the lattice curvature tensor, the rank two tensor of the spatial derivatives of the orientation field

Syntax

kappa = curvatureTensor(M, cs)

By its 3 x 3 matrix in a crystal frame.

kappa = ebsd.curvature()

From the orientation gradients of a map.

Description

The curvature is what the dislocation density tensor is derived from, dislocationDensity(kappa). A map of the plane gives no derivative along z, so the third column of a curvature computed from it is NaN.

Input

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

Keywords

keyword	default	description
`rank`		the rank of the tensor; for this class always two
`doubleConvention`		read and write a Voigt matrix with the factors of two off the diagonal
`frame`		the reference frame of the coefficients, instead of giving it positionally
`density`		the mass density of the material, carried along
`unit`		the physical unit of the coefficients, a string carried along
`name`		the name of the tensor, carried along
`Kelvin`		read a 6 x 6 matrix in the Kelvin (Mandel) notation
`dtype`		the NumPy type of the coefficients

Output

kappa curvatureTensor

Members

curvatureTensor	the lattice curvature tensor, the rank two tensor of the spatial derivatives of the orientation field
dislocationDensity	convert lattice curvature to the Nye dislocation density tensor
fitDislocationSystems	rho, factor = fitDislocationSystems(kappa, dS): the dislocation densities that account for the curvature with the least total line energy, one signed density per system, NaN where no combination of them reproduces it

MATLAB’s curvatureTensor_index

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/curvatureTensor_index_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.

The class curvatureTensor