Dear Huy,
In order to minimise the information needed to describe a crystal
structure, we use space groups that define the symmetry of the unit cell.
Each space group has a different set of symmetry opperators that can
generate multiple atoms in the unit cell when you only give the atomic
coordinates of one of the atoms, as they are all related by the inherent
symmetry of the space group.
For most of the unit cell ('general positions'), you can apply all of the
symmetry opperators and generate all of the related positions but on
'special sites' applying all of the symmetry opperators will generate more
than one atom at a position. The easy way of visuallising this is by
having an atom one side of a mirror plane. The mirror plane generates a
second atom, equal distance from the opposite face of the mirror plane. As
you move the first atom closer and closer to the mirror plane the two
atoms get closer until they sit on top of each other, when the atom
resides on the plane itself. Obviously in a real system two atoms do not
sit on top of each other but in fact there is just one atom. This is known
as overgeneration, as the symmetry opperators of the space group have
gnereated more atoms than there actually are.
Some refinement programs deal with overgeneration internally, such as
GSAS, but fullprof requires you to correct for overgeneration. The way you
do this is to look up the multiplicity of the specific atomic site for
that atom in the International Tables for Crystallography, then divide it
by the multiplicity of the general position and put this value into
fulprof as the the occupation number. i.e. fullprof would generate two
atoms on the mirror plane so you must set the occupancy to 0.5. That way
the total number of atoms on the site is 2 x 0.5 = 1.
This complicates things when a site in your crystal is also deficient. If
you do not have unity occupancy then you must multiply the occupancy (SOF)
that you do have by the correction value for overgeneration.
So for your Mg2Sn you are right that the occupancies that you need to put
in for Mg and Sn are 8/192 and 4/192 respectively if you have unity
occupancy on the sites but if you also need to take into account any site
deficiencies then you must further multiply these values by your SOF
values.
I hope that answered your question, and am sure that Juan (that wrote
fullprof, just over the road from you) has probably already replied with a
better answer.
Ross
> Dear all,
>
> As a newbie in FullProf (and also in crystallography) I'm being
> confused with the parameter "Occupation number" (Occ).
>
> In fact, as indicated in the FullProf Manual:
>
> /"Occupation number i.e. chemical occupancy × site multiplicity (can be
> normalised to the multiplicity of the general position of the group)."/
>
> What is the meaning of this "Occupation number" and difference between
> "Occupation number" and SOF ?
>
> Could anyone help me to explain how to find the value of chemical
> occupancy, site multiplicity ? And how can the Occupation number be
> "/normalised to the multiplicity of the general position of the group/" ?
>
> I have tried to calculate for Mg2Sn (Fm3m), with Mg at the site 8c and
> Sn at 4a, then Occupation number of Mg is 8/192 and that of Sn is 4/192.
> Is this right ?
>
> Thanks in advance for your any help.
>
> Huy LE-QUOC,
> LPSC/CRPMN - CNRS
> 53 rue des Martyrs, Grenoble 38026, FRANCE
>
>
>
