Do you really want to know how it works...or do you only want know the positions for a structure? For the second case you should use software (e.g. like PowderCell or any of the numerous software developed for this or mostly for much more complicated tasks as fundamental.) In case you are really interested in the opportunity, how to derive all coordinates....use the International Tables for Crystallography, Vol. I. There is more described than you can imagine at the moment (BEHIND the well known space-group tables!).

Shortly: you have to apply all symmetry element on each position in order to get all possible. Then you need to sort out since every position can exist only once.

Do you really want to know how it works...or do you only want know the positions for a structure? For the second case you should use software (e.g. like PowderCell or any of the numerous software developed for this or mostly for much more complicated tasks as fundamental.) In case you are really interested in the opportunity, how to derive all coordinates....use the International Tables for Crystallography, Vol. I. There is more described than you can imagine at the moment (BEHIND the well known space-group tables!).

Shortly: you have to apply all symmetry element on each position in order to get all possible. Then you need to sort out since every position can exist only once.

Dear Bahman,

I suggest you use VNL package for building the structure of your simulations. Here is the link of this software : https://quantumwise.com/

I hope it helps,

Samaneh

Dear Samaneh,

Thank you very much for your response.As you know, these positions usually provide by crystallography packages. However, I am rather trying to understand how to realize the fraction positions by both of Wyckoff positions and space groups.

Warmly,

Bahman

Then this book might be helpful :

"Modeling Materials: Continuum, Atomistic and Multiscale Techniques" by Ellad Tadmor and Ronald Miller.

Samaneh

you have to use the International Table of Crystallography vol A (ITA vol A).

in your case you have 4 different atomic species located at 4 different Wyckoff sites; each Wyckoff site is characterized by an its own symmetry. for example Sr is located at the 8c site: the number 8 stands for the multiplicity of the site, that is there are 8 equivalent positions inside the cell with this symmetry. so, given the symmetry of the site, it is necessary to know only 1 position among the 8 of this specific Wyckoff site, because the reamaining 7 are given by symmetry and you can find them listed in ITA vol A. the letter 'c' has not a specific meaning; letters are used only to list the different wyckoff site.

so the crystallographic cell of your compound will host 8 atoms of Sr, 4 of Al, 4 of Ta and 24 of O, that is Sr8Al4Ta4O24. you can see that this is exactly the stoichiometry Sr2AlTaO6.

Dear

Dneshian

go to http://www.cryst.ehu.es/cgi-bin/cryst/programs/nph-table?from=getwp

Click on desired space group. You can find Multiplicity , Wyckoff letter , Site symmetry , Coordinates of atom.

Dear Alberto,

Thank you very much for your helpful response to my question. your response is very close to what I am looking for actually. However, I did not understand where you told me you can find other 7 positions of Sr atoms from the table. this is exactly my problem.I can only see 2 of 8 ( c) positions for fm-3m space group in this table. how can I find other 6 positions?

I use this link for wyckoff positions of space group fm-3m:

http://www.cryst.ehu.es/cgi-bin/cryst/programs/nph-wp-list?gnum=225

Looking forward to hearing from you

With the best regards,

Bahman Daneshian

I cannot succed in opening your link, but in any case I guess it refers to the table of the space group 225. So if you look at this table in ITA vol A, you can see that face centering conditions hold for the atomic positionts. these face centering conditions are: (0,0,0); (0,1/2,1/2); 1/2,0,1/2); 1/2,1/2,0)(. In this table only the position pertaining to the condition (0,0,0) are listed, the remaining can be easily calculated by adding (0,1/2,1/2) and so on.

so, in the case of Sr you have the following position in 8c: (1/4,1/4,1/4) and (1/4,1/4,3/4) for (0,0,0).

for (0,1/2,1/2) you will obtain (1/4,3/4,3/4) and (1/4,3/4,1/4)

you can try to do the same for the remaining (1/2,0,1/2) and (1/2,1/2,0) to obtain all the 8 positionss

PS: you can find these centering condition in the table just below the word "coordinates"s