ResearchOne Page Summary: Twinning

Dingyi SunUpdated: December 15, 2016

One Page Summary: Twinning

Dingyi Sun

Updated: December 15, 2016

Figure 0.1: HRTEM twin example from[1].

Materials have a variety of mechanisms by which they accommodatedeformation; one such mechanism is known as twinning . From a crystallo-graphic view, twinning involves the reorientation of a material’s lattice abouta planar discontinuity such that the lattice on one side of this discontinuity canbe treated as a rotation or a reflection of the lattice on the other, as visualizedthrough high-resolution transmission electron microscopy in Figure 0.1. Twin-ning appears in a variety of materials of all different crystal structures. Forexample, Lu et al. [2] highlights some of the importance of twin boundariesin copper, a face-centered cubic material. Similarly, Christian and Mahajan[3] reviews a variety of previous works that have examined the prevalence oftwinning in hexagonal close-packed structures.

In the interest of space, we will limit this summary document to looking only at twinning in hexagonal close-packedmagnesium. Due to the high strength-to-weight ratio, alloys based around hexagonal close-packed materials are verypromising materials for future industrial applications (e.g. lightweight vehicle components for better fuel efficiency).

Slip Systems Twin Systems

Basal Prismatic

Pyramidal I Pyramidal II

Tension

Compression

Figure 0.2: Common mechanisms of deformation in HCP materials.

Unfortunately, the anisotropy of the crystalstructure lends itself to poor ductility. Assuch, the mechanisms of deformation accom-modation in these materials need to be fullyunderstood. There are a variety of questionssurrounding twinning, one of which is theanswering of which crystallographic planesaround which twins can form. This is an areathat Christian and Mahajan [3] began to probedecades ago; for hexagonal close-packed ma-terials, it was hypothesized that a significantnumber of twin modes could be visualized.However, this comes somewhat in contrastwith many contemporary works, which haveargued that only a limited number of twin-ning systems may appear in these materials.Indeed, of all of the modes proposed, the com-munity has settled on the f10N12g

˝10N11

˛ten-

sion and f10N11g˝10N12

˛compression twins as

the two dominant twin modes alongside the variety of slip systems represented in Figure 0.2.However, various anomalies have been observed experimentally and have gone mostly unexplained. For instance,

Li and Zhang [4] and Liu et al. [5] observe twin planes outside of the two popular modes, and Brown et al. [6] arguesthat some of their neutron powder diffraction peaks do not match with these previous arguments. Consequently, ourgroup is interested in resolving these anomalies. Using a novel framework that draws on lattice theories seen in Bilbyand Crocker [7], Pitteri [8], and Ball and James [9, 10], we attempt to find all of the possible twin modes and then useatomistic simulations and establish metrics for which of the predicted twins are likely to be visualized. Our findingsshow that there are actually quite a significant number of modes around which twins can form - particularly in hexagonalclose-packed materials - and some of these modes do correlate to these earlier experimental observations.

1

ResearchOne Page Summary: Twinning

Dingyi SunUpdated: December 15, 2016

References[1] Y.B. Wang, M.L. Sui, and E. Ma. In situ observation of twin boundary migration in copper with nanoscale twins

during tensile deformation. Philosophical Magazine Letters, 87(12):935–942, 2007.

[2] K. Lu, L. Lu, and S. Suresh. Strengthening Materials by Engineering Coherent Internal Boundaries at theNanoscale. Science, 324:349–352, 2009.

[3] J.W. Christian and S. Mahajan. Deformation Twinning. Progress in Materials Science, 39:1–157, 1995.

[4] B. Li and X.Y. Zhang. Global strain generated by shuffling-dominated f10N12g˝10N1N1

˛twinning. Scripta Materialia,

71:45–48, 2014.

[5] B.Y. Liu, J. Wang, B. Li, L. Lu, X.Y. Zhang, Z.W. Shan, J. Li, C.L. Jia, J. Sun, and E. Ma. Twinning-like latticereorientation without a crystallographic twinning plane. Nature Communications, 10.1038(4297):1–6, 2014.

[6] D.W. Brown, S.R. Agnew, M.A.M. Bourke, T.M. Holden, S.C. Vogel, and C.N. Tomé. Internal strain and textureevoluhtion during deformation twinning in magnesium. Materials Science and Engineering A, 399:1–12, 2005.

[7] B.A. Bilby and A.G. Crocker. The theory of the crystallography of deformation twinning. Proceedings of theRoyal Society A, 288(1413):240–255, 1965.

[8] M. Pitteri. On the kinematics of mechanical twinning in crystals. Archive for Rational Mechanics and Analysis25.IV, 88(1):25–57, 1985.

[9] J.M. Ball and R.D. James. Fine phase mixtures as minimizers of energy. Archive for Rational Mechanics andAnalysis 11.XII, 100(1):13–52, 1987.

[10] J.M. Ball and R.D. James. Proposed Experimental Tests of a Theory of Fine Microstructure and the Two-WellProblem. Philosophical Transactions: Physical Sciences and Engineering, 338(1650):389–450, 1992.

2