Extension of the classical theory for types I and II twinning

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 c...

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Bibliographic Details
Published in:Journal of materials research 2021-07, Vol.36 (13), p.2615-2622
Main Authors: Hirth, J. P., Wang, J.
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Biomaterials
Chemistry and Materials Science
Inorganic Chemistry
Materials Engineering
Materials research
Materials Science
Nanotechnology
Orientation
Rotation
Topology
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Summary: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.
ISSN:0884-2914
2044-5326
DOI:10.1557/s43578-020-00003-6