Geology Reference
In-Depth Information
O-lattice. For best fit, and therefore presumably minimum energy, this plane will
pass as much as possible through O-lattice points. Since the O-lattice points
represent sites of a maximum degree of coincidence of the two crystal structures,
and since the regions halfway between these points [that is, the intersections with
the cell walls in the sense of Wigner-Seitz cells (Wigner and Seitz
1933
)] represent
regions of maximum misfit, the grain boundary can be viewed as made up of
regions of good fit separated by dislocation lines having a Burgers vector equal to
a crystal lattice vector and a spacing corresponding to the periodicity of the
O-lattice (the elements of dislocation theory are summarized in
Chap. 6
). These
dislocations are known as primary grain boundary dislocations. Such a description
of a grain boundary corresponds well with observation in the case of small-angle
boundaries but it is more a geometrical formalism for high-angle grain boundaries
where the dislocation cores will overlap, even allowing for some relaxation along
the grain boundary to maximize the areas of good fit. However, it is generally held
that, to minimize energy, the structure of the core of high-angle grain boundaries
will adjust itself to conform as far as possible to the nearest low energy config-
uration, such as that of a CSL of low R, and that the remaining misfit will be
concentrated in a further network of dislocations known as secondary grain
boundary dislocations. Burgers vectors of the latter dislocations are vectors of the
DSC lattice, thus revealing the significance of its introduction (note that in
imagining the formation of such a dislocation, the Volterra cut must be made in the
grain boundary itself). Such dislocations have also been imaged by TEM although
their smaller Burgers vectors make the imaging more difficult. Both types of grain
boundary dislocation are described as intrinsic dislocations since they represent
aspects of the intrinsic structure of the ideal or equilibrium grain boundary core
formed between two perfect crystals. It may also be noted that steps or ledges in
the boundary can be intrinsically associated with grain boundary dislocations.
Just as a perfect dislocation can have defects introduced into it, so defects can
be added to the ideal grain boundary, in particular, vacancies and other disloca-
tions known as extrinsic dislocations. Extrinsic dislocations can be imagined as
arising when a boundary is formed between two imperfect crystals or when a
crystal dislocation is moved from the grain interior into the boundary. In the latter
case the dislocation may dissociate into other grain boundary dislocations having
Burgers vectors of both the crystal lattice and the DSC lattice if it is energetically
favorable to do so. If a sufficient number of dislocations is introduced, the structure
of the grain boundary core may be regarded as being transformed by incorporating
a regular array of the new dislocations as intrinsic grain boundary dislocations.
One of the principal differences between intrinsic and extrinsic dislocations lies in
the absence of long range stress fields around the former on account of their
regular spacing, while extrinsic dislocations can show a stress field that appre-
ciably penetrates the adjacent grains.
The analytical or atomistic approach. The geometrical approach to the grain
boundary core structure just outlined takes little account of the nature of the crystal
structure and bonding type and has naturally found most application in metals
where the structure is simple and the bonding non-directional and non-polar. In the
