Standard Orientations edit page

This section displays some of the standard orientations that are build into MTEX. The full list of predefined orientations consists of

  • 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');

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),...
  ];

3d Euler angle space

Lets first visualize the orientations in the three dimensional Euler angle space

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

A second common way of visualizing the orientation space are sections with fixed Euler angle phi2

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 the three dimensional axis angle space the orientation appear inside the fundamental sector

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

In the major pole figures the predefined orientations appear at the following spots

plotx2north
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

For inverse pole figure the situation is as follows. Note that the different size of the markers has been chosen to avoid overprinting.

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'));

Defining an Model ODF

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 (m-3m → 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
plotIPDF(odf,r)
hold on
plotIPDF(odf,r,'contour','lineColor','k','linewidth',2)
hold off
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