Conventions

The following conventions are adopted within pyXem.

Physical Units

When physical units are used it is anticipated that we have:

  1. Diffraction plane units of reciprocal Angstroms i.e. g = 1/d.

  2. Atomic structure coordinates in Angstroms.

  3. Scan coordinates in nanometres.

Diffraction Pattern Coordinates

Following alignment and calibration of two-dimensional diffraction data in the ElectronDiffraction class coordinates in the two-dimensional diffraction pattern are Cartesian coordinates referred to an origin at the center of the diffraction pattern with the lower right hand quadrant positive. Coordinates may also be expressed as polar coordinates with the positive rotation an anticlockwise rotation. These conventions are depicted below:

_images/axis_conventions_pyxem.png

Crystallographic Axes

Atomic structures are manipulated in pyXem using the diffpy.Structure module and crystallographic conventions are therefore primarily inherited from there. Unless otherwise stated it will be assumed that a crystal structures is described in the standard setting as defined in the International Tables for Crystallography

Crystal orientations/rotations are typically described with respect to an orthonormal basis, which must be related to the crystallographic basis in a consistent manner. For further discussion see, for example, the following article by Rowenhorst et al. In pyXem it is assumed that these axes are related according to the metric tensor defined in a diffpy.structure.lattice object.

Rotations

These are in the rzxz convention, as defined in transforms3d. This means that we rotate about z (by alpha), then the new x (by beta), and finally the new z (by gamma), as illustrated below:

_images/euler_angles.png