Geology Reference
In-Depth Information
2. Partially covalent character of bonding may be of significance especially where
Si-O and Al-O bonds are involved, associated with high Peierls stresses.
3. Chemical substitution and non stoichiometry may be common, involving a rich
variety of structural defects.
4. Many mineral structures are of low symmetry, resulting in low multiplicity of
slip systems and hence in difficulty of meeting intragranular strain compati-
bility requirements in rocks.
Requirements deriving from covalent bond character or electrostatic repulsion
of ions of unlike charge are factors additional to the long-range elastic strain
energy (dependent purely on the Burgers vector and the elastic constants) in
determining the most favored slip direction and slip plane in minerals. Thus, the
metallurgical rule that slip occurs in the direction of closest packing (shortest
Burgers vector) is less strictly followed in minerals. For example, in calcite the
most commonly observed slip direction \2021[ is that of the third-shortest
Burgers vector (length 0.81 nm, compared with 0.50 nm for the shortest repeat
distance, that in the a axis direction).
Frank (
1951
) suggested, on the basis of a simplistic thermodynamic argument,
that when the Burgers vector exceeds a value of the order of 0.5-1 nm there will
be a tendency to form a hollow core in the dislocation of diameter Gb
2
=
4p
2
c
;
or
somewhat smaller when nonlinear elasticity near the core is taken into account,
where G is the shear modulus and c the surface energy: see Nabarro (
1984a
,
b
) for
the case of anisotropic crystals. Little direct evidence for such an effect has come
so far from electron microscopy of minerals and possibly other types of core
response meet the situation. However, the existence of such a tendency may
conceivably be a factor favoring such phenomena as the segregation of impurity
atoms in the core, the fast diffusion of atoms along the core or the formation of a
non crystallographic core as proposed for ice (Di Persio and Escaig
1984
, Perez
et al.
1975
).
6.3 Dislocation Interactions
So far, we have dealt with the properties of an isolated single dislocation in an
otherwise perfect crystal. We now consider the interaction of dislocations with
other types of crystal defect, including boundaries, and the mutual interaction of
dislocations. These interactions, together with the interactions with the crystal
itself (as discussed in
Sects. 6.2.3
-
6.2.7
), are very important because of their
influence on the mobility of dislocations and hence on the plastic deformation of
crystals. Such interactions have to be taken into account in developing theories of
the flow resistance of crystals under external stress (
Sect. 6.6
), much of the
complexity of which arises from the variety of the interactions. The magnitude of
interaction can, in principle, be expressed as the change DE in the energy of the
dislocation in the presence of the entity with which it is interacting. The force
