The crystallography, in detail

The crystallography of the thesis, in detail

Every structural statement of the thesis, what it rests on, and how firmly. The laboratory diffractometer did what it can do; the point is to know which structural facts the thesis has, which it infers, and which it needs, because that is what the beam time must deliver.

The data and the refinement

One instrument. Bruker D6, Cu Kα (Annex A); the 2\(\theta\) range, step, counting time, software, refined parameters and zero-shift or displacement treatment are not stated. Mn, Co and Fe fluoresce under Cu Kα (their K edges lie below 8.05 keV), which raises the background of exactly these samples unless the detector discriminates energy.
What was refined. Cells of every material (Tables II.3, II.5, II.7–II.9), Rwp, Rexp and \(\chi^2\) for the NMA lines, Li–O distances for two tables (which need a refined oxygen position), and a Li/Ni antisite fraction for two materials: 3.5 % in NMA and 2.2 % in La–NMA (p. 90).
The proxy. For every material, mixing is read from I(003)/I(104), with 1.2 as the threshold of good ordering. The ratio also moves with preferred orientation of platelet crystallites, absorption and the oxygen position; it is a proxy, not an occupancy.
The scattering. In NMA, Ni carries 72 % of the X-ray scattering power and Li 1 %; in neutrons Ni carries 54 %, O 42 %, and Mn scatters with the opposite sign. The contrast page has the numbers.

The structural claims and what they rest on

Claim of the thesis	What it rests on	Status, and what would settle it
Every material is a single-phase layered \(R\bar{3}m\) oxide (Chapter II).	Indexing and the absence of extra laboratory peaks.	Plausible at the laboratory detection limit. Surface \(\mathrm{Li_{2}CO_{3}}\)/LiOH, rock-salt and La/Y/Sc-rich phases at the per-cent level are below it. F08.
Each dopant reduces Li/Ni mixing (pp. 77, 90, 98, 106).	A rising I(003)/I(104); refined antisite for NMA and La–NMA only.	In tension with charge balance. Mn\(^{4}\)⁺, Sb\(^{5}\)⁺ and Mg\(^{2}\)⁺ require more Ni\(^{2}\)⁺, not less (0.05–0.15 per formula unit). Refined occupancies (neutrons + X-rays) and the Ni K edge settle it. F01, F03.
Pristine NCA's ratio "remains above the critical threshold of 1.2" (p. 77).	I(003)/I(104) = 1.05 (Table II.5).	Contradicted by its own value. F01.
Fe/Sb co-doping slightly lowers c/a, "from 4.944 to 4.9359" (pp. 79, 107).	Table II.5.	The table shows the reverse (\(4.9359 \to 4.944\) for NCA). F07.
Pristine NMA: a = 2.860, c = 14.30 Å, c/a = 5.00 (Tables II.7–II.9).	Rietveld.	Two cells for one powder: Table II.3 gives 2.9042 / 14.3489 Å. c/a = 5.00–5.08 for the NMA family is unusual for this composition (\(\approx 4.94\text{–}4.95\) is typical). A calibration or zero-shift problem is likely. F07.
Mn replaces Co in the Mn–NCA series; Mg, Y, La and Sc replace Mn; Na replaces Li.	Cell shifts with ionic radius; EDS homogeneity; the absence of extra peaks.	Assumed. No site is measured; La\(^{3}\)⁺ (1.03 Å) and Y\(^{3}\)⁺ (0.90 Å) on the octahedral metal site are unusual, and surface segregation is invisible to laboratory diffraction. F03, F04.
Sb is Sb\(^{5}\)⁺ after calcination (p. 79).	Assertion; §II.3.2 still lists Sb\(^{3}\)⁺ among the trivalent dopants.	Not measured. Sb K-edge XANES settles it. F05.
The Fe/Sb–NMA composition is \(\mathrm{LiNi_{0.8}Mn_{0.15}Sb_{0.05}Fe_{0.05}Al_{0.05}O_2}\) (§II.4.4).	Nominal formula.	Does not close: 1.10 metals per formula unit; Table II.10's own theoretical wt% give \(\approx\) Ni₀.₇₆Mn₀.₀₈Fe₀.₀₅Sb₀.₀₅Al₀.₀₆. F05.
Lithium: a modest deficiency of 0.6–0.9 wt% (p. 70).	ICP, Table II.4.	Larger than it sounds. 0.91–0.93 Li per transition metal, a 7–9 % deficit; bulk and surface not separated. F02.
Fe/Sb, Mg, Y, La improve thermal stability.	TGA of lithiated powders.	A different quantity. Thermal stability of a cathode is the oxygen release of the charged material; in situ heating diffraction of charged electrodes measures it. F06.
Retention follows the reduced mixing (Chapter III).	Correlation between the ratio and cycling.	Inferred. No structure of any electrode after cycling. F09.

Measured: none of the claims above is measured in the sense of a refined occupancy or valence with an uncertainty. Inferred / assumed / plausible: consistent with the data, which cannot establish it. In tension / contradicted / does not close / not measured.