I wonder how octahedral and tetrahedral site preferences occur in a AB2O4 spinel? Does it change for inverse or normal spinels? Can I calculate by hand? What is/are the key parameter(s) for formation of spinel?
Many ferrites are spinel and they have AB2O4 structure. Their crystal structures have Fd-3m symmetry and I wonder how octahedral and tetrahedral site preferencies occur.
(Sorry for correction. Tablets do not support java I guess).
ah...I see. Sorry, I was talking about the phase ferrite which is Fe (or austenite). You are talking about the "material class" which are magnets. Sorry again, my fault.
For spinel the occupation of 2+ and 3+ ions is theoretically fixed.
For magnetite (incerse spinel) it means that one half of the trivalent Fe ions – site at Wyckhoff position 8a - occupies only one-eighth of all 64 tetrahedral interstices of the ccp oxygen array, whereas the residual fraction of trivalent and all divalent Fe ions (Wyckhoff position 16d) randomly fills one half of the available 32 octahedral interstices within the oxygen framework.
see also
Article Exploring structural similarities between crystal phases usi...
In order to fit the site occupancies, you will need to do a Reitveld refinement on the data. If you haven't done this before then you should read the documentation well and follow the online tutorials. There are many programs available. I use GSAS since it has been an open source program which has been improved and expanded for 30 years or so.
I am not sure how accurate you know your composition and about which A and B you are talking. If A and B are similar in atomic number I would not be that optimistic using XRD since the scattering factor are perhaps not significantly different. Moreover, since you are talking about doped material...the reliability of a correct interpretation only by Rietveld is decreasing since the main implemented structure model becomes more and more "critical". If we then take some other problems into account, e.g. non-stochiometry as known for magnetite-maghemite (disorder effects), I am not sure how far you will come with XRD. Nevertheless, it is worth to give it a try. Or it is worth to think about Neutron diffraction as Lawrence proposed.