OOF2: The Manual

Name

Bunge (Bunge) — Bunge angles for defining a rotation which operates on the lab axes, bringing them into coincidence with the crystal axes, in the order z, x, z.

Synopsis

Bunge(phi1,theta,phi2)

Details

  • Base class: Orientation
  • Parameters:

    phi1
    First rotation, about z axis, in degrees. Type: A real number in the range [-180, 180].
    theta
    Second rotation, about x axis, in degrees. Type: A real number in the range [0, 180].
    phi2
    Third rotation, about z axis, in degrees. Type: A real number in the range [-180, 180].

Description

A Bunge object represents the orientation of a three dimensional object, assumed to be a crystal, in three dimensional space in terms of three angles, \(\phi_1\), \(\Theta\), and \(\phi_2\), corresponding to rotations which bring the lab (or screen) axes \(\hat{\mathrm{\bf x}}\), \(\hat{\mathrm{\bf y}}\), and \(\hat{\mathrm{\bf z}}\) into coincidence with the crystalline \(\hat{\mathrm{\bf a}}\), \(\hat{\mathrm{\bf b}}\), and \(\hat{\mathrm{\bf c}}\), axes, respectively. This is the conventional usage of the texture community, and is the opposite of the usual sense for rotations in OOF2.

With this important difference, it resembles the X convention, in that the axis selection and ordering are the same. The \(\phi_1\) rotation is about the initial laboratory axis \(\hat{\mathrm{\bf z}}\), the second \(\Theta\) rotation is about the rotated laboratory \(\hat{\mathrm{\bf x}}\) axis, and the third \(\phi_2\) rotation is about the rotated \(\hat{\mathrm{\bf z}}\) axis.

The OOF2 implementation of this method actually constructs the usual OOF2 rotation matrix (which takes the crystalline axes into the laboratory axes), but does so from the conventionally specified Bunge parameters. Users familiar with the Bunge convention can thus use previously obtained or instrument provided angles directly.