Three types of coordinate system are used frequently in ATOMS: the observer Cartesian system; the natural structure system; and a Clinographic system.
The observer system is fixed with respect to the display screen or paper of dot-matrix or pen-plotter copy. The origin is at the center of the screen or paper, and the x axis points directly toward the observer. The y axis points to the observer's right and the z axis vertically, both in the plane of the screen or paper.
The atomic coordinates and the parameters of crystal faces if present are given in terms of the natural structure axis system, although in the case of molecules this may itself be a Cartesian system. Once all the atoms and faces have been generated, their coordinates are converted to Cartesian coordinates. Except for crystals using rhombohedral axes, the natural c axis is originally placed parallel to the observer z axis, and the natural b axis is aligned in the y-z plane (or in crystallographic terminology the a* axis is parallel to x). If rhombohedral crystal axes are chosen, the three-fold symmetry axis is parallel to z, and the the vertical plane containing the first rhombohedral axis is aligned in the x-z plane.
This conversion defines the "original'' orientation of the structure. After the location of atoms and faces, and before the initial display, the orientation may optionally be modified by the rotations in the Initial Orientation dialog in the Input2 menu, by the alignment of a Slice of a crystal, and by clinographic rotation, defined in the next paragraph.
Clinographic Viewing. One of the standard methods of drawing crystals (external morphology) is clinographic projection, in which the crystal is in effect viewed from above and slightly to the right of the a axis, or to be more precise, in towards the center along the vector [621] referred to cubic or Cartesian axes. If the option for clinographic viewing is chosen, after the faces, atoms etc. are found, the structure and its associated Cartesian system are rotated -18.4 degrees on the z axis, then 9.5 degrees on the y axis.
After the drawing appears, additional rotations may be made either on (1) specified vectors in the natural structure system; (2) the observer Cartesian axes; or (3) if clinographic viewing is on, the rotated Cartesian axes, or clinographic system. The clinographic system does not rotate with the crystal; it is always related to the observer system by the two rotations given above.
If clinographic viewing is not on, the clinographic and observer systems have the same orientation, and if the natural structure system is Cartesian or cubic all three systems have the same orientation.
Summary of axial systems:
1) Observer Cartesian system. Reference system, fixed with respect to the display screen or paper.
2) Natural or structure system. Fixed with respect to the atomic structure. Atom coordinates are initially given in this system. The axes are the unit-cell edges in the case of crystals. Axes may have unequal lengths and may be at angles of other than 90 degrees.
3) Clinographic system. Only applies when clinographic projection or viewing is on. Axes are those of the observer Cartesian system, but rotated in a certain manner to avoid a straight-on view of the structure.
If Perspective viewing is not selected, the drawing is a direct projection in the x axis direction (observer system). If perspective viewing is selected, the atoms are projected onto the y-z plane from a point on the x- axis at the specified distance in the positive direction (toward the observer).
In ATOMS, a, b and c (or A, B and C) refer to the natural structure axes. The three axes may sometimes have these names although it is conventional in some systems to use a1, a2 and a3 if the axes are equal by symmetry. The letters x, y and z usually refer to the observer Cartesian axes. If it is necessary to refer to the clinographic system, this is mentioned explicitly. The fractional atomic coordinates are also referred to as x, y and z, but these are usually identified explicitly.