The balance between the energies of the symmetric twin boundaries and asymmetric basal/prismatic interfaces in hcp metals
Introduction
Deformation twinning is frequent in metals with hexagonal close packed (hcp) structure such as magnesium [1]. Particularly, twinning makes significant contribution to plastic deformation and accommodates the deformation about 〈c〉 axis. The room for twinning activity occurs due to relative hardness of non-basal slip [2], [3]. There are several twinning modes observed, however, the most frequent one is so-called “tension” twinning on twinning plane .
Despite a great effort to understand deformation twinning, some details of its mechanism are subject of discussion. For example, the presence of basal–prismatic (BP) interfaces. As a consequence, the twin boundaries can consist of the symmetrical and non-symmetrical / facets, the later represent a termination of one grain by the basal plane and on the other side by the prismatic plane. The BP interfaces have low formation energies that are comparable to the energy of a twin boundary [4], [5], [6] and therefore it is expected that the occurrence of this interface can affect the kinetics of twin boundary migration.
The objective of this paper is to study the relationship between the symmetric twin boundary facets and asymmetric facets formed by the BP interfaces in twin embryo.
Section snippets
Equilibrium shape of the twin embryo
It was observed in computer simulations that the growing twin embryo is delimited by the conjugate and twin boundaries that are almost perpendicular one to the other [5], [7], [8]. For the ideal c/a ratio, the angle between them is about 86.6°. Presence of conjugate facets was also observed experimentally in Zn in twin tips [9], [10]. At the corner between these symmetric facets, asymmetric BP interfaces can be found [7], [8]. The resulting twin embryo shape in
Twin boundary motion
The twins possess well known atomic structure studied already for long time [13], [14], [15].
Notice that in the hcp lattices, the separation of the neighbouring atomic planes is not constant. For instance, the prismatic planes are separated alternatively a√3/6 (about 0.289 a) or a√3/3 (about 0.577 a). Consequently, at the regions with perturbed crystal structure, the narrow spaced neighbouring atomic planes can coalesce into essentially one atomic plane that can be denoted as a
Discussion
The energies of the twin boundary and of the BP interface were calculated for Liu potential [17] in [5] and [18]. Their ratio for the planar infinite defects of 1.42 (γBP = 173 and γTw = 122 mJm−2) is close to √2, i.e. to the critical value obtained from our analysis. This fact indicates that ratio lBP/lTw tends to become close to zero. In principle, such situation is in agreement with a classical lamellar shape of twin, where the BP facets could appear nearby the twin tip only. It is worth
Conclusions
The basal/prismatic interfaces are the only relatively low energy facets of the tension twins in magnesium. Their energy is comparable with the energy of symmetric twin boundaries. The consideration of Gibbs-Wullf construction allows to conclude that the ratio lengths of basal/prismatic and facets will be low in equilibrium twin embryos. Significant occurrence of basal/prismatic facets could be associated with the non-equilibrium states and observed stages of twin growth.
Acknowledgments
The authors gratefully acknowledge the financial support of the Czech Science Foundation (ProjectsNo. 16-14599S).
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2019, Mechanics of MaterialsCitation Excerpt :These dislocations interact with and modify the twin boundary by converting the coherent boundary into an incoherent, faceted boundary with residual dislocation content (Pond et al., 1999; Serra and Bacon, 1996; Serra et al., 2002; Barrett and El Kadiri, 2014). This modified boundary should have different stored energy than the idealized coherent twin boundary, and will depend on the specific twin-defect interactions that are dominant during deformation (Paidar and Ostapovets, 2017; Paidar et al., 2018). It is likely that for the same magnesium alloy loaded along two orientations that promote twinning, the measured value of βint could differ wherein particular stress states promote different twin-twin and twin-dislocation interactions.
Dislocation content of non-classical twin boundaries in hexagonal metals
2018, Acta Physica Polonica A