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comparecell: Compare two unit cells

The "comparecell" program compares 2 unit cells.

The program will try to assemble the first unit cell given by making linear combinations of the cell axes of the second unit cell.

On the output a list will be shown of all possible transformations of the second unit cell that create the first one. Trivial transformations will be removed.

For each solution the following parameters are listed:

The "Rotation angle", in degrees.
The "Rotation vector in the laboratory coordinate system"
The "Rotation vector in the a*,b*,c* (or hkl) coordinate system"
The "Rotation vector in the a,b,c coordinate system"
A "Figure of merit", representing the r.m.s. difference between the superposition matrix and the given rotation matrix. This number is 0.00 for a perfect fit.
The "twin law", if applicable.
The "Superposition matrix", showing the relations between the h,k,l vectors of the two lattices.

This program can also be used to compare a unit cell with itself. Any non-trivial solutions that come out of such a run could be a possible cause of twinning.

If you find 2 unit cells using e.g. dirax, the second lattice is often less well-defined than the first. In such a case, the rotation vector and rotation angle coming out of "comparecell" can be rough approximations of the real values. The ntrans program can be used in such cases to "synthesize" unit cells that have the exact relation. e.g. if "comparecell" tells you that the second cell is approximately a 179.4 degree rotation around the 1,0,24 direction in direct space, you could try to use "ntrans", and rotate the first cell 180 degrees around the c axis. Frequently, cells synthesized this way are better approximations of the lattice than the original dirax result. See also the twin chapter in the ndirax manual.

Usage

comparecell [options] <two .x or .rmat files>

Accepted options

The program accepts all options for controlling the way the unit cell is treated, plus:

trivial=s: Eliminate trivial transformations in the given crystal system. By default the crystal system of the first unit cell will be used.
lencrit=#.#: Criterion to decide whether two lengths are identical. Default value is 0.03 signifying 3% length difference is allowed.
angcrit=#.#: Criterion to decide whether two angles are identical. Default value is 1.0 degrees.
matcrit=#.#: Criterion to decide whether the volume of 2 unit cells is identical. Default value is 0.1, signifying 10% difference is allowed. degrees.

Example output

no203[205]2view%3% comparecell ia.rmat iar.rmat nostandardize
{Input cell : a=6.6717 b=7.6644 c=8.1339 alpha=94.419 beta=108.616 gamma=111.586 P
 Volume     : 357.48; System: triclinic; Point group: -1}
{Input cell : a=6.6717 b=7.6644 c=8.1339 alpha=94.419 beta=108.616 gamma=111.586 P
 Volume     : 357.48; System: triclinic; Point group: -1}
==============================================================================
Solution number :   1
---------------------
New Cell: a=6.6717 b=7.6644 c=8.1339 alpha=94.419 beta=108.616 gamma=111.586

Figure of Merit (0=ideal)         :   0.00
Rotation angle  (degrees)         :  180.000
Rotation vector (laboratory)      :   0.2025  0.5997  0.7742
Rotation vector (reciprocal cell) :   5.00 -2.11 -1.95
Rotation vector (direct cell)     :   1.00  0.00  0.00

Superposition matrix              :  H' = +1.000 * H                      
                                     K' = -0.845 * H -1.000 * K           
                                     L' = -0.778 * H            -1.000 * L
==============================================================================

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