From:   TOPHAM::COCKCROFT    "Jeremy Karl Cockcroft" 26-NOV-2002 17:32:49.96
To:     SMTP%"oomotoso@nrcan.gc.ca"
CC:     COCKCROFT
Subj:   RE: Symmetry Operators

Hello Dipo,

>Could you please show the mathematical derivation of symmetry operators in
>the general rectlinear system?  I tried the 3-fold symmetry in cartesian
>coordinates but got a different operator than the one that you gave (-x/2
>-sqrt3y/2, sqrt3x/2 - y/2, z) in the text.  I got (-sqrt3x/2 - y/2, x/2 -
>sqrt3y/2, z).

I have added in a supplementary web page showing the proof:
        http://pd.cryst.bbk.ac.uk/pd02/symm1/cartsym.htm

Looking at your result, it corresponds to a rotation of 150 degrees. In the
above web page, I give the matrix form for a 120 degree rotation, but it can
be used for any arbitrary angle theta if one substitutes 120 for theta in it.

Hope this helps - please get back to me if it doesn't.

Thanks again for all comments - they really are useful,

Jeremy Karl.

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Dr Jeremy Karl Cockcroft        Email: cockcroft@img.cryst.bbk.ac.uk
School of Crystallography       Tel: 020 7631 6849 (office) or 6853 (laboratory)
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