Introduction

All-solid-state rechargeable lithium ion batteries using oxide-based solid electrolytes have the potential to drastically improve the high energy, high power and safety of current lithium-ion batteries1,2. Thin-film type solid-state batteries have been prepared using thin film electrodes (micron- or submicron-order) prepared by physical vapor deposition approaches, including sputtering and pulsed laser deposition3,4. They have been commercialized and shown to be capable of >10,000 charge–discharge cycles5. To further increase the energy density of batteries, many researchers are currently focusing on bulk-type solid-state batteries. However, these batteries are known to have key performance problems. In particular, two issues are directly connected with the power density of batteries: the bonding of solid-solid hetero-interface between electrode and solid electrolyte, and thinning of the solid electrolyte separator5,6,7,8.

Various oxide electrolytes, such as perovskite-type Li3xLa2/3−x□1/3−2xTiO3 (LLTO), LISICON, and NASICON have been widely investigated. In particular, garnet-type Li7−x La3A2−x 4+B x 5+O12 (A = Zr, B = Nb, Ta) derivatives are considered promising candidate materials due to their high Li+ conductivity (around 10−4 S cm−1 at room temperature) and wide electrochemical window. They are neither oxidized nor reduced in a wide voltage range9,10,11,12,13. The control of balance in the Li+-occupying sites of tetragonal-24d/octahedral-96h is found to be primarily responsible for both the Li+ conductivity and stability under air moisture. Furthermore, Narayanan et al. demonstrated that incorporating external defects, such as replacing Y with Nb (Li5+2xLa3Nb2−xYxO12), enhanced the Li+ conductivity by two orders of magnitude in Li5La3Nb2O12 14.

It is generally believed that practical all-solid-state lithium ion batteries should ideally be fabricated by a solid-phase process for achieving dense solid interfaces. Since the architectures at interface, including both material density and purity, strongly affect the electrochemical performance and interfacial resistance, we need to consider how to bond interfaces of polycrystalline ceramic powders while suppressing the side reactions that increase the interfacial resistance15,16. Existing literatures on solid-solid homo- and heterojunction formation suggest that lowering the reaction temperature is effective for suppressing the sub-phase formation, promoted by the introduction of a buffer layer into the interface8 or using new discontinuous heating processes5. However both these conventional and new heating process under historical powder-based process often have technical limitations on the thinning of dense sintering bodies, as comparing to that of vacuum phase processing. Since the densification reaction is caused by diffusion of chemical species in solids based on the chemical potential gradient formed at the boundary of the contact interface between individual particles, the filling of the raw material powder closely in a crucible at the preliminary forming stage before sintering effectively form a dense sintered body densely. Furthermore, the use of raw materials having a non-uniform shape also makes it difficult to effectively fill the voids.

Very recently, solid electrolyte thin films, fabrication by using pulsed laser deposition (PLD)17,18, radio-frequency magnetron sputtering19, sol-gel process20, and aerosol deposition21 have been reported. Even though it was expected that such solid electrolyte thin film provides low electrical resistance and increasing volumetric energy density for all-solid-state battery, their lithium ion conductivities at room temperature were in the range of 10−7–10−5 S·cm−1, which is nearly two digits lower than sintered pellets samples. These film fabrication methods are efficient for fabricating uniform film and controlling the film thickness, however in some cases, it is difficult to control elementary composition and microstructures. Especially, except for epitaxial growth on a single crystal substrate18, there is no effective way for controlling the crystal growth orientation and grain boundary structures. Moreover, increasing substrate temperature during deposition and/or post-annealing should be needed to obtain well-crystallized films. Since high temperature treatments may lead to undesired reactions at the interface or uncontrolled diffusion between electrode and solid electrolyte, these methods are not recommended in some cases for fabricating all-solid-state batteries.

Based on the above considerations, here we demonstrate the formation of cubic phase stoichiometric Li5La3Nb2O12 crystal layers that are less than 30-μm thick, via the conversion of ultra-thin Nb substrate in a LiOH flux. We further discuss the reaction mechanism and crystallographic characteristics related to the crystal layer formation based on cross-sectional electron microscopic analysis. In addition, heterojunction formation between Li5La3Nb2O12 and LiCoO2 ceramics (which is the most popular cathode active material) was performed through a similar approach.

Results

Growth of Li5La3Nb2O12 crystal layer

The Li5La3Nb2O12 crystal layers were prepared on a Nb substrate by the flux growth method using a LiOH flux, in which LiOH·H2O and La2O3 powders reacted with the Nb substrate. Time-dependent XRD measurements were performed. As shown in Fig. 1, the formation of Li5La3Nb2O12 was initiated at 500 °C for 1 min. The diffraction lines were assigned to cubic phase Li5La3Nb2O12, perovskite LiLa2NbO6, and Nb, respectively. Perovskite LiLa2NbO6 is considered an intermediate phase which lacks Li and La compared to the stoichiometric composition of Li5La3Nb2O12. In fact, there are no reports on the formation of stable LiLa2NbO6 phase during the synthesis of Li5La3Nb2O12. Neither is the LiLa2NbO6 phase found in the ternary phase diagram of Li2O-La2O3-Nb2O5 system22. We further carried out computational studies to predict the LiLa2NbO6 phase formation in Li2O-La2O3-Nb2O5 system under various temperatures and pressures. As shown in Fig. 2 (a),(b), the LiLa2NbO6 phase was not formed when the starting materials were mixed in either stoichiometric or non-stoichiometric compositions. All these results indicate that the LiLa2NbO6 phase is not thermodynamically stable.

Figure 1
figure 1

Time-dependent XRD patterns of the Nb substrate during reaction in a molten LiOH flux with La2O3 at 500 °C in air: (a) 10 min, (b) 60 min, and (c) 600 min.

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Figure 2
figure 2

Phase diagram of Li-La-Nb-O system with respect to the chemical potential of Li and temperature with different molar ratios of La/Nb: (a) La/Nb = 1.5 and (b) La/Nb = 2.

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The formation of Li5La3Nb2O12 progressed with increasing holding time. The cubic phase Li5La3Nb2O12 was obtained as a single phase after 10 h. It is interesting to note that the Li5La3Nb2O12 phase was the major product during the early stages of the reaction, despite the unreacted La2O3 and LiOH remaining in the flux. Furthermore, no diffraction pattern assignable to niobium oxides such as Nb2O5 was detected during the growth process. In contrast, in-situ XRD measurement in atmosphere without using the LiOH flux revealed that the metal Nb substrate surface was oxidized to Nb2O5 at 500 °C (Fig. S1). Very similar results were observed in our previous reports that describe the formation of hollow-structured LiCoO2, LiMn2O4, and LiNi0.5Co0.2Mn0.3O2 from the conversion of electrodeposited Co, Mn, and stacked Ni/Co/Mn dots in molten salts at high temperatures, respectively23,24. Based on these results, the oxide formation on the Nb substrate could limit the reaction kinetics, since the amount of dissolved oxygen is normally small in the molten salts.

Next, we carried out time-dependent SEM observations coupled with XRD measurements to further understand the reaction and growth mechanisms (Fig. 3). Two different kinds of morphologies, the spirally-grown flat shape and the 3D polyhedral shape, were formed on the Nb substrate after heating at 500 °C for 1 min in molten LiOH. The flat-shaped crystal layer developed laterally as the reaction continued, and the polyhedral crystals multiplied simultaneously. Finally, after 10 h, the surface of Nb substrate was completely covered with polyhedral crystals with well-defined faces. The individual polyhedral crystals have a wide range of diameters, with the mean diameter ~30 μm. The face angle analysis suggests that the crystal surface was dominantly surrounded by larger {211} and smaller {110} faces. Such crystallographic features dovetail with those of Li5La3Nb2O12 single crystals that were homogeneously grown from LiOH flux (with LiOH·H2O, La2O3, and Nb2O5 powders reacting in a crucible)25.

Figure 3
figure 3

Time-dependent SEM images of the Nb substrate during reaction in a molten LiOH flux with La2O3 at 500 °C in air: (a) as-purchased Nb substrate, after (b) 10 min, (c) 60 min, and (d) 600 min.

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Cross-sectional SEM observation revealed that the polyhedral crystals grew directly from the Nb surface (Fig. 4). There were no detectable defects such as voids, spaces, and twins at the interface. The spirally grown flat crystalline layer was hardly observed at the interface. This result strongly suggests the possible limiting reaction suggested above. If the formation of LiLa2NbO6 through the reaction of LiOH·H2O and La2O3 powders with Nb2O5 layer limits the whole reaction, LiLa2NbO6 and/or Nb2O5 layer should remain at the interface. Thus, the thickness of Li5La3Nb2O12 crystal layer will be determined by the initial thickness of the oxidized Nb layer prior to the reaction. Indicating that the self-diffusion rate of Nb is not much faster than the diffusion of O2 in the molten LiOH flux. If the self-diffusion rate of Nb is much faster than the diffusion of O2 in the molten LiOH flux, the anisotropic atomic motion at the boundary layer, which is a consequence of the different diffusion rates, will prompt the formation of voids and spaces at the interface.

Figure 4
figure 4

(a) Cross-sectional SEM image and (b-e) SEM-EDS elemental mapping of the Li5La3Nb2O12 crystal layer on Nb substrate: (b) SEM-image, (c) Nb, (d) La, and (e) O.

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Cross-sectional SEM observation also indicates that each individual crystal seems to connect to neighboring crystals through the formation of tilted grain boundaries. In order to characterize their 3D crystallographic orientation in the selected area near the grain boundaries, we performed cross-sectional TEM observations of the sliced Li5La3Nb2O12 crystal layer which was created using FIB-milling. The cross-sectional TEM images and SAED patterns are shown in Fig. 5(a). “L” and “R” in the diffraction patterns mean patterns observed from the left and right grains in the TEM image, respectively. All the images and diffraction patterns were taken from the same sample. These are images tilted 24.3°, with the horizontal arrow direction (the [001]* axis of R grain) in the diffraction pattern of the R region as the tilt axis. Therefore, the angle between these two directions can be estimated as 24.1°. The image and diffraction pattern shown on the right side are taken from the same position with 24.3° tilting around the [00 l] axis of the R region. The analysis of these diffraction patterns revealed that the [201] direction (in L grain) and the [110] direction (R grain) are almost in agreement. From the above observations, it became clear that the crystal orientation is aligned three-dimensionally in this crystal region. Figure 5(b) shows a stereo diagram based on a number of cross-sectional TEM observations for the FIB-milled Li5La3Nb2O12 crystal layers. Superimposed on it are the stereo diagrams for the case where the incident [211], [110], and [210] incidence as the poles from cross-sectional TEM observation. It can be seen that the crystal planes {120} and {112}, which appeared on the surface at each incidence angle, are close to each other and enclosed by the circle in the figure. This result suggests that there may be a direct correlation with crystal orientation of crystal habit which appears in different grains.

Figure 5
figure 5

(a) Cross-sectional TEM images and SAED patterns of FIB-milled thin Li5La3Nb2O12 crystal layer. “L” and “R” in the diffraction pattern mean diffraction patterns observed from the left and right grains in the TEM image, respectively. (b) A stereo diagram based on cross-sectional TEM observations of the sample.

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We have reported the Li+ conductivity of the sinter bodies prepared from the Li5La3Nb2O12 crystals of which it was grown from LiOH flux under same recipe described in this paper25. The Li+ conductivity was of 5 × 10−6 S·cm−1 at room temperature, as evaluated by conventional electrochemical impedance spectroscopy. Unfortunately, reproducible data on the Li+ conductivity for the Li5La3Nb2O12 crystal layers have not yet to acquire because any symmetrical cells, Li| Li5La3Nb2O12 crystal layer|Li for non-blocking geometry and Au | Li5La3Nb2O12 crystal layer |Au for blocking geometry were not obtained at this time. It is difficult to make free-standing film required for making symmetrical cells due to the strong adhesion strength to the Nb substrate. We are now going to demonstrate AC impedance measurement of the Li5La3Nb2O12 crystal layers by using micro-probe technique26. We will report our new findings near feature in elsewhere soon.

Molecular dynamics simulation to evaluate the lithium ion conductive characteristics at the tilted grain boundary of Σ3 (2–1–1) = (1–21)

A stoichiometric equilibrium atomic model was calculated by using MD simulation for understanding the atomic arrangement and determining the Li ion conductivity at the tilted grain boundary of Σ3 (2–1–1) = (1–21), as a one representative grain boundary model. Figure 6 displays the trajectories with respect to the available La (light brown), Nb (blue), O (red), and Li (yellow) crystallographic sites and calculated via MD simulations for a temperature of 1300 K and duration of 500 ps. Trajectories of the framework atoms revealed that there was hardly any migration of the La, Nb, and O atoms. In addition, Fig. 7 displays the radial distribution function (RDF) plots obtained for the Li-Li, La-La, Nb-Nb, and O-O interactions in the bulk and at the grain boundary, from the MD simulations conducted at 700 K and total duration of 500 ps. The results in Fig. 8 suggest no remarkable differences among the La, Nb, and O sites as compared to the Li atoms, indicating that only small atomic rearrangements were present at the crystallographic sites of the Σ3 (2–1–1) = (1–21) titled grain boundary model. Interestingly, the grain boundary formation energy was estimated as 0.23 J m−2, which is markedly smaller than that of cubic-Li7La3Zr2O12 (0.52 J m−2)27. It indicates that the tilted grain boundary represented by the Σ3 (2–1–1) = (1–21) models is one of the most stable grain boundaries in the Li5La3Nb2O12 system. This computationally predicted trend is consistent with the thermodynamically stable faces of the Li5La3Nb2O12 crystals grown from a molten LiOH flux25.

Figure 6
figure 6

Trajectories of the Li, La, Nb, and O framework atoms obtained for Σ3 (2–1–1) = (1–21) at a temperature of 1300 K.

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Figure 7
figure 7

RDFs for the Li, La, Nb, and O interactions in the bulk (black) and at the tilted grain boundary Σ3 (2–1–1) = (1–21) model (red): (a) Li-Li, (b) La-La, (c) Nb-Nb, (d) O-O, (e) La-Li, (f) Nb-Li, (g) O-Li, (h) Li-O, (i) La-O, and (j) Nb-O.

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Figure 8
figure 8

(a) Arrhenius plots of the Li+ conductivity calculated for isotropic 3D Li diffusion path in the bulk garnet Li5La3Nb2O12 along the a, b, and c axes. (b) Fitted Li+ conductivity at 300 K derived from the MSD analysis.

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Figure 8(a) describes the computationally predicted apparent Li+ conductivities of the bulk and the Σ3 (2–1–1) = (1–21) models, including the average and separate conductivities along the a, b, and c axes. It should be noted that the Li+ conductivities of the utilized grain boundary model included bulk conductivities, because of the presence of bulk regions in the model. The corresponding Li+ diffusion coefficients and conductivities at a specified temperature can be evaluated from the slopes of MSD plotted against time and the Nernst-Einstein equation, respectively. The values of the fitted Li ionic conductivity at 300 K, which were obtained from the Arrhenius plots for the models, are summarized in Fig. 8(b). The computationally predicted bulk Li+ conductivity is in good agreement with data in previous reports28. However, it was almost two orders of magnitude higher than the experimental value evaluated by electrochemical impedance spectroscopy for the pelletized samples.

The grain boundary conductivity in the cubic Li5La3Nb2O12 is lower than the bulk one, regardless of the orientations. In particular, the conductivities along the c-axis (perpendicular to the grain boundary) are the lowest, being one order of magnitude lower than the bulk value. To our best knowledge, this study reports for the first time that the conductivity along the direction perpendicular to the grain boundaries primarily contributes to the reduction in the total ion conductivity. Most previous electrochemical impedance spectroscopic studies of garnet-based solid electrolytes could not distinguish the tilted grain boundary contribution driven by atomic arrangements within the overall material resistance, thus underestimating the experimental bulk conductivity. Furthermore, the elemental substation of Nb with Zr, leading to form Li7La3Zr2O12 was known to enhance bulk Li+ conductivity through changing the Li+ occupancy at 24d/96 h sites12, we newly discovered that the substitution made significant degradation of the grain boundary conductivity at the Σ3 (2–1–1) = (1–21). Our molecular dynamics simulation to the Li+ conductivity in Li7La3Zr2O12 revealed that the fitted Li ionic conductivity at 300 K were ca. 38.1 mS·cm−1 in bulk and 0.7 mS·cm−1 in the grain boundary. The grain boundary conductivity decreased nearly three orders than that of bulk. It was quite different from the Li5La3Nb2O12 system. We believe our results here strongly suggest that the observed discrepancy between the experimental and computational Li+ conductivities may be attributed to the effect of the grain boundary resistance on the atomic arrangement.

Growth of Li5La3Nb2O12 crystal layer on LiCoO2 ceramics

We applied the same methodology to stack the Li5La3Nb2O12 crystal layer on LiCoO2 ceramics through the direct growth from the LiCoO2 surface. Sputtered thin Nb film was deposited prior to the growth, and was used as the Nb source instead of a metallic Nb substrate. The LiCoO2 ceramic surface turned to a brilliant color after the deposition. Time-dependent XRD holding at 500 °C reveals that the perovskite LiLa2NbO6 phase was dominantly formed during the initial stage of reaction (Fig. 9). This phase was sequentially transformed into cubic Li5La3Nb2O12 as the reaction time increased. The cubic Li5La3Nb2O12 phase with garnet framework was eventually obtained as a single phase after 10 h, without any sub-phase formation. Note that an excessively long reaction time was found to promote the formation of byproduct phases, such as Li0.5La2Co0.5O4, at the heterophase interface. This is thought to be due to the mutual diffusion of Co in LiCoO2 and La in Li5La3Nb2O12 at the interface. Time-dependent SEM observation was used to characterize the growth and development of Li5La3Nb2O12 crystal layer on the LiCoO2 surface. As shown in Fig. 10(a),(b), the initial surface morphology was drastically changed with increasing reaction time. Numerous polyhedral crystals having well-defined faces gradually covered the surface. Prolonged reaction time promoted the growth of the individual crystals, and their size distribution became simultaneously broader. These time-dependent crystal growth characteristics in molten LiOH flux strongly support that the crystal growth is driven by Ostwald’s ripening. The whole surface was covered by the Li5La3Nb2O12 crystal layer after 10 h (Figs 9(e) and 10(e)). However, further reaction caused voids to form on the crystal surface due to the Li7La3Nb2O12 phase formation. In addition, many large pin-holes were formed at the grain boundaries, driven by over growth of the Li5La3Nb2O12 crystal (Fig. 10(f)). Interestingly, the formation of pin-holes and the Li0.5La2Co0.5O4 phase occurred simultaneously.

Figure 9
figure 9

Time-dependent XRD patterns of LiCoO2 ceramic substrates: (a) as-purchased, (b) after Nb deposition, (c) held at 500 °C for 1 h, (d) 5 h, (e) 10 h, and (f) 20 h.

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Figure 10
figure 10

Time-dependent SEM images of LiCoO2 ceramic substrates: (a) as-purchased, (b) after Nb deposition, (c) held at 500 °C for 1 h, (d) 5 h, (e) 10 h, and (f) 20 h.

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Cross-sectional SEM combined with EDS mapping clearly showed that the elemental distribution in Co is very different from those of Nb and Zr (Fig. S2), meaning that the ultra-thin Nb film, sequentially formed Nb2O5 layer, and LiLa2NbO6 and Li5La3Nb2O12 crystal layers mitigated the sub-phase (Li0.5La2Co0.5O4) formation during the growth. M. Bitzer et al. reported that the formation of unwanted Li0.5La2Co0.5O4 phase at the LiCoO2/Li7Li3Zr2O12 interface of which it appears that La diffused from the Li7Li3Zr2O12 electrolyte into the LiCoO2 cathode during calcination. They further claimed that the Li0.5La2Co0.5O4 phase formation at the electrode/electrolyte interface resulted in significant Li+ conductivity fading29. We believe that the fabrication route which achieve the suppression of sub-phase formation at the hetero-interface will be an ideal avenue to produce thin and dense ceramic separators. In fact, no electrical short-cut was observed in the stacking structures of Li5La3Nb2O12 crystal layer and LiCoO2 ceramics after the deposition of In metal as a counter electrode (an anode).

Discussion

We have studied the direct growth of cubic Li5La3Nb2O12 and related compounds on solid substrates. The conversion of Nb substrate in molten LiOH flux formed crystal layers with well-defined faces, and each individual crystal is connected to neighboring ones. Cross-sectional TEM observation coupled with SAED pattern analysis implied the formation of tilted grain boundaries that are composed of [211], [110], and [210] faces. We further found that the ultra-thin Nb film naturally mitigates sub-phase formation at the interface during the growth process, since the formation of niobium oxides on the substrate limits the reaction kinetics. We believe that our approach having robustness against side reactions at the interface could possibly lead to the production of ideal ceramic separators with a thin and dense interface. The LiCoO2 ceramics used in this study (1 mm in thickness) was too thick for solid batteries and could not perform as such at this stage. However, as long as the electrode layer can be made as thin as 100 μm, the stacking layer will operate as a solid battery.

Materials and Methods

Materials

Metal Nb substrate (Nilaco Corporation) La2O3, and LiOH·H2O (Wako Pure Chemical Industries) were used for the preparation of the Li5La3Nb2O12 crystal layer. The Nb substrate was cut into small pieces with dimension of 10 mm × 15 mm prior to use. LiCoO2 ceramics (φ = 13 mm × 1 mm thick) were purchased from KCM Corporation. All commercial materials were used without further purification.

Characterization

The morphological and elemental mapping analyses of the grown crystal layers were carried out using field-emission scanning electron microscopy (FE-SEM) coupled with an analyzer for energy dispersive X-ray spectroscopy (EDX) (JEOL, JSM-7600F). An acceleration voltage of 15 kV was used. Pass energy was controlled to be The phases and structures of the crystals were identified using X-ray diffraction (XRD) analysis with Cu Kα radiation. The X-ray diffractometer (RIGAKU, Miniflex II) was operated at 30 kV and 20 mA, with 2θ = 10–80°. For the cross-sectional TEM observation and crystallographic orientation analysis of the Li5La3Nb2O12 crystal layer on Nb substrate, thin specimens were prepared by a focused ion beam apparatus with Ga gun (FIB, JIB-4000, JEOL). Selected area electron diffraction (SAED) patterns and bright-field TEM images were obtained using a 200kV electron microscope (TOPCON EM-002B).

Growth of Li5La3Nb2O12 crystal layer through conversion of metallic Nb substrate in molten LiOH flux

We applied similar recipe of the flux growth of polyhedral shaped Li5La3Nb2O12 single crystals the crystal layer formation25. La2O3 (0.305 g) and LiOH·H2O (0.295 g) were mixed in an alumina crucible 30 mL in volume for 30 min. To adjust the solute concentration to 5 mol%, 2.431 g of LiOH·H2O powder was further added as a flux. A Nb substrate was gently placed a the mixture and then heated to 500 °C at a rate of 500 °C·h−1 in an electric furnace. The substrate was cooled to 300 °C at a rate of 100 °C·h−1, and then naturally cooled to room temperature in the furnace. The substrate was separated from the mixture by washing with warm water for three times to remove the remaining flux, completely. Finally, the substrate was dried at 60 °C in air for 10 h.

Molecular dynamics simulation of the phase diagram of Li-La-Nb-O system

The Vienna ab initio simulation package30,31 was used with the generalized gradient approximation (GGA-PBE sol) + U 32 and projector-augmented wave methods33. For the GGA + U calculations, the U value for the d-orbitals of Nb was set to 1.5 eV, based on previous reports34. An energy cutoff of 500 eV and a k-point mesh were chosen, so that the product of the number of k-points and the number of atoms in the unit cell was greater than 1000. To construct the phase diagram of the Li-La-Nb-O system, we obtained the possible compositions from Inorganic Crystal Structure Database (ICSD) and optimized the structures of related oxides (in this case they are Li2O, Li2O2, La2O3, NbO2, Nb2O5, LiNbO2, LiNbO3, LiNb3O8, Li3NbO4, Li8Nb2O9, LaNbO4, LaNbO7, LiLaNb2O7, LiLa2NbO6, and Li5La3Nb2O12). The total energy, E total (X), obtained by DFT calculations was assumed as the sum of chemical potentials μ(Y): E total (Li5La3Nb2O12) = 5(Li+) + 3(La) + 2(Nb) + 12(O). The chemical potential of oxygen molecule was set as zero in the horizontal axis, and that of lithium metal was set as zero in the vertical axis. The energy correction for O2 molecules was used for all calculations as reported by Wang et al.35. At the boundaries between two phases, the chemical potentials of each atom were assumed to be equal in the two phases. The boundaries between two phases were calculated by simultaneous equations. For example, the boundary between Li5La3Nb2O12 and (La3NbO7 + Nb2O5) phases was calculated by the following equations:

$$\begin{array}{c}{E}_{total}({{\rm{Li}}}_{{\rm{5}}}{{\rm{La}}}_{{\rm{3}}}{{\rm{Nb}}}_{{\rm{2}}}{{\rm{O}}}_{{\rm{12}}})=5\,\mu ({\rm{Li}})+3\,\mu ({\rm{La}})+2\,\mu ({\rm{Nb}})+12\,\mu ({\rm{O}})\\ {E}_{total}({{\rm{La}}}_{{\rm{3}}}{{\rm{NbO}}}_{{\rm{7}}})=3\,\mu ({\rm{La}})+\mu \,({\rm{Nb}})+7\,\mu ({\rm{O}})\\ {E}_{total}({{\rm{Nb}}}_{{\rm{2}}}{{\rm{O}}}_{{\rm{5}}})=2\,\mu ({\rm{Nb}})+5\,\mu ({\rm{O}})\end{array}$$
(1)

We obtained the phase diagram of Li-La-Nb-O system by calculating all the possible simultaneous equations similar to the ones given above. Note that the molar ratio of La/Nb is fixed as 2 and 1.5 in the phase diagrams. We convert the chemical potential of oxygen to the temperature and oxygen partial pressure using the following equation36,

$${\mu }_{O}=\frac{1}{2}({E}_{{O}_{2}}^{DFT}+({G}_{{O}_{2}}^{0}(T)-{G}_{{O}_{2}}^{0}(0K))+{k}_{B}T\,\mathrm{ln}(\frac{{P}_{{O}_{2}}}{{p}^{0}}))$$
(2)

where \({E}_{{O}_{2}}^{DFT}\) is the energy of one O2 molecule obtained by DFT calculations. \({G}_{{O}_{2}}^{0}\) is the Gibbs free energy of the gaseous O2 phase under the standard pressure \({p}^{0}\) as a function of temperature, which is estimated by assuming an ideal gas on the basis of experimental results37.

Molecular dynamics simulation to evaluate the tilted grain boundary of Σ3 (2–1–1) = (1–21)

Molecular dynamics (MD) simulations were performed using a Born-like description of the ionic crystal lattice38. The long-range Coulombic interactions were summed via the Ewald method39, whereas the short-range interactions were described using the parameterized Buckingham pair potentials40. The latter were summed to the cut-off value of 10.5 Å, beyond which the influence of the potential was considered negligible. The lattice energy is defined as

$${E}_{L}=\sum _{i}\sum _{j > i}[\frac{{q}_{i}{q}_{j}}{4\pi {\varepsilon }_{0}{r}_{ij}}+{A}_{ij}\exp (\frac{-{r}_{ij}}{{\rho }_{ij}})-(\frac{{C}_{ij}}{{r}_{ij}^{6}})]$$
(3)

where \({r}_{ij}\) is the separation between ions i and j, q i and q j are the ion charges, and \({\varepsilon }_{0}\) is the permittivity of the free space. The Buckingham potential parameters, \({A}_{ij}\), \({\rho }_{ij}\), and \({C}_{ij}\), were specific to the pairs of interacting species. The simulation parameters are listed in Table S1 41.

The DL POLY simulation package42 was used for all MD calculations, and the corresponding time step was equal to 1 fs. First, the initial models were equilibrated for 20 000 time steps (20 ps) in the isothermal isobaric (NPT) ensemble at a temperature of 300 K. During this initial period, the volume of the cell was allowed to relax with time. The Nosé-Hoover thermostat and barostats43,44 were used to control the temperature and pressure, respectively. Afterwards, the temperature was elevated from 700 to 1700 K at a rate of 10 K per 5 ps; and the NPT dynamic simulations were conducted for 100 ps, during which the cell angles were allowed to relax. After equilibration at 1700 K, the obtained structure was cooled to a desired temperature, which allowed the lattice to fully equilibrate in a shorter simulation time compared to that required for directly heating the system to the target temperature. Cooling was performed via an iterative procedure, which involved decreasing the temperature in steps of 10 K accompanied by dynamic simulations with durations of 5 ps. For each studied temperature, MD simulations containing 500 000 time steps (500 ps) were performed using the constant volume and temperature (NVT) ensemble, in order to obtain statistical information about diffusion rates. The bulk Li5La3Nb2O12 calculations were performed using the 3 × 3 × 3 unit cell superstructure with cubic symmetry and containing 4752 atoms.

The GB energy, \({\gamma }_{GB}\), is defined as

$${\gamma }_{GB}=\frac{1}{2A}({E}_{GB}-N{E}_{bulk})$$
(4)

where A is the GB area, E GB is the lattice energy of the GB model, E bulk is the lattice energy per atom, and N is the number of atoms in the particular GB model. To investigate the ionic transport properties of a particular structure, the mean square displacement (MSD) of the ions was monitored as a function of time at different temperatures. For a system with N ions, the MSD of ion i at position r i (t + t 0) and time t with respect to its initial position r i (t 0) is defined as

$$\langle {r}^{2}(t)\rangle =\langle \frac{1}{N}\sum _{i=0}^{N}{({r}_{i}(t+{t}_{0})-{r}_{i}({t}_{0}))}^{2}\rangle .$$
(5)

The Li diffusion coefficient, D, can be calculated from the MSD slopes plotted against time45:

$$\langle {|{r}_{i}(t+{t}_{0})-{r}_{i}({t}_{0})|}^{2}\rangle =6Dt+B$$
(6)

where B is the atomic displacement parameter related to thermal vibrations. The Li ionic conductivity, \({\sigma }_{Li}\), can be calculated by using the Nernst-Einstein equation46:

$${\sigma }_{Li}={c}_{Li}{({z}_{Li}F)}^{2}\frac{{D}_{Li}}{RT}$$
(7)

where \({c}_{Li}\) is the Li carrier density, \({z}_{Li}\) is the Li charge, F is Faraday’s constant, R is the gas constant, and T is the temperature. The Li ionic conductivity values were obtained in the temperature range of 700–1700 K.

Growth of Li5La3Nb2O12 crystal layer on LiCoO2 ceramics

A thin Nb film was deposited on the LiCoO2 ceramics by RF-driven Ar sputtering under 0.67 Pa. The back pressure, input power, and flow rate of Ar gas were controlled to be 2.0 × 10−3 Pa, 300 W, and 3.0 sccm, respectively. The 1 mm thick LiCoO2 ceramics with sintering density of >98% was gently placed on the mixture of La2O3 (0.305 g) LiOH·H2O (0.295 g) and then heated to 500 °C at a rate of 500 °C·h−1 in an electric furnace. After maintaining this temperature for a designated period, the crucible was cooled to 300 °C at the rate of 100 °C·h−1, and then naturally cooled to room temperature in the furnace. The substrate was separated from the mixture by washing with warm water for three times to remove the remaining flux. Finally, the substrate was dried at 60 °C under air for 10 h.