Boundary Plots edit page

Here we describe how to visualize grain boundary properties, e.g., misorientation angle, misorientation axes. Therefore lets start by importing some EBSD data and reconstructing the grain structure.

close all; plotx2east

% import the data
mtexdata forsterite

% restrict it to a sub-region of interest.
ebsd = ebsd(inpolygon(ebsd,[5 2 10 5]*10^3));

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

% smooth the grains a bit
grains = smooth(grains,4);
ebsd = EBSD
 
 Phase  Orientations     Mineral         Color  Symmetry  Crystal reference frame
     0   58485 (24%)  notIndexed                                                 
     1  152345 (62%)  Forsterite  LightSkyBlue       mmm                         
     2   26058 (11%)   Enstatite  DarkSeaGreen       mmm                         
     3   9064 (3.7%)    Diopside     Goldenrod     12/m1       X||a*, Y||b*, Z||c
 
 Properties: bands, bc, bs, error, mad
 Scan unit : um
 X x Y x Z : [0 36550] x [0 16750] x [0 0]
 Normal vector: (0,0,1)

The grain boundary segments of a list of grains are stored within the field

gB = grains.boundary
gB = grainBoundary
 
 Segments    length   mineral 1   mineral 2
      869  27592 µm  notIndexed  Forsterite
       36   1562 µm  notIndexed   Enstatite
       42   1361 µm  notIndexed    Diopside
     1398  56197 µm  Forsterite  Forsterite
      654  26372 µm  Forsterite   Enstatite
      522  20750 µm  Forsterite    Diopside
       35   1296 µm   Enstatite   Enstatite
      134   5802 µm   Enstatite    Diopside
       23    951 µm    Diopside    Diopside

We may use the plot command to visualize the grain boundaries in the map

% plot phases and grain boundaries
plot(ebsd)
hold on
plot(gB,'lineWidth',2)
hold off

Specific boundaries

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

grains(45).boundary

% lets highlight this specific grain by its boundary
hold on
plot(grains(45).boundary,'lineWidth',4,'lineColor','DarkBlue')
hold off
ans = grainBoundary
 
 Segments   length   mineral 1   mineral 2
       81  3365 µm  Forsterite  Forsterite
       16   720 µm  Forsterite   Enstatite
        9   386 µm  Forsterite    Diopside

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

hold on
plot(grains.boundary('Fo','En'),'linecolor','DarkGreen','linewidth',4)
hold off

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.

hold on
plot(grains.innerBoundary,'linecolor','red','linewidth',4)
hold off

Misorientation angle

The boundary misorientation is the misorientation between the two neighboring pixels of a boundary segment. Depending of the misorientation angle one distinguishes between high angle and low angle grain boundaries. In MTEX we can visualize the boundary misorientation angle by the commands

close all
gB_Fo = grains.boundary('Fo','Fo');
plot(grains,'translucent',1,'micronbar','off')
legend off
hold on
plot(gB_Fo,gB_Fo.misorientation.angle./degree,'linewidth',4)
hold off
mtexColorbar('title','misorientation angle')

The misorientation axes in crystal coordinates

Similarly as the rotational angle we may colorize the grain boundaries also according the misorientation axes. First of all we have to decide whether we want to visualize the rotational axis in crystal or coordinate system. Second we have to define a color key that translates rotational axes into colors.

Lets start with the rotational axes in crystal coordinates

% computed the axes in specimen coordinates
axes = gB_Fo.misorientation.axis

% define a color key
colorKey = HSVDirectionKey(axes);

% compute colors
color = colorKey.direction2color(axes);

hold on
plot(gB_Fo,'lineColor','black','linewidth',6) % some black background for contrast
plot(gB_Fo,color,'linewidth',4)
hold off
mtexColorbar('visible','off')
axes = Miller (Forsterite)
 size: 1398 x 1

As a colorbar replacement we plot the color key and on top of it the misorientation axes at the grain boundaries

figure(2)
plot(colorKey)
hold on
plot(axes,'MarkerFaceAlpha',0.1,'MarkerEdgeAlpha',0.3,'MarkerColor','black')
hold off

The misorientation axes in specimen coordinates

Analyzing the misorientation axis in specimen coordinates is a bit more involved as it requires to extract the two neighboring orientations to each boundary segment. To do this we use the ebsdId stored in the boundary segments.

figure(1)

% first we reduce the number of boundary segments a bit
% in order to avoid that the plot becomes to messy
gB_red = reduce(gB_Fo,5)

% next we extract for every boundary segment the two orientations at both
% sides
ori = ebsd('id',gB_red.ebsdId).orientations

% the two orientations we use to compute the misorientation axis in
% specimen coordinates
axes = axis(ori(:,1),ori(:,2))

% plot the projection of the misorientation axis on the measurement surface
hold on
quiver(gB_red,axes,'autoScaleFactor',0.4,'color','black')
hold off
gB_red = grainBoundary
 
 Segments    length   mineral 1   mineral 2
      280  11373 µm  Forsterite  Forsterite
 
ori = orientation (Forsterite → xyz)
  size: 280 x 2
 
axes = vector3d
 size: 280 x 1

Full Misorientation Colorization

In order to visualize the full misorientation, i.e., axis and angle, one has to define a corresponding color key. One option is the color key described in the paper by S. Patala, J. K. Mason, and C. A. Schuh, Improved representations of misorientation information for grain boundary, Prog. Mater. Sci., vol. 57, no. 8, pp. 1383-1425, 2012.

% plot the grains
close all
plot(grains,'micronbar','off')
legend off

% define the color key
colorKey = PatalaColorKey(gB_Fo);

hold on
plot(gB_Fo,'linewidth',7)
hold on
color = colorKey.orientation2color(gB_Fo.misorientation);
plot(gB_Fo,squeeze(color),'linewidth',4)
hold off

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

figure(2)
plot(colorKey,'layout',[3,4])

% and plot the misorienations on top
plot(gB_Fo.misorientation,...
  'MarkerFacecolor','none','add2all','MarkerSize',4)

Lets illustrate this color coding also at a iron sample.

% import the data
mtexdata csl

% grain segmentation and smoothing
[grains,ebsd.grainId] = calcGrains(ebsd('indexed'));
grains = smooth(grains,2);
gB = grains.boundary('iron','iron');

% and plot image quality + orientation
close all
plot(ebsd,log(ebsd.prop.iq),'figSize','large')
mtexColorMap black2white
setColorRange([.5,5])
hold on
plot(grains,grains.meanOrientation,'FaceAlpha',0.4)

% define the color key and colorize the grain boundaries
colorKey = PatalaColorKey(gB)
color = colorKey.orientation2color(gB.misorientation);
hold on
plot(gB,squeeze(color),'linewidth',4,'smooth')
hold off
ebsd = EBSD
 
 Phase   Orientations  Mineral         Color  Symmetry  Crystal reference frame
    -1  154107 (100%)     iron  LightSkyBlue      m-3m                         
 
 Properties: ci, error, iq
 Scan unit : um
 X x Y x Z : [0 511] x [0 300] x [0 0]
 Normal vector: (0,0,1)
 
colorKey = 
  PatalaColorKey with properties:

          CS1: [1×1 crystalSymmetry]
          CS2: [1×1 crystalSymmetry]
    antipodal: 1

At the end we plot the colorized misorientation space in axis angle sections. Note that in this plot misorientations mori and inv(mori) are associated.

plot(colorKey,'axisAngle',(5:5:60)*degree,'layout',[3,4])

plot(gB.misorientation,'points',300,'add2all',...
  'MarkerFaceColor','none','MarkerEdgeColor','w')
plotting 300 random orientations out of 20356 given orientations