Geology Reference
In-Depth Information
energy itself that is minimized by the complex motions or reorganization in the
core zone. However, the amplitude of the Peierls potential, and hence the Peierls
stress, need not be reduced and in fact may be increased by the core spreading,
rendering the dislocation less mobile (Vitek 1985 ).
If the discrete structural or topological disruptions in the core of a dislocation
are distributed over a region of sufficiently large dimensions that the long-range
stress field can no longer be regarded as deriving from a single linear singularity,
then the dislocation can be called an extended dislocation. Such a dislocation can
generally be regarded as made up of component partial dislocations separated by
ribbons of planar defect or fault ( Sect. 6.2.1 ). Any perfect dislocation with Burgers
vector ¼ can be dissociated into a set of j dislocations having Burgers vectors ¼ j
such that ¼ ¼ P ¼ j
without affecting the displacements at distances large com-
pared with the spacing of the new dislocations. However, if ¼ is already a mini-
mum or primitive lattice translation, the components b ¼ will not generally be lattice
translations and so will give rise to partial dislocations. Further, provided that
b 1 þ b 2 þ ... þ b j \b 2 and that the spacings of the partial dislocations are dis-
tinctly larger than their core diameters, the total elastic energy will be reduced by
the dissociation from approximately Gb 2 toward P j Gb j as the spacing of the
partial dislocations becomes large. However, additional energy must be provided
for the ribbons of planar defect separating the partial dislocations, in proportion to
the area of the ribbons. There will therefore be an equilibrium spacing corre-
sponding to the minimization of the sum of the elastic and planar defect energies.
In practice, the equilibrium spacing can be used to estimate the surface energy of
the planar defect or fault ribbon; typical values are in the range 0.01-0.1 Jm- 2
(Amelinckx 1979 ; Carter 1984 ). The terms glide dissociation and climb dissoci-
ation are often used to distinguish the cases where the partial dislocation lines and
fault ribbons lie in a plane that, respectively, contains the Burgers vector of the
parent perfect dislocation (Fig. 6.8 ) and is inclined to their Burgers vector. In the
case of screw dislocations, the distinction disappears, at least geometrically, since
some sort of distinction may still, in principle, be made dynamically in terms of
planes of easy and difficult glide. The glide and climb motion of dissociated
dislocations involves a coupling between the individual partials through the energy
of the strip of stacking fault joining them. Processes such as cross-slip appear to
require a temporary recombination of the partials, while, in the case of climb, the
nucleation of jogs is thought sometimes to involve local loop formation (for
example Carter 1984 ; Cherns 1984 ).
In an ordered structure (Sect. 2.), the actual periodicity is that of the superlattice
and so, strictly, the Burgers vector will be a multiple of the Burgers vector for the
disordered structure. In practice, dislocations in ordered structures are commonly
still described with reference to the lattice defined for the disordered structure.
A unit dislocation in the ordered structure is then referred to as a superdislocation.
The superdislocation can be, and is likely to be, dissociated into a pair of normal
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