Defects in deformation twins in plagioclase

Abstract

The topological model is applied to analyze defects associated with albite and pericline twins in plagioclase. Twin growth occurs by the motion of twinning disconnections. The same twinning disconnections are shown to produce both twins. The topological model is used to predict the atomic details of the disconnections. High-resolution transmission electron microscopy results verify the model predictions. Early work on the possibility of pseudo-twinning is also discussed.

Appendix 1: Lattice site and atom exchanges

Almost all Burgers vectors in twins connect prefect lattice sites that are perfect translational t vectors in dichromatic spaces. However, there are a few cases where the vectors shear and shuffle to alternate sites in a process called synchroshear (Kronberg 1957). A better term is synchroshuffle, since the displacements are not the long-range ones defined by the Burgers vector. These are not perfect displacement vectors and create a special type of imperfect dislocation or disconnection. Examples of synchroshuffle include twinning, e.g., in alumina (Kronberg 1957), and phase transformations, e.g., in spinel (Poirier 1981) and Laves phases (Hazzledine and Pirouz 1993). The synchroshear displacements are of two kinds, knock-on and coupled pairs (Anderson et al. 2017). Synchroshear usually occurs in crystals with a basis, i.e., a structural group of atoms, or in simple structures a pair of atoms, at a lattice site that has point-group symmetry. For example, with a basis of 2, the dipole groups can be labeled as A and B. For more common cases, the shuffle or shear exchanges are A–A and B–B. For the synchronous cases the exchanges are A–B and B–A. To maintain stoichiometry there must be equal numbers of A–B and B–A exchanges. There are analogous displacements that we describe as anti-site exchanges. These arise during disconnection motion and entail atoms shuffling (or, less likely shearing) to the wrong site chemically. Again, there must be balanced A–B and B–A shifts.

Synchroshuffle was applied to twinning in alumina in the original work of Kronberg (1957). Often in twinning, the displacements are similar synchroshuffles. In twinning, the synchroshear/shuffle constraints often can be partly relaxed, as illustrated in the main text. For example, in a simulation of ($10\overline{ 1} 2$) twinning in Zr (Khater et al. 2013), knock-on, B–A and B–A exchanges (called swaps) occur. However, since the shuffle vectors simply complete perfect vector displacements from matrix to twin, no added fault is created. Thus, the distinction as an exchange is not as important. However, the exchange is of interest with regard to the atomic mechanism of motion. In contrast, the anti-site shuffles are important since they create local disorder, corresponding to a disorder fault in the wake of a moving disconnection. We describe the fault as a disorder fault since there is no incorrect layer stacking as in a stacking fault.