4.4 Extended Defects
91
Fig. 4.31 Schemes of a–c
pure tilt and d–f pure twist
boundary, dislocation
formation in (c) pure tilt
and f twist boundaries
(a)
(b)
(c)
(d)
(e)
(f)
(a)
(b)
(c)
0
1
3
2
4
5
-4
6
5
4
3
2
1
0
(d)
(e)
Fig. 4.32 a Scheme of a small-angle (pure tilt) grain boundary. b Model of edge dislocations in a {110} plane in Ge. c
Relation of dislocation distance d and tilt angle θ for various small-angle grain boundaries in Ge. Solid line is relation
d = 4.0 × 10 −8 /θ. d Optical image of an etched (CP–4 etch) Ge sample with a small-angle grain boundary. Adapted
from [359]. e HRTEM image of a small-angle grain boundary in Si with dislocations highlighted. From [360]
tilt SAGB are shown. The dislocation spacing is inversely proportional to the tilt angle θ . An image of
a twist SAGB is shown in Fig. 4.33.
Special large angle boundaries possess (for a certain angle) a coincident site lattice (CSL). Some of
these grain boundaries have a low energy and are thus commonly observed. The ratio of lattice points
of the CSL and the lattice unit cell is an odd integer number n; the corresponding grain boundary is
then labeled SAGB are also termed 1. 3 grain boundaries are always twin boundaries. An