Geology Reference
In-Depth Information
acting on the dislocation will then be oDE
=
ox where x is the coordinate in the
direction of the motion.
6.3.1 Interaction with Point Defects
Many deformation effects are controlled by the interaction of dislocations with the
structural perturbations associated with vacancies, self-interstitials, and impurity
or solute atoms, referred to conveniently as point defects (
Sect. 1.2.2
). The
interaction being a mutual one, the local concentration of point defects will also
tend to be influenced by the presence of the dislocation. The actual local con-
centration will depend on whether or not equilibrium has been established and, in
case of equilibrium, will be determined by considerations of entropy as well as of
the local atomic interaction energies.
It is useful to distinguish three aspects of the interaction of point defects with a
dislocation:
1. Atomic bonding interactions at the scale of the dislocation core (chemical
aspect).
2. Elastic interactions with the linear elastic stress field of the dislocation (elastic
aspect).
3. Electrostatic interactions between charges that may exist on the dislocations
and point defects (electrostatic aspect).
In the next three paragraphs, we elaborate a little on the nature of these aspects
of interaction (for general references, see Friedel
1964
, Chap. 13; Hirth and Lothe
1982
, Chap. 14; Nabarro
1967
, Chap. 6).
Because of the gross structural distortion in the core of a dislocation it may be
expected that site occupancy, compared with the normal topological arrangement
of atoms for the perfect crystal, may be seriously modified, for example,
by substitution of impurity atoms, by changes in the concentration of solute atoms
in solid solutions (such as Mg/Fe ratio in olivine), or by nonoccupancy of normally
occupied sites. That is, relative to a local singularity in structure produced simply
by reuniting the two surfaces of a hypothetical cut after their relative translation by
the Burgers vector, a modification or reconstruction of bonding relationship may
often be expected in the core since its energy would be thereby reduced, and
segregation or redistribution of impurity or solute atoms may be involved in the
modification. The actual core structure can, in principle, be obtained from ab initio
or similar quantum mechanical calculations but, in practice, a more rudimentary
approach in terms of interaction with vacancies and solute or impurity atoms is
usually taken, expressed in terms of binding energies for the interaction, deter-
mined more or less empirically (Hirth and Lothe
1982
, p. 512). The effect of the
segregation of vacancies or solute atoms to the dislocation core will be to modify
the Peierls potential, decreasing it in case of attractive interaction; if the Peierls
valley is thereby deepened and its walls steepened, the effect will be accompanied
