Geology Reference
In-Depth Information
E
kn
;
although depending in form on the form assumed for the Peierls potential, can
commonly be approximated as
(
)
3
4
s
s
p
E
kn
¼
E
k
1
ð
6
:
13a
Þ
according to Kocks et al. (
1975
, p. 187), where E
k
is the kink energy (
Sect. 6.2.4
)
and s
p
the Peierls stress. A value for E
km
seems to be more difficult to estimate
(Hirth and Lothe
1982
, p. 534); it is probably somewhat less than E
kn
but may still
be quite significant (Hirsch
1985
). Further development of the theory needs to take
into account the finite lengths of dislocation segments between nodes that limit the
free run of kinks (Hirth and Lothe
1982
, p. 545). For a discussion of the role of
kinks in the dislocation velocity in germanium and silicon, see, for example,
Louchet and George (
1983
) and Jones (
1983
).
In the majority of situations, the intrinsic behavior just considered will probably
be masked by the influence of extrinsic factors affecting dislocation velocity.
These factors may include any of the dislocation interactions listed in
Sect. 6.3
which have a local pinning effect on the dislocation. The treatment by Hirth and
Lothe (
1982
, Chap. 16) of the velocity of jogged dislocations provides an approach
to the treatment of a wider range of local pinning effects.
More generally, if the glide velocity of a dislocation is determined by rate of
thermally activated crossing of barriers of any sort, and if we express the velocity as
v
¼ð
DA
=
l
Þ
m
ð
6
:
13b
Þ
where A is the area swept out by a dislocation segment of length l in a single
activation event, and m is the frequency of such events, given by (3-12 g), then we
obtain
exp
DE
sb DA
2
DA
v
¼
2v
0
DA
l
sinh
sbDA
2kT
ð
6
:
14
Þ
kT
where, in addition to DA and l just defined, v
0
is the attempt frequency (now of the
order of the vibration frequency for a dislocation segment, say, 10
10
-10
11
s
-1
Friedel
1964
), DE
the activation energy and DA
the activation area.
In practice, it is usually difficult, a priori, to assign values to the parameters
l
;
DA
;
DA
and DA
in (
6.14
) and so it is common to adopt a more empirical
approach and attempt to fit experimental observations to expressions that are
analogous to the approximate forms in Eqs. (
3.12d
) and (
3.12e
)
in
Sect. 3.2.4
,
namely:
m
¼
A
0
s
m
exp
Q
RT
ð
6
:
15
Þ
and
m
¼
m
0
exp
Q
sbDA
RT
ð
6
:
16
Þ
