Hello,

It is unlikely you will be able to determine relevant mixing ratio in this scenario from refinement using powder laboratory XRD. You might refine some trends measuring "long scan" (>12 hours measurements), with a perfect sample preparation (zero level, no preferential orientation, known instrument parameters, ....), with good sample quality (and you might not be able to compare 2 samples). From litterature on such scenarios, ratios are determined using other technics.

If you want to stick with XRD my recommendation would be to use single crystal XRD (if available, and if you have single crystal sample) which bring high quality datas (and less painful refinement). Or if you dont need precise mixing ratio (and if there is enough reported litterature) try to see if your refined cell parameters are closer of reported cell parameters of Li-rich or reported of Ni-rich (so you can estimate from your refined cell parameters in which case you are).

Otherwise my best recommandation would be to use other technics (such as Inductively Coupled Plasma Spectroscopies) to get the correct ratios. You can use XRD after and the refinement will be easier knowing which ratio values you are expecting.

Then if you want to stick with the "12hours measurement powder XRD" version using fullprof software (i dont know about the other software as I am mostly not using them), you will have to use linear restraints. It is too long to explain how to prepare your pcr for it here (and might be described in the fullprof manual / tutorial), but I could provide / fill an example if needed.

you duplicate the sites you expect to be mixed, and add identifier codes with coeficient so if occupancies values decrease on Site1_duplicate1, it will increase along the refinement in Site1_Duplicate2) and add an additional restraint so Site1_duplicate1 + Site1_duplicate2 = Maximum occupancy of Site1. You will need perfect data, good understanding of the structure, and perfect comprehension of how fullprof refinement work to do this, there is a lot of refined parameters so it can easily bring false refinement.

Hope this helps,

Bastien Leclercq,

If one cation replaces another cation, then the occupation number will help to understand the composition.

If you are using the Fullprof suite, initially put the number of Li atoms in OCC and Ni as zero, then refine both. Ensure the sum of refined OCCs of Li and Ni is equal to the initial OCC of Li.

You may refer Article The influence of nickel substitution on the structural and g...

First, you likely need high resolution data to determine average site occupancies. Assuming you have data sufficient for this kind of analysis, I recommend this article for reference:

Chem. Mater. 2020, 32, 3, 1002–1010

Article Thermodynamics of Antisite Defects in Layered NMC Cathodes: ...

Example input files for TOPAS are provided, though you can implement this kind of parameterization in many software packages. Be wary of the parameters that correlate with site occupancies (e.g., displacement parameters).