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On Tue, 2006-05-02 at 17:14 -0400, Qun Wan wrote:
> I Have a question about permuting crystal indices. When I compare two
> crystal data sets to get crossR value to know how isomorphous they
> are, I need to permute the indices of one of the crystal. Both of my
> crystals have space group P212121. I was told to permute HKL to LKH,
> HLK, and KHL. I do not have a clear mind the principle. For example,
> by whole arrangement, there will be 6 possibilities for the
> permutation. Why only four exist here? The second question is more
> important: if I want to change from HKL to KHL, the new indices are
> (0 -1 0 -1 0 0 0 0 -1), not (0 1 0 1 0 0 0 0 1). Why there
> is minus sign in the indices?
>
> Could anyone recommend me one paper or book to read to solve my puzzle?
The instructions you were given conflict with my knowledge. I believe
the permutations you mention will all result in a change of handedness.
Assuming that both your data sets were properly collected and have the
same handedness, you should retain that handedness, and allowable
permutations for HKL would be KLH or LHK. These permutations retain the
order of axes in a cyclical fashion.
By convention, axes of similar symmetry are listed in order from
shortest to longest. Since your space group is P 2(1) 2(1) 2(1), all
three axes have equivalent symmetry.
Of course, I don't know about your particulars, maybe a change of
handedness is a good thing if you have some left-handed alpha helices
you are trying to clear up, or some such.
Cheers,
--
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I think we're all bugs and mice, and are only different expressions
of an all-inclusive cheese. - Charles Fort
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David J. Schuller
modern man in a post-modern world
MacCHESS, Cornell University
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