Geology Reference
In-Depth Information
the CSL consists of those lattice points of the two coexisting crystal lattices that
coincide in space. The fraction of the lattice points that coincide is designated
by 1
=
R, where R is an integer. A low value of R and therefore a relatively small
CSL unit cell represents a rather special orientational and translational rela-
tionship between two grains. For more general relationships a CSL may or may
not exist.
3. The O-lattice (Bollmann
1970
): Given the crystal lattices defined in each grain
as before, an O-lattice is formed by any set of equivalent points within the unit
cells of the two coexisting crystal lattices that coincide in space. These points
are then called O-points (analogous to the pattern of light areas in a trans-
mission Moiré pattern in two dimensions). An O-lattice exists for all rela-
tionships between two grains. If a CSL exists, it represents a special case of an
O-lattice in which the O-points are crystal lattice points. Other special cases
arise where the relationship between the two crystal lattices is a rotation about a
common low-index axis or a matching of planes across the boundary. Thus, the
O-lattice is fundamental to all considerations of grain boundary core structure.
However, it is to be understood that it is only the O-points that define the
O-lattice and that we have to consider additionally the pattern of crystal lattice
points that fall within the O-lattice unit cells. This pattern may vary from one
cell to the next and may or may not be periodic. Thus, there are special rela-
tionships between the two crystal lattices for which there is a finite number of
different patterns within the unit cells (called ''pattern elements'' by Bollmann),
or even a single one, and the total pattern is then periodic. In the latter case, the
number N
0
of crystal unit cells per period of the pattern is a measure of the
overall degree of coincidence of all points within the crystal lattice unit cells,
N
0
being smaller the better this fit, in a manner somewhat analogs to that in
which R is a measure of the degree of crystal lattice site coincidence but with
more profound implications for the energy of a grain boundary configuration.
4. The DSC lattice (''displacement shift complete'') (Sutton and Balluffi
1995
): In
defining the DSC lattice, it is assumed that the two crystals are in a special or
optimal relationship (having either a CSL of low R or, at least, an O-lattice of
low N
0
) so that there is a periodicity in the pattern of crystal lattice points, as
just discussed. The DSC lattice is then derived from all displacements con-
necting pairs of crystal lattice points in this pattern which preserves the overall
pattern; it is the coarsest lattice that can accommodate all the crystal lattice
points of the two crystals (note: not all the DSC lattice sites or equivalent points
are occupied by crystal lattice points, the pattern itself having the periodicity
not of the DSC lattice but of a multiple or sublattice of the CSL or the
O-lattice). The DSC lattice has a sort of reciprocal relationship to the corre-
sponding CSL or O-lattice in the sense that the higher is R or N
0
the smaller is
the spacing of the DSC lattice.
So far we have considered the relationships between the two crystals that are to
share a boundary. Now we consider the location and structure of the boundary
itself. A grain boundary can be viewed as a particular plane located within the
