Grain Reconstruction

By grain reconstruction we mean the subdivision of the specimen, or more precisely the measured surface of the specimen, into regions of similar orientation which we then call grains. Note that there is no canonical definition of what is a grain. The grain reconstruction method that is default in MTEX is based on the definition of high angle grain boundaries which are assumed at the Mittelsenkrechten between neighbouring measurements whenever their misorientation angle exceeds a certain threshold. According to this point of view grains are regions surrounded by grain boundaries.

In order to illustrate the grain reconstruction process we consider the following sample data set

close all; plotx2east

% import the data
mtexdata forsterite

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

% make a phase plot
plot(ebsd)

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, x, y
 Scan unit : um

Basic grain reconstruction

We see that there are a lot of not indexed measurements. For grain reconstruction, we have three different choices how to deal with these unindexed regions:

By default, MTEX uses the first method.

The second parameter that is involved in grain reconstruction is the threshold misorientation angle indicating a grain boundary. By default, this value is set to 10 degrees.

All grain reconstruction methods in MTEX are accessible via the command calcGrains which takes as input an EBSD data set and returns a list of grain.

grains = calcGrains(ebsd,'angle',10*degree)

grains = grain2d
 
 Phase  Grains  Pixels     Mineral  Symmetry  Crystal reference frame
     0    1139    4052  notIndexed                                   
     1     244   14093  Forsterite       mmm                         
     2     177    1397   Enstatite       mmm                         
     3     104     759    Diopside     12/m1       X||a*, Y||b*, Z||c
 
 boundary segments: 10422 (523078 µm)
 inner boundary segments: 0 (0 µm)
 triple points: 905
 
 Properties: meanRotation, GOS

The reconstructed grains are stored in the variable grains. Note that also the notIndexed measurements are grouped into grains. This allows later to analyze the shape of these unindexed regions.

To visualize the grains we can plot its boundaries by the command plot.

% start overide mode
hold on

% plot the boundary of all grains
plot(grains.boundary,'linewidth',1.5)

% stop overide mode
hold off

Filling notindexed holes

It is important to understand that MTEX distinguishes the following two situations

A location marked as notindexed is interpreted by MTEX as at this position, there is no crystal, whereas for a location that does not occur in the data set is interpreted by MTEX as: it is not known whether there is a crystal or not. Just to remind you, the later assumption is nothing special as it applies at all locations but the measurement points.

A location that does not occur in the data is assigned in MTEX to the same grain and phase as the closest measurement point - this may also be a notindexed point. Hence, filling holes in MTEX means to erase them from the list of measurements, i.e., instead of telling MTEX there is no crystal we are telling MTEX: we do not know what there is.

The extremal case is to say whenever there is a not indexed measurement we actually do not know anything and allow MTEX to freely guess what happens there. This is realized by removing all not indexed measurements or, equivalently, computing the grains only from the indexed measurements

% compute the grains from the indexed measurements only
grains = calcGrains(ebsd('indexed'))

plot(ebsd)

% start overide mode
hold on

% plot the boundary of all grains
plot(grains.boundary,'linewidth',1.5)

% mark two grains by location
plot(grains(11300,6100).boundary,'linecolor','DarkGreen','linewidth',5,...
  'DisplayName','grain A')
plot(grains(12000,4000).boundary,'linecolor','DarkBlue','linewidth',5,...
  'DisplayName','grain B')

% stop overide mode
hold off

grains = grain2d
 
 Phase  Grains  Pixels     Mineral  Symmetry  Crystal reference frame
     1     103   14093  Forsterite       mmm                         
     2      32    1397   Enstatite       mmm                         
     3      71     759    Diopside     12/m1       X||a*, Y||b*, Z||c
 
 boundary segments: 3784 (185218 µm)
 inner boundary segments: 12 (605 µm)
 triple points: 240
 
 Properties: meanRotation, GOS

We observe, especially in the marked grains, how MTEX fills notindexed regions and connects otherwise separate measurements to grains. As all information about not indexed regions were removed the reconstructed grains fill the map completely

plot(grains,'linewidth',2)

Inside of grain B, there is a large not indexed region and we might argue that is not very meaningful to assign such a large region to some grain but should have kept it not indexed. In order to decide which not indexed region is large enough to be kept not indexed and which not indexed regions can be filled it is helpful to know that the command calcGrains also separates the not indexed regions into "grains" and we can standard grain functions like area or perimeter to analyze these regions.

[grains,ebsd.grainId,ebsd.mis2mean] = calcGrains(ebsd);
notIndexed = grains('notIndexed')

notIndexed = grain2d
 
 Phase  Grains  Pixels     Mineral  Symmetry  Crystal reference frame
     0    1139    4052  notIndexed                                   
 
 boundary segments: 8694 (436378 µm)
 inner boundary segments: 0 (0 µm)
 triple points: 868
 
 Properties: meanRotation, GOS

We see that we have 1139 not indexed regions. A good measure for compact regions vs. cluttered regions is the quotient between the area and the boundary length. Lets, therefore, plot the "not indexed grains" colorized by this quotient

% plot the not indexed regions colorcoded according the the quotient between
% number of measurements and number of boundary segments
plot(notIndexed,log(notIndexed.grainSize ./ notIndexed.boundarySize))
mtexColorbar

Regions with a high quotient are blocks which can be hardly correctly assigned to a grain. Hence, we should keep these regions as not indexed and only remove the not indexed information from locations with a low quotient.

% the "not indexed grains" we want to remove
toRemove = notIndexed(notIndexed.grainSize ./ notIndexed.boundarySize<0.8);

% now we remove the corresponding EBSD measurements
ebsd(toRemove) = [];

% and perform grain reconstruction with the reduces EBSD data set
[grains,ebsd.grainId,ebsd.mis2mean] = calcGrains(ebsd);

plot(grains,'lineWidth',2)

We see that that all the narrow not indexed regions have been assigned to the surounding grains while the large regions have been left unindexed. Finally, the image with the raw EBSD data and on top the grain boundaries.

% plot the raw data
plot(ebsd)

% start overide mode
hold on

% plot the boundary of all grains
plot(grains.boundary,'linewidth',1.5)

% mark two grains by location
plot(grains(11300,6100).boundary,'linecolor','DarkGreen','linewidth',4,...
  'DisplayName','grain A')
plot(grains(12000,4000).boundary,'linecolor','DarkBlue','linewidth',4,...
  'DisplayName','grain B')

% stop overide mode
hold off

Non convex data sets

By default MTEX uses the convex hull when computing the outer boundary for an EBSD data set. This leads to poor results in the case of non convex EBSD data sets.

% cut of a non convex region from our previous data set
poly = 1.0e+04 *[...
  0.6853    0.2848
  0.7102    0.6245
  0.8847    0.3908
  1.1963    0.6650
  1.1371    0.2880
  0.6853    0.2833
  0.6853    0.2848];

ebsdP = ebsd(ebsd.inpolygon(poly));

plot(ebsdP,'micronBar','off')
legend off

% compute the grains
grains = calcGrains(ebsdP('indexed'));

% plot the grain boundary
hold on
plot(grains.boundary,'linewidth',1.5)
hold off

We see that the grains badly fill up the entire convex hull of the data points. This can be avoided by specifying the option tight for the determination of the outer boundary.

plot(ebsdP,'micronBar','off')
legend off

% compute the grains
grains = calcGrains(ebsdP('indexed'),'boundary','tight');

% plot the grain boundary
hold on
plot(grains.boundary,'linewidth',1.5)
hold off