how to detect triple points

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Calculation of triple points |

Index triple points by phase |

Index triple points by grains |

Index triple points by grain boundary |

Boundary segments from triple points |

MTEX automatically computes triple points during grain reconstruction. They are acessable similarly to grain boundaries as an property of the grain list.

% import some EBSD data set mtexdata small % compute grains grains = calcGrains(ebsd('indexed')); % extract all triple points tP = grains.triplePoints

tP = triplePointList points mineral 1 mineral 2 mineral 2 15 Forsterite Forsterite Forsterite 7 Forsterite Forsterite Enstatite 4 Forsterite Enstatite Enstatite 8 Forsterite Forsterite Diopside 16 Forsterite Enstatite Diopside 4 Forsterite Diopside Diopside 2 Enstatite Enstatite Diopside 1 Enstatite Diopside Diopside 11 Diopside Diopside Diopside

You may index triple points by the adjacent phases. The following command gives you all triple points with at least one phase being Forsterite

`tP('Forsterite')`

ans = triplePointList points mineral 1 mineral 2 mineral 2 15 Forsterite Forsterite Forsterite 7 Forsterite Forsterite Enstatite 4 Forsterite Enstatite Enstatite 8 Forsterite Forsterite Diopside 16 Forsterite Enstatite Diopside 4 Forsterite Diopside Diopside

The following command gives you all triple points with at least two phases being Forsterite

tP('Forsterite','Forsterite')

ans = triplePointList points mineral 1 mineral 2 mineral 2 15 Forsterite Forsterite Forsterite 7 Forsterite Forsterite Enstatite 8 Forsterite Forsterite Diopside

Finaly, we may mark all inner Diopside triple points

% smooth the grains a bit grains = smooth(grains,2); % and plot them plot(grains); % on top plot the triple points hold on plot(tP('Diopside','Diopside','Diopside'),'displayName','Di-Di-Di','color','b') hold off

Since, triple points are asociated to grains we may single out triple points that belong to a specific grain or some subset of grains.

% find the index of the largest grain [~,id] = max(grains.area); % the triple points that belong to the largest grain tP = grains(id).triplePoints; % plot these triple points plot(grains(id),'FaceColor',[0.2 0.8 0.8],'displayName','largest grains'); hold on plot(grains.boundary) plot(tP,'color','r') hold off

Triple points are not only a property of grains but also of grain boundaries. Thus we may ask for all triple points that belong to Fosterite - Forsterite boundaries with misorientation angle larger then 60 degree

% all Fosterite - Forsterite boundary segments gB_Fo = grains.boundary('Forsterite','Forsterite') % Fo - Fo segments with misorientation angle larger 60 degree gB_large = gB_Fo(gB_Fo.misorientation.angle>60*degree) % plot the triple points plot(grains) hold on plot(gB_large,'linewidth',2,'linecolor','w') plot(gB_large.triplePoints,'color','m') hold off

gB_Fo = grainBoundary Segments mineral 1 mineral 2 255 Forsterite Forsterite gB_large = grainBoundary Segments mineral 1 mineral 2 55 Forsterite Forsterite

On the other hand we may also ask for the boundary segments that build up a triple point. These are stored as the property boundaryId for each triple points.

% lets take Forsterite triple points tP = grains.triplePoints('Fo','Fo','Fo'); % the boundary segments which form the triple points gB = grains.boundary(tP.boundaryId); % plot the triple point boundary segments plot(grains) hold on plot(gB,'lineColor','w','linewidth',2) hold off

Once we have extracted the boundary segments adjecent to a triple point we may also extract the corresponding misorientations. The following command gives a n x 3 list of misorientations where n is the number of triple points

mori = gB.misorientation

mori = misorientation size: 15 x 3 crystal symmetry : Forsterite (mmm) crystal symmetry : Forsterite (mmm) antipodal: true

Hence, we can compute for each triple point the sum of misorientation angles by

sumMisAngle = sum(mori.angle,2);

and my visualize it by

plot(grains,'figSize','large') hold on plot(tP,sumMisAngle ./ degree,'markerEdgeColor','w') hold off mtexColorMap(blue2redColorMap) CLim(gcm,[80,180]) mtexColorbar

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