Miller.multiplicity edit page

number of directions symmetrically equivalent to m

Description

The multiplicity of a crystal direction is the size of its orbit under the crystal symmetry, i.e. the number of distinct symmetrically equivalent directions - 6 for {100}, 12 for {110}, 8 for {111} and 48 for {321} in m-3m. This is the multiplicity as the term is used crystallographically, e.g. the factor scaling the intensity of a reflection in powder diffraction.

Up to MTEX 6 this returned the reciprocal quantity, numSym(CS)/n, i.e. the order of the stabilizer - the number of symmetry operations that fix m. See https://github.com/mtex-toolbox/mtex/issues/2584. The two multiply to the order of the group, so the old value is numSym(m.CS) ./ multiplicity(m).

Syntax

n = multiplicity(m) % number of <Miller.Miller.html Miller> indices equivalent to m

Input

m Miller

Output

n integer

See also

vector3d.symmetrise orientation.multiplicity fibre.multiplicity

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/Miller.multiplicity.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.