the distribution of the misorientation angle: of a misorientation density, of a list of misorientations, or of the uniform density of two crystal frames

Syntax

density, omega = calcAngleDistribution(mdf)

The angle distribution of a misorientation density.

density, omega = calcAngleDistribution(mdf, omega=np.linspace(0, 60, 31)*degree)

At the angles given.

density, omega = calcAngleDistribution(mori)

A histogram of misorientations.

density, omega = calcAngleDistribution(mori, edges=np.linspace(0, 63, 22)*degree)

With the bin edges given.

ad, omega = calcAngleDistribution(cs)

The uniform distribution of one crystal frame.

ad, omega = calcAngleDistribution(cs, cs2)

The uniform one of two crystal frames.

ad, omega = calcAngleDistribution(cs, np.linspace(0, 60, 61)*degree)

At the angles given.

Description

The result depends on the input:

a crystal frame, or two: the distribution of the uniform density, the area of the axis sector of the fundamental region at each angle times sin^2(omega/2), scaled to mean one over the angles.
an SO3Fun: that uniform distribution times the mean of the function over the axes at each angle, scaled by the same factor, so that a uniform density gives the uniform distribution.
misorientations: a histogram of the disorientation angles in percent, summing to 100, with omega the centres of the bins, zero in every bin for no misorientations.

The angles are in radians and end at the largest angle of the fundamental region; angles given beyond it are dropped. They may also be given positionally, after the second frame. MATLAB returns the same two outputs in this order.

Input

`f`	SO3Fun, a misorientation density; orientation, misorientations; or crystalFrame
`cs2`	crystalFrame, the second frame of the uniform distribution (positional)

Keywords

keyword	default	description
`omega`	`None`	the angles at which the distribution is computed, 200 up to the largest angle by default (SO3Fun and frames)
`edges`	`None`	the bin edges of the histogram, by default between 4 and 49 bins up to the largest angle, one per 20 misorientations (misorientations)
`resolution`	`0.5*degree`	the spacing of the axes sampled at each angle (SO3Fun)

Output

`density`	ndarray, the values of the distribution
`omega`	ndarray, the angles they belong to

Used on

AngleDistributionFunction

MATLAB’s orientation.calcAngleDistribution

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/orientation.calcAngleDistribution_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.

orientation.calcAngleDistribution