In order to understand the magnetic behaviour of ferrite nanoparticles, one needs to know the exact distribution of metallic cations among the tetrahedral and octahedral lattice sites. Therefore, one needs to explore the theoretical/experimental methods with which cation distribution can be determined accurately. I raised this question assuming that the integrated insensities from the X-ray diffraction measurements is one among them.
X-rays are scattered off electrons. If the number of electrons between two alternative cations is large enough, an assignment can be done. What considers "large enough" depends on the quality of the experiment, the wavelength of the radiation that is used, and the quality of the absorption correction.
One complication is that there can be a significant correlation in the determination between the thermal motion amplitude of an atom and the total number of electrons in an atom. One can make a misassignment of atom types if the thermal motion is over- or underestimated.
One solution to find out how reliable the results are is by replacing the atom types and calculating the goodness of fit for both alternatives. From statistical considerations you should be able to see whether the distinction power is large enough.
Why do you not perform EXAFS measurements? It should give you information about the short range order around one of the element you are looking for.
You can have a very quick and rough answer takiing any Rietveld software and doing a couple simulations! If you can't get enough contrast with neutrons, then go for anomalous diffraction (working above and below absorption edges). This is somehow routine at synchrotron sources and, depending on your system, you might get already some information collecting your pattern on a lab diffractometer at two different energies (different tubes) and doing a combined refinement.
Be warned, though, that in your case things can be more complex than expected. If your particles are really nano, then you'll see a large line profile broadening and some issues can arise when doing a Rietveld refinement (apparent strange behavior of the lattice parameter). Moreover anisotropic broadening is likely to happen if the shape of your particles is not spherical (and this is an often sought result) or contain defects.
Things can be more complicated if you have partial ordering on the sites.
I would also expect to see differences in the occupancy between core and surface: in that case I agree with Fabiola that EXAFS (or DAFS, easily done if you do your diffraction experiment on a synchroton diffraction beamline) can also be a good complement.
Have a further check at the literature and if you have a strong enough case you can easily apply for beamtime either through the conventional route or via one of the faster mail-in services (for sure I know BM-11 at APS for synchrotron or POWGEN at ORNL for neutrons, but I think most facilities have this service).
What if we could create a 2D X-ray Imaging system that could operate at MILLIONS of fps (video frames per second 12-24Bits) and sub-micron spatial resolution? Would it change the paradigm?
There are scintillators (phosphors) available with short enough decay time to achieve this objective and so are available the imaging devices these days.
@Ravi, no that would not change anything for the assignment. Sub-micron positional accuracy is not going to help anything, and millions of fps are not very useful since we're not looking for time resolving here. Besides, there are only millions of photons per second in a home system, and the higher flux of photons arrive in very short pulsed batches in a synchrotron.
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