Explains how to detect orthotropic symmetry in an ODF.

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A synthetic example |

Reconstruct an ODF from simulated EBSD data |

Detect the sample symmetry axis in the reconstructed ODF |

Sample symmetry in an ODF computed from pole figure data |

We start by modeling a orthotropic ODF with cubic crystal symmetry.

CS = crystalSymmetry('cubic'); SS = specimenSymmetry('222'); % some component center ori = [orientation('euler',135*degree,45*degree,120*degree,CS,SS) ... orientation('euler', 60*degree, 54.73*degree, 45*degree,CS,SS) ... orientation('euler',70*degree,90*degree,45*degree,CS,SS)... orientation('euler',0*degree,0*degree,0*degree,CS,SS)]; % with corresponding weights c = [.4,.13,.4,.07]; % the model odf odf = unimodalODF(ori(:),'weights',c,'halfwidth',12*degree) % lets plot some pole figures h = [Miller(1,1,1,CS),Miller(2,0,0,CS),Miller(2,2,0,CS)]; plotPDF(odf,h,'antipodal','silent','complete')

odf = ODF crystal symmetry : m-3m specimen symmetry: 222 Radially symmetric portion: kernel: de la Vallee Poussin, halfwidth 12° center: Rotations: 4x1 weight: 1

Next we simulated some EBSD data, rotate them and estimate an ODF from the individual orientations.

% define a sample rotation %rot = rotation('euler',0*degree,0*degree,1*degree); rot = rotation('euler',15*degree,12*degree,-5*degree); % Simulate individual orientations and rotate them. % Note that we loose the sample symmetry by rotating the orientations ori = rot * calcOrientations(odf,1000) % estimate an ODF from the individual orientations odf_est = calcODF(ori,'halfwidth',10*degree) % and visualize it figure, plotPDF(odf_est,h,'antipodal',8,'silent');

ori = orientation size: 1 x 1000 crystal symmetry : m-3m specimen symmetry: 1 odf_est = ODF crystal symmetry : m-3m specimen symmetry: 1 Harmonic portion: degree: 28 weight: 1

We observe that the reconstructed ODF has almost orthotropic symmetry, but with respect to axed different from x, y, z. With the following command we can determine an rotation such that the rotated ODF has almost orthotropic symmetry with respect to x, y, z. The second argument is some starting direction where MTEX locks for a symmetry axis.

[odf_corrected,rot_inv] = centerSpecimen(odf_est); figure plotPDF(odf_corrected,h,'antipodal',8,'silent') % the difference between the applied rotation and the estimate rotation angle(rot,inv(rot_inv)) / degree

progress: 100% progress: 100% progress: 100% progress: 100% ans = 0.8195

In the next example we apply the function `centerSpecimen` to an ODF estimated from pole figure data. Lets start by importing them

fname = fullfile(mtexDataPath,'PoleFigure','aachen_exp.EXP'); pf = loadPoleFigure(fname); plot(pf,'silent')

In a second step we compute an ODF from the pole figure data

odf = calcODF(pf,'silent') plotPDF(odf,h,'antipodal','silent')

odf = ODF crystal symmetry : 432 specimen symmetry: 1 Radially symmetric portion: kernel: de la Vallee Poussin, halfwidth 5° center: 4790 orientations, resolution: 5° weight: 1

Finally, we detect the orthotropic symmetry axes a1, a2, a3 by

[~,~,a1,a2] = centerSpecimen(odf,yvector) a3 = cross(a1,a2) annotate([a1,a2,a3],'label',{'RD','TD','ND'},'backgroundcolor','w','MarkerSize',8)

progress: 100% progress: 100% progress: 100% progress: 100% progress: 100% a1 = vector3d size: 1 x 1 resolution: 0.71° x y z 0.0499876 0.998745 0.00325886 a2 = vector3d size: 1 x 1 x y z -0.99875 0.0499879 0 a3 = vector3d size: 1 x 1 resolution: 0.71° x y z -0.000162903 -0.00325478 0.999995

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