OOF2: The Manual

Name

X (X) — Goldstein's X convention for 3D orientations, using rotations which bring the crystal axes into coincidence with the lab axes, in the order z, x, z.

Synopsis

X(phi,theta,psi)

Details

  • Base class: Orientation
  • Parameters:

    phi
    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].
    psi
    Third rotation, about z axis, in degrees. Type: A real number in the range [-180, 180].

Description

An X object represents the orientation of a three dimensional object, assumed to be a crystal, in three dimensional space in terms of Euler angles conventionally denoted φ, θ and ψ. In the X convention, these operate similarly to the Abg Euler angles, in that the defined rotation takes the crystal basis vectors \(\hat{\mathrm{\bf a}}\), \(\hat{\mathrm{\bf b}}\) and \(\hat{\mathrm{\bf c}}\) into coincidence with the lab (or screen) basis vectors \(\hat{\mathrm{\bf x}}\), \(\hat{\mathrm{\bf y}}\), and \(\hat{\mathrm{\bf z}}\), respectively. The first rotation is by φ about the \(\hat{\mathrm{\bf c}}\) axis, the second by θ about the rotated \(\hat{\mathrm{\bf b}}\) axis, and the third by ψ about the rotated \(\hat{\mathrm{\bf c}}\) axis.

This rotation scheme is one member of a family of rotation schemes, all of which differ only in the order in which the rotation axes are specified for the successive rotations associated with the Euler angles. The nomenclature is not standardized, but the choice of X to denote this convention comes from the second edition of "Classical Mechanics" by H. Goldstein.