Analysis of the extended defects in 3C-SiC.pdf - Nelson Mandela ...

47
When this is incorporated into the Darwin-Howie-Whelan equations it modifies the
equations to be,
d
dz
g
2i(
s
g
i
g g
'
e
' g q '
g
g
dR
g ) g
i
'
(4.37)
g
dz
which only constitutes a change in the excitation error to an effective excitation error
given by,
dR(r)
( r) s g
(4.38)
dz
eff
sg g
4.3. Image Contrast for Selected Defects
4.3.1 Line Defects
As discussed in section 2.4 a dislocation is a linear lattice defect which may be
characterised by a Burgers vector b and a dislocation line direction u. It may be
characterised as being of edge character with b·u = 0 or screw character with b || u or
a mixture of both. In general the displacement field of a dislocation is given by,
1 sin 2
1
2
cos
R b
be
b u
ln r
(4.39)
2
4(
1
)
2(
1
)
4(
1
)
where υ is Poissons’s ratio, be the edge component of the Burgers vector and (r,θ)
polar coordinates in a plane perpendicular to the dislocation line direction.
4.3.2 Stacking Faults
The aim of this section is not to describe the full process of simulating an inclined
stacking fault with its associated partial dislocations but rather to describe a relatively
easy way of obtaining one-dimensional intensity profiles of stacking fault fringes. The
procedure uses a scattering matrix approach discussed in Section 4.2.5 with the