The high-entropy garnet LLZTTSO was synthesized by conventional solid-state reaction. The starting materials Li₂CO₃, La(OH)₃, ZrO₂, TiO₂, Ta₂O₅, and Sb₂O₅ were mixed in stoichiometric amounts with 5 wt% Li₂CO₃ in excess. One batch of the synthesis is to obtain around 5 g target products. The starting powder was ball-milled in a ZrO₂ milling jar filled with hexane and ZrO₂ beads for 2 h at a rotation speed of 300 rpm in a planetary milling machine (Fritsch Pulverisette). Afterwards, the powder was dried at 80°C to evaporate hexane. After collected through a 300-mesh sieve, the dried powder was placed on a gold sheet inside an alumina crucible for calcination. The calcinations were performed in air at various temperatures (800°C, 850°C, and 950°C) for 12 h. After cooling down to 400°C in the furnace, the crucibles were transferred into a drying chamber for further cooling. After the temperature reached room temperature, the calcined powder was ball-milled again in hexane at a rotation speed of 300 rpm for 2 h. After dried at 80°C, the powder went through a 300-mesh sieve and was stored in desiccator. The calcined powder was pressed to form pellets at 13.7 MPa by using uniaxial hydraulic press, and the pellets were subsequently pressed at 150 MPa in an isostatic press. The obtained pellets were sandwiched between two gold sheets and sintered in an alumina crucible. The sintering was performed in air at 1,050°C for 2, 6, or 12 h. After cooling down to 400°C in the furnace, the crucibles were transferred into a drying chamber for further cooling. After the temperature reached room temperature, the sintered pellets were collected and stored in desiccator.

Serving as the control samples, garnets Li₇La₃Zr₂O₁₂ (LLZO), Li₇La₃ZrTiO₁₂ (Ti-LLZO), Li₆La₃ZrTaO₁₂ (Ta-LLZO), and Li₆La₃ZrSbO₁₂ (Sb-LLZO) were prepared in the same way. The calcination and final sintering were performed at 850°C for 12 h and 1,050°C for 12 h, respectively.

The samples were characterized for their phase purities by XRD on a Bruker D4 Endeavor device (Bruker, Germany) using Cu Kα radiation equipped with a 1D detector LynxEye. The qualitative phase analyses were done using Panalytical’s HighScore software, and LeBail profile fitting for lattice parameters of the investigated samples were carried out using the software Jana2006 (Petříček, Dušek, and Palatinus, 2014) based on the structure model in the cubic space group of Ia-3d (ICSD 158372), which is described by Murugan et al. (Murugan et al., 2007). The quantitative phase analysis was carried out using the software PowderCell (Kraus and Nolze, 1996). The apparent densities of sintered pellets were determined by Archimedes’ Method. For microstructural investigation on cross-section, samples were embedded in EpoFix epoxy resin (Struers, Germany) and mirror-polished. Back-scattered electron (BSE) images and energy-dispersive X-ray spectroscopy (EDS) analysis were taken by a scanning electron microscope (SEM) (TM3000 tabletop microscope, Hitachi).

After polished on 400, 800, 1,500, and 4,000 grid sandpapers, the sintered LLZTTSO pellets were transferred into an Ar-filled glovebox. The pellets were polished again on 4,000 grid sandpaper to remove possible impurities. Two lithium metal foils with a diameter of 6 mm were pressed onto both sides of the pellets. Such Li|LLZTTSO|Li symmetric assembly was then sealed in a pouch bag with two Ni bars as current collectors for electrochemical characterization.

Electrochemical impedance spectroscopy (EIS) was measured in the frequency range from 10 MHz to 1 Hz with an electrical field perturbation of 50 mV using an impedance analyzer by Novocontrol Technologies, or in the frequency range from 1 MHz to 0.1 Hz with an electrical field perturbation of 10 mV using a frequency response analyzer by Solartron Analytical. A fitting of the impedance spectrum was conducted in the software ZView (Scribner). For the determination of the critical current density (CCD) of LLZTTSO, a VMP-300 multi-potentiostat (BioLogic) combined with a climate chamber (Vötsch VT4002EMC) was used. The current density was increased stepwise from 25 μA cm⁻²–300 μA cm⁻² with an interval of 25 μA cm⁻². The stripping/plating process was controlled by limiting the areal capacity of 0.1 mAh cm⁻², and repeated 5 times for each step.

First-principle density functional theory (DFT) calculations were performed to obtain the theoretical lattice parameters and density of garnet structures, information essential for the analysis of measured data. These calculations utilized the gpu-enabled 7.2 version of plane-wave Quantum Espresso code (Giannozzi et al., 2009; Giannozzi et al., 2020). We employed ultrasoft pseudopotentials (Vanderbilt, 1990) and the PBEsol exchange-correlation functional (Perdew et al., 2008), which have been shown to give good structural parameters for cathode materials in lithium-ion batteries (Kowalski et al., 2021; Ting and Kowalski, 2023). The pure cubic phase-LLZO atomic bulk structure was modeled with a space group of Ia-3d and a unit cell formula of Li₅₆La₂₄Zr₁₆O₉₆.

The spatial distribution of elements within the multi-doped LLZO was modeled with the Special Quasirandom Structure (SQS) method (Zunger et al., 1990), implemented through the Alloy Theoretic Automated Toolkit (ATAT) package (van de Walle et al., 2013). This approach creates a unit cell with an atomic arrangement that mimics the disorder found in a fully random solid solution. A plane-wave cutoff energy of 50 Ry and a Monkhorst-Pack 4 × 4 × 4 k-point mesh were employed to ensure convergence of the results (Monkhorst and Pack, 1976). All structures underwent full optimization, adhering to a convergence threshold of 10^–5 Ry and 10^–4 Ry/a₀ (where a₀ is the Bohr radius) for energy and forces, respectively.

In the case of ideal mixing of n species, the configurational entropy per mole, S _conf , was calculated using the Stirling’s approximation: S c o n f = − R ∙ ∑ i = 1 n x i ∙ ⁡ ln ⁡ x i , where R is the universal gas constant, and x _i the concentration ratio of element i.

When considering garnet structures, the formula for configurational entropy was adapted to include sublattices: S c o n f = − R ∙ ∑ s m s ∙ ∑ i x i , s ∙ ⁡ ln ⁡ x i , s , where m _s denotes the multiplicity of a sublattice s, and x _{i,s} represents the mole fractions of species i on the sublattice s sites.

We have chosen Ta⁵⁺, Sb⁵⁺, and Ti⁴⁺ as doping cations on the Zr site due to the commonality of Ta⁵⁺ as a dopant in most investigated Li-garnets, the similar ionic radius of Sb⁵⁺ (0.62 Å) to Ta⁵⁺ (0.64 Å), and the known ability of Ti⁴⁺ to suppress lithium dendrite formation (Gao et al., 2021; Zhu et al., 2021). Deviating from the equimolar Li₆La₃Zr_0.5Ti_0.5Ta_0.5Sb_0.5O₁₂ composition, we have slightly reduced the Ti content from 0.5 per formula unit (pfu) to 0.3 pfu in LLZTTSO. This adjustment is based on the stability of Ti⁴⁺ within the garnet structure against Li metal (Shao et al., 2017). LLZTTSO powders were synthesized at different calcination temperatures (800°C, 850°C, and 950°C). XRD results (Figure 1A) indicate the formation of a cubic garnet phase at 800°C, accompanied by intermediate products such as LaTiO₃ and La₂Zr₂O₇ in the powder. The phase formation of LaTiO₃ could be attributed to the reduction of La₂Ti₂O₇ induced by Li₂CO₃ (Zhang et al., 2022). With the increased calcination temperature, the quantity of these intermediate products diminishes, and the powder calcined at 950°C exhibits the cubic garnet phase exclusively. Subsequently, all three calcined powders were pelletized and sintered at 1,050°C. As depicted in Figure 1B, pure cubic garnet phases are observed in all samples after sintering regardless the dwell time (2, 6 or 12 h) and the purity of the calcined powders. The sharpening reflections of sintered pellets, compared to the broader reflections of calcined powder, also indicate the increase in crystallinity. In comparison, undoped LLZO and Ti-LLZO prepared under the same condition exhibit a tetragonal structure, while Ta- and Sb-LLZO are presented in the cubic form (Figure 1C). This suggests that the doping by aliovalent element on Zr site stabilize the cubic phase, consistent with the finding by Logéat et al. (Logéat et al., 2012). Profile fitting of the XRD pattern of LLZTTSO (Figure 1D) reveals a lattice parameter of a = 12.87239 (13) Å, in good agreement with the predicted value by the computational method (12.877 Å), affirming the successful synthesis of LLZTTSO (Table 2). Additionally, the calculated configurational entropy values are 3.71R, 5.84R, and 7.10R for undoped LLZO, mono-doped LLZO (e.g., Ta-LLZO and Sb-LLZO), and LLZTTSO, respectively. It is noteworthy that for undoped LLZO, the cubic phase exhibits a theoretical configurational entropy of 3.71R per mole of formula unit, in contrast to the tetragonal phase, where the configurational entropy is 0, attributable to the complete occupation of lattice sites. With the increase of configuration entropy, the tetragonal phase turn into cubic phase in the samples. We postulate that this high configurational entropy contributes to stabilize the cubic phase at elevated temperatures.

The LLZTTSO pellets prepared from powder calcined at 800°C and 850°C have similar relative densities above 70%, whereas those made from powder calcined at 950°C have much lower relative densities below 70% (Table 3). A dwell time of 6 h is found optimal for achieving the highest density, and an extension to 12 h results in a decrease in density. The LLZTTSO pellet calcined at 850°C and subsequently sintered at 1,050°C for 6 h attains the highest relative density of 80.6%. In contrast, both Ta-LLZO and Sb-LLZO exhibit relative densities lower than 60%. This discrepancy underscores the superior sintering performance of high-entropy garnet LLZTTSO compared to mono-doped garnets, suggesting that the introduction of Ti in this system may enhance the sintering process. To prevent Al³⁺-diffusion from the alumina crucible into the pellets, gold sheets are utilized as sintering substrates in our processing. However, the sintering temperature is constrained by the melting point of gold, which is 1,064°C. Consequently, sintering is performed only at 1,050°C, a temperature that may not be sufficiently high to fully densify the samples. The use of platinum as a substrate, with its significantly higher melting point of 1768°C, could be a more effective option for obtaining dense pellets. Alternatively, advanced sintering technologies, such as field-assisted sintering technique (Bram et al., 2020) or ultrafast high-temperature sintering (Wang et al., 2020b) utilizing carbon materials as substrates, are also viable approaches for preparing high-entropy garnets.

Figure 2 depicts BSE-SEM images on the fracture surface of the sintered LLZTTSO pellets, providing insights into the microstructure and highlighting the impact of calcination temperature and sintering time on the material. All LLZTTSO pellets exhibit noticeable porosity, consistent with the relative density results obtained. Garnet grain sizes range from 2 to 4 µm. Pellets produced from the powder calcined at 800°C and 850°C (Figures 2A–D) display distinct intergranular grain boundaries and pores along grain junctions. Some densified regions are already evident, indicating a progression from an intermediate to a final sintering stage. In contrast, pellets from powders calcined at 950°C (Figure 2E) are in an intermediate sintering stage, displaying continuous pore channels through the pellets. This suggests that LLZTTSO powder calcined at lower temperatures exhibits superior sinterability compared to that calcined at higher temperatures. Comparatively, Ta-LLZO (Figure 2F) exhibits a microstructure similar to LLZTTSO, transitioning from the intermediate to the final sintering stage. On the other hand, Sb-LLZO (Figure 2G) shows small necks at particle junctions and continuous pore channels through the pellets, indicating the transition from initial to intermediate sintering stage. The microstructure of Ti-LLZO (Figure 2H) differs significantly from all other samples, with particles undergoing coarsening rather than densification, resulting in larger grain sizes up to 10 µm. The intergranular spaces are filled with side phases (dark regions in the BSE-SEM image), potentially corresponding to the LaTiO₃ phase detected by XRD. This Ti-containing phase is also detected in the LLZTTSO powder calcined at 800°C or 850°C, and may contribute to sintering, possibly through a reactive sintering mechanism along with another side phase, La₂Zr₂O₇ (Zheng et al., 2022). This observation might explain the higher relative density of LLZTTSO obtained from the powders calcined at 800°C or 850°C compared to those calcined at 950°C. EDS element mapping of LLZTTSO (Figure 2I) shows homogeneous distribution of La, Zr, Ta, Sb, and Ti within the investigated region, aligning with the characteristic features of high entropy materials.

The electrochemical properties of the LLZTTSO sintered pellets prepared from powder calcined at 850°C are evaluated. The Nyquist plot of LLZTTSO sintered at 1,050°C for 6 h (Figure 3A) exhibits two semicircles. An equivalent circuit consisting of two parallel elements of resistor (R) and constant phase element (CPE) is used to fit the two semicircles. The first semicircle at high frequency range having a capacitance of 4.89 × 10⁻¹¹ F represents the bulk contribution of LLZTTSO, whereas the second semicircle at medium to low frequency having a capacitance of 4.22 × 10⁻⁸ F represents the grain boundary contribution of LLZTTSO. The impedance contribution of Li/LLZTTSO-interface is missing. A possible explanation can be that this part impedance is buried in the second semicircle, as the fitting result of the second CPE shows large error, especially in the capacitance, and it is also difficult to distinguish them by simply applying another parallel (R) (CPE) element. From these results we obtain the bulk and total conductivity of LLZTTSO at 25°C as 0.099 and 0.088 mS cm⁻¹, respectively. In addition, the sample sintered from the 950°C calcination powder also has a bulk conductivity of 0.098 mS cm⁻¹ (Supplementary Figure S3), but a lower total conductivity of 0.016 mS cm⁻¹ due to the higher porosity. As shown in Figure 3B, the total ionic conductivity of LLZTTSO sintered at 1,050°C for 12 h is 0.046 mS cm⁻¹ at 25°C, surpassing the total ionic conductivity of Ta-LLZO and Sb-LLZO (0.023 and 0.0053 mS cm⁻¹, respectively). This conductivity enhancement can be attributed to the higher density of LLZTTSO achieved through the high-entropy strategy. Figure 3C presents the Arrhenius plots of LLZTTSO pellets sintered at 1,050°C for different dwell time (e.g., 6 h or 12 h). The sample with a dwell time of 6 h exhibits higher conductivity and a lower activation energy of 0.497 eV, while the sample with dwell time of 12 h has a higher activation energy of 0.507 eV. The obtained activation energy values, though higher than those reported for other HEGs (Fu and Jacob, 2022; Stockham et al., 2023), may be influenced by the low density of LLZTTSO resulting from the relatively low sintering temperature and the consequent formation of suboptimal grain boundaries (Naqash et al., 2019). It is noteworthy that the impact of the local structure created by different dopants is not addressed in this study, which could contribute to the observed increased energy barrier for Li⁺ diffusion.

Subsequently, the LLZTTSO pellet with the highest ionic conductivity underwent the critical current density test (Figure 4A). The capacity-controlled CCD measurement at 25°C, with the capacity of Li stripping/plating limited to 0.1 mAh cm⁻² for each polarization step, reveals flat plateaus for the current densities smaller than 0.1 mA cm⁻², indicating favorable Li plating/stripping behavior. At 0.125 mA cm⁻², the polarization curve increases slightly at the end stage of each step, suggesting possible void formation at the Li/LLZTTSO interface. Despite void formation, the measured polarization voltages remain constant within the cycling steps with the same current densities, underscoring the highly reversible void formation and refilling process. A soft short circuit occurs at 0.30 mA cm⁻², with the highest reached current density before short-circuit being 0.275 mA cm⁻². The impedance spectra in Figure 4B reveal that the first semicircle at high-to-medium frequency range, representing the solid electrolyte, remains unchanged after each cycling step, indicating the robust stability of LLZTTSO against Li metal. In contrast, the second semicircle at medium and low frequency ranges, representing the grain boundary and Li/LLZTTSO-interface, increases, suggesting the possible Li filament formation at the grain boundary and void formation at the Li/LLZTTSO-interface after cycling. Notably, no interfacial modification on LLZTTSO was performed prior to attaching Li metal, and the Li metal was not even molten to improve the interface. Considering the high porosity of the LLZTTSO sample, the achievement of the high CCD of 0.275 mA cm⁻² is particularly noteworthy.