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Recurrence properties of O-lattices and the classification of grain boundaries

Recurrence properties of O-lattices and the classification of grain boundaries A recurrence relation is shown to exist between O-lattices of rotation-related grain boundaries (GBs) when a suitable parametrization of the rotation angle is introduced. This relation allows the basis vectors of any O-lattice to be calculated by a simple vector addition if the basis vectors of any two orientations are known. Its main usefulness, however, lies in the fact that it induces a partition of the angular space into disjoint sets, which groups grain boundaries into a finite number of equivalence classes, each represented by a special singular boundary (normal form). This shows that the O-lattice theory contains within it a much sought after general classification scheme for interfaces independent of the crystal system and therefore completely general. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A Foundations of Crystallography International Union of Crystallography

Recurrence properties of O-lattices and the classification of grain boundaries

Recurrence properties of O-lattices and the classification of grain boundaries


Abstract

A recurrence relation is shown to exist between O-lattices of rotation-related grain boundaries (GBs) when a suitable parametrization of the rotation angle is introduced. This relation allows the basis vectors of any O-lattice to be calculated by a simple vector addition if the basis vectors of any two orientations are known. Its main usefulness, however, lies in the fact that it induces a partition of the angular space into disjoint sets, which groups grain boundaries into a finite number of equivalence classes, each represented by a special singular boundary (normal form). This shows that the O-lattice theory contains within it a much sought after general classification scheme for interfaces independent of the crystal system and therefore completely general.

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References (4)

Publisher
International Union of Crystallography
Copyright
Copyright (c) 2006 International Union of Crystallography
Subject
grain boundaries, O-lattices, recurrence properties
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S0108767306025293
pmid
16926489
Publisher site
See Article on Publisher Site

Abstract

A recurrence relation is shown to exist between O-lattices of rotation-related grain boundaries (GBs) when a suitable parametrization of the rotation angle is introduced. This relation allows the basis vectors of any O-lattice to be calculated by a simple vector addition if the basis vectors of any two orientations are known. Its main usefulness, however, lies in the fact that it induces a partition of the angular space into disjoint sets, which groups grain boundaries into a finite number of equivalence classes, each represented by a special singular boundary (normal form). This shows that the O-lattice theory contains within it a much sought after general classification scheme for interfaces independent of the crystal system and therefore completely general.

Journal

Acta Crystallographica Section A Foundations of CrystallographyInternational Union of Crystallography

Published: Aug 23, 2006

Keywords: grain boundaries ; O -lattices ; recurrence properties .

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