the texture average of a single crystal tensor over an ODF, a list of orientations or a map; MATLAB’s calcTensor

Syntax

TV = calcTensor(odf, T)

Over an ODF, the Voigt average.

TR = calcTensor(odf, T, 'Reuss')

The inverse averaged and inverted.

TH = calcTensor(odf, T, average='Hill')

The mean of the Voigt and the Reuss average.

TV = calcTensor(ori, T, weights=w)

Over a weighted list of orientations.

TV, TR, TH = calcTensor(ebsd, T1, T2, 'all')

Over a map, one tensor per phase.

Description

The average decides how the rotated tensors are combined:

‘Voigt’, the default: the mean of the tensor rotated by the orientations.
‘Reuss’: the inverse of the mean of the rotated inverses.
‘Hill’: the mean of the Voigt and the Reuss average.
‘all’: the three of them.

Over an ODF the average is exact, since a rotated tensor of rank R is a polynomial of degree R in the rotation. MATLAB’s geometric mean (‘geometric’) is not offered.

Over a map every indexed phase takes the tensor of its crystal frame, the tensors given in any order, and a phase without a tensor is refused: select the phases first, ebsd[[‘Forsterite’, ‘Enstatite’]].

Input

`x`	SO3Fun, orientation or EBSD
`T`	tensor, the single crystal tensor; for a map one per phase

Keywords

keyword	default	description
`average`	`'Voigt'`	‘Voigt’, ‘Reuss’, ‘Hill’ or ‘all’; also given as a string after the tensors
`weights`	`None`	one weight per orientation or pixel

Output

`T`	the average, of the class of T; with ‘all’ the three averages Voigt, Reuss, Hill

Used on

CPOSeismicProperties, TensorAverage

MATLAB’s EBSD.calcTensor

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/EBSD.calcTensor_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.

EBSD.calcTensor