Elsevier

Materials Letters

Volume 198, 1 July 2017, Pages 93-96
Materials Letters

The balance between the energies of the symmetric (101¯2) twin boundaries and asymmetric basal/prismatic interfaces in hcp metals

https://doi.org/10.1016/j.matlet.2017.03.178Get rights and content

Highlights

  • Symmetric twin boundaries and asymmetric basal/prismatic interfaces are compared.

  • Equilibrium shape of twin embryo is illustrated.

  • The relationship between the twin boundary and BP interface energies is derived.

  • Migrating elements of twin boundary facets are discussed.

Abstract

The energies of grain boundaries with different inclination of the boundary plane for a misorientation close to 90° about the [12¯10] axis in hexagonal close packed metals are discussed. On the basis of large scale computer simulations with an empirical potential for magnesium, it can be illustrated that the basal/prismatic interfaces possess special properties.

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 (101¯2).

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 (101¯2) and non-symmetrical (0001)/(101¯0) 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 (101¯2) twin embryo

It was observed in computer simulations that the growing twin embryo is delimited by the conjugate (101¯2) and (101¯2¯) 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 {101¯2} facets was also observed experimentally in Zn in (101¯2) 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 {101¯2} 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 (101¯0) 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 (101¯2) 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 (101¯2) tension twins in magnesium. Their energy is comparable with the energy of symmetric (101¯2) twin boundaries. The consideration of Gibbs-Wullf construction allows to conclude that the ratio lengths of basal/prismatic and (101¯2) 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).

References (18)

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