Fadila El Kouihen's thesis made cobalt-low NCA and cobalt-free NMA cathodes, doped them in four design lines and coated one for solid-state cells. It refined their cells on laboratory Cu Kα data and read their Li/Ni mixing from an intensity ratio, I(003)/I(104). Every argument it builds is about where the nickel goes. This page shows what each probe can see in these cathodes, what every material will be measured with, and which structural question each measurement answers.
A powder pattern measures a site's total scattering. X-rays weigh each atom by its electrons, Z; neutrons by its coherent scattering length, b, which is negative for lithium and manganese. Two occupants of a site can be separated only by a probe in which they differ, and a valence by none: that needs the absorption edge.
The NMA reference, LiNi0.8Mn0.15Al0.05O2 in R3̄m. For each question, two models that differ by that question alone; the structure factors of both from diff-ref-struct's core; the change of the powder pattern measured.
The twelve materials as the thesis designed them: the cobalt line from NCA to the cobalt-free NMA, and the branches that dope or coat NCA and NMA. Colour by what the thesis determined, or by how many probes are planned. The squares under each value are the planned determinations. Select a material for what was refined, what does not close, and what each measurement will determine for it.
Cells with a bold frame are the key set K9, measured with high-resolution neutrons. "n/a": the thesis gives no value for that material in that mode. Ni²⁺ is computed from the nominal formula with the usual valences; the Fe/Sb–NMA formula as printed has 1.10 metals and gives 0.55.
● the probe that answers the question; ○ one that does not answer it alone but fixes a quantity the answer needs (a composition, a lattice, a valence). "Home" is the work before beam time: the lithium balance, surface species, XPS and Mössbauer, lab XRD with an internal standard.
In the refinement sense: a ○ probe does not answer the question by itself, but measures something the answering probe's refinement needs, a fixed value that cuts down what the answer can be. In Rietveld terms it supplies a constraint or a restraint.
So the circle is a supporting measurement: it does not see the answer, it removes the alternatives.
Read the grid as probabilities. No single technique determines these cathodes, but each one rules out part of what they could be, and together they leave little room. The spirit enters twice: it decides which experiments to ask for, and later how their results are analysed together.
Every structural parameter has a probe that sees it (●) and others that remove what it trades off against (○). For the mixing both diffraction probes see it, so the design is the joint refinement; for the identity of the metal only neutrons see it; for the valence only the edge. The next step after the contrast computed above is the expected width of each answer for each combination, from the same structure factors with realistic counts.
One structural model of each material, and every measurement a term in its probability: the ID22 and D2B patterns as two likelihoods sharing the cell and the metal layer; ICP, titration and XANES as priors on the composition, the surface lithium and the Ni valence, with their uncertainties. The result is a distribution: how much Ni sits on the Li layer, how much of it is Mn, how sure the combined data are.
| Parameter | Seen by (likelihood) | Narrowed by (prior, constraint) | What the combination removes |
|---|---|---|---|
| Ni on the Li layer | D2B, ID22 | ICP; charge balance; Ni K edge (Ni²⁺) | the correlation of mixing with displacement parameters, absorption and preferred orientation |
| Ni or Mn on the Li layer | D2B | ID22 resonant at the Ni K edge; ICP Mn | a metal on the Li layer of unknown identity |
| Li content | D2B | washed ICP; titration of LiOH and Li₂CO₃ | surface lithium counted as bulk |
| Ni²⁺ fraction | Ni K XANES | refined Li-layer Ni; charge balance | a valence inferred from a formula |
| Dopant site (Y, La, Mg, Sc, Na) | ID22 (Y, La), D2B (Mg, Sc) | Y K, La K, Sc K EXAFS; second-phase fractions | a site read from a cell shift |
| Fe, Sb valence and the formula | Fe K, Sb K XANES | Mössbauer; ICP; joint refinement | a formula with 1.10 metals and an asserted Sb⁵⁺ |
diff-ref-struct already shows the path of a refinement in configuration space (its Explore module); the Bayesian layer, posterior distributions over the same parameters, is the extension this project would use first on real data.
Separate proposals that cite each other and the garnet proposals of the companion project. Shift counts are estimates, to be checked with each instrument's contact. A shift is 8 h.