3D Grains edit page

Grains as three dimensional objects are stored in MTEX as variables of type grain3d. Basic properties and operations are described in the sections Properties of Three-Dimensional Grains and Operations with Three-Dimensional Grains.

In this section we discuss how to import three dimensional grains from Dream3d and Neper.

Import Grains from Dream3d

In order to import grain data we use the command grain3d.load 

% specify the file name
fname = fullfile(mtexDataPath,'EBSD','SmallIN100_MeshStats.dream3d');
grains = grain3d.load(fname);

% for triangulated data sets it may be useful to plot them without lines
plot(grains,grains.meanOrientation,'LineStyle','none','micronbar','off')

% use a nice plotting convention
how2plot = plottingConvention.default3D;
setCamera(how2plot)

Dream3d stores the boundary faces with an arbitrary winding, i.e., the normal computed from the vertex order points randomly into or out of the grain. MTEX therefore runs orientFaces as part of the import, so that face normals, grain volumes and boundary.grainId are directly usable. Should you need the raw winding as stored in the file, switch this off with

grainsRaw = grain3d.load(fname,'noOrientFaces');

Without oriented faces, more than half of the grains of this data set come out with a negative volume, since their normals point inwards

[nnz(grainsRaw.volume < 0), nnz(grains.volume < 0)]
ans =
   419     0

Similarly as with two dimensional grains we can select individual grains by arbitrary constraints. For instance we can find the largest grain by

% index of the grain with the largest volume
[~,id] = max(grains.volume)

plot(grains(id),'edgeAlpha',0.15,'micronBar','off')
setCamera(how2plot)
id =
   623

Slicing the 3d grains by a plane using the command slice results in 2d grains comparable to what can be reconstructed from 2d EBSD maps.

% define the plane by a normal direction and a point
plane = plane3d(vector3d(1,1,1),vector3d(-20,20,-15));

% compute the sliced grains
grains2 = slice(grains,plane)

% plot them
plot(grains2,grains2.meanOrientation,'micronbar','off')

setCamera(how2plot)
grains2 = grain2d (y↓→x)
 
 Phase  Grains  Pixels  Mineral  Symmetry         Color
     2     187     187  unknown       432  LightSkyBlue
 
 boundary segments: 7177 (655 µm)
 inner boundary segments: 0 (0 µm)
 triple points: 269
 
 Properties: meanRotation, Id3d

It might be reasonable to adjust the plotting convention such that the normal direction grains2.N points out of screen.

how2plot2 = plottingConvention;
how2plot2.outOfScreen = grains2.N;
how2plot2.east = vector3d(1,-1,0);

setCamera(how2plot2), axis off, xlabel('') , ylabel('')

Import Grains from Neper

Neper is a software package for the simulation of three dimensional microstructures. After installation it can be directly called by MTEX. The general workflow is explained here. Here we use it to quickly generate a copper microstructure with specific texture and specific distribution of boundary normals.

% set up the communication with Neper
neper.init;
neper.geometry = "cube(2,2,1)";

% define a texture
cs = crystalSymmetry.load('quartz.cif','color','lightblue');
odf = fibreODF(cs.cAxis,vector3d(1,1,1));

numGrains = 300;
grains = neper.simulateGrains(numGrains,odf,'silent')
% or you can load an existing tessellation file
%grains = grain3d.load('allgrains.tess','CS',cs)
========================    N   e   p   e   r    =======================
Info   : A software package for polycrystal generation and meshing.
Info   : Version 4.9.1-4
Info   : Built with: gsl|muparser|opengjk|openmp|nlopt|libscotch (full)
Info   : Running on 12 threads.
Info   : <https://neper.info>
Info   : Copyright (C) 2003-2022, and GNU GPL'd, by Romain Quey.
========================================================================

 
grains = grain3d (y↓→x)
 
 Phase  Grains  Volume  Mineral  Symmetry  Crystal reference frame
     2     300       4   Quartz       321        X||a*, Y||b, Z||c
 
 boundary faces: 2032
 
 Properties: meanRotation
% colorize by mean orientation
plot(grains,grains.meanOrientation,'micronbar','off','faceAlpha',0.5)
setCamera(how2plot)

Slicing

Let us slice this 3d data set as well

% make all slices passing through the center point of the cube
P0 = vector3d(0.5,0.5,0.5);

% with normal (0,0,1)
N = vector3d(0,0,1);

grains_2d = grains.slice(N,P0)

plot(grains_2d,grains_2d.meanOrientation,'micronbar','off','linewidth',3)
setCamera(how2plot)
grains_2d = grain2d (y↓→x)
 
 Phase  Grains  Pixels  Mineral  Symmetry         Color
     2      99      99   Quartz       321  LightSkyBlue
 
 boundary segments: 298 (41 µm)
 inner boundary segments: 0 (0 µm)
 triple points: 165
 
 Properties: meanRotation, Id3d

Grains intersecting a slice

Using the function intersected we can identify all grains that intersect a given plane. Lets simply add 3d the shapes of all grains intersecting the plane.

isInter = grains.intersected(N,P0);

hold on
plot(grains(isInter),grains(isInter).meanOrientation,'faceAlpha',0.6,'linewidth',0.5)

%[a,b,c] = grains(isInter).principalComponents;
%plotEllipsoid(grains(isInter).centroid,a,b,c,'faceAlpha',0.5)
hold off

setCamera(plottingConvention.default3D)

Plot the normal directions of a single grain

The following code shows how to visualize the face normals

% multiplication with I_GF flips the boundary normals to point out of the
% grain
id = 3;
dir = full(grains(id).I_GF(1,:)).' .* grains(id).boundary.N

plot(grains(id))
hold on
quiver(grains(id).boundary,dir)
hold off
dir = vector3d (y↓→x)
 size: 8 x 1
       x       y       z
       1       0       0
       0       0       1
   -0.12   0.993 0.00632
  -0.705  -0.128  -0.697
  0.0244  -0.988  -0.155
  -0.908  -0.289  -0.303
  -0.912   0.304  -0.277
   0.106   0.129  -0.986