Deformation Mechanisms: Crystal Plasticity - Materials Science for Structural Geology - page 137

cross-slip motion through the formation of a constriction in the extended dislo-
cation. Such a process can be thermally activated and models have been proposed
by Schoeck and Seeger ( 1959 ), Seeger et al. ( 1959 ) and Wolf ( 1960 ), on the one
hand, and by Friedel ( 1959 , 1964 , p. 164) and Escaig ( 1968a , b ), on the other hand,
for situations where the dislocation is less or more dissociated in the cross-slip
plane than in the primary plane, respectively (see also Schoeck 1980 ; see also
Vanderschaeve and Escaig 1979 ). The theoretical discussions have centered
mainly on estimating the activation energy for the dislocation motion in the cross-
slip plane, predicting that in some cases the activation energy will depend on the
stress and in other cases not.
In the case of only slightly dissociated dislocations, the energy barrier associ-
ated with the constriction mentioned above can be viewed formally as a sort of
Peierls barrier and the motion of the constriction as analogous to the migration of a
kink. This view is particularly appropriate in cases where the dissociation is dif-
ficult to resolve but the core can be regarded as being extended somewhat outside
the cross-slip plane, as in a zonal dislocation (cf. b.c.c. metals: Hirth and Lothe
1982 , p. 369; cf. b.c.c. metals: Louchet 1979 ; Vitek 1985 ).

6.4.3 Climb Velocity of Edge Dislocations

We consider only the case of a pure edge dislocation under the influence of a
normal stress r applied parallel to its Burgers vector (for the case of a mixed
dislocation and a general stress, see Hirth and Lothe 1982 , p. 562). The first
estimate of the climb velocity v can be made using the formalism of Sect. 3.2.4 if
we regard the mobile entity as a dislocation segment of length equal to the
structure repeat distance b 1 parallel to the dislocation and we write v ¼ b 2 v where
b 2 is the structure repeat distance in the direction of climb and m the jump fre-
quency. From relation ( 6.6b ) the climb force on such a segment is rbb 1 ; which can
be written in molar terms as rV m where V m is the molar volume. In the case of
relatively low stresses such that rV m RT , we can then apply ( 3.12d ) to obtain

exp DG
RT

v ¼ b 2 v ¼ b 2 V m rm 0
RT

ð 6 : 18 Þ

where DG is the molar activation energy. If the thermally activated event is
essentially one of volume self-diffusion, we can treat v 0 exp ð DG = RT Þ as the
diffusional jump rate C which, from ( 3.32 ), is equal to D = afb 3 where D is the
diffusion coefficient, af a numerical factor of order unity, and b 3 the jump distance.
Thus, in the approximation that af is put equal to unity and b 2 ; b 3 equal to the
Burgers vector b,( 6.18 ) becomes

v DV m r
bRT

ð 6 : 19 Þ