Actually, there is a confusion about the occupation of atoms in any crystal system. Many people said in different different way and they are correlated with chemical formula of the crystal system also. But it is not cleared about it. So, I want to clear about the meaning of occupation of atoms in any crystal system.
It is relatively easy, the atomic positions depends of the space group. If you visist, for example, the web page (free) http://crystdb.nims.go.jp/index_en.html, you will found a particular compound, its space group and the atomic positions (Wykoff positions).
Any problem do not hesitate to contact me
Pedro
Thank you very much Dr. Pedro for positive response. Your suggestion will help me.
You need to find the Crystallographic information file (.cif) for the compound you are dealing with. There you will find the site multiplicity for each and every Wyckoff site of an atom in a unit cell. If each and every multiple sites are completely field ; the occupancy of that site is 1(100%), if some vacancy i.e. due to defect defect then occupancy is less than 1 means less than 100%.
See the excerpt from the CIF file of LaMnO3. Here all site occupancy is 1 for each La, Mn and O sites. But multiplicity of O site is 18 ( see 18e Wyckoff position ). So here, over all atomic occupancy of O is 1 (100%), Mn and La : 0.33 (33%) in comparison to Oxygen in side the unit cell. If some how Mn atoms are only 16.5% then the chemical formula will be LaMn0.5O3.
There are three items dealing with "number of atoms" at a specific site. The site occupation factor (sof) gives the probability to find the atom at a specific site. The value ranges from nearly 0 (no atome) to a maximum of 1 (100%, site alsways occuoied by this atom). The multiplicity of a site tells the number of atom positions produced by the symmetry of a space group from a single site noted in structure descriptions. CIF, the standard way of telling about a structure, uses sof values. Some programs do not use this a value as it is, but combine this values with the multiplicity of the site (M) and the multiplicity of a general site (site with highest multiplicity (Mmax) for a given space group). Therefore some pograms use the small values of occ=sof*M/Mmax instead of occ=sof.
The multiplicity of a site combined with the Wyckoff letter is forming the Wyckoff position consiting of a number followed by a letter.
sof depends on the structure
M depends on spacegroup and site
occ depends also on the program for refinement
Many many thanks to Dr. Robert for your valuable answer. I think that your answer will be more effective for me. So, I can say that occupation of atoms at a specific site means the contribution of atoms to filled that specific site for any particular system which will be maximum(1 or 100%) for without doping atoms or without any vacancy of atoms in that site in general. Am I right or wrong?
You are right.
Many compounds show sof=1 for all sites. For example NaCl, space group Fm-3m, has two sites (4a and 4b) occupied, both with M=4 and sof=1
atom x y z sof
Cl 0 0 0 1
Na 1/2 1/2 1/2 1
(vice versa is also valid)
If you assume 1% Br as a dopand
Cl 0 0 0 0.99
Br 0 0 0 0.01
Na 1/2 1/2 1/2 1
If you assume 1% vacancies
Cl 0 0 0 0.99
Na 1/2 1/2 1/2 0.99
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