Orientation Sections

A three dimensional cloud of orientations is hard to read on paper, so the usual compromise is a stack of two dimensional slices through orientation space. Which slices, and how they are cut, is a matter of convention - each of them keeps some structure recognisable and hides other.

plottingConvention.default('y↑→x');

cs = crystalSymmetry('432')
ss = specimenSymmetry('222')

ori = orientation.rand(100,cs,ss)

cs = crystalSymmetry (⊙c→a)
 
  symmetry: 432    
  elements: 24     
  a, b, c : 1, 1, 1
 
 
ss = orthorhombic specimenSymmetry (y↑→x)
 
 
ori = orientation (432 → y↑→x (222))
  size: 100 × 1

phi2 Sections

The most common cut fixes the third Euler angle. Each plot is one value of \(\varphi_2\), with \(\varphi_1\) and \(\Phi\) spanning the plane.

plotSection(ori,'phi2')

The points have no preferred orientation, but they are not uniform in the rectangular Euler coordinates: the volume element contains \(\sin\Phi\), so points thin out near \(\Phi=0\). Real textures add structure on top of that baseline, as spots or lines running through several sections. The classical rolling fibres of cubic metals are read this way, see Euler Angle Sections.

Sigma Sections

Sigma sections cut differently, along \(\sigma = \varphi_1 - \varphi_2\). They need fewer plots to cover the same region and keep a texture component together instead of splitting it across sections.

plotSection(ori,'sigma')

Why they are the better default for cubic material, and how to read them, is Sigma Sections.

Further Section Types

plotSection also takes 'phi1' for sections of the first Euler angle and 'axisAngle' for sections of constant rotational angle. The number of sections is set with the option 'sections'.

plotSection(ori,'axisAngle','sections',6)

Sections of a density rather than of a list of orientations are the same plots applied to an ODF, which is what these views are mostly used for - see Plotting an ODF. Do not contour a scatter of orientations directly: computing an ODF first and plotting that is both faster and better founded, and MTEX warns when asked to do otherwise.

Next

The full three dimensional views these sections cut through are 3D Plots.