the coincidence site lattice misorientations of order sigma of the lattice of the crystal frame cs, MATLAB’s CSL

Syntax

mori = CSL(3, cs)

The twin of a cubic lattice.

mori = CSL([3, 5, 7], cs)

Several orders at once.

mori = CSL(5, cs, 'I')

Of the lattice centred I.

mori = CSL(7, cs, delta=0.01)

Near coincidences within a misfit of the metric.

Description

The misorientations are from cs to cs with grain exchange, one per coincidence class, ascending in sigma and then in angle: CSL(3, cs) is the twin of a cubic lattice. An order without coincidences, such as an even one of a cubic lattice, contributes none.

Any lattice is searched for the rotations that take sigma times every lattice vector onto a lattice vector, where MATLAB reads a table of the cubic ones. The lattice is the Bravais lattice of cs, centred as cs.centering says or as a letter given; the cubic P, I and F lattices share their coincidences.

A metric with rational ratios, a cubic one or a hexagonal one with c^2/a^2 rational, has exact coincidences. With a misfit delta > 0 the metric is replaced by the one of the smallest denominators within the relative misfit delta, and its coincidences are the near ones of the real lattice, the constrained coincidence site lattices of a hexagonal metal: c^2/a^2 = 2.52 of titanium is 5/2 within delta = 0.01.

MATLAB’s delta, a search radius about the angle or axis of its table, is not this one.

Input

`sigma`	the order, an integer or a list of them
`CS`	crystalFrame, whose lattice is searched
`args`	a letter P, I, F, A, B, C or R, the centring of the lattice instead of cs.centering

Keywords

keyword	default	description
`delta`	`0`	the relative misfit of the metric within which rational ratios replace it; 0 keeps the metric as it is

Output

mori orientation from cs to cs, antipodal, one per coincidence class

References

H. Grimmer, W. Bollmann, D. H. Warrington, Coincidence-site lattices and complete pattern-shift lattices in cubic crystals, Acta Cryst. A 30 (1974) 197-207
H. Grimmer, Acta Cryst. A 40 (1984), the coincidence site lattices of any lattice

Used on

CSLBoundaries, Twinning

MATLAB’s CSL

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/CSL_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.

CSL