The slides explains theoretical means of visualizing orientation with respect to arbitrarily assign frames.

1. 1
DESCRIPTION OF MICROSTRUTURE
 Microstructure can include all of the features of internal
structure of heterogeneous materials at a variety of length
scales.
(e.g. phase, grain size, lattice orientation, dislocation, voids, interatomic spacing) 10-8 m
10-10 m
10-7 m
10-5 m
10-3 m
The crystal orientation, g, can be defined by a
set of three rotations (φ1, Φ, φ2) that relate
the crystal frame to the sample reference
frame.
X
Z
Y
[001]
[010]
[100]
crystal
g
 The distribution of crystal lattice orientations in a polycrystalline
metal (also referred to as texture or ODF) is taken as the main
descriptor of microstructure.

2. Projections: Pole Figures (PF)
 Orientations can be plotted as a two dimensional projections.
A pole figure of pole relative to the sample reference frame.
 Example: (001) pole figure.
 Note that the three point shown in the pole figure are three symmetrically equivalent planes
in the crystal. (The clear points correspond to point extending into the bottom half of the
sphere.

3. Projections: Inverse Pole Figure (IPF)
 An inverse pole figure shows the position of a sample
direction relative to the crystal reference frame.
 Example: [001] inverse pole figure.
 Note because of the symmetry in the crystal, multiple points appear on the full IPF. If the
IPF is plotted using the unit triangle, then only one point per orientation will appear in the
plot.