the dislocation density or Nye tensor, the rank two tensor derived from the curvature tensor of an orientation field

Syntax

alpha = dislocationDensityTensor(M, cs)

By its 3 x 3 matrix in a crystal frame.

alpha = dislocationDensity(kappa)

From a curvature tensor.

Description

Fitting it against a list of dislocationSystem gives the densities of the geometrically necessary dislocations, calcGND. Constructed from a curvatureTensor, the coefficients are taken over as they are; dislocationDensity(kappa) computes the tensor from the curvature.

Input

M 3 x 3 matrix, or an array (…, 3, 3) of them
cs crystalFrame the coefficients refer to

Keywords

keyword default description
rank None the rank of the tensor; for this class always two
doubleConvention None read and write a Voigt matrix with the factors of two off the diagonal
frame None the reference frame of the coefficients, instead of giving it positionally
density None the mass density of the material, carried along
unit None the physical unit of the coefficients, a string carried along
name None the name of the tensor, carried along
Kelvin False read a 6 x 6 matrix in the Kelvin (Mandel) notation
dtype None the NumPy type of the coefficients

Output

alpha dislocationDensityTensor

See also

tensor, curvatureTensor, dislocationSystem, calcGND

MATLAB’s dislocationDensityTensor.dislocationDensityTensor

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/dislocationDensityTensor.dislocationDensityTensor_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.