Triple points edit page

Triple points are automaticaly computed during grain reconstruction. They are accessable similarly to grain boundaries as the property triplePoints of the grain list. When analyzing triple points it is a good idea to use the option removeQuadruplePoints in calcGrains to convert all quadruple points into triple points.

% import some EBSD data set
mtexdata small silent

% compute grains
grains = calcGrains(ebsd('indexed'),'removeQuadruplePoints');
%grains = calcGrains(ebsd('indexed'));

% smooth the grains a bit
grains = smooth(grains,2);

% plot the grains
plot(grains);

% extract all triple points
tP = grains.triplePoints;

% and plot the on top
hold on
plot(tP,'color','b','linewidth',2)
hold off

Index triple points by phase

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 3
     15  Forsterite  Forsterite  Forsterite
      8  Forsterite  Forsterite   Enstatite
      4  Forsterite   Enstatite   Enstatite
      8  Forsterite  Forsterite    Diopside
     19  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 3
     15  Forsterite  Forsterite  Forsterite
      8  Forsterite  Forsterite   Enstatite
      8  Forsterite  Forsterite    Diopside

Finaly, we may mark all inner Diopside triple points

hold on
plot(tP('Diopside','Diopside','Diopside'),'displayName','Di-Di-Di','color','darkred','linewidth',2)
hold off

Index triple points by grains

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','linewidth',2)
hold off

Index triple points by grain boundary

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','linewidth',2)
hold off
gB_Fo = grainBoundary
 
 Segments   mineral 1   mineral 2
      255  Forsterite  Forsterite
 
gB_large = grainBoundary
 
 Segments   mineral 1   mineral 2
       55  Forsterite  Forsterite

Boundary segments from triple points

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 (Forsterite → Forsterite)
  size: 15 x 3
  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','MarkerSize',8)
hold off
mtexColorMap(blue2redColorMap)
CLim(gcm,[80,180])
mtexColorbar

Angles at triple points

The angles at the triplepoints can be accessed by tP.angles. This is a 3 column matrix with one column for each of the three angles enclosed by the boundary segments of a triple point. Obviously, the sum of each row is always 2*pi. More interestingly is the difference between the largest and the smallest angle. Lets plot this for our test data set.

plot(grains,'figSize','large')
hold on
tP = grains.triplePoints;
plot(tP,(max(tP.angles,[],2)-min(tP.angles,[],2))./degree,'markerEdgeColor','w','MarkerSize',8)
hold off
mtexColorMap LaboTeX
setColorRange([0,180])
mtexColorbar