Zakaria Kharbouch's thesis made 38 Ga-stabilised LLZO garnets in two families and refined two quantities per garnet, the lattice parameter and the phase fractions, on laboratory Cu Kα data. Every argument it builds on them is about lithium and about which site each dopant takes. This page shows what each probe can see in these garnets, what every one of the 38 compositions 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 does not follow Z and is negative for lithium and hydrogen. Two occupants of a site can be separated only by a probe in which they differ.
The Ga–Ta reference, Li6.3Ga0.2La3Zr1.9Ta0.1O12 in I4̄3d, built from the neutron structure of cubic LLZO. 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 38 compositions of the thesis, each family branching from its co-doped reference into three La-site series. Colour by what the thesis determined, or by how many probes are planned. The squares under each value are the planned determinations. Select a cell for what was refined, what does not close, and what each measurement will determine for that composition.
The thesis gives phase fractions and Li₂ZrO₃ only for the Ta family; Sc cells show "n/a" in those modes. Cells with a bold frame are the key set K12, re-made fresh for the high-resolution neutron work. Nominal vacancies are 7 − Li from the weighing formula, M on the La site.
● 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 site occupancy). "Home" is the work before beam time: fresh samples under argon, ICP-OES, TGA–MS, 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 garnets, but each one rules out part of what they could be, and together they leave little room. That is the spirit of the project, in two moments: it decides which experiments to ask for, and later it decides how their results are analysed together.
Every structural parameter has a probe that sees it (●) and others that remove what it trades off against (○). A proposal is good when, for each question, the two are both in the plan. The contrast computed above is the first step: the pattern change says which probe sees a parameter. The next step is the expected width of the answer for each combination of probes, from the same structure factors with realistic counts, so that the shifts go where they narrow the answer most.
One structural model of each composition, and every measurement a term in its probability: the ID22 and D2B patterns as two likelihoods sharing the lattice and the heavy atoms; ICP-OES and TGA as priors on the composition and the protons, with their own uncertainties, not as hard constraints; EXAFS coordination numbers as a prior on the Y site fraction. The result is not one set of numbers with esd's but a distribution: how much Li sits on 12a, 12b and 48e, and how sure the combined data are of it.
| Parameter | Seen by (likelihood) | Narrowed by (prior, constraint) | What the combination removes |
|---|---|---|---|
| Li per site, 12a 12b 48e | D2B, D20 | ICP total Li; TGA protons; charge balance | the trade-off of Li occupancy against displacement parameters; H mistaken for Li |
| Ga on 12a, acentric O1/O2 | D2B | ID22 lattice, profile and heavy atoms; ICP Ga | Ga and the distortion fitted against an uncertain cell and peak shape |
| Al on 12a | ICP | D2B site scattering | an Al content with no site, or a site with no Al content |
| Y on La or on Zr | EXAFS (Y K edge) | ID22 La-site occupancy; ICP Y; resonant diffraction | a site fraction inferred from a lattice parameter alone |
| Ba, Rb in the garnet | D2B (Ba), ID22 (Rb) | ID22 BaZrO₃ fraction; ICP; Rb K EXAFS | a solubility read from a second phase instead of the garnet |
| Phase fractions, powder and pellet | ID22 | D2B (Li₂ZrO₃ contrast); ICP Zr/La | fractions that do not close the mass balance |
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: no facility takes one combined X-ray and neutron proposal for materials. Shift counts are estimates, to be checked with each instrument's contact. A shift is 8 h.