very close
chemical affinity between solid and melt.
2. When c
SS
=
2\c
SL
\c
SS
;
then cos h
¼
c
SS
=
2c
SL
and 0\h\60
:
The melt will
tend to take up a prismatic configuration in the 3-grain junctions (grain edges)
and the volume fraction at which equilibrium interconnection occurs will
decrease from about 21 % to about 0.6 % as h increases from 0 to 60 (Wray
1976
). In contrast, the volume fraction at which complete wetting or separation
