Tutorials

Crystallographic texture is the statistical distribution of crystal orientations in a specimen. MTEX reaches that distribution from two main kinds of measurement: orientation maps and diffraction pole figures.

Each tutorial below follows one short, reproducible analysis from data import to an interpreted result. Open a tutorial in the MATLAB editor, run it section by section, and change one choice at a time.

edit EBSDTutorial;

A tutorial is a worked route, not a measurement protocol. Parameters such as reconstruction thresholds and smoothing widths depend on the specimen and the scientific question. The linked chapters explain those choices.

Before you start

General Concepts introduces the MTEX object model. One variable usually holds a vectorized list of measurements or grains, and selecting a subset is how an analysis narrows its question.

Notation and Conventions states MTEX's choices for angles, Euler angles, and the direction of an orientation. It distinguishes planes from directions and covers crystal-axis alignment, plotting conventions, units, and the names used in examples.

Before the diffraction route, read Miller Indices and Specimen Symmetry. They introduce Miller indices and the specimen invariance used in pole-figure reconstruction.

Choose the route that matches your measurement

Electron backscatter diffraction (EBSD) records a phase and an orientation at each sampled position on a polished surface. The resulting orientation map retains spatial information: it says what was measured and where it was measured.

Start with EBSD, which imports and audits a map. It plots phase and orientation maps, reconstructs grains, and plots pole figures and inverse pole figures. Continue with Grains to compare pixel and grain orientations. It selects and measures grains and previews boundaries between phases. Then use Grain Boundaries to analyse their interfaces.

Before importing your own map, read Reference Frame. A reference frame is the coordinate system in which the data are expressed. It is distinct from crystal symmetry and from the plotting convention that lays the frame out on screen.

X-ray and neutron diffraction measure many crystals together. For one selected lattice plane, a pole figure records intensity over specimen directions. It describes an illuminated volume but does not retain the spatial position of each contributing crystal.

Start with Pole Figure Data, which imports and corrects measured pole figures. It reconstructs an ODF and checks it against the measurements. Continue with ODFs for ODFs estimated from orientations and for model ODFs.

Where the two routes meet

An orientation distribution function (ODF) is a continuous density over crystal orientations. It can be estimated from individual EBSD orientations or reconstructed from diffraction pole figures.

The ODF is therefore a common representation for texture from either route. An EBSD orientation list can also be projected directly into pole figures when that is the comparison the experiment requires. Continue with ODFs from either route. It estimates an ODF from individual EBSD orientations, reconstructs one from pole figures, and defines a model ODF.

VPSC starts from a third kind of input: simulated texture from the visco-plastic self-consistent deformation code. It is intended for readers who already have modelling output rather than measurements.

Continue into the chapters

The worked EBSD route leads into EBSD, Grains, and Grain Boundaries. The diffraction route leads into Pole Figures, and both routes meet again in ODF.

The objects used throughout these chapters begin with Vectors and Crystal Geometry. Return to those foundations when directions, rotations, orientations, or symmetry become the subject rather than merely an input.

Further reading