Geology Reference
In-Depth Information
nucleation of new kinks. The new kinks are necessarily nucleated as kink pairs
unless the nucleation occurs where the dislocation ends at an interface or junction,
or unless the kink is produced by intersection by another dislocation of the same
Burgers vector moving on another slip plane. The latter two origins for new kinks
are probably, in general, of minor importance for dislocation mobility in materials
of high Peierls stress, the dislocation mobility in these being thought rather to
depend strongly on the thermal nucleation of kink pairs, at least in certain ranges
of temperature.
The energy of a kink, E
k
;
can be expressed approximately as
2
E
k
2b
np
2
E
0
l
E
p
l
ð
6
:
10
Þ
(Hirth and Lothe
1982
, p. 254) where n
;
E
0
and E
p
are as defined by (
6.8
) for a
length l of dislocation line. Putting
ð
E
0
=
l
Þ¼
aGb
2
and
ð
E
p
=
l
Þ¼ð
b
=
np
Þ
Gb
2
as in
Sect. 6.2.3
, we obtain
b
2
Gb
3
2a
np
E
k
ð
6
:
11
Þ
That is, E
k
is of the order of
ð
1
=
5
Þ
b
1
=
2
Gb
3
within a factor of two or three, where
b is the same numerical parameter as in (
6.9
). The value of E
k
can thus be expected
to vary from less than 0.1 eV for the close-packed metals to the order of 1 eV for
covalent crystals. A more refined calculation indicates that E
k
is several times
larger in screw dislocations than in edge dislocations (Hirth 1982, p. 256, where
the relationship between E
k
and the width of the kink is also discussed). The
energy of a kink pair is almost 2E
k
for all but very small separations of the
individual kinks.
When the kink energy is relatively large, it is necessary to raise the temperature
quite substantially in order to make possible a significant rate of kink pair
nucleation by thermal activation and so facilitate dislocation glide in face of a high
Peierls barrier. This situation is presumed to explain why plastic deformation is
only achieved at elevated temperatures in materials such as germanium and silicon
and it probably also underlies the difficulty of deforming minerals such as quartz
and the framework silicates. Raising the temperature in these cases may also
facilitate the surmounting of the secondary Peierls barriers along the potential
ridge, promoting the mobility of the kinks thus nucleated. For further review of the
role of kink nucleation and mobility, see Hirth and Lothe (
1982
, pp. 532-545),
Philibert (
1979
) and Guyot and Dorn (
1967
).
A jog consists also of a unit step in an otherwise straight dislocation line but,
instead of the step lying within the slip plane as for a kink; it now has a component
normal to the slip plane. A jog is probably commonly formed in a dislocation as a
result of intersection by another dislocation having a Burgers vector inclined to the
slip plane of the first dislocation (intersection by a dislocation with Burgers vector
lying in the slip plane of the first dislocation would produce a kink in it; see Hull
