Thin and Dense Solid-solid Heterojunction Formation Promoted by Crystal Growth in Flux on a Substrate

In this work, we demonstrate the direct growth of cubic Li5La3Nb2O12 crystal layer on the LiCoO2 substrate through the conversion of ultra-thin Nb substrate in molten LiOH flux. The initial thickness of the Nb layer determines that of the crystal layer. SEM and TEM observations reveal that the surface is densely covered with well-defined polyhedral crystals. Each crystal is connected to neighboring ones through the formation of tilted grain boundaries with Σ3 (2–1–1) = (1–21) symmetry which show small degradation in lithium ion conductivity comparing to that of bulk. Furthermore, the sub-phase formation at the interface is naturally mitigated during the growth since the formation of Nb2O5 thin film limits the whole reaction kinetics. Using the newly developed stacking approach for stacking solid electrolyte layer on the electrode layer, the grown crystal layer could be an ideal ceramic separator with a dense thin-interface for all-solid-state batteries.

increase the interfacial resistance 15,16 . 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 interface 8 or using new discontinuous heating processes 5 . 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 sputtering 19 , sol-gel process 20 , and aerosol deposition 21 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 substrate 18 , 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 Li 5 La 3 Nb 2 O 12 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 Li 5 La 3 Nb 2 O 12 and LiCoO 2 ceramics (which is the most popular cathode active material) was performed through a similar approach.  Fig. 2 (a),(b), the LiLa 2 NbO 6 phase was not formed when the starting materials were mixed in either stoichiometric or non-stoichiometric compositions. All these results indicate that the LiLa 2 NbO 6 phase is not thermodynamically stable.

Growth of Li
The formation of Li 5 La 3 Nb 2 O 12 progressed with increasing holding time. The cubic phase Li 5 La 3 Nb 2 O 12 was obtained as a single phase after 10 h. It is interesting to note that the Li 5 La 3 Nb 2 O 12 phase was the major product during the early stages of the reaction, despite the unreacted La 2 O 3 and LiOH remaining in the flux. Furthermore, no diffraction pattern assignable to niobium oxides such as Nb 2 O 5 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 Nb 2 O 5 at 500 °C (Fig. S1). Very similar results were observed in our previous reports that describe the formation of hollow-structured LiCoO 2 , LiMn 2 O 4 , and LiNi 0.5 Co 0.2 Mn 0.3 O 2 from the conversion of electrodeposited Co, Mn, and stacked Ni/Co/Mn dots in molten salts at high temperatures, respectively 23,24 . 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 Li 5 La 3 Nb 2 O 12 single crystals that were homogeneously grown from LiOH flux (with LiOH·H 2 O, La 2 O 3 , and Nb 2 O 5 powders reacting in a crucible) 25 .
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 LiLa 2 NbO 6 through the reaction of LiOH·H 2 O and La 2 O 3 powders with Nb 2 O 5 layer limits the whole reaction, LiLa 2 NbO 6 and/or Nb 2 O 5 layer should remain at the interface. Thus, the thickness of Li 5 La 3 Nb 2 O 12 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 O 2 in the molten LiOH flux. If the self-diffusion rate of Nb is much faster than the diffusion of O 2 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.
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 Li 5 La 3 Nb 2 O 12 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   This result suggests that there may be a direct correlation with crystal orientation of crystal habit which appears in different grains.
We have reported the Li + conductivity of the sinter bodies prepared from the Li 5 La 3 Nb 2 O 12 crystals of which it was grown from LiOH flux under same recipe described in this paper 25 . 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 Li 5 La 3 Nb 2 O 12 crystal layers have not yet to acquire because any symmetrical cells, Li| Li 5 La 3 Nb 2 O 12 crystal layer|Li for non-blocking geometry and Au | Li 5 La 3 Nb 2 O 12 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 Li 5 La 3 Nb 2 O 12 crystal layers by using micro-probe technique 26 . 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-Li 7 La 3 Zr 2 O 12 (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 Li 5 La 3 Nb 2 O 12 system. This computationally predicted trend is consistent with the thermodynamically stable faces of the Li 5 La 3 Nb 2 O 12 crystals grown from a molten LiOH flux 25 .   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 reports 28 . 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 Li 5 La 3 Nb 2 O 12 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 Li 7 La 3 Zr 2 O 12 was known to enhance bulk Li + conductivity through changing the Li + occupancy at 24d/96 h sites 12 , 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 Li 7 La 3 Zr 2 O 12 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 Li 5 La 3 Nb 2 O 12 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 Li 5 La 3 Nb 2 O 12 crystal layer on LiCoO 2 ceramics.
We applied the same methodology to stack the Li 5 La 3 Nb 2 O 12 crystal layer on LiCoO 2 ceramics through the direct growth from the LiCoO 2 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 LiCoO 2 ceramic surface turned to a brilliant color after the deposition. Time-dependent XRD holding at 500 °C reveals that the perovskite LiLa 2 NbO 6 phase was dominantly formed during the initial stage of reaction (Fig. 9). This phase was sequentially transformed into cubic Li 5 La 3 Nb 2 O 12 as the reaction time increased. The cubic Li 5 La 3 Nb 2 O 12 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 Li 0.5 La 2 Co 0.5 O 4 , at the heterophase interface. This is thought to be due to the mutual diffusion of Co in LiCoO 2 and La in Li 5 La 3 Nb 2 O 12 at the interface. Time-dependent SEM observation was used to characterize the growth and development of Li 5 La 3 Nb 2 O 12 crystal layer on the LiCoO 2 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 Li 5 La 3 Nb 2 O 12 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 Li 7 La 3 Nb 2 O 12 phase formation. In addition, many large pin-holes were formed at the grain boundaries, driven by over growth of the Li 5 La 3 Nb 2 O 12 crystal (Fig. 10(f)). Interestingly, the formation of pin-holes and the Li 0.5 La 2 Co 0.5 O 4 phase occurred simultaneously.
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 Nb 2 O 5 layer, and LiLa 2 NbO 6 and Li 5 29 . 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

Discussion
We have studied the direct growth of cubic Li 5 La 3 Nb 2 O 12 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 LiCoO 2 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. Metal Nb substrate (Nilaco Corporation) La 2 O 3 , and LiOH·H 2 O (Wako Pure Chemical Industries)
were used for the preparation of the Li 5 La 3 Nb 2 O 12 crystal layer. The Nb substrate was cut into small pieces with dimension of 10 mm × 15 mm prior to use. LiCoO 2 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 Li 5 La 3 Nb 2 O 12 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 Li 5 La 3 Nb 2 O 12 crystal layer through conversion of metallic Nb substrate in molten
LiOH flux. We applied similar recipe of the flux growth of polyhedral shaped Li 5 La 3 Nb 2 O 12 single crystals the crystal layer formation 25 . La 2 O 3 (0.305 g) and LiOH·H 2 O (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·H 2 O 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 package 30,31 was used with the generalized gradient approximation (GGA-PBE sol) + U 32 and projector-augmented wave methods 33 . For the GGA + U calculations, the U value for the d-orbitals of Nb was set to 1.5 eV, based on previous reports 34 . 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 Li 2 (Li 5 La 3 Nb 2 O 12 ) = 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 O 2 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 Li 5 La 3 Nb 2 O 12 and (La 3 NbO 7 + Nb 2 O 5 ) phases was calculated by the following equations: 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 equation 36 ,

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 lattice 38 . The long-range Coulombic interactions were summed via the Ewald method 39 , whereas the short-range interactions were described using the parameterized Buckingham pair potentials 40 . 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 where r ij is the separation between ions i and j, q i and q j are the ion charges, and ε 0 is the permittivity of the free space. The Buckingham potential parameters, A ij , ρ 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 package 42 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 barostats 43,44 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 Li 5 La 3 Nb 2 O 12 calculations were performed using the 3 × 3 × 3 unit cell superstructure with cubic symmetry and containing 4752 atoms.
The GB energy, γ GB , is defined as

GB GB bulk
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 The Li diffusion coefficient, D, can be calculated from the MSD slopes plotted against time 45 : where B is the atomic displacement parameter related to thermal vibrations. The Li ionic conductivity, σ Li , can be calculated by using the Nernst-Einstein equation 46 : Li Li Li Li 2 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 Li 5 La 3 Nb 2 O 12 crystal layer on LiCoO 2 ceramics. A thin Nb film was deposited on the LiCoO 2 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 LiCoO 2 ceramics with sintering density of >98% was gently placed on the mixture of La 2 O 3 (0.305 g) LiOH·H 2 O (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.