Imaging of dislocations
5.5.5 Imaging of dislocations
Image contrast from imperfections arises from the the diffraction of electrons by crystals. In the case of
dislocations the displacement vector R is essentially equal to b, the Burgers vector of the dislocation, since atoms near the core of the dislocation are displaced parallel to b. In physical terms, it is easily seen that if a crystal, oriented off the Bragg condition,
i.e. s 6D 0, contains a dislocation then on one side of the dislocation core the lattice planes are tilted into the reflecting position, and on the other side of the dislocation the crystal is tilted away from the reflecting position. On the side of the dislocation in the reflecting position the transmitted intensity,
Figure 5.39 Schematic diagram showing the dependence of
i.e. passing through the objective aperture, will be the dislocation image position on diffraction conditions .
158 Modern Physical Metallurgy and Materials Engineering
Figure 5.40 (a) Application of the g.b D 0 criterion. The effect of changing the diffraction condition (see diffraction pattern inserts) makes the long helical dislocation B in (a) disappear in (b) (after Hirsch, Howie and Whelan, 1960; courtesy of the
Royal Society) .
however, a dislocation goes out of contrast when the Figure 5.41a. In general, the contrast from a stacking reflecting plane operating contains its Burgers vector,
fault will not be uniformly bright or dark as would and this fact is commonly used to determine the Burg-
be the case if it were parallel to the foil surface, ers vector. To establish b uniquely, it is necessary to
but in the form of interference fringes running par- tilt the foil so that the dislocation disappears on at least
allel to the intersection of the foil surface with the two different reflections. The Burgers vector must then
plane containing the fault. These appear because the
be parallel to the direction which is common to these diffracted intensity oscillates with depth in the crystal two reflecting planes. The magnitude of b is usually
as discussed. The stacking fault displacement vector the repeat distance in this direction.
R , defined as the shear parallel to the fault of the por- The use of the g.b D 0 criterion is illustrated in
tion of crystal below the fault relative to that above the Figure 5.40. The helices shown in this micrograph
fault which is as fixed, gives rise to a phase difference have formed by the condensation of vacancies on to
˛D
screw dislocations having their Burgers vector b par- side of the fault. It then follows that stacking-fault con- allel to the axis of the helix. Comparison of the two pictures in (a) and (b) shows that the effect of tilt-
for which g.R D n. This is equivalent to the g.b D 0 ing the specimen, and hence changing the reflecting
criterion for dislocations and can be used to deduce R. plane, is to make the long helix B in (a) disappear
The invisibility of stacking fault contrast when in (b). In detail, the foil has a [0 0 1] orientation and
g.R D 0 is exactly analogous to that of a dislocation the long screws lying in this plane are 1/2[1 1 0]
when g.b D 0, namely that the displacement vector is and 1/2[1 1 0]. In Figure 5.40a the insert shows the
parallel to the reflecting planes. The invisibility when
0 2 0 reflection is operating and so g.b 6D 0 for either
g.R D
1, 2, 3, . . . occurs because in these cases the
A or B, but in Figure 5.40b the insert shows that vector R moves the imaging reflecting planes normal the 2 2 0 reflection is operating and the dislocation B
to themselves by a distance equal to a multiple of the is invisible since its Burgers vector b is normal
spacing between the planes. From Figure 5.41b it can
be seen that for this condition the reflecting planes are 2⊳ C ⊲ 1 2 ð 1 ð 2⊳ C 0 D 0 for the dislocation B, and is
to the g-vector, i.e. g.b D 2 2 0.1/2[1 1 0] D ⊲ 1 2 ð 1ð
once again in register on either side of the fault, and, as therefore invisible.
a consequence, there is no interference between waves from the crystal above and below the fault.