Pole Figures & Orientation Fibers

Diffraction Geometry

Rodrigues Space

σ = °

Orbit: drag · Zoom: scroll · Click blue ring to compute orientation fiber

Pole Figures

1 Choose a crystal system and lattice parameters

2 Set a Miller index (hkl)

3 Choose an X-ray energy to compute the Bragg circle

4 Click on the blue circle to see the orientation fiber

5 Fold the fiber into the fundamental zone

6 Sweep around the circle to see the full orientation surface

7 Calculate pole figures on the detector

Lattice System

a Å

Miller Index (hkl)

h k l

X-ray Energy

Fold into Fundamental Zone

Map every point on the fiber by all crystal symmetries and keep the one closest to identity.

Sweep Animation

Sweep the point around the Bragg circle to visualize the full surface of orientations contributing to this reflection.

Calculate Pole Figures

Integrate the ODF along each fiber and project intensities onto a flat detector.

About ⓘ

For a crystal with lattice planes (hkl) and d-spacing d, Bragg’s law 2d sinθ = λ determines the scattering angle. With the beam along x, the plane normal must lie on a cone at angle 90°−θ_B from the beam — the blue circle on S². Each point on that circle defines a scattering direction; the set of crystal orientations producing that diffraction spot forms a fiber in orientation space, shown as a yellow curve in Rodrigues representation.

Pole Fig­ures & Orientation Fibers