Geology Reference
In-Depth Information
boundaries, see the three-yearly proceedings of the International Conferences on
Intergranular and Interphase Boundaries. Farver and Yund (
1995
) and Keller,
Hauzenberger and Abart (
2007
) deal with diffusion in interphase boundaries.
1.3.3 Solute Segregation, Extra Phases, and Void Space
at Grain Boundaries
In considering the segregation of impurities or heterogeneity in chemical com-
position in or near grain boundaries, a distinction must first be made between
equilibrium and non-equilibrium situations. At equilibrium, segregation appears to
be confined to the core regions of grain boundaries, of the order of 1 nm in
thickness or less. Observations have been mainly carried out on metals, involving
measurements on grain boundary energies and direct analyses on grain boundary
fracture surfaces using Auger electron spectroscopy (Hondros
1976
; Seah and
Hondros
1973
). However, a few observations on ceramics and minerals, such as
aluminium oxide (for example, Johnson
1977
) suggest that similar effects may be
expected in rocks although the quantitative aspects may be rather different because
of differences in defect formation energies and, in ionic materials, the concen-
tration of electrical charge in grain boundaries tends to be an important additional
factor (Hall
1982
; Kingery
1974
). Similar considerations can also be expected to
apply to individual dislocations and to low angle or subgrain boundaries.
The reason for grain boundary segregation is envisaged to lie in the existence of
a variety of sites different from those in the interior of the grains, a situation
analogs to that at the surface of a crystal although less pronounced. Thus, ther-
modynamical considerations similar to those for surfaces have been applied
(Hondros and Seah
1977
; McLean
1957
), involving the equivalent of a Langmuir
adsorption isotherm expressing the concentration of a species in the boundary in
terms of the concentration of available sites and an energy of segregation or
binding energy; typically 0-20 kJ mol
-1
for solute impurities in metals (Seah and
Hondros
1973
), comparable to that for physisorption (Atkins
1986
, p. 772). The
segregation commonly amounts to less than a monolayer, especially at high
temperatures. However, multilayers of two or more atoms thickness have also been
observed, analogous to multilayer adsorption of gases on surfaces (Seah and
Hondros
1973
), For non-metallic materials space charge effects may lead to some
broadening of the profile of segregation (Hall
1982
; Yan et al.
1983
) but it is not
clear that this effect is generally very important (Johnson
1977
); for example, Tiku
and Kröger (
1980
) find the effect on conductivity in Al
2
O
3
to be small. There have
been suggestions that in some cases the segregation may lead to new structures in
the grain boundary core (Guttmann
1977
) and atomistic aspects have been con-
sidered (Vitek and Wang
1982
). The extent of segregation can be expressed by a
grain boundary enrichment ratio relative to the grain interiors. Enrichment ratios
from unity to 10
5
have been shown to be inversely related to the solid solubility in
