Selecting Grains edit page

In this section we discuss how to select grains by properties. We start our discussion by reconstructing the grain structure from a sample EBSD data set.

% load sample EBSD data set
mtexdata forsterite silent

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

% remove all not indexed pixels
ebsd = ebsd('indexed');

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

% smooth them
grains = smooth(grains,5);

% plot the orientation data of the Forsterite phase
plot(ebsd('fo'),ebsd('fo').orientations)

% plot the grain boundary on top of it
hold on
plot(grains.boundary,'lineWidth',2)
hold off

Selecting grains by mouse

The most easiest way to select a grain is by using the mouse and the command selectInteractive which allows you to select an arbitrary amount of grains. The index of the selected grains appear as the global variable indSelected in your workspace

selectInteractive(grains,'lineColor','gold')

% this simulates a mouse click
pause(0.1)
simulateClick(9000,3500)
pause(0.1)

global indSelected;
grains(indSelected)

hold on
plot(grains(indSelected).boundary,'lineWidth',4,'lineColor','gold')
hold off
Grain selected: 94
 
ans = grain2d
 
 Phase  Grains  Pixels     Mineral  Symmetry  Crystal reference frame
     1       1     323  Forsterite       mmm                         
 
 boundary segments: 107 (4116 µm)
 inner boundary segments: 0 (0 µm)
 triple points: 10
 
 Id   Phase   Pixels   phi1   Phi   phi2          GOS
 94       1      323    131    64    250   0.00796443

Indexing by orientation or position

One can also to select a grain by spatial coordinates without user interaction. This is done using the syntax grains(x,y), i.e.,

x = 12000; y = 4000;

hold on
plot(grains(x,y).boundary,'linewidth',4,'linecolor','blue')

plot(x,y,'marker','s','markerfacecolor','k',...
  'markersize',10,'markeredgecolor','w')
hold off

Alternatively one can also select all grains with a certain orientation. Lets find all grains with a similar orientation as the one marked in gold. As threshold we shall use 20 degree

% select grains by orientation
grains_selected = grains.findByOrientation(grains(indSelected).meanOrientation,20*degree)

hold on
plot(grains_selected.boundary,'linewidth',4,'linecolor','gold')
hold off
grains_selected = grain2d
 
 Phase  Grains  Pixels     Mineral  Symmetry  Crystal reference frame
     1       4     524  Forsterite       mmm                         
 
 boundary segments: 204 (8292 µm)
 inner boundary segments: 0 (0 µm)
 triple points: 23
 
  Id   Phase   Pixels   phi1   Phi   phi2          GOS
  26       1        1    130    68    258            0
  62       1      181    131    64    245   0.00699418
  94       1      323    131    64    250   0.00796443
 123       1       19    144    74    250    0.0103623

Indexing by a Property

In order the generalize the above concept lets remember that the variable grains is essentially a large vector of grains. Thus when applying a function like area to this variable we obtain a vector of the same lenght with numbers representing the area of each grain

grain_area = grains.area;

As a first rather simple application we could colorize the grains according to their area, i.e., according to the numbers stored in grain_area

plot(grains,grain_area)

As a second application, we can ask for the largest grain within our data set. The maximum value and its position within a vector are found by the Matlab command max.

[max_area,max_id] = max(grain_area)
max_area =
   4.1013e+06
max_id =
   208

The number max_id is the position of the grain with a maximum area within the variable grains. We can access this specific grain by direct indexing

grains(max_id)
ans = grain2d
 
 Phase  Grains  Pixels     Mineral  Symmetry  Crystal reference frame
     1       1    1545  Forsterite       mmm                         
 
 boundary segments: 295 (11687 µm)
 inner boundary segments: 0 (0 µm)
 triple points: 31
 
  Id   Phase   Pixels   phi1   Phi   phi2        GOS
 208       1     1545    167    81    251   0.012969

and so we can plot it

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

Note that this way of addressing individual grains can be generalized to many grains. E.g. assume we are interested in the largest 5 grains. Then we can sort the vector grain_area and take the indices of the 5 largest grains.

[sorted_area,sorted_id] = sort(grain_area,'descend');

large_grain_id = sorted_id(2:5);

hold on
plot(grains(large_grain_id).boundary,'linecolor','Orange','linewidth',4)
hold off

Indexing by a Condition

By the same syntax as above we can also single out grains that satisfy a certain condition. I.e., to access are grains that are at least one quarter as large as the largest grain we can do

condition = grain_area > max_area/4;

hold on
plot(grains(condition).boundary,'linecolor','Yellow','linewidth',4)
hold off

This is a very powerful way of accessing grains as the condition can be build up using any grain property. As an example let us consider the phase. The phase of the first five grains we get by

grains(1:5).phase
ans =
     2
     1
     1
     1
     2

Now we can access or grains of the first phase Forsterite by the condition

condition = grains.phase == 1;
plot(grains(condition))

To make the above more directly you can use the mineral name for indexing

grains('forsterite')
ans = grain2d
 
 Phase  Grains  Pixels     Mineral  Symmetry  Crystal reference frame
     1     118   14093  Forsterite       mmm                         
 
 boundary segments: 3541 (147821 µm)
 inner boundary segments: 14 (312 µm)
 triple points: 257
 
 Properties: meanRotation, GOS

Logical indexing allows also for more complex queries, e.g. selecting all grains perimeter larger than 6000 and at least 600 measurements within

condition = grains.perimeter>6000 & grains.grainSize >= 600;

selected_grains = grains(condition)

plot(selected_grains)
selected_grains = grain2d
 
 Phase  Grains  Pixels     Mineral  Symmetry  Crystal reference frame
     1       4    5248  Forsterite       mmm                         
 
 boundary segments: 875 (35941 µm)
 inner boundary segments: 0 (0 µm)
 triple points: 79
 
  Id   Phase   Pixels   phi1   Phi   phi2          GOS
  99       1     1448    166   127    259    0.0134158
 119       1     1047     89    99    224   0.00765479
 122       1     1208    153    68    237   0.00807919
 208       1     1545    167    81    251     0.012969

The grainId and how to select EBSD inside specific grains

Besides, the list of grains the command calcGrains returns also two other output arguments.

plot(grains)
largeGrains = grains(grains.grainSize > 50);

text(largeGrains,largeGrains.id)

The second output argument grainId is a list with the same size as the EBSD measurements that stores for each measurement the corresponding grainId. The above syntax stores this list directly inside the ebsd variable. This enables MTEX to select EBSD data by grains. The following command returns all the EBSD data that belong to grain number 33.

ebsd(grains(33))
ans = EBSD
 
 Phase  Orientations   Mineral      Color  Symmetry  Crystal reference frame
     3      1 (100%)  Diopside  Goldenrod     12/m1       X||a*, Y||b*, Z||c
 
    Id   Phase   phi1   Phi   phi2   bands   bc    bs   error   mad       x      y   grainId
 37553       3     80    16    152       7   65   113       0   0.7   11000   2550        33
 Scan unit : um

and is equivalent to the command

ebsd(ebsd.grainId == 33)
ans = EBSD
 
 Phase  Orientations   Mineral      Color  Symmetry  Crystal reference frame
     3      1 (100%)  Diopside  Goldenrod     12/m1       X||a*, Y||b*, Z||c
 
    Id   Phase   phi1   Phi   phi2   bands   bc    bs   error   mad       x      y   grainId
 37553       3     80    16    152       7   65   113       0   0.7   11000   2550        33
 Scan unit : um

The following picture plots the largest grains together with its individual orientation measurements.

plot(ebsd(grains(max_id)),ebsd(grains(max_id)).orientations)
hold on
plot(grains(max_id).boundary,'lineWidth',2)
hold off

Boundary grains

Sometimes it is desirable to remove all boundary grains as they might distort grain statistics. To do so one should remember that each grain boundary has a property grainId which stores the ids of the neigbouring grains. In the case of an outer grain boundary, one of the neighbouring grains has the id zero. We can filter out all these boundary segments by

% ids of the outer boundary segment
outerBoundary_id = any(grains.boundary.grainId==0,2);

% plot the outer boundary segments
plot(grains)
hold on
plot(grains.boundary(outerBoundary_id),'linecolor','red','linewidth',2)
hold off

Now grains.boundary(outerBoundary_id).grainId is a list of grain ids where the first column is zero, indicating the outer boundary, and the second column contains the id of the boundary grain. Hence, it remains to remove all grains with these ids.

% next we compute the corresponding grain_id
grain_id = grains.boundary(outerBoundary_id).grainId;

% remove all zeros
grain_id(grain_id==0) = [];

% and plot the boundary grains
plot(grains(grain_id))

finally, we could remove the boundary grains by

grains(grain_id) = []

However, boundary grains can be selected more easily be the command isBoundary.

plot(grains(~grains.isBoundary))