What are the crystallographically equivalent sites in a crystal unit cell?

[Useful nucleus]

Given a crystal structure and the cell edges (a,b,c) , angles (alpha, beta, gamma) and the fractional coordinates of all atoms in the unit cell. Also given an arbitrary unoccupied site P by fractional coordinates (s1,s2,s3). How can I determine all the sites that are crystallographically equivalent to P within the single unit cell.

Any help is appreciated.

 

[Dr Transport]

if you apply the operations of the group to the point, you should find the equivalent positions.

 

[Useful nucleus]

For the non-expert like me, are there tabulations of these operations for each group in a simple representation (like matrix multiplication) ?
I searched but what I get is usually the so-called "Wycoff postions" , which I do not know if it is relevant to my question.

 

[kanato]

Yes, the Wyckoff positions are the sets of the sites with independent symmetry. That is, each Wyckoff position is a site with different symmetry than the other Wyckoff positions. The Wyckoff positions are named based on the number of equivalent sites, ie. the 2a position refers to a two sites that are symmetry equivalent. These are tabulated for every space group in various places; you can find lists on the web like this one: http://www.cryst.ehu.es/cgi-bin/cryst/programs/nph-wp-list
The "hard" part is determining which space group is correct for your crystal. The space group is determined by the crystal structure and the coordinates of the atoms. But there are programs written to do that, like the findsym program: http://stokes.byu.edu/findsym.html

 

[Useful nucleus]

Thank you very much! That helps a a lot!