On the role of deformation twinning in domain reorganization and grain reorientation in ferroelastic crystals
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On the role of deformation twinning in domain reorganization and grain reorientation in ferroelastic crystals Peter M¨ullnera) and Waltraud M. Kriven Department of Materials Science and Engineering, University of Illinois at Urbana – Champaign, 105 South Goodwin Avenue, Urbana, Illinois 61801 (Received 27 December 1995; accepted 26 March 1997)
The response of ferroelastic crystals on an applied stress is considered, and a distinction is seen between the reorganization of the domain structure within a grain at low stress and the reorientation of whole grains at high stress. The procedures are modeled in the framework of defect theory, i.e., by twinning dislocations and deformation twinning. The reorganization is controlled by the motion of pre-existing twinning dislocations. Since the Peierls stress of the twinning dislocations is very small, domain reorganization occurs under a very small load. The process of grain reorientation involves the nucleation of dislocations and, therefore, it requires a much higher stress. This concept is confirmed by comparison with experiments.
I. INTRODUCTION
Crystals are called ferroelastic if their stress-strain behavior exhibits a hysteresis characterized by the spontaneous strain and the coercive stress.1 It is known that the origin of the spontaneous strain is the reorientation of the domains. Thereby the whole domain changes its orientation. The domain structure is a consequence of a transformation from a high temperature high symmetry phase to a low temperature low symmetry phase. Due to this transformation, the shape of the unit cell changes, as well as the shape of each individual grain [Figs. 1(a) and 1(b)]. The grains do not fit together perfectly anymore. Thus, they have to be deformed in order to avoid decohesion at grain boundaries— decohesion, in fact, is one option to relaxing the transformation strains.2 Another possible mechanism of relaxation is the incorporation of twins [Fig. 1(c)]. Since the function of these twins is to accommodate strain, they are in fact deformation twins.3 (These deformation twins must not be confused with the transformation twins: Deformation twins always develop within a matrix and under a mechanical load; i.e., they accommodate strain. On the contrary, transformation twins develop simultaneously during a phase transformation as symmetry equivalent options. The driving force is a chemical but not a mechanical force. Transformation twins cannot reasonably be classified as matrix and twin.) These twins are by definition individual grains. However, for the sake of clarity, we shall use the following convention throughout this paper: Convention: A ferroelastic grain (or briefly grain) is a region that has formerly, i.e., in the parent phase, a)
New address: Max-Planck-Institut f¨ur Metallforschung, Seestrasse 92, D-70174 Stuttgart, Germany. J. Mater. Res., Vol. 12, No. 7, Jul 1997
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been a single grain. A ferroelastic twin/domain (or briefly
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