The fact base

The fact base: 38 compositions

Every number the thesis gives for each composition, one row each, transcribed from Tables III-1, III-S1, III-2, IV-1 and IV-3 of the manuscript of 17 October 2026, with the quantities derived here: the nominal lithium content and vacancies per formula unit, the arithmetic check of each refinement, the \(\mathrm{Li_{2}ZrO_{3}}\) per garnet formula unit. The source is data/compositions.yml, written by analysis/facts.py; this is the table the samples of the proposals are chosen from and the one the beam-time results will be written into.

Ga-M-Ta · Chapter III

Phase fractions in wt% (Table III-S1), calcined powders, 900 °C; density, \(\sigma\) and Eₐ on pellets sintered at 1200 °C (Tables III-1, III-2). Li and Vac.: nominal, per formula unit, M on the La site. Flags: \(\chi^2\) printed against (Rwp/Rexp)² where they differ by more than 15 %; the lattice parameter of Table III-1 where it is not the rounding of Table III-S1. \(\mathrm{Li_{2}ZrO_{3}}\) per garnet formula unit computed from the wt% and the nominal molar masses.

M	x	Nominal formula	Li	Vac.	a (Å), III-S1	c-LLZO	t-LLZO	Second phase (wt%)	Rwp	Rexp	\(\chi^2\)	ρ (%)	\(\sigma\) (mS \(\mathrm{cm}^{-1}\))	Eₐ (eV)
ref.	0	Li6.3Ga0.2La3Zr1.9Ta0.1O12	6.3	0.7	12.97735	100	—	—	5.25	1.54	5.65 ≠ 11.62	87.6	0.15	0.42
Ba	0.03	Li6.33Ga0.2La2.97Ba0.03Zr1.9Ta0.1O12	6.33	0.67	12.98148	100	—	—	5.18	1.62	12.9 ≠ 10.22	88.5	0.18	0.42
Ba	0.05	Li6.35Ga0.2La2.95Ba0.05Zr1.9Ta0.1O12	6.35	0.65	12.97843	100	—	—	5.82	1.51	11.7 ≠ 14.86	87.9	0.19	0.41
Ba	0.1	Li6.4Ga0.2La2.9Ba0.1Zr1.9Ta0.1O12	6.4	0.6	12.96941	100	—	—	5.91	1.55	14.5	91	0.24	0.38
Ba	0.15	Li6.45Ga0.2La2.85Ba0.15Zr1.9Ta0.1O12	6.45	0.55	12.97538	95.69	—	BaZrO3 4.31	6.32	1.73	13.4	89.9	0.17	0.39
Ba	0.2	Li6.5Ga0.2La2.8Ba0.2Zr1.9Ta0.1O12	6.5	0.5	12.97817	96.61	—	BaZrO3 3.39	5.75	1.5	14.6	90.1	0.14	0.41
Ba	0.3	Li6.6Ga0.2La2.7Ba0.3Zr1.9Ta0.1O12	6.6	0.4	12.97912	96.24	—	BaZrO3 3.76	5.79	1.65	12.3	90.2	0.12	0.41
Rb	0.03	Li6.36Ga0.2La2.97Rb0.03Zr1.9Ta0.1O12	6.36	0.64	12.98746	81.47	16.26	Li2ZrO3 2.27 0.13 per f.u.	13.3	3.41	15.2	90.1	0.11	0.41
Rb	0.05	Li6.4Ga0.2La2.95Rb0.05Zr1.9Ta0.1O12	6.4	0.6	12.98962 III-1: 12.989	83.79	16.22	—	6.4	1.21	27.9	88.9	0.059	0.45
Rb	0.1	Li6.5Ga0.2La2.9Rb0.1Zr1.9Ta0.1O12	6.5	0.5	12.99185	79.28	20.72	—	6.59	1.61	16.9	89.1	0.061	0.46
Rb	0.15	Li6.6Ga0.2La2.85Rb0.15Zr1.9Ta0.1O12	6.6	0.4	12.99334 III-1: 12.996	88.21	9.98	Li2ZrO3 1.82 0.103 per f.u.	7.72	1.73	19.9	89.2	0.057	0.45
Rb	0.2	Li6.7Ga0.2La2.8Rb0.2Zr1.9Ta0.1O12	6.7	0.3	13.00058 III-1: 13.000	95.51	3.43	Li2ZrO3 1.05 0.059 per f.u.	6.01	4.48	11.5 ≠ 1.8	89.3	0.076	0.43
Rb	0.3	Li6.9Ga0.2La2.7Rb0.3Zr1.9Ta0.1O12	6.9	0.1	13.00099	87.92	12.08	—	6.07	1.6	14.5	89.5	0.079	0.41
Y	0.03	Li6.3Ga0.2La2.97Y0.03Zr1.9Ta0.1O12	6.3	0.7	12.98339	84.19	11.65	Li2ZrO3 4.16 0.243 per f.u.	6.04	1.61	13.6	91.5	0.14	0.39
Y	0.05	Li6.3Ga0.2La2.95Y0.05Zr1.9Ta0.1O12	6.3	0.7	12.98477 III-1: 12.984	93.21	4.07	Li2ZrO3 2.73 0.157 per f.u.	4.77	1.67	8.11	90.8	0.11	0.38
Y	0.1	Li6.3Ga0.2La2.9Y0.1Zr1.9Ta0.1O12	6.3	0.7	12.98598	87.73	6.35	Li2ZrO3 5.91 0.35 per f.u.	5.48	1.66	10.8	93.1	0.24	0.38
Y	0.15	Li6.3Ga0.2La2.85Y0.15Zr1.9Ta0.1O12	6.3	0.7	12.98466 III-1: 12.984	90.35	4.48	Li2ZrO3 5.17 0.303 per f.u.	4.22	1.71	6.08	90.9	0.63	0.34
Y	0.2	Li6.3Ga0.2La2.8Y0.2Zr1.9Ta0.1O12	6.3	0.7	12.99372	82.18	3.58	Li2ZrO3 14.24 0.919 per f.u.	5.45	1.73	9.87	95.3	1.04	0.32
Y	0.3	Li6.3Ga0.2La2.7Y0.3Zr1.9Ta0.1O12	6.3	0.7	12.99365	82.92	8.85	Li2ZrO3 8.23 0.494 per f.u.	5.44	1.64	11	90.5	0.23	0.37

Ga-M-Sc · Chapter IV

Lattice parameters to two decimals (Table IV-1), not re-refined with the Chapter III protocol; no phase fractions are given for this family. \(\sigma\) at room temperature only (Table IV-3); bulk and grain-boundary conductivities resolved for the Y series only.

M	x	Nominal formula	Li	Vac.	a (Å), IV-1	Phases (Fig. IV-1, §IV.3.1)	ρ (%)	\(\sigma\)ₜ (mS \(\mathrm{cm}^{-1}\))	\(\sigma\)_b / \(\sigma\)_gb
ref.	0	Li6.5Ga0.2La3Zr1.9Sc0.1O12	6.5	0.5	13.07	c-LLZO + t-LLZO (text, section IV.3.1) / single cubic (Fig. IV-2a refinement, Table IV-1)	91.2	0.451	—
Ba	0.03	Li6.53Ga0.2La2.97Ba0.03Zr1.9Sc0.1O12	6.53	0.47	13.07	c-LLZO + t-LLZO	87.6	0.278	—
Ba	0.05	Li6.55Ga0.2La2.95Ba0.05Zr1.9Sc0.1O12	6.55	0.45	13.06	c-LLZO + t-LLZO	90.8	0.361	—
Ba	0.1	Li6.6Ga0.2La2.9Ba0.1Zr1.9Sc0.1O12	6.6	0.4	13.07	c-LLZO + t-LLZO + BaZrO3	86.8	0.282	—
Ba	0.15	Li6.65Ga0.2La2.85Ba0.15Zr1.9Sc0.1O12	6.65	0.35	13.07	c-LLZO + t-LLZO + BaZrO3	84.8	0.189	—
Ba	0.2	Li6.7Ga0.2La2.8Ba0.2Zr1.9Sc0.1O12	6.7	0.3	13.05	c-LLZO + t-LLZO + BaZrO3	87	0.162	—
Ba	0.3	Li6.8Ga0.2La2.7Ba0.3Zr1.9Sc0.1O12	6.8	0.2	13.06	c-LLZO + t-LLZO + BaZrO3	85.2	0.137	—
Rb	0.03	Li6.56Ga0.2La2.97Rb0.03Zr1.9Sc0.1O12	6.56	0.44	13.07	c-LLZO + t-LLZO (traces) + Sc2O3	96.2	0.903	—
Rb	0.05	Li6.6Ga0.2La2.95Rb0.05Zr1.9Sc0.1O12	6.6	0.4	13.07	c-LLZO + t-LLZO (traces) + Sc2O3	94.5	0.642	—
Rb	0.1	Li6.7Ga0.2La2.9Rb0.1Zr1.9Sc0.1O12	6.7	0.3	13.07	c-LLZO + t-LLZO (traces) + Sc2O3	94.3	0.723	—
Rb	0.15	Li6.8Ga0.2La2.85Rb0.15Zr1.9Sc0.1O12	6.8	0.2	12.99	c-LLZO + t-LLZO (traces) + Sc2O3	91.7	0.377	—
Rb	0.2	Li6.9Ga0.2La2.8Rb0.2Zr1.9Sc0.1O12	6.9	0.1	13.00	c-LLZO + t-LLZO (traces) + Sc2O3	90.7	0.183	—
Rb	0.3	Li7.1Ga0.2La2.7Rb0.3Zr1.9Sc0.1O12	7.1	-0.1	13.00	c-LLZO + t-LLZO (traces) + Sc2O3	93	0.116	—
Y	0.03	Li6.5Ga0.2La2.97Y0.03Zr1.9Sc0.1O12	6.5	0.5	13.05	c-LLZO	76	0.024	0.059 / 0.041
Y	0.05	Li6.5Ga0.2La2.95Y0.05Zr1.9Sc0.1O12	6.5	0.5	13.05	c-LLZO	75.2	0.036	0.102 / 0.056
Y	0.1	Li6.5Ga0.2La2.9Y0.1Zr1.9Sc0.1O12	6.5	0.5	13.04	c-LLZO	74.3	0.006	0.013 / 0.013
Y	0.15	Li6.5Ga0.2La2.85Y0.15Zr1.9Sc0.1O12	6.5	0.5	13.04	c-LLZO + Y2O3	74.7	0.007	0.016 / 0.014
Y	0.2	Li6.5Ga0.2La2.8Y0.2Zr1.9Sc0.1O12	6.5	0.5	13.03	c-LLZO + Y2O3	72.8	0.007	0.013 / 0.018
Y	0.3	Li6.5Ga0.2La2.7Y0.3Zr1.9Sc0.1O12	6.5	0.5	13.03	c-LLZO + Y2O3	75.3	0.02	0.08 / 0.027

How to read it

Nominal Li assumes M on the La site; Y on the Zr site would add one Li per Y. The vacancies are \(7 - \mathrm{Li}\); the literature's critical value for the cubic garnet is 0.4–0.5 (thesis, p. 63).
Past full lithium. Ga–Rb–Sc at x = 0.20 and 0.30 are weighed with 6.9 and 7.1 Li per formula unit: no vacancies left at all, and at x = 0.30 more lithium than fully stuffed LLZO holds. Either part of the Rb or the Li does not enter the garnet, or it is tetragonal; the thesis sees only traces of tetragonal garnet. The measured Li content (G02) and the Rb on the La site (G06) will say which.
Two families, two footings. The Ga–M–Ta lattice parameters come from the V4.0 refinements with all phases; the Ga–M–Sc ones from the earlier protocol, two decimals, 0.06–0.09 Å higher. Compare within a family, not across.
Powders and pellets. The structural columns are for calcined powders, the density and conductivity columns for sintered pellets.
Where the beam time will add columns: refined Li per formula unit and its distribution (12a, 12b, 48e), Ga and Al on 12a, Ba or Rb or Y on the La site, Y on the Zr site, the acentric distortion, phase fractions of pellets, ICP composition, H content, all with esd.