Pergamon
Scripta Metallurgica et Materialia,Vol. 3l, No. 12, pp. 1657-1662. 1994
Copyright ©1994 ElsevierScience Ltd
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BETWEEN DISLOCATION AND DISCLINATION MODELS FOR TWINS
Peter Miillner* and A. E. Romanov**
* Institute of Metallurgy, Swiss Federal Institute of Technology,
8092 Ztirich, Switzerland
** Ioffe Physico-Technical Institute, Polytechnicheskaya 26,
194021 St. Petersburg, Russia
(Received July 19, 199411
1. Introduction
As result of a lot of theoretical and experimental work on the field of dislocations, the understanding of the
plasticity of crystalline materials deforming by dislocation mechanisms is broad and manyfold [e.g. 1-3]. However,
many materials deform not only by the movement of ordinary perfect and dissociated dislocations (glide plasticity);
other mechanisms such as the cooperative motion of partial dislocations involved in deformation twinning and strain
induced martensite transformation contribute to deformation as well (transformational plasticity, [e.g. 4-6]). The
understanding of glide plasticity is based on the properties of individual dislocations [e.g. 7]. The basis of
transformational plasticity are cooperative ensembles of partial dislocations; the description of those ensembles in
terms of individual dislocations is rather complex and therefore the transformational plasticity is by far not as well
understood based on dislocations as glide plasticity is. However, special types of those ensembles form
disclinations, the properties of which are given in a recent overview [8].
It was 1968 when a twin was proposed for the first time to be described in terms of disclinations [9].
Recently it was shown that under deformation conditions the front of a deformation twin in fact forms a disclination
dipole [10-12]. The present paper aims to review the elastic properties of a deformation twin in terms of
disclinations, in order to give an elementary tool for the treatment of the manyfold problems of twinning and strain
induced martensite formation. In order to give an example of the overall applicability of the disclination model, a
recrystallisation twin is described also.
2. Twi.n models
2.1 Twinning dislocation~
A twin in the fcc lattice can be considered as a set of stacking faults on succesive {111} planes (twinning
plane; in the following the twinning plane is the d-plane, using Tompsons notation [13]). Each stacking fault is
bounded by a partial dislocation (a twinning dislocation) which, in principle, can be any of the X8 Shockley
dislocations (X can be A, B, or C), independent of all the other twinning dislocations.
a) Recrystallisation twin
During recrystallisation, long range stresses get cancelled. Therefore, the sum of the Burgers vectors of all
twinning dislocations is zero. And thus, one third of the dislocations must be AS, another third must be BS, and
another third must be C~. Among all possible stackings fulfilling that condition, the regular stacking of alternating
AS, BS, and C8 is that with the lowest short range stresses and therefore the most probable.
b) Deformation twin
The dislocations of a deformation twin carry the twinning shear which is 1/~/2. That shear results only if all
twinning dislocations have the same Burgers vector. Therefore, a strong stress field is caused by a deformation
twin.
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