A method of EBSD.

the weighted Burgers vector: the net Burgers vector of the dislocations crossing the map per unit area, by the integral or the gradient method; MATLAB’s weightedBurgersVec

Syntax

W = weightedBurgersVec(ebsd)

In specimen coordinates, a 3 x 3 loop.

W = weightedBurgersVec(ebsd, windowSize=2)

Around a loop of 5 x 5 pixels.

W = ebsd.orientations.inv() * weightedBurgersVec(ebsd) # in crystal coordinates

W = weightedBurgersVec(ebsd, gradient=True)

From the orientation gradient.

Description

The weighted Burgers vector of Wheeler et al. is computed by one of two methods:

the integral method, the default: the crystal coordinates of the specimen x and y axes summed around a square loop of 2 windowSize + 1 pixels about every pixel. It needs a gridded map of one indexed phase. A loop that leaves the map, meets a non indexed pixel or, after calcGrains, leaves the grain gives NaN, so a larger window leaves more pixels NaN.
the gradient method, gradient=True: the column of Nye’s tensor along the normal of the map, from the curvature of the nearest neighbours. It runs on a list and on a map of several phases as well.

The vectors are in the specimen frame, per scan unit. windowSize is a whole number of at least 1.

Input

ebsd EBSD, of one indexed phase and gridified for the integral method

Keywords

keyword	default	description
`windowSize`	`1`	the half width of the loop of the integral method, in pixels
`stencil`	`'oneSided'`	the stencil of the derivatives of the gradient method, ‘oneSided’, ‘lattice’ or ‘full’
`gradient`	`False`	use the gradient method instead of the integral one

Output

`W`	vector3d of the shape of the map, in the specimen frame

References

J. Wheeler, E. Mariani, S. Piazolo, D.J. Prior, P. Trimby, M.R. Drury, The weighted Burgers vector: a new quantity for constraining dislocation densities and types using electron backscatter diffraction on 2D sections through crystalline materials, J. Microscopy 233 (2009) 482-494

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.weightedBurgersVec_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.weightedBurgersVec