If I've understood your question correctly, you want to know how to model fractional atomic occupancies. I don't know SIESTA specifically, but in general there are two choices:

1. Use an approximate mean-field method which allows for fractional atomic occupation. The simplest is probably the Virtual Crystal Approximation (VCA) [1][2] which basically constructs the atomic (pseudo-)potential from a weighted average of the Fe and Al. A more sophisticated method is the Coherent Potential Approximation (CPA) [3][4][5] which basically constructs a potential to reproduce the weighted-average scattering properties of Fe and Al (actually it's usually done in a Green's function method).

2. Model a larger system with many repeats of the primitive unit cell, and replace the appropriate fraction of atoms. 

Method 1 is the quickest to perform computationally, since it allows you to use a small simulation system and use the fractional occupations directly. However it relies on the properties of interest depending linearly on the atomic potentials (VCA) or properties (CPA), which is an approximation (essentially it's Vegard's law).

It is generally found that VCA only works well for metallic alloys, whereas CPA is applicable more generally; though there are modifications to VCA which try to incorporate the concepts of CPA (e.g. ref. [6][7]). I don't know SIESTA very well, but I think it does have VCA at least (see page 15, ref. [8]).

Method 2 is the most realistic, but requires a larger system to be simulated. For example in your case the smallest simulation system you could use would be comprised of 4 primitive cells, giving you 4 Fe1 sites (and 4 Fe2 sites etc.); you can then put 3 Fe atoms and 1 Al atom on the 4 Fe1 sites, giving you the 75% : 25% occupation you require. Do the same for the other sites, and you have your model.

You will also need to consider whether the system is ordered or disordered -- i.e. in the real system is every 4th Fe1 site occupied by Al, or are they randomly occupied by Fe and Al with probabilities 0.75 and 0.25 respectively. In the ordered case you can construct a simulation system of that ordered phase, but for the disordered case you will usually need:

(a) a simulation system N times larger, with 4N Fe1 sites, so that you can randomly occupy N sites with Al (N being a convergence parameter);

and (b) to construct several different realisations of the system (i.e. with a different random choice of the N sites to put Al on) so that you can be sure your results are representative, i.e. are valid beyond the exact atomic ordering you happened to choose.

Hope that helps,

Phil Hasnip

[1] L. Nørdheim, Ann. Phys. (Leipzig) 9, 607 (1931).

[2] T. Muto, Sci. Pap. Inst. Phys. Chem. Res. (Jpn.) 34, 377 (1938).

[3] P. Soven, Phys. Rev. 156, 809 (1967).

[4] P. Soven, Phys. Rev. 178, 1136 (1969).

[5] J. S. Faulkner, Prog. Mat. Sci. 27, 187 (1982).

[6] N. J. Ramer and A. M. Rappe, Phys. Rev. B 62, R743(R) (2000)

[7] C.-J. Yu and H. Emmerich, J. Phys.: Condens. Matter 19 306203 (2007).

[8] http://departments.icmab.es/leem/siesta/Documentation/Manuals/siesta-3.2-manual.pdf (accessed 2014-10-21)

Dear Guilherme,

 Our Site Occupancy Disorder (SOD) program:

 https://sites.google.com/site/rgrauc/sod-program

can help you deal with these situations, by generating the symmetrically different configurations in a given supercell. It also helps to perform a statistical mechanics analysis of the spectrum of energies for the whole ensemble, so you can describe both ordered and disordered solids. Hope it helps. 

 Kind regards,

Ricardo.

Thanks for the answer Phil and Ricardo, I will try what you guys told me!

I put in attached what I'm trying to do! 

The problem is , the way I'm trying to do,  I put more atoms, (before 40 atoms, after 160 atoms) and this requires much the computer!!

But in that case I made... I'm considering the ordered system... and the disordered is more correct to my case

Hi Phil Hasnip, 

I used the VCA to generate the mix pseudopotential...

But when I change my fdf, and run the Siesta appear this error:

SPLIT: ERROR Orbital with angular momentum L= 2 not bound in the atom

SPLIT: ERROR a cut off radius must be explicitly given

ERROR STOP from Node: 0

ERROR STOP from Node: 0

application called MPI_Abort(MPI_COMM_WORLD, 1) - process 0

I'm trying to find the error... but until now... I found nothing!!

I put in attached my new FDF...

Using the VCA program, when I mixed 65% of Fe and 35% of Al... appeared the error that a put in my last post...

But I tried 90% of Fe and only 10% of Al... and it works!! But I need more... do you know what it's happening?!

The l=2 angular momentum corresponds to the d-states (presumably 3d) and it's likely that this won't be bound for large Al concentrations (since it won't be for pure Al). It appears that SIESTA requires the state to be bound, so this will restrict the proportion of Al you can use though I can't say by how much -- clearly it'll be somewhere in the range 10% to 35%, judging by your simulations.

Remember that you can increase the total Al by choosing one particular site and substituting a whole Fe for a whole Al, then using VCA for the others. This has the disadvantage of re-introducing a kind of order and a periodic-image interaction, but it will allow you to go to higher overall Al substitutions than VCA alone.

I do have a couple of queries regarding your VCA proportions:

1) In the top figure, the Fe2 site occupancies don't add up to 100% -- is this just a typing mistake? It's unlikely to be physically meaningful.

2) In the top figure, it looks like you're breaking the stoichiometry with the VCA substitutions; is this intentional?

Hope that helps,

Phil

Hi Phil...

Yeah... I made a mistake... it's only 15% of Al on the site Fe2...

and for the second question... it's intentional the breaking the stoichiometry... for two reason... the first one

1 - compound was synthesized by the high-energy ball milling route , and this method don't respect much the stoichiometry;

2 - Using the Rietveld method, the best fitting was obtained with this occupation.

I will try more here and I'll read more to see if I finding something!! And if I find the answer... I post here!

Really thanks for the help Phil!