the grain boundary normal distribution in the crystal frame, estimated from the traces of the boundaries in a planar section; with a misorientation the grain boundary character distribution

Syntax

gbnd = calcGBND(gB, ebsd)

The normals from the orientations of the pixels.

gbnd = calcGBND(gB, grains)

The normals from the mean orientations of the grains.

gbnd = calcGBND(gB, ebsd, halfwidth=5*degree, nonneg=True)

A smaller halfwidth, a nonnegative kernel.

gbcd = calcGBND(gB, grains, moriRef)

The character distribution of one misorientation.

gbcd = calcGBND(gB, grains, moriRef, oneSide=True) # only the first side of a symmetric relation

Description

A section shows only the trace of every boundary; the boundary plane may be inclined about it at any angle. The orientations on both sides turn each trace into the crystal frame, and a kernel over the unknown inclination spreads it to the compatible normals. Summed over all boundaries, weighted by their lengths, this gives an antipodal density of the normals, normalised so that a uniform distribution of planes is one.

The boundaries must hold one pair of phases, gB[‘Magnesium’, ‘Magnesium’] for instance. With a map, the orientations of the two pixels of every segment are used, which requires boundaries that were not resampled: smooth them with smoothBoundary(grains, simplify=False, refine=False), or pass the grains to use their mean orientations.

With a misorientation moriRef, only the boundaries near it count, weighted by their distance to it, and the normals are given in the crystal frame of its first side: the grain boundary character distribution. A relation that is its own inverse, a twin, takes both sides of every boundary unless oneSide=True.

Input

`gB`	grainBoundary, the boundaries of one pair of phases
`source`	EBSD, the map the boundaries were computed from, or grain2d, the grains
`moriRef`	orientation, the misorientation of the character distribution

Keywords

keyword	default	description
`halfwidth`	`10*degree`	the halfwidth of the density estimation, of the kernel in the normals, and, with moriRef, how far a misorientation may lie from it
`nonneg`	`False`	a nonnegative kernel of the inclination, a Gaussian in the cosine to the trace, instead of the solution of the integral equation, which may ring and be negative
`bump`	`False`	a bump kernel of the inclination, constant within the halfwidth
`oneSide`	`False`	with a moriRef that is its own inverse, take only the first side of every boundary

Output

gbnd S2FunHarmonic, antipodal, in the crystal frame of the phase, or of the first side of moriRef

References

D.M. Saylor, G.S. Rohrer, Determining crystal habits from observations of planar sections, J. Am. Ceram. Soc. 85 (2002) 2799-2804
R. Hielscher, R. Kilian, E. Wünsche, Efficient computation of the grain boundary normal distribution from two dimensional EBSD data, not yet published

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/grainBoundary.calcGBND_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.

grainBoundary.calcGBND