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The Type-II Twin Boundary (TB) is a critical interface in functional materials whose irrational Miller-index identity has recently drawn significant research interest. This study establishes general structural characteristics of the Type-II twin interface, utilizing TBs in Shape Memory Alloys (SMAs) - TiPd, TiPt, and AuCd - as study targets. It is shown how the irrational identity of each TB is explained by the Terrace-Disconnection (T-D) structural topology. It is proposed that the terrace is the rational-plane nearest to the irrational TB in the reciprocal space, having in- tegral Miller-indices of least magnitude. Crystallographic-registry on this terrace requires non- trivial coherence-strains. A novel kinematic-origin of the coherence-strain is proposed, coming directly from a transformation of the classical twinning deformation-gradient. This trans- formation revealed that the classical twinning-shear partitions into the coherence-strain and a new metric termed the “terrace-shear” . It is shown that the magnitude of shear relating the twin- structure to the matrix is the terrace-shear and not the twinning-shear, contrary to classical un- derstanding. Furthermore, the Burgers vector of the twinning disconnection is shown to be related directly to the terrace-shear. The energy of each Type-II interface is determined from ab initio Density Functional Theory (DFT) calculations. It is shown that the energy-minimal atomic- structure on the terrace requires determination of a “lattice-offset” that is non-trivial and un- known apriori. In summary, this study expounds on T-D topological structure of Type-II twin interfaces, establishing methods to identify rational terraces, coherence strains, ab initio planar TB energies and revealing a unique partitioning of the twinning-shear exhibited by this class of interfaces.
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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 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.
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- Award ID(s):
- 1661686
- PAR ID:
- 10231273
- Date Published:
- Journal Name:
- Journal of Materials Research
- ISSN:
- 0884-2914
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Type II and IV twins with irrational twin boundaries are studied by high-resolution transmission electron microscopy in two plagioclase crystals. The twin boundaries in these and in NiTi are found to relax to form rational facets separated by disconnections. The topological model (TM), amending the classical model, is required for a precise theoretical prediction of the orientation of the Type II/IV twin plane. Theoretical predictions also are presented for types I, III, V, and VI twins. The relaxation process that forms a faceted structure entails a separate prediction from the TM. Hence, faceting provides a difficult test for the TM. Analysis of the faceting by the TM is in excellent agreement with the observations.more » « less
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null (Ed.)The structure of type II twins in 10M Ni-Mn-Ga is modeled using the topological method. This method predicts the same twinning parameters as the kinematic model of Bevis and Crocker. Furthermore, topological modeling provides mechanistic insight into boundary migration rates, the twinning stresses and their temperature dependence. A type II twin is envisaged to form from a precursor, which is its type I conjugate. Disconnections on the precursor k_1 plane align into a tilt wall, which, after the relaxation of the rotational distortions, forms the type II boundary parallel on average to the k_2 plane. The component defects may align into a sharp wall or relax by kinking into a less orderly configuration. Both interfaces can host additional glissile disconnections whose motion along a boundary produces combined migration and shear. The ease of motion of these defects increases with their core width, and this, in turn, decreases with increasing sharpness of the boundary. Some experimental evidence in other materials suggests that type II twins can reduce their interfacial energy by adopting a configuration of low-index facets, which reduces twin boundary mobility. Topological modeling suggests that such a coherently faceted structure is unlikely in 10M Ni-Mn-Ga, in agreement with the high mobility of type II twin boundaries.more » « less
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Abstract The abrupt occurrence of twinning when Mg is deformed leads to a highly anisotropic response, making it too unreliable for structural use and too unpredictable for observation. Here, we describe an in-situ transmission electron microscopy experiment on Mg crystals with strategically designed geometries for visualization of a long-proposed but unverified twinning mechanism. Combining with atomistic simulations and topological analysis, we conclude that twin nucleation occurs through a pure-shuffle mechanism that requires prismatic-basal transformations. Also, we verified a crystal geometry dependent twin growth mechanism, that is the early-stage growth associated with instability of plasticity flow, which can be dominated either by slower movement of prismatic-basal boundary steps, or by faster glide-shuffle along the twinning plane. The fundamental understanding of twinning provides a pathway to understand deformation from a scientific standpoint and the microstructure design principles to engineer metals with enhanced behavior from a technological standpoint.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1557/s43578-020-00003-6
