Misorientations at grain boundaries

Analyse misorientations along grain boundaries

Import EBSD data and select a subregion

plotx2east
mtexdata forsterite
%
% correct EBSD spatial coordinates
%
%
%             O************O xmax,ymax
%             *            *
%             * selected   *
%             * subregion  *
%             *            *
%   xmin,ymin O************O
%
xmin = 7000;
ymin = 4500;
xmax = 20000;
ymax = 8100;
region = [xmin ymin xmax-xmin ymax-ymin];

plot(ebsd)
rectangle('position',region,'edgecolor','r','linewidth',2)

% select EBSD data within region and printout to command window
condition = inpolygon(ebsd,region); % select indices by polygon
ebsd = ebsd(condition);

Grain modelling prototcole - using indexed points and segmentation angle

and re-calculate grain model to cleanup grain boundaries

% segmentation angle typically 10 to 15 degrees
seg_angle = 10;

% minimum indexed points per grain between 5 and 10
min_points = 10;

% Restrict to indexed only points
[grains,ebsd.grainId,ebsd.mis2mean] = calcGrains(ebsd('indexed'),'angle',seg_angle*degree);

% Remove small grains with less than min_points indexed points
grains = grains(grains.grainSize > min_points);

% Re-calculate grain model to cleanup grain boundaries with less than minimum index points
% used ebsd points within grains having the minium indexed number of points (e.g. 10 points)
ebsd = ebsd(grains);
[grains,ebsd.grainId,ebsd.mis2mean] = calcGrains(ebsd('indexed'),'angle',seg_angle*degree);

% smooth grains
grains = smooth(grains,4)
 
grains = grain2d  
 
 Phase  Grains  Pixels     Mineral  Symmetry  Crystal reference frame
     1      46   12891  Forsterite       mmm                         
     2      11    1287   Enstatite       mmm                         
     3      10     448    Diopside     12/m1        X||a*, Y||b, Z||c
 
 boundary segments: 2957
 triple points: 95
 
 Properties: GOS, meanRotation
 

plot the data

%plot(ebsd('fo'),ebsd('fo').orientations,'micronbar','off')
plot(grains('fo'),grains('fo').meanOrientation,'micronbar','off','figSize','large')
hold on
plot(grains.boundary)
hold off
  I'm going to colorize the orientation data with the 
  standard MTEX colorkey. To view the colorkey do:
 
  oM = ipdfHSVOrientationMapping(ori_variable_name)
  plot(oM)

Visualize the misorientation angle at grain boundaries

% Use boundary('Fo','Fo') to chose only Fo-Fo boundaries
gB = grains.boundary.reorder;
gB_FoFo = gB('Fo','Fo');

% visualize the misorientation angle
% draw the boundary in black very thick
hold on
plotOrdered(gB_FoFo,'linewidth',4);

% and on top of it the boundary colorized according to the misorientation
% angle
hold on
plotOrdered(gB_FoFo,gB_FoFo.misorientation.angle./degree,'linewidth',2);
%plot(gB_FoFo,gB_FoFo.misorientation.angle./degree,'linewidth',5);
hold off
mtexColorMap jet
mtexColorbar('title','misorientation angle')

Visualize the misorientation axes in specimen coordinates

Computing the misorientation axes in specimen coordinates can not be done using the boundary misorientations only. In fact, we require the orientations on both sides of the grain boundary. Lets extract them first.

% do only consider every third boundary segment
Sampling_N=3;
gB_FoFo = gB_FoFo(1:Sampling_N:end);

% the following command gives a Nx2 matrix of orientations which contains
% for each boundary segment the orientation on both sides of the boundary.
ori = ebsd(gB_FoFo.ebsdId).orientations;

% the misorientation axis in specimen coordinates
gB_axes_FoFo = axis(ori(:,1),ori(:,2));

% axes can be plotted using the command quiver
hold on
quiver(gB_FoFo,gB_axes_FoFo,'linewidth',1,'color','k','autoScaleFactor',0.3)
hold off

Note, the shorte the axes the more they stick out of the surface. What may be a bit surprising is that the misorientations axes have some abrupt changes at the left hands side grain boundary. The reason for this is that the misorientations angle at this boundary is close to the maximum misorientation angle of 120 degree. As a consequence, slight changes in the misorientation may leed to a completely different disorientation, i.e., a different but symmetrically equivalent misorientation has a smaller misorientation angle.