A Synthesis and Crystal Chemical Study of the Fast Ion Conductor Li_7–3xGa_xLa₃ Zr₂O₁₂ with x = 0.08 to 0.84

Abstract

Fast-conducting phase-pure cubic Ga-bearing Li₇La₃Zr₂O₁₂ was obtained using solid-state synthesis methods with 0.08 to 0.52 Ga³⁺ pfu in the garnet. An upper limit of 0.72 Ga³⁺ pfu in garnet was obtained, but the synthesis was accompanied by small amounts of La₂Zr₂O₁₂ and LiGaO₃. The synthetic products were characterized by X-ray powder diffraction, electron microprobe and SEM analyses, ICP-OES measurements, and ⁷¹Ga MAS NMR spectroscopy. The unit-cell parameter, a₀, of the various garnets does not vary significantly as a function of Ga³⁺ content, with a value of about 12.984(4) Å. Full chemical analyses for the solid solutions were obtained giving: Li_7.08Ga_0.06La_2.93Zr_2.02O₁₂, Li_6.50Ga_0.15La_2.96Zr_2.05O₁₂, Li_6.48Ga_0.23La_2.93Zr_2.04O₁₂, Li_5.93Ga_0.36La_2.94Zr_2.01O₁₂, Li_5.38Ga_0.53La_2.96Zr_1.99O₁₂, Li_4.82Ga_0.60La_2.96Zr_2.00O₁₂, and Li_4.53Ga_0.72La_2.94Zr_1.98O₁₂. The NMR spectra are interpreted as indicating that Ga³⁺ mainly occurs in a distorted 4-fold coordinated environment that probably corresponds to the general 96h crystallographic site of garnet.

Short abstract

Fast-conducting cubic Ga-bearing Li₇La₃Zr₂O₁₂ (LLZO) has been synthesized using solid-state methods with 0.08 to 0.52 Ga³⁺ pfu in the garnet. An upper limit of 0.72 Ga³⁺ pfu in the garnet was obtained, but the synthesis product contained small amounts of La₂Zr₂O₁₂ and LiGaO₃. The NMR spectra are interpreted as indicating that Ga³⁺ mainly occurs in a distorted 4-fold coordinated environment that corresponds to the “non-standard” general 96h crystallographic site.

Introduction

Research has shown that Al-bearing Li₇La₃Zr₂O₁₂ (LLZO) with a cubic garnet structure has high ion conductivity (approximately 10^–4 S·cm^–1).¹ At room temperature, end-member LLZO is tetragonal (I4₁/acd) and it has a lower conductivity compared to the “high temperature” cubic modification (Ia-3d).² The tetragonal phase has a fully ordered arrangement of Li⁺ ions. It has been proposed that by doping LLZO with supervalent cations the cubic structure is stabilized by introducing vacancies at the Li positions, which act to increase the entropy and reduce the free energy.³ The stabilization of cubic LLZO through Al³⁺ was first reported in 2011^4,5 and confirmed many times thereafter.⁶⁻¹⁷ Attention has since been directed also at other dopant cations. Because gallium is located directly below aluminum in the periodic table, it should show similar crystal-chemical behavior as Al³⁺ in LLZO. Indeed, the stabilization of cubic LLZO through Ga³⁺ has been reported.¹⁷⁻¹⁹

In spite of the amount of recent study that has been made on the LLZO group of phases, certain aspects are still not understood. Emphasis has been placed on measuring Li-ion conductivity often at the expense of careful compositional and crystal-chemical characterization of the garnet under consideration. The latter are important, if not essential, in order to understand the precise stability and conductivity behavior of LLZO. In terms of Ga-bearing LLZO, there is no information about the amount of Ga³⁺ that can be incorporated and its site distribution with the garnet structure.

To obtain a more detailed understanding of the role of super valent cations in LLZO, we synthesized a series of Li_7–3xGa³⁺_xLa₃Zr₂O₁₂ garnets and carefully characterized them chemically and structurally. Characterization was done using X-ray powder diffraction (XRPD) measurements, electron microprobe analysis (EMPA), inductively coupled plasma optical emission spectroscopy (ICP-OES) measurements, and ⁷¹Ga magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy.

Experimental Section

A series of Li_7–3xGa³⁺_xLa₃Zr₂O₁₂ garnets with intended mole fractions of Ga³⁺ (x_int) of 0.08–0.84 pfu was synthesized by high-temperature sintering in air. The starting materials were Li₂CO₃ (99%, Merck), La₂O₃ (99.99%, Aldrich), ZrO₂ (99.0%, Aldrich), and Ga₂O₃ (99.0%, Aldrich). To begin, the starting materials were weighed out in their intended stoichiometric proportions together with an excess of 10 wt % Li₂CO₃ to compensate for Li₂O loss during synthesis. After intimate mixing in a ball mill for 8 h, the starting mix was cold-pressed into pellets of 10 mm diameter and 5 mm height. The pellets were placed in a Pt crucible and heated at a rate of 5 °C/min to 900 °C and calcinated for 4 h. The resulting pellets were then removed from the oven, were allowed to cool, and were ground for 15 min and pressed again into pellets. The final sintering step was done at 1050 °C for 17 h in air. A small amount of a given compacted sintered pellet, taken from the middle of the pellet, was ground and used for the XRPD, ⁷¹Ga MAS NMR, and ICP-OES measurements. A polycrystalline chip was used for microprobe analysis.

XRPD measurements were performed with Cu Kα radiation using a Siemens D8 diffractometer. This was done to characterize the synthetic products in terms of the phases present and to determine the symmetry and unit-cell dimension of the garnet. Data were collected between 10° and 70° 2θ. The unit-cell lattice parameter, a₀, and grain size were determined by Rietveld refinement using the program Topas V2.1 (Company Bruker).

EMPA was done using a JEOL JXA 8100 Superprobe at the Institute of Mineralogy and Petrography at the University of Innsbruck. Small polycrystalline chips, taken from the larger sintered pellets, were embedded in an epoxy holder, and the surface was ground and then polished using diamond paste. Special attention was made with regard to grain sizes, grain boundaries, and textures during analysis. Back-scattered electron (BSE) images were taken to identify small amounts of non-garnet phases. Wavelength-dispersive (WDS) measurements for the elements La, Zr, and Ga were undertaken to characterize the synthetic products in terms of their composition and chemical homogeneity. Analytical measuring conditions were 15 kV accelerating voltage and a 10 nA beam current. The following synthetic standards were used: GaAs (99.99%, Aldrich) for Ga, La-phosphate, LaP₅O₁₄, for La, and zircon, ZrSiO₄, for Zr. Measuring times were 20 s at the peak maximum and 10 s for the lower and upper peak background. Twenty point measurements, made on five different garnet grains, were performed to obtain representative compositions for each garnet composition.

ICP-OES measurements, using a Horiba Jobin Yvon Ultima 2 device, were made to determine the Li contents at the University of Ulm, Germany. About 50 mg of garnet, taken from a sintered pellet, were divided into two batches in order to be able to determine the analytical reproducibility. The samples were prepared by placing 15 mg of garnet in 2 mL of aqua regia (HCl + HNO₃), followed by heating to ensure dissolution of the garnet. Deionized water was then added to obtain 20 mL of solution. One mL aliqouts were used for the ICP-OES measurements.

⁷¹Ga MAS NMR spectra were recorded at room temperature on the same Ga³⁺-bearing samples that were characterized by XRPD, EMPA, and ICP-OES measurements using a Bruker ASX 400 spectrometer at Ruhr University in Bochum, Germany. MAS NMR spectra were collected at 122 MHz (9.4 T) with a spinning rate of 12.5 kHz using a 4 mm MAS probe. Spectra were recorded with a single pulse sequence; the pulse length was 0.6 μs. The spectral width was 125 kHz corresponding to a radio frequency tip angle of about 15 ± 5°. The signal-to-noise ratio was optimized by a pulse delay of 0.4 s using full relaxation for short pulses. Line broadening of 100 Hz was applied and the first 4–8 points of 1 k measured free induction decay (FID) points were removed because of the strong distortion and low signal. The count of the spectral points was 8 k. Typically, about 10⁶ scans were acquired for samples with x_int < 0.36 and about 2 × 10⁵ for samples with x_int ≥ 0.24. Line shapes were simulated using the STARS simulation package (Varian), with manual adjustment of parameters to match the quadrupolar line shapes typical of the spectra for the samples with x_int = 0.24 to x_int = 0.64. The ⁷¹Ga chemical shifts are reported relative to aqueous 1 M Ga(NO₃)₃.

Results

Garnet Composition and Lattice Constant

The XRPD patterns of the various Li_7–3xGa_xLa₃Zr₂O₁₂ garnets with x_int = 0.08, 0.16, 0.24, 0.36, 0.54, 0.64, and 0.84 are shown in Figure 1, together with the pattern of Li_7–xAl_xLa₃Zr₂O₁₂ with x = 0.24 (ICSD no. 261302). All garnet compositions exhibit reflections indicating cubic symmetry. There are no indications of reflection splitting indicating a tetragonal garnet phase. All diffraction patterns of garnet with x_int from 0.08 to 0.54 do not show the presence of any other phase. In the diffraction pattern of the sample with x_int = 0.64, just one weak reflection is observed and it can be assigned to La₂Zr₂O₇ occurring at roughly the 1% level. For the garnet with x_int = 0.84, about 4% LiGaO₂ and 6% La₂Zr₂O₇ are calculated from Rietveld analysis. The unit-cell constant, a₀, and a determination of the amounts of the different phases were evaluated by Rietveld analysis. The results are summarized in Table 1 and shown in Figure 2. The unit-cell constant of garnet with x_int = 0.08 is 13.034(6) Å, and this value decreases slightly to 12.971(4) Å for garnet with x_int = 0.24. More Ga-rich garnets have a similar a₀ value of 12.979(5) for the sample with x_int = 0.84. The a₀ values are similar to Al-bearing LLZO with a₀ = 12.975(1) Å or to Fe-bearing LLZO with a₀ = 12.986(1) Å.^5,20

Figure 1.

XRPD patterns of Li_7–3xGa_xLa₃Zr₂O₁₂ garnet solid solutions with x_int = 0.08−0.84. The diffraction pattern (red) of cubic Li_7–3xAl_xLa₃Zr₂O₁₂ with x = 0.24 is shown for comparison. Only the strongest reflections of non-garnet phases are observed at high Ga³⁺ contents and their positions are highlighted with a gray background.

Table 1. Unit-Cell Parameter of Li_7–3xGa_xLa₃Zr₂O₁₂ with x_int = 0.08–0.84 and the Amount of Phases in the Different Syntheses Obtained by Rietveld Refinement.

xint	a0 [Å]	LLZO [%]	La2Zr2O7 [%]	LiGaO2 [%]
0.08	13.034(6)	100	0	0
0.16	12.981(2)	100	0	0
0.24	12.971(4)	100	0	0
0.36	12.969(1)	100	0	0
0.54	12.979(9)	100	0	0
0.64	12.973(2)	>99	<1	0
0.84	12.979(5)	90	6	4

Figure 2.

Lattice parameter, a_o, and amount of phases obtained in the synthesis experiments as a function of the intended Ga³⁺ concentration in LLZO.

The X-ray reflections for Ga-bearing LLZO are broader than those of Al-bearing LLZO and increase, especially at small 2θ, with increasing Ga³⁺ concentration.

Phase Identification and Compositional Homogeneity (EMPA)

BSE images of polycrystalline chips made with the EPMA are shown in Figure 3. Examination reveals only garnet and no other phases for compositions from x_int = 0.08 up to x_int = 0.54. Garnet crystal diameters are ∼10 μm. La₂Zr₂O₇ could be identified in the sample with x_int = 0.64 pfu and La₂Zr₂O₇ and LiGaO₃ in the sample with x_int = 0.84 pfu. The density of the various samples appears to increase with increasing Ga³⁺ content.

Figure 3.

BSE images of the various Li_7–3xGa_xLa₃Zr₂O₁₂ samples with x_int = 0.08–0.84. Only garnet crystals are observed from x_int = 0.08 to x_int = 0.54. The dark regions are holes in the surface of the sample. The orange circle shows the phase LiGaO₃, and green circles show La₂Zr₂O₇. The diameter of each total sample circle is 30 μm.

Chemical Composition (EMPA and ICP-OES)

The chemical analyses obtained using EMPA and ICP-OES measurements are reported in Tables 2 and 3 and shown in Figure 4. Ga, La, and Zr were measured by electron microprobe. Because Li cannot be measured by electron microprobe analysis, the Li₂O content of those syntheses that yielded only garnet was measured by ICP-OES.

Table 2. EMPA (Ga, La, Zr) and ICP-OES (Li) Results for Li_7–3xGa_xLa₃Zr₂O₁₂ with x_int = 0.08–0.84 in wt %.

xint	Ga2O3	Li2Oa	La2O3	ZrO2	total
0.08	0.73(4)	11.83	57.16(12)	29.79(35)	99.51(51)
0.16	1.83(8)	10.49	56.49(70)	29.88(35)	98.69(14)
0.24	2.78(8)	10.42	56.57(23)	29.63(35)	99.40(50)
0.36	4.31(10)	9.90	55.86(57)	29.11(35)	99.18(10)
0.54	6.15(4)	9.06	55.91(19)	28.59(35)	99.71(33)
0.64	6.92(11)	8.37b	54.98(78)	28.65(17)	100.00
0.84	8.33(9)	7.80b	54.65(73)	28.29(17)	100.00

^aMeasured by ICP-OES. Data were normalized to 100 wt % for the elemental oxides. Values in brackets are the standard deviation based on 20 point analyses.

^bValues were calculated according to [Li₂O] = 100 – [Ga₂O₃] – [La₂O₃] – [ZrO₂].

Table 3. Crystal Chemical Formulae of the Li_7–3xGa_xLa₃Zr₂O₁₂ Samples^a.

xint	Ga3+	Li+	La3+	Zr4+
0.08	0.06(1)	7.08	2.93(1)	2.02(2)
0.16	0.15(1)	6.50	2.96(3)	2.05(3)
0.24	0.23(1)	6.48	2.93(2)	2.04(2)
0.36	0.36(1)	5.93	2.94(1)	2.01(3)
0.54	0.53(2)	5.38	2.96(3)	1.99(2)
0.64	0.60(2)	4.82	2.96(1)	2.00(1)
0.84	0.72(1)	4.53	2.94(1)	1.98(2)

^aCalculated using the values given in Table 2 on the basis of 12 oxygen atoms per formula unit [pfu].

Figure 4.

Plot of measured vs intended compositions for Li_7–3xGa_xLa₃Zr₂O₁₂ with x_int = 0.08–0.84. The black lines correspond to intended garnet compositions, the blue lines to the EMPA measured values, and the red line to the ICP-OES measurements. The gray area corresponds to those bulk compositions where non-garnet phases are present in the synthetic product.

Crystal Chemical Formula

The measured Ga³⁺ concentrations of the various single phase garnet samples (x_obs) are close to the nominal values of the starting material: x_int= 0.08 → x_obs = 0.06(1), x_int = 0.16 → x_obs = 0.15(1), x_int = 0.24 → x_obs = 0.23(1), x_int = 0.36 → x_obs = 0.36(1), and x_int = 0.54 → x_obs = 0.53(2). When additional non-garnet phases are present, the Ga³⁺ content in LLZO is lower than that in the starting material: x_int = 0.64 → x_obs = 0.60(2) and x_int = 0.84 → x_obs = 0.72(1). The Li content measured with ICP-OES (Li_obs) agrees satisfactorily with the Li content (Li_theo) of the starting material: x_int = 0.08, Li_theo = 6.82 → Li_obs = 7.08; x_int = 0.16, Li_theo = 6.55 → Li_obs = 6.50; x_int = 0.24, Li_theo = 6.31 → Li_obs = 6.48; x_int = 0.36, Li_theo = 5.92 → Li_obs = 5.93; and x_int = 0.54, Li_theo = 5.41 → Li_obs = 5.38. For more Ga-rich samples having additional non-garnet phases, the Li content was calculated based on [Li₂O] = 100 – [Ga₂O₃] – [La₂O₃] – [ZrO2] and gives for x_int = 0.64, Li_theo = 5.08 → Li_obs = 4.82(7), and x_int = 0.84, Li_theo = 5.41 → Li_obs = 4.53(5).

Figure 4 shows that measured La and Zr contents are close to their stoichiometric values of 3.0 and 2.0, respectively, with a maximum deviation of ∼2% pfu (considering the standard deviations). The calculated chemical formulas of the various garnet solid solutions using the EMPA and ICP-OES results are

The chemical formulas of the garnet solid solutions with additional non-garnet phases in the synthetic products are

We note that the La³⁺ content in all LLZO samples appears to be slightly too low. This may possibly reflect a systematic analytical artifact related to the La standard used or in the correction procedure. Other reasons could be a possible substitution of La³⁺ by Li⁺ or Zr⁴⁺ at the dodecahedral site.

⁷¹Ga MAS NMR Spectra

Spectra for the samples with x_int = 0.16, 0.24, 0.36, 0.54, 0.64, and 0.84 are shown in Figure 5. ⁷¹Ga (spin quantum number I = 3/2, natural abundance 39.6%) is a quadrupole nucleus; the interaction of its rather large quadrupole moment (Q = 10.7 × 10^–30 m²) with the surrounding electric field gradient results in a central line that is perturbed by second-order effects. Their shape can be simulated well with a single set of NMR parameters, namely an isotropic chemical shift, δ, of 244(2) ppm, a quadrupolar coupling constant, C_Q, of 4.0(2) MHz, and an asymmetry parameter, η_Q, of 0.46(3). The spectrum of the sample with x_int = 0.84, which has a slightly different line shape than those in the spectra of the other garnets (Figure 5), also has a NMR resonance with the major component at δ = 244(2) ppm. The spectra for samples with Ga³⁺ contents, x_int ≥ 0.36, show the best signal to background ratios.

Figure 5.

⁷¹Ga MAS NMR spectra of Li_7–3xGa³⁺_xLa₃Zr₂O₁₂ garnets with x_int = 0.08–0.84. Asterisks (*) mark spinning side bands. The spectra on the right are shown over a smaller range of chemical shift values. The spectrum shown in red is simulated for the sample with x_int = 0.36.

We interpret these spectra, as well as that for x_int = 0.24, as indicating that Ga³⁺ is located at a single structural site in LLZO. The observed δ values indicate Ga³⁺ with 4-fold coordination.²¹ The rather large η_Q value indicates that Ga³⁺ is located at a structural site with no axial symmetry. This might exclude the special crystallographic tetrahedrally coordinated site 24d in garnet with site symmetry −4 from consideration. It should be noted, however, that the local symmetry around Ga³⁺ could be lower than that determined by diffraction measurements. The interpretation of the spectrum of the sample with x_int = 0.16 is difficult because the single resonance could be assigned to a small amount of Ga³⁺ located at a site with a smaller C_Q. The spectrum of the sample with x_int = 0.84 could indicate the presence of two Ga-bearing phases. The major phase is clearly Ga-bearing LLZO and the second possibly minor LiGaO₂. The latter was identified by XRPD measurements. LiGaO₂ has similar NMR parameters of δ = 242(2), C_Q = 3.89(5), and η_Q = 0.37(2) and line shape as Ga-bearing LLZO.²¹ This spectrum could represent the superposition of a garnet phase and LiGaO₂. A similar situation may be shown in the spectrum with x_int = 0.64, although no LiGaO₂ was detected by XRPD or EPMA.

Discussion

The main goal of this study is to investigate the degree of solid solution and crystal-chemical properties of Ga-bearing LLZO garnet. To understand our discussion, we provide a short description of the crystal structure of cubic LLZO garnet.

Li₇La₃Zr₂O₁₂ with cubic symmetry Ia-3d has O^2– ions that are located at general crystallographic positions, 96h. They form an oxygen-ion framework with interstices occupied by the La³⁺ at the 8-fold coordinated position 24c (point symmetry 222) and by Zr⁴⁺ at the 6-fold coordinated position 16a (point symmetry −3). Li⁺ is partially located at the 4-fold coordinated 24d position (point symmetry −4) as well as the 6-fold coordinated 48g positions (point symmetry 2) and a “4-fold” coordinated 96h position (point symmetry 1). The latter two sites are empty in the conventional garnet structure.²² The crystal structure is illustrated in Figure 6.

Figure 6.

Crystal structure of cubic LLZO. The blue dodecahedrally coordinated sites (24c) are occupied by La³⁺ and the green octahedrally coordinated sites (16a) by Zr⁴⁺. The yellow spheres correspond to tetrahedrally coordinated sites (24d), the orange spheres to octahedrally coordinated sites (48g) and the purple to “4-fold” coordinated sites (96h). These three latter sites can potentially be occupied by Li.

Allen et al. were the first to study Ga³⁺ incorporation in Li-oxide garnet.²³ They investigated the conductivity behavior of a garnet of composition Li_6.75La_3.00Zr_1.75Ta_0.250_12.00 and two compositions with Ga³⁺ or Al³⁺ doping. The samples were prepared from a coprecipitated precursor and calcinated by solid-state sintering. Garnet without Ga³⁺ or Al³⁺ showed a slightly higher Li-ion conductivity, σ, at room temperature (σ = 8.7 × 10^–4 S·cm^–1) than garnet of composition Li_6.15La_3.00Zr_1.75Ta_0.25Ga_0.20O_12.00 (σ = 4.1 × 10^–4 S·cm^–1) and Li_6.15La_3.00Zr_1.75Ta_0.25Al_0.20O_12.00 (σ = 3.7 × 10^–4 S·cm^–1). They proposed that Ga³⁺ mainly occupies the 96h site, whereas Al³⁺ is located at 24d based on considering the work of Geller et al., who reported that Ga³⁺ preferred 6-fold coordination in garnet (16a).²⁴ Howard et al. synthesized cubic garnet of composition Li_5.50Ga_0.50La₃Zr₂O₁₂ using solid-state sintering methods.¹⁷ A ⁷¹Ga MAS NMR spectrum showed a single resonance with a chemical shift of ∼221 ppm. They proposed, in contrast to Allen et al., that Ga³⁺ occupies the tetrahedrally coordinated special crystallographic 24d site. A third investigation of Ga-bearing LLZO garnet was undertaken by El Shinawi and Janek.¹⁸ Here, a series of Li_7–xGa_xLa₃Zr₂O₁₂ garnets, synthesized using sol–gel methods, with x = 0.1, 0.2, 0.3, 0.4, 0.5, and 1.0, were prepared. XRPD analysis indicated the presence of additional non-garnet phases for LLZO compositions with x = 0.1, 0.2, 0.5, and 1.0 Ga³⁺ pfu. They measured only small Ga³⁺ contents directly in garnet. Instead, most Ga³⁺ was concentrated at grain boundaries. The non-garnet phases were: (i) La₂Zr₂O₇, which was present in compositions with x = 0.1, 0.2, 0.5, and 1.0 Ga³⁺ pfu, and (ii) LiGaO₂, together with another La³⁺- or Zr⁴⁺-containing phase, for samples with x > 0.5 Ga³⁺ pfu. In terms of the garnet, they observed increasing ion conductivity with increasing Ga³⁺ content.

Our work demonstrates that single phase Ga-bearing LLZO can be synthesized with up to x = 0.53 Ga³⁺ pfu. A Ga³⁺ content of up to x = 0.72 Ga³⁺ pfu in garnet can be obtained, but herein it is associated with small amounts of additional non-garnet phases. Our results differ from the unspecified minor amount of Ga³⁺ incorporated in LLZO as observed by El Shinawi and Janek.¹⁸ We think this reflects the different sample preparation and synthesis route. For example, in the case of the synthesis of Al-bearing LLZO it has been shown that LiAlO₂ can occur at grain boundaries or that the Al³⁺ is incorporated in the garnet, depending upon the exact synthesis conditions.²⁵

Previous studies of Ga-bearing Li-oxide garnet have proposed that Ga³⁺ can reside at 24d¹⁷ or at 96h²⁴. We think that the large η_Q value that is greater than 0.40, together with the relatively large ionic radius of Ga³⁺ (r^[6) = 0.62 Å),²⁶ argues for local “4-fold” coordination. We think that this occurs at the 96h site (site symmetry: 1 ⇒ η_Q ≠ 0). Both observations argue against the proposal that Ga³⁺ is located at the “standard garnet” tetrahedrally coordinated 24d site (site symmetry: −4 ⇒ η_Q = 0).

To understand the behavior of Ga³⁺ better, one can also consider the case of Al³⁺ in LLZO garnet. The latter are better understood in terms of their crystal chemistry, and ²⁷Al NMR spectra and can be used as a guide to interpret our ⁷¹Ga NMR results. It has been proposed that a relationship between ²⁷Al and ⁷¹Ga in NMR spectra exists for δ as is given by²⁷

Taking δ(⁷¹Ga) ≈ 246 ppm for LLZO from our work, we calculate 88 ± 5 ppm for δ(²⁷Al). An ²⁷Al NMR resonance with this chemical shift value has been measured for Al-bearing LLZO.^4,5,7,8 It was assigned to Al³⁺ at the 96h site by DFT calculations.²⁸ This analysis also argues, albeit indirectly, for the presence of Ga³⁺ at 96h in Li_7–3xGa³⁺_xLa₃Zr₂O₁₂ garnets.

Author Contributions

All authors have given approval to the final version of the manuscript.

The research was supported by Austrian Science Fund (FWF): project number P25702.

The authors declare no competing financial interest.