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Identification of singular interfaces with Δgs and its basis of the O-lattice

  • IIB 2010
  • Published:
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Abstract

This article identifies singular interfaces according to singularity in terms of structural defects, including dislocations and ledges. Defect singularities are defined by the elimination of one or more classes of defects, which must be present in the vicinal interfaces. In addition to the three commonly classified structural interfaces, a new type of interface—the CS-coherent interface—is introduced. Singularities in dislocation and ledge structures have been integrated in the study of orientation relationships (OR). The dislocation structures are determined through the O-lattice theory, originally proposed by Bollmann. The basic concepts of the O-lattice and related formulas from the original theory and extended studies are briefly reviewed. According to the theory, singular interfaces exhibiting singularity in the dislocation structures have been identified. An interface that is singular with respect to the interface orientation must be normal to at least one Δg, a vector connecting two reciprocal points from different lattices. An interface that is singular also with respect to the OR must obey one or more Δg parallelism rules. The selection of proper Δgs for different preferred states of interfaces are explained. Identification of singular interfaces with measurable Δgs provides a convenient and effective approach to the interpretation of the observed facets and ORs. The ambiguity about the selection of the deformation matrix (A) for the O-lattice calculation and the advantage of the O-lattice approach over the approach using the Frank–Bilby equation for the calculation of the interfacial dislocations are clarified. Limitations of the present approach and further study are discussed.

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Notes

  1. Σ is the ratio of the unit cell volume of the CSL to that of a crystal lattice.

  2. The O-lattice has been defined as a lattice of origins according to Bollmann [9, 11]. In this sense, the “O” is the abbreviation of origin. However, it can also be considered as the abbreviation of “zero” [11], as used in early publications by Bollmann, e.g. [9]. In this article, the letter O is adopted, since it is well-accepted pronunciation in the community with the O-lattice applications.

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Acknowledgements

Financial support from National Nature Science Foundation of China (No. 50971076) and National Basic Research Program of China (No. 2009CB623704) from Chinese Ministry of Science and Technology are gratefully acknowledged. The Authors wish to thank Professors A.P. Sutton and R.C. Pond for valuable discussions during iib 2010, to Mr. X.-F. Gu and Mr. Z.-Z. Shi for kind assistance in preparation of the manuscript, and to Mr. C. Ocier and Ms. S. Hadian for helpful proof reading, and to the reviewers for kind helps in providing many useful corrections and suggestions especially in English writing.

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  1. X.-P. Yang

    Present address: Bruker Nano GmbH, Schwarzschildstrasse 12, 12489, Berlin, Germany

Authors and Affiliations

  1. Department of Materials Science and Engineering, Laboratory of Advanced Materials, Tsinghua University, Beijing, 100084, China

    W.-Z. Zhang & X.-P. Yang

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  1. W.-Z. Zhang
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  2. X.-P. Yang
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Correspondence to W.-Z. Zhang.

Additional information

Dedicated to W. Bollmann, the inventor of the O-lattice.

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Zhang, WZ., Yang, XP. Identification of singular interfaces with Δgs and its basis of the O-lattice. J Mater Sci 46, 4135–4156 (2011). https://doi.org/10.1007/s10853-011-5431-x

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