Explains how to detect and quantify twin boundaries
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|Data import and grain detection|
|Properties of grain boundaries|
|Merge twins along twin boundaries|
|Calculate the twinned area|
|Setting Up the EBSD Data for the Merged Grains|
Lets import some Magnesium data that are full of grains and segment grain within the data set.
% load some example data mtexdata twins % segment grains [grains,ebsd.grainId,ebsd.mis2mean] = calcGrains(ebsd('indexed'),'angle',5*degree); % remove two pixel grains ebsd(grains(grains.grainSize<=2)) = ; [grains,ebsd.grainId,ebsd.mis2mean] = calcGrains(ebsd('indexed'),'angle',5*degree); % smooth them grains = grains.smooth(5); % visualize the grains plot(grains,grains.meanOrientation) % store crystal symmetry of Magnesium CS = grains.CS;
I'm going to colorize the orientation data with the standard MTEX colorkey. To view the colorkey do: oM = ipfColorKey(ori_variable_name) plot(oM)
Now we can extract from the grains its boundary and save it to a separate variable
gB = grains.boundary
gB = grainBoundary Segments mineral 1 mineral 2 600 notIndexed Magnesium 3164 Magnesium Magnesium
The output tells us that we have 3219 Magnesium to Magnesium boundary segments and 606 boundary segements where the grains are cut by the scanning boundary. To restrict the grain boundaries to a specific phase transistion you shall do
gB_MgMg = gB('Magnesium','Magnesium')
gB_MgMg = grainBoundary Segments mineral 1 mineral 2 3164 Magnesium Magnesium
A variable of type grain boundary contains the following properties
These can be used to colorize the grain boundaries. By the following command, we plot the grain boundaries colorized by the misorientation angle
We observe many grain boundaries with a large misorientation angle of about 86 degrees. Those grain boundaries are most likely twin boundaries. To detect them more precisely we define first the twinning as a misorientation, which is reported in literature by (1,1,-2,0) parallel to (2,-1,-1,0) and (-1,0,1,1) parallel to (1,0,-1,1). In MTEX it is defined by
twinning = orientation.map(Miller(1,1,-2,0,CS),Miller(2,-1,-1,0,CS),... Miller(-1,0,1,1,CS),Miller(1,0,-1,1,CS))
twinning = misorientation size: 1 x 1 crystal symmetry : Magnesium (6/mmm, X||a*, Y||b, Z||c*) crystal symmetry : Magnesium (6/mmm, X||a*, Y||b, Z||c*) Bunge Euler angles in degree phi1 Phi phi2 Inv. 330 93.6529 330 0
The followin lines show that the twinning is actually a rotation about axis (-2110) and angle 86.3 degree
% the rotational axis round(twinning.axis) % the rotational angle twinning.angle / degree
ans = Miller size: 1 x 1 mineral: Magnesium (622, X||a*, Y||b, Z||c*) h -1 k 2 i -1 l 0 ans = 86.3471
Next, we check for each boundary segment whether it is a twinning boundary, i.e., whether boundary misorientation is close to the twinning.
% restrict to twinnings with threshold 5 degree isTwinning = angle(gB_MgMg.misorientation,twinning) < 5*degree; twinBoundary = gB_MgMg(isTwinning) % plot the twinning boundaries plot(grains,grains.meanOrientation) %plot(ebsd('indexed'),ebsd('indexed').orientations) hold on %plot(gB_MgMg,angle(gB_MgMg.misorientation,twinning),'linewidth',4) plot(twinBoundary,'linecolor','w','linewidth',2,'displayName','twin boundary') hold off
twinBoundary = grainBoundary Segments mineral 1 mineral 2 1649 Magnesium Magnesium I'm going to colorize the orientation data with the standard MTEX colorkey. To view the colorkey do: oM = ipfColorKey(ori_variable_name) plot(oM)
Grains that have a common twin boundary are assumed to inherite from one common grain. To reconstruct those initial grains we merge grains together which have a common twin boundary. This is done by the command merge.
[mergedGrains,parentId] = merge(grains,twinBoundary); % plot the merged grains %plot(ebsd,ebsd.orientations) hold on plot(mergedGrains.boundary,'linecolor','k','linewidth',2.5,'linestyle','-',... 'displayName','merged grains') hold off
The second output argument paraentId of merge is a list with the same size as grains which indicates for each grain into which common grain it has been merged. The id of the common grain is usually different from the ids of the merged grains and can be found by
ans = 16
Hence, we can find all childs of grain 16 by
childs = grains(parentId == mergedGrains(16).id)
childs = grain2d Phase Grains Pixels Mineral Symmetry Crystal reference frame 1 8 1698 Magnesium 6/mmm X||a*, Y||b, Z||c* boundary segments: 442 triple points: 25 Id Phase Pixels GOS phi1 Phi phi2 6 1 40 0.00752395 178 90 236 14 1 254 0.0113434 81 25 187 17 1 4 0.0135723 80 26 189 19 1 38 0.00595743 95 145 186 24 1 774 0.0102947 178 90 235 28 1 45 0.0107243 81 26 188 29 1 293 0.00910428 94 146 185 33 1 250 0.0106861 179 89 235
We can also answer the question about the relative area of these initial grains that have undergone twinning to total area.
twinId = unique(gB_MgMg(isTwinning).grainId); % compute the area fraction sum(area(grains(twinId))) / sum(area(grains)) * 100
ans = 73.5716
Note that the Id's of the merged grains does not fit the grainIds stored in the initial ebsd variable. As a consequence, the following command will not give the right result
plot(mergedGrains(16).boundary,'linewidth',2) hold on plot(ebsd(mergedGrains(16)),ebsd(mergedGrains(16)).orientations) hold off
In order to update the grainId in the ebsd variable to the merged grains, we proceed as follows.
% copy ebsd data into a new variable to not change the old data ebsd_merged = ebsd; % update the grainIds to the parentIds ebsd_merged('indexed').grainId = parentId(ebsd('indexed').grainId)
ebsd_merged = EBSD Phase Orientations Mineral Color Symmetry Crystal reference frame 0 46 (0.2%) notIndexed 1 22794 (100%) Magnesium light blue 6/mmm X||a*, Y||b, Z||c* Properties: bands, bc, bs, error, mad, x, y, grainId, mis2mean Scan unit : um
Now the variable ebsd_merged can be indexed by the merged grains, i.e.
plot(ebsd_merged(mergedGrains(16)),ebsd_merged(mergedGrains(16)).orientations) hold on plot(mergedGrains(16).boundary,'linewidth',2) hold off
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