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Anisotropic indentation pile-up in single crystals

C. Zambaldi, MPI für Eisenforschung, Düsseldorf, Germany
Published in March 2012, version 2013-10-23

The calculator below takes an experimentally measured orientation as input and returns the Euler angles after the convention defined in Zambaldi & Raabe (Acta Mater. 2010). Further, it gives the in-plane rotation angles that will rotate the measured pile-up pattern according to the convention. Thereby the inverse pole figure of indentation patterns can be constructed from several indents in various orientations. IPF templates are available.

The Euler angles should be after Bunge convention (Z-X-Z) and rotate the laboratory frame into the crystal frame.

Define crystal system
Improper rotations
Number of symmetry operators: 24

Euler angles (°) Label:

Euler angles (deg) ("")

Euler angles in the fundamental zone: .

The corresponding Z-vector (the indentation axis) in crystal coordinates: VAL

Euler angles after convention: VAL

Spherical coordinates zeta and eta: VAL (deg)

The in-plane rotation to backrotate the experimental orientation into the one defined by convention [1] is VAL.

When rotating the actual topography data by this angle, keep in mind that it might be necessary to apply an additional in-plane rotation to align the data coordinate system with the RD-TD axes of the Euler angles.

To construct the inverse pole figure of pile-up topographies:

  1. Rotate the topography counter-clock-wise by VAL degrees
  2. Place it in the IPF at coordinates [X,Y] = VAL (stereographic projection).
If the given values change by switching the "improper rotations" option on and off, this means that the topography has to be mirrored through the plane that connects the two adjacent regions in the full and reduced inverse pole figure.