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A plane-displacement diagram showing the four twinning elements, planes and directions, is fundamental to the classical theory of twinning. One aspect of the classical theory of type I and II twinning is shown to be inapplicable when the twin rotation is large. We employ the topological model with certain nonlinear characteristics to deduce a modified set of twinning elements. For twinning associated with a small rotation, both the classical theory and the topological model for type I and II twinning are shown, which give the same set of twinning elements. However, only the topological model is applicable for the large rotation case. As for the classical model, the twin plane in the type II twinning case is irrational unless it, and the type I twin is compound. Often, this irrational plane is close to a low-index orientation for a given orientation relationship. Then it can be favorable for the interface to break up into low-index, rational facets, separated by disconnections. This occurs without changing the orientation relationship. We apply the topological model to describe both the irrational type II twins and faceting in NiTi. The results agree with TEM observations. 

Twin–twin interactions (TTIs) take place when multiple twinning modes and/or twin variants are activated and interact with each other. Twin–twin junctions (TTJs) form and affect subsequent twinning/detwinning and dislocation slip, which is particularly important in determining mechanical behavior of hexagonal metals because twinning is one major deformation mode. Atomic-level study, including crystallographic analysis, transmission electronic microscopy (TEM), and molecular dynamics (MD) simulations, can provide insights into understanding the process of TTIs and structural characters associated with TTJs. Crystallographic analysis enables the classification of TTIs and the prediction of possible interfaces of twin–twin boundaries (TTBs), characters of boundary dislocations, and possible reactions of twinning dislocations and lattice dislocations at TTBs. MD simulations can explore the process of TTIs, microstructures of TTJs, atomic structures of TTBs, and stress fields associated with TTJs. The predictions based on crystallographic analysis and the findings from MD can be partially verified by TEM. More importantly, these results provide explanation for microstructural characters of TTJs and guidance for further TEM characterizations. 

A different type of defect, the coherency disclination, is added to disclination types. Disconnections that include disclination content are considered. A criterion is suggested to distinguish disconnections with dislocation content from those with disclination content. Electron microscopy reveals unit disconnections in a low albite grain boundary, defects important in grain boundary sliding. Disconnections of varying step heights are displayed and shown to define both deformed and recovered structures.

 

Abstract A topological model (TM) is presented for the complex crystal structures characteristic of some minerals. We introduce a tractable method for applying the TM to characterize defects in these complex materials. Specifically, we illustrate how structural groups, each with a motif containing multiple atoms, provide lattices and structures that are useful in describing dislocations and disconnections in interfaces. Simplified methods for determining the shuffles that accompany disconnection motion are also described. We illustrate the model for twinning in albite owing to its potential application for constraining the rheological properties of the crust at conditions near the brittle-plastic transition, where plagioclase is a major constituent of common rock types. While deformation twins in plagioclase are often observed in crustal rocks, the interpretation of the stress states at which they form has not advanced. The concept of structural groups makes an analysis of the twinning process easier in complex minerals and explicitly predicts the interface structure of the deformation twins.