Geology Reference
In-Depth Information
of a large number of dislocations distributed through the crystal. The dislocation is
thus the basic entity at the atomic scale underlying the mechanisms of slip and
mechanical twinning. Brief histories of the notion of a dislocation are given by
Nabarro (
1967
, Chap. 1), Jouffrey (
1979
) and Hirth (
1985
).
The idea of the propagation of dislocations as the mechanism of slip in crystals
was first put forward independently in 1934 by Orowan (
1934
), Polanyi (
1934
) and
Taylor (
1934
). This picture has been abundantly verified observationally since the
1950s (Hirth and Lothe
1982
, p. 9) and a very large body of literature on both
observation and theory has appeared. A comprehensive account of the theory of
dislocations in crystals cannot be attempted within the scope of the present volume
but the principal properties will be summarized in the following sections. For
general accounts of dislocation theory, the classic texts are Cottrell (
1953
), Friedel
(
1964
), Nabarro (
1967
) and Hirth and Lothe (
1982
), while succinct accounts will
be found in Weertman and Weertman (
1964
,
1992
), Nicolas and Poirier (
1976
),
Haasen (
1978
) and Poirier (
1985
) and in many other topics and reviews in
materials science. Groh et al. (
1979
) have also published a useful compilation of
papers in French on a broad range of dislocation topics.
Figure
6.6
depicts the type of dislocation with which we are concerned here and
which has been called by Nabarro (
1967
) the Burgers type to distinguish it from
the more general types associated with the names of Weingarten, Volterra and
Somigliana. Such a dislocation is a line that that can be thought of as the boundary
of a surface in which the body is imagined to have been cut and across which the
material on one side is imagined to have been translated homogeneously relative to
the material on the other side before repairing the cut to restore continuity of the
material. The virtual translation vector b is known as the Burgers vector. In the
case of crystals, b is normally equal to a translation vector of the crystal lattice, in
which case the dislocation is called a perfect dislocation; the minimum possible
value of b is thus the minimum lattice parameter except when a nonprimitive unit
cell is chosen. If b is not a translation vector of the lattice, the dislocation is known
as a partial dislocation, which necessarily bounds a surface of faulting in the
crystal structure. Where a dislocation line is normal to the Burgers vector it is said
to be of pure edge character and, where parallel to the Burgers vector, of pure
screw character; otherwise, it is of mixed character.
The essential nature of a dislocation is revealed by considering a Burgers
circuit, which is a notional path through a sequence of lattice sites forming a
closed loop around the dislocation. If a path is followed through a corresponding
sequence of lattice sites in a perfect crystal, this path fails to close and the vector
required to close the gap is the Burgers vector of the dislocation. Taking the sense
of the Burgers vector to be positive when going from finish to start of the circuit
(FS), a sense or sign can then be attributed to a given segment of dislocation line
such that the Burgers circuit is seen to be performed in a clockwise sense when
looking in the positive direction along the dislocation line (RH). Conversely, if one
first chooses a positive sense for the dislocation line, the positive sense of the
Burgers vector can be defined by the reverse argument. This FS/RH sign con-
vention is, however, not always followed and an opposite convention is also
