the crystal axes a, b, c in Cartesian coordinates, from the cell of a lattice; MATLAB’s calcAxis, what crystalFrame builds its axes with

Syntax

axes = crystalAxes(lattice, abc, abg)
X   a*, Z   c. 
axes = crystalAxes(lattice, abc, abg, alignment=['X||a', 'Z||c*'])

Another alignment.

axes = crystalAxes(lattice, abc, abg, alignment=['EDAX'], rotate=rot)

The vendor’s alignment, turned.

Description

The default alignment puts a* along x and c along z. An alignment names the lattice direction a Cartesian axis lies along: a, b, c, their reciprocals a, b, c*, m = a + b or d = a + b + c.

  • X or Y named, no Z: Z lies along c, or along c* when a direct axis was named
  • Z alone named: X takes the partner of the usual setting
  • ‘EDAX’, ‘TSL’ or ‘OIM’: the vendors’ alignment X||a for the triclinic, trigonal and hexagonal lattices, where a and a* differ

A length of 0 is filled from the others and an angle of 0 from its partners, as MTEX fills them; a cell the lattice does not allow is refused unless check=False.

Input

lattice latticeType, the lattice system
abc the lengths a, b, c of the cell
abg the angles alpha, beta, gamma of the cell, in radians; by default those of the lattice

Keywords

keyword default description
alignment () a list of strings like ‘X||a’, ‘Z||c*’ or a vendor’s name
rotate None a rotation, or a 3 x 3 matrix, applied to the aligned axes
uniqueAxis 1 the index of the unique axis of a monoclinic lattice, 0 to 2 for a to c
check True refuse a cell the lattice does not allow: unequal lengths a and b of a trigonal, hexagonal or tetragonal lattice, unequal lengths of a cubic one, angles not 90 degree with the unique axis of a monoclinic one

Output

axes a (3, 3) array, the axes a, b, c in Cartesian coordinates, one per row

See also

crystalFrame, reciprocalAxes, CrystalReferenceSystem

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/crystalAxes_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.