Everything measured on a polished surface is a section through something three-dimensional, and a section is a biased witness. Cut a box of grains with a plane and the circles you see are almost never through the middle of a grain, so the sizes are systematically too small. Cut an elongated grain across rather than along and it looks equiaxed. The boundary you measure is a line where a surface met your section, and its inclination is simply gone.
Three-dimensional data removes these compromises. It comes from serial sectioning - polish, map, repeat - from diffraction techniques that see into the volume, or from simulated microstructures generated for modelling.
plottingConvention.default('y↑→x');
fname = fullfile(mtexDataPath,'EBSD','SmallIN100_MeshStats.dream3d');
grains = grain3d.load(fname);
plot(grains,grains.meanOrientation,'LineStyle','none','micronbar','off')
What is drawn is the outside of the volume. The grains behind it are present in the data, which is the point, and also the reason a three-dimensional data set takes more care to look at than a map.
What three dimensions actually buy
Three things, and they are worth separating because they need different amounts of data.
Volume instead of area. A grain has a real size rather than a sectioned one, so the size distribution needs no stereological correction and no assumption about shape.
The whole boundary. The interface between two grains is a surface, so the two numbers that a section could not give - the inclination of the boundary plane - are measured rather than inferred. All five parameters of a boundary become available at once, per boundary, which is the single biggest gain.
Real neighbourhood. Two grains that appear to touch in a section may not, and two that do touch may not appear to. Only in three dimensions is the contact network of the grains the actual one.
The data is shaped differently
A 2D map is a list of measurements on a grid. A 3D grain structure is usually a mesh: grains bounded by faces, faces bounded by edges, with the geometry carried by vertices. It is not a stack of pixels, and code written for maps does not carry over unchanged.
The practical consequences are that faces have an orientation which may need fixing on import, that plotting means deciding what to hide, and that everything is larger - which is why a subset is usually selected before anything expensive.
Where to start
3D-Grains is the entry point: importing a volume, what the resulting grain3d object contains, and how to draw it.
Properties and Operations are the three-dimensional counterparts of the measuring and selecting pages in Grains. Not everything has a counterpart yet, and those pages say which.
Neper Interface connects MTEX to Neper, which generates synthetic polycrystals. This is more useful than it may sound: a simulated microstructure has a known answer, which makes it the honest way to test whether an analysis does what you think.
Next
The two-dimensional case is EBSD, Grains and Grain Boundaries, and those chapters are where the concepts are introduced. The boundary character that three dimensions finally makes fully measurable is discussed under Boundary Normal Distribution.