Grain Boundaries

Overview about colorizing grain boundaries

On this page ...
The grain boundary
Visualizing special grain boundaries
Phase boundaries
Subboundaries
Misorientation
Classifying special boundaries

Let's import some EBSD data and compute the grains.

close all
mtexdata forsterite
plotx2east

ebsd = ebsd('indexed');
[grains,ebsd.grainId] = calcGrains(ebsd);

% remove very small grains
ebsd(grains(grains.grainSize<=5)) = [];

% and recompute grains
[grains,ebsd.grainId] = calcGrains(ebsd);

% smooth the grains a bit
grains =smooth(grains,4)
 
ebsd = EBSD  
 
 Phase  Orientations     Mineral        Color  Symmetry  Crystal reference frame
     1  151466 (82%)  Forsterite   light blue       mmm                         
     2   25635 (14%)   Enstatite  light green       mmm                         
     3     7306 (4%)    Diopside    light red     12/m1       X||a*, Y||b*, Z||c
 
 Properties: bands, bc, bs, error, mad, x, y, grainId
 Scan unit : um
 
 
grains = grain2d  
 
 Phase  Grains  Pixels     Mineral  Symmetry  Crystal reference frame
     1     426  151466  Forsterite       mmm                         
     2     200   25635   Enstatite       mmm                         
     3     142    7306    Diopside     12/m1       X||a*, Y||b*, Z||c
 
 boundary segments: 33636
 triple points: 1347
 
 Properties: GOS, meanRotation
 

The grain boundary

The grain boundary of a list of grains can be extracted by

gB = grains.boundary

plot(gB)
 
gB = grainBoundary  
 
 Segments   mineral 1   mineral 2
     1355  notIndexed  Forsterite
      198  notIndexed   Enstatite
       36  notIndexed    Diopside
    13890  Forsterite  Forsterite
    10857  Forsterite   Enstatite
     5167  Forsterite    Diopside
      598   Enstatite   Enstatite
     1259   Enstatite    Diopside
      276    Diopside    Diopside

Accordingly, we can access the grain boundary of a specific grain by

grains(267).boundary

plot(grains(267).boundary)
 
ans = grainBoundary  
 
 Segments   mineral 1   mineral 2
      304  Forsterite  Forsterite
      126  Forsterite   Enstatite
       97  Forsterite    Diopside

let's combine it with the orientation measurements inside

% define the colorcoding such that the meanorientation becomes white
oM = ipdfHSVOrientationMapping(grains(267));
oM.inversePoleFigureDirection = grains(267).meanOrientation * oM.whiteCenter;
oM.maxAngle = 5*degree;

% get the ebsd data of grain 267
ebsd_931 = ebsd(grains(267));

% plot the orientation data
hold on
plot(ebsd_931,oM.orientation2color(ebsd_931.orientations))
hold off

Visualizing special grain boundaries

Phase boundaries

For a multi-phase system, the location of specific phase transistions may be of interest. The following plot highlights all Forsterite to Enstatite phase transitions

close all
plot(grains,'faceAlpha',.3)
hold on
plot(grains.boundary('Fo','En'),'linecolor','r','linewidth',1.5)
hold off

Subboundaries

Another type of boundaries is boundaries between measurements that belong to the same grain. This happens if a grain has a texture gradient that loops around these two measurements.

close all
plot(grains.boundary)
hold on
plot(grains.innerBoundary,'linecolor','r','linewidth',2)

Misorientation

Basically there are two ways to visualize misorientations along the grain boundary. The simplest way is to colorize the grain boundaries with respect to the misorientation angle.

close all
gB_Fo = grains.boundary('Fo','Fo');
plot(grains,'translucent',.3,'micronbar','off')
legend off
hold on
plot(gB_Fo,gB_Fo.misorientation.angle./degree,'linewidth',1.5)
hold off
mtexColorbar('title','misorientation angle')

The more sophisticated way is to colorize the misorientation space and apply the color to the respective grain boundaries.

close all
plot(grains,'translucent',.3,'micronbar','off')
legend off
hold on

% this reorders the boundary segement a a connected graph which results in
% a smoother plot
gB_Fo = gB_Fo.reorder;

oM = patalaOrientationMapping(gB_Fo);

plot(gB_Fo,'linewidth',4)
% on my computer setting the renderer to painters gives a much more
% pleasent result
set(gcf,'Renderer','painters')
hold on

plot(gB_Fo,oM.orientation2color(gB_Fo.misorientation),'linewidth',2)

hold off

Lets visualize the color key as axis angle sections through the misorientation space

plot(oM)

Classifying special boundaries

Actually, it might be more informative, if we classify the grain boundaries after some special property.

We can mark grain boundaries after its misorientation angle is in a certain range

close all

mAngle = gB_Fo.misorientation.angle./ degree;
hist(mAngle)

[~,id] = histc(mAngle,0:30:120);
plot(gB,'linecolor','k')

hold on
plot(gB_Fo(id==1),'linecolor','b','linewidth',2,'DisplayName','>40^\circ')
plot(gB_Fo(id==2),'linecolor','g','linewidth',2,'DisplayName','20^\circ-40^\circ')
plot(gB_Fo(id==3),'linecolor','r','linewidth',2,'DisplayName','10^\circ-20^\circ')
plot(gB_Fo(id==4),'linecolor','y','linewidth',2,'DisplayName','< 10^\circ')

hold off

Or we mark the rotation axis of the misorientation.

close all
plot(gB)
hold on

ind = angle(gB_Fo.misorientation.axis,xvector)<5*degree;

plot(gB_Fo(ind),'linecolor','b','linewidth',2,'DisplayName','[100]')
Warning: Symmetry mismatch 
Warning: Symmetry mismatch 

Or we mark a special rotation between neighboured grains. If a linecolor is not specified, then the boundary is colorcoded after its angular difference to the given rotation.

rot = rotation('axis',vector3d(1,1,1),'angle',60*degree);
ind = angle(gB_Fo.misorientation,rot)<10*degree;

close all
plot(gB)
hold on
plot(gB_Fo(ind),'lineWidth',1.5,'lineColor','r')

legend('>2^\circ','60^\circ/[001]')
Warning: Ignoring extra legend
entries. 

Another kind of special boundaries is tilt and twist boundaries. We can find a tilt boundary by specifying the crystal form, which is tilted, i.e. the misorientation maps a lattice plane of on grain onto the others grain lattice plane.

where are neighbored orientations. TODO

%close all
%plot(grains.boundary)
%hold on
%plot(grains.boundary,'property',Miller(1,1,1),'delta',2*degree,...
%  'linecolor','r','linewidth',1.5)
%plot(grains.boundary,'property',Miller(0,0,1),'delta',2*degree,...
%  'linecolor','b','linewidth',1.5)
%
%legend('>2^\circ',...
%  '\{111\}',...
%  '\{001\}')