Grain Neighbors edit page

In this section we discuss how to analyze the neighbouring relationships between grains. While most of this can be done also on the level of grain boundaries an local misorientations it is for large data sets sometimes useful to consider misorientations between the meanorienations of grains. We shall use the following Magnesium data set of our explainations.

% load sample EBSD data set
mtexdata twins silent
CS = ebsd('indexed').CS;

% reconstruct grains
[grains, ebsd.grainId] = calcGrains(ebsd('indexed'),'angle',5*degree);

grains = smooth(grains,5);

% plot the grains
plot(grains,grains.meanOrientation)

Central for the analysis of grain to grain relationships is the function grains.neighbours. It return a list of pairs of neighbouring grain ids. Each row of the list containes the ids of two neighbouring grains. In the following lines choose the row number 170 and outline the corresponding grains

pairs = grains.neighbors;

hold on
plot(grains(pairs(170,:)).boundary,'LineWidth',4,'linecolor','b')
hold off

In order to compute the misorentation between these two grains we can do

mori = inv(grains(pairs(170,1)).meanOrientation) * grains(pairs(170,2)).meanOrientation
mori = misorientation (Magnesium → Magnesium)
 
  Bunge Euler angles in degree
     phi1     Phi    phi2
  107.142 58.9469  309.49

This can be generalized to compute the misorientations between neighbouring grains using

mori = inv(grains(pairs(:,1)).meanOrientation) .* grains(pairs(:,2)).meanOrientation

close all
histogram(mori.angle./degree)
xlabel('misorientation angle')
mori = misorientation (Magnesium → Magnesium)
  size: 251 x 1

We observe a high peak at about 85 degree. This angle corresponds to twinning. In Magnesium the twinning orientation relationship is given by

twinning = orientation.map(Miller(0,1,-1,-2,CS),Miller(0,-1,1,-2,CS),...
  Miller(2,-1,-1,0,CS),Miller(2,-1,-1,0,CS))
twinning = misorientation (Magnesium → Magnesium)
 
 (1-101) || (10-11)   [01-11] || [01-1-1]

In order to determine the percentage of twinnig pairs we do

% which of the pairs are twinning
isTwinning = angle(mori,twinning) < 3*degree;

% percentage of twinning pairs
100 * sum(isTwinning) / length(isTwinning)
ans =
   37.0518

It is important to understand that the list returned by grains.neighbours containes only pairs such that both grains are contained in grains. This allows the syntax grains('phaseName') to extract only neighbour relation ships within one phase.

In some case, e.g. if we ask for all neighbouring grains to a given grains, it is useful to replace this constraint by the condition that at least one grain should by part of grains. This can be accomplished by the option 'full'.

% get all pairs containing grain 83
pairs = grains(83).neighbors('full');

% remove center grain 83 from this list
pairs(pairs == 83) = [];

plot(grains,grains.meanOrientation,'micronbar','off')
hold on
plot(grains(pairs).boundary,'lineColor','blue','lineWidth',3)
hold on
plot(grains(83).boundary,'lineColor','red','lineWidth',3)
hold off