Geology Reference
In-Depth Information
g
2
in which the shear plane intersects K
1
and K
2
, the shear plane being defined as
the plane containing the normals of K
1
and K
2
and itself being normal to the
intermediate principal strain axis, that is, the plane of the circular section most
nearly parallel to the longest dimension of the deformation twin in the shear plane;
it is, in general, parallel to the composition plane, the plane across which the two
twin individuals would join with best fit or least interfacial energy to form a
so-called coherent boundary.
In crystals of relatively low symmetry, either K
1
and g
2
have rational crystal-
lographic indices and K
2
, g
1
are irrational (defining type I twins), or K
2
, g
1
are
rational and K
1
, g
2
irrational (type II twins). In the case of type I twinning, the twin
individuals are related by a reflection with respect to K
1
or by a twofold rotation
about the normal to K
1
. In the case of type II twinning, the symmetry relationship
is a twofold rotation about g
2
or a reflection with respect to the plane normal to g
2
.
However, in higher symmetry crystals, all four elements K
1
, K
2
, g
1
, g
2
can be
rational and the four types of symmetry relationship just mentioned become
equivalent, giving rise to so-called compound or degenerate twins, in which the
composition plane can then also be always referred to as the twinning plane. In all
cases, the twinning is fully specified by either K
1
and g
2
or K
2
and g
1
,as
appropriate. However, a convenient alternative, often used, is to specify the
twinning in terms of the plane K
1
,
the direction g
1
and the magnitude of the shear
c
¼
2cot/
¼
2cos/ (Fig.
6.5
).
For further discussion of the geometry and crystallography of mechanical
twinning, see Cahn (
1953
,
1954
), Hall (
1954
), Pabst (
1955
), Klassen-Neklyndova
(
1964
), Christian (
1965
, Chap. 20) and Hirth and Lothe (
1982
, Chap. 23).
It should be borne in mind that some treatments in the metallurgical literature refer
only to relatively high symmetry crystals and do not make some of the distinctions
in terminology that are appropriate for lower symmetry crystals.
Martensitic or displacive phase transformations constitute a more general class
of shear deformation processes related to mechanical twinning. In these, instead of
the crystal structure being restored as in twinning, albeit with a new orientation, a
new structure is produced by the shearing, namely, that of a polymorphous phase.
Mechanical twinning is thus a special case of this more general class of trans-
formations. Ideal kinking (Orowan
1942
; Paterson and Weiss
1966
) can also be
regarded as having some analogy to twinning and it has even at times been
described as ''irrational twinning'' but it is better viewed as a special type of
deformation band, that is, a particular heterogeneous distribution of slip (see
review by Cahn
1953
).
At the atomic scale, slip and twinning and displacive transformation take place
by the movement of dislocations, the properties of which we now consider. Later
in the chapter (
Sects. 6
and
7
) we consider slip and twinning in terms of dislocation
motion.
