Use of the CSL symmetrically equivalent descriptions tables in the DSC lattice base computation

Bleris, G. L.; Doni, E.; Karakostas, Th.; Antonopoulos, J. G.; Delavignette, P.

doi:10.1107/s0108767385000940

Cited by 9 publications

(2 citation statements)

References 10 publications

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“…This procedure is more efficient than the one proposed by Bleris, Doni, Karakostas, Antonopoulos & Delavignette (1985).…”

Section: 13mentioning

confidence: 92%

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Fundamentals for the description of hexagonal lattices in general and in coincidence orientation

Grimmer¹,

Warrington²

1987

Acta Cryst Sect A

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The connection between the rotation matrix in hexagonal lattice coordinates and an angle-axis quadruple is given. The multiplication law of quadruples is derived. It corresponds to multiplying two matrices and gives the effect of two successive rotations. The relation is given between two quadruples that describe the same relative orientation of two lattices owing to their hexagonal symmetry; a unique standard description of the relative orientation is proposed. The restrictions satisfied by rotations generating coincidence site lattices (CSL's) are derived for any value of the axial ratio p = c~ a. It is shown that the law for cubic lattices, where the multiplicity 2 of the CSL is equal to the lowest common denominator of the elements of the rotation matrix, does not always hold for hexagonal lattices. A generalization of this law to lattices of arbitrary symmetry is given and another, quicker, method of determining £ for hexagonal lattices is derived. Finally, convenient algorithms are described for determining bases of the CSL and the DSC lattice.

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“…This procedure is more efficient than the one proposed by Bleris, Doni, Karakostas, Antonopoulos & Delavignette (1985).…”

Section: 13mentioning

confidence: 92%

“…Karakostas, Antonopoulos & Delavignette (1985). Let us consider the same example (tz = 8, 1, = 3, m = 7, U = V --0, W = 3) as they do to illustrate our method and to compare it with theirs.…”

Section: Determination Of Bases For the Csl And Dsc Lattices Generatementioning

confidence: 99%

Fundamentals for the description of hexagonal lattices in general and in coincidence orientation

Grimmer¹,

Warrington²

1987

Acta Cryst Sect A

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Coincidence‐Site Lattices in the Rhombohedral System

Doni

Fanides

Bleris

1986

Cryst. Res. Technol.

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Coincidence orientations in the rhombohedra1 system are exanlined by means of the CSL model. The rotation matrix R producing a CSL, the generating function Z and the equivalent descriptions of the same CSL in direct and reciprocal space are analytically coinputed. As an application, Tables of CSLs for the approximation of typical rhombohedral materials are presented. Koinzidenzorientierungen in den1 rhombohedrischen System werden anhand d esKoinzidenzplatzgitters-Models untersucht. Die Rotationsmatrix R, die ein Koinzidenzplatzgitter erzeugt, die erzeugende Funktion Z und die iiquivalenten Beschreibungen desselben Koinzidenzplatzgitters im norrnalen und reziproken h u m werden analytisch berechnet. Als Anwendung werden Koinzidenzplatzgittertabellen fiir die Niiherungsrechnung typischer rhombohedrischer Materialien gegeben.

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Study of special triple junctions and faceted boundaries by means of the CSL model

Doni

Bleris

1988

Phys. Stat. Sol. (a)

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Sufficient work has been made until now on the grain boundaries (GBs) multi‐junctions in different polycrystalline cubic materials by using electron microscopy. In the present work the main characteristics of the majority of the junctions reported are theoretically investigated. In fact triple junctions (TJs) show a very systematic geometrical relationship, as far as the thermodynamically favorable grain boundaries are concerned. Thus the possible intersection of three grain boundaries is examined by using the analytical expression of the CSL rotation matrix and the CSL symmetry for cubic system. The general properties obtained are applied on TJs containing low ∑ value grain boundaries and the resulting junctions are examined according to their stability.

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Use of the CSL symmetrically equivalent descriptions tables in the DSC lattice base computation

Cited by 9 publications

References 10 publications

Fundamentals for the description of hexagonal lattices in general and in coincidence orientation

Fundamentals for the description of hexagonal lattices in general and in coincidence orientation

Coincidence‐Site Lattices in the Rhombohedral System

Study of special triple junctions and faceted boundaries by means of the CSL model

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