OOF2: The Manual
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.
- First rotation, about z axis, in degrees. Type: A real number in the range [-180, 180].
- Second rotation, about x axis, in degrees. Type: A real number in the range [0, 180].
- Third rotation, about z axis, in degrees. Type: A real number in the range [-180, 180].
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
convention, these operate similarly to the Abg Euler angles, in that the defined
rotation takes the crystal basis vectors
into coincidence with the lab (or screen) basis vectors
, respectively. The first rotation is by φ about the
axis, the second by θ about the rotated
and the third by ψ about the rotated
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.