Standard Orientations edit page

Rolling, drawing and recrystallisation produce the same few orientations again and again, and those have names - Cube, Goss, Brass, Copper. Naming a component is how a texture is described in one sentence, and MTEX has the standard ones built in, so a measured texture can be compared against them directly.

The predefined orientations are

Cube, CubeND22, CubeND45, CubeRD
Goss, invGoss
Copper, Copper2
SR, SR2, SR3, SR4
Brass, Brass2
PLage, PLage2, QLage, QLage2, QLage3, QLage4

For visualization we fix a generic cubic crystal symmetry and orthorhombic specimen symmetry

cs = crystalSymmetry('m-3m');
ss = specimenSymmetry('orthorhombic');

% the standard components are defined relative to the rolling frame -
% RD to the north, TD to the west and ND out of the page
specimenFrame.rolling.makeDefault

and select a subset of the above predefined orientations

components = [...
  orientation.goss(cs,ss),...
  orientation.brass(cs,ss),...
  orientation.cube(cs,ss),...
  orientation.cubeND22(cs,ss),...
  orientation.cubeND45(cs,ss),...
  orientation.cubeRD(cs,ss),...
  orientation.copper(cs,ss),...
  orientation.PLage(cs,ss),...
  orientation.QLage(cs,ss),...
  ];

Each component is named in the legends below by the lattice plane and direction it stands for, as \((hkl)[uvw]\) - the plane facing the sheet normal and the direction along the rolling direction, which is what orientation.byMiller takes.

Three Dimensional Euler Angle Space

The first view puts every component at its three Bunge Euler angles.

close all
for i = 1:length(components)
  plot(components(i),'bunge','MarkerSize',10,'MarkerColor', ind2color(i),...
    'DisplayName',round2Miller(components(i),'LaTex'))
  hold on
end
legend('show','interpreter','LaTeX','location','southoutside','numColumns',3,'FontSize',1.2*getMTEXpref('FontSize'));
hold off

Two Dimensional phi2 Sections

The classical way of showing the same thing on paper: sections of fixed \(\varphi_2\), in which the rolling components line up in recognisable patterns, see Euler Angle Sections.

close all
for i = 1:length(components)
  plotSection(components(i), 'add2all', 'MarkerColor', ind2color(i),...
    'DisplayName', round2Miller(components(i),'LaTex'))
end

legend('show','interpreter','LaTeX','location','southeast','FontSize',1.2*getMTEXpref('FontSize'));

Three Dimensional Axis Angle Space

In axis angle space the components sit inside the fundamental region of the cubic-orthorhombic pair, see Fundamental Region.

close all
for i = 1:length(components)
  hold on
  plot(components(i),'axisAngle','MarkerSize',10,'MarkerColor', ind2color(i),...
    'DisplayName',round2Miller(components(i),'LaTex'))
  axis off
end
legend('show','interpreter','LaTeX','location','southoutside','numColumns',3,'FontSize',1.2*getMTEXpref('FontSize'));

Pole Figures

Where each component puts the major lattice planes. This is the view a measured pole figure is compared against. For Goss, the \(\{110\}\) family has a pole in the centre because the \((011)\) plane faces the sheet normal. Cube puts \(\{100\}\) poles in the centre and on the two axes of the rim.

h = Miller({1,0,0},{1,1,0},{1,1,1},{3,1,1},cs);

close all
for i = 1:length(components)
  plotPDF(components(i),h,'MarkerSize',10,'MarkerColor', ind2color(i),...
    'DisplayName',round2Miller(components(i),'LaTex'))
  hold on
end
hold off

legend('show','interpreter','LaTeX','location','northeast','numColumns',2,'FontSize',1.2*getMTEXpref('FontSize'));

Inverse Pole Figures

The same components seen from the specimen side: which crystal direction lies along X, Y and Z. The markers are drawn in decreasing size so that components falling on the same spot stay visible.

r = [vector3d.X,vector3d.Y,vector3d.Z];

close all
for i = 1:length(components)
  plotIPDF(components(i),r,'MarkerSize',(12-i)^1.5,'MarkerColor', ind2color(i),...
    'DisplayName',round2Miller(components(i),'LaTex'))
  hold on
end
hold off

legend('show','interpreter','LaTeX','location','northeast','numColumns',2,'FontSize',1.2*getMTEXpref('FontSize'));

From a Component to a Model Texture

A named component is a single orientation, and a real texture is a spread around one. Giving the component a halfwidth turns it into a model ODF, which is what the measured data is actually fitted against, see Modeling ODFs.

odf = unimodalODF(components(3),'halfwidth',7.5*degree)

plotPDF(odf,h)
hold on
plotPDF(odf,h,'contour','lineColor','k','linewidth',2)
hold off

odf = SO3FunRBF (m3̅m → y↓→x (mmm))
 
  unimodal component
  kernel: de la Vallee Poussin, halfwidth 7.5°
  center: 1 orientations
 
  Bunge Euler angles in degree
  phi1    Phi   phi2 weight
     0      0      0      1

What was a single point is now a spread about seven degrees wide. The same in the inverse pole figures,

plotIPDF(odf,r)
hold on
plotIPDF(odf,r,'contour','lineColor','k','linewidth',2)
hold off

and in phi2 sections, with all the components drawn on top so it is visible which one the model was built around.

plotSection(odf)

hold on
plotSection(odf,'contour','lineColor','k','linewidth',2)

for i = 1:length(components)

  plotSection(components(i),'MarkerSize',10,'filled','DisplayName',round2Miller(components(i),'LaTex'))

end

hold off

Fibres of Orientations follows the named fibre components through orientation space. Modeling ODFs develops the model textures introduced above.

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/OrientationStandard.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.

Standard Orientations