Revealing Atomic-Scale Ionic Stability and Transport around Grain Boundaries of Garnet Li7La3Zr2O12 Solid Electrolyte

For real application to the all-solid-state batteries, understanding and control of the grain boundaries (GBs) are essential. However, the in-depth insight into the atomic-scale defect stabilities and transports of ions around the GBs is still far from understood. Here, the first-principles investigation on the promising garnet Li 7 La 3 Zr 2 O 12 solid electrolyte GBs has been carried out. Our study reveals a GB-dependent behavior for the Li-ion transport correlated to the diffusion network. Especially, the  3(112) tilt GB model exhibits a quite high Li-ion conductivity comparable to that in bulk, and a fast intergranular diffusion contrary to the former concepts. Moreover, the preference of the electron accumulation at the  3(112) GB was uncovered in terms of the lower Li interstitial formation energies. This phenomenon is further enhanced by the presence of the Schottky-like defect, leading to the increase in the electronic conductivity at GBs, which plays a key role in the Li dendrite growth.


Introduction
Li-ion battery as an important energy storage device has been extensively applied to many fields, such as portable devices and electric vehicles. 1,2 Due to the existence of weakness of the organic liquid electrolyte in the traditional Li-ion battery (e.g. flammable), all-solid-state battery (ASSB) containing an inorganic solid electrolyte is one of the most promising candidates of the next-generation battery owing to its improved safety and cycle stability. [3][4][5] Through the long-term development, a variety of high-performance solid electrolytes (SEs) has been successfully synthesized, whose ion conductivities are comparable with the traditional liquid electrolytes. [6][7][8][9] Among of them, the garnet-type Li7La3Zr2O12 (LLZO) as a superior solid electrolyte has attracted great interest, 8,10,11 thanks to its high conductivity (~ 10 -4 S/cm), wide electrochemical window (~ 6 eV) 12 . More attractively, LLZO shows good compatibility with the ultimate anode material, Li metal, to achieve an ASSB with a significantly high energy density. [13][14][15][16][17] As most of the synthesized LLZO SEs are polycrystalline, the grain boundary (GB) has an inevitable influence on their performances. However, until now, this underlying GB effect has not been thoroughly understood yet. For example, numerous works have reported the resistance at GB related to the decrease in the ion conductivity in LLZO, [18][19][20][21] while some other studies have observed contradictory results, where the sample with small grain size has higher conductivity than that containing large-sized grains, indicating the faster ion transport at the GBs. [22][23][24] Moreover, GBs are expected to contribute to the Li dendrite growth in LLZO, [25][26][27] which leads to the short-circuiting of the cell 22,[28][29][30][31] . It is reported that the inhomogeneous depletion 30 and low ion conductivity 32 at the GB are responsible for the dendrite growth.
Particularly, recent works have proposed that the dendrite propagation originates from the high electronic conductivity, 28,33 which is reported to be appeared at the GB 34 .
Thoroughly unraveling these serious GB issues require a comprehensive understanding of the ion diffusion, defect chemistry, and electronic properties at GB. Especially, the Li-ion conductivity at the GB has been revealed using the classical simulation method, where the GB resistance is sensitive to the GB structure and temperature. 21 However, the in-depth atomistic mechanism of Li-ion transportation at GBs has not been established yet. First-principles simulation based on the atomistic model as a powerful way can provide comprehensive results about the properties of SE. Especially for LLZO, it has been extensively used to explain the phase transition 35 , migration mechanism 36 , electrochemical window 12 , defect chemistry 37 , and the phenomena on the surface and at the interface with Li metal 38,39 . Unfortunately, as far as we know, there is no report of the study on these significant GB issues based on the firstprinciples simulation.
Herein, we have reported a study on the atomistic diffusion and defect chemistry of ions at the GBs of LLZO using the first-principles density functional theory (DFT), aiming to discover the GB effects on the ion conductivity and dendrite growth within LLZO SE. We have observed the distortion and decomposition of ZrO6 unit at the GBs. It is revealed that Li + diffusivity is strongly dependent on the migration network determined by the GB atomistic structure.
Especially, the 3(112) GB model with the analogous migration network shows the comparable conductivity with that of bulk, whereas the 1(110) GB model exhibits the significantly slow diffusivity. Moreover, through the calculated defect formation energies, the enrichment of Li interstitials at the GB has been observed, introducing the extra electron localized at the GB and leading to the enhanced electronic conductivity, which is a key in the dendrite growth. To the best of our knowledge, this study is the first work for simulating the GB in SE using first-principles method thus far. We believe that this work provides a novel perspective for elucidating the GB effect on the SE.     Those defect distributions around GBs will be investigated in future works.
The calculated Ef for V Li × at 24d and 96h sites in bulk are approximate to 3.6 eV (Figure 3a), which is in good agreement with the previously calculated values (3.54 eV). 46 Interestingly, we have found that there are several V Li × with significantly higher Ef at the 1(110) GB, whose maximum value (4.3 eV) is about 0.7 eV larger than that in bulk. These sites with remarkably high Ef will lead to the large barriers for Li + migrating from neighboring sites to these sites, which is one of the main reasons for the low Li + conductivity at this GB. Through analyzing the Li-Li coordination environments of the considered vacancies ( Figure S8a), we found that, only for the sites at the GB with the elevated Ef, the coordination number within the cutoff radius of 2.7 Å is zero, indicating that these sites have the longer interatomic distances and the weaker electrostatic repulsion interactions with the neighbouring Li-ions. This is a potential origin of these high Ef.  It is well known that the DFT calculation based on the PBE functional usually underestimates the band gap. Therefore, we have adopted the screened hybrid functional Furthermore, the excess electrons show a strong preference to be localized in the GB regions.
These electrons, whose states are close to the conduction bands, would show the potentially high mobility, and high capability to combine with the excess Li ions to trigger the nucleation of Li 0 inside the SE. 33,34,53 Meanwhile, these excess electrons may lead to the redistribution of the electric field. 54 The GB with high electronic conductivity will facilitate the Li penetrations.
All of these factors are critical for the dendrite propagation inside LLZO SE.
It is noteworthy that Li creep and plastic flow driven by the built-up pressure at the LLZO/Li interface during electrodeposition are also critical for the dendrite formation. 51,55,56 The current study focuses on the impact of the microstructure structure of GB, and provides a potential reason for the high electronic conductivity of LLZO, which has been widely reported as another major origin of the dendrite formation within SE. 17,33,34,53 Our study shows that the Methods GB structure construction. The GB models were constructed based on the Zr sublattice to preserve the ZrO6 octahedron in the initial structure. To suppress the interaction between the neighbouring equivalent GBs, the distance between them are above 15 Å. All the Li sites are occupied in the initial GB models, and we performed a two-step procedure to search the energetically favorable Li distribution. First, we selected a series of different occupations of 24d and 96h sites in the GB models (Table S1) on the basis of the experimentally observed occupations (0.564 for 24d site and 0.442 for 96h site) . For each occupation, 10 structures were randomly constructed with the exclusion of the electrostatically unfavorable neighboring sites (distance between two Li-ions < 1.8 Å) and geometrically optimization is conducted ( Figure S1a,b). The lowest-energy models of 1(110) and 3(112) GBs were adopted as input First-principles calculation. The DFT method was employed within the generalized gradient approximation of the Perdew, Burke, and Ernzernhof functional as implemented in the Vienna ab initio simulation package. 58 Electron−ion interactions were described using projector-augmented wave pseudopotentials 59 , with the following valence electrons: 2s 1 for Li, 2s 2 2p 4 for O, 5s 2 4d 2 for Zr, and 5s 2 5p 6 5d 1 6s 2 for La. A plane-wave kinetic-energy cutoff of 520 eV and a k-spacing of 0.25 Å -1 in reciprocal space were used to achieve reliable results.
First-principle molecular dynamic (FPMD) simulations were performed in the canonical (NVT) ensemble using the Nosé-Hoover thermostat 60 at 700 and 1000 K for bulk, 1(110) and 3(112) GB models, with a time step of 1 fs. Additional MD simulations at 850 and 1200 K were carried out for bulk. In the MD simulations, in order to trade off the computational cost and accuracy, the kinetic-energy cutoff and k-spacing were set to 450 eV and 0.5 Å -1 in reciprocal space, respectively. The detailed methods for calculating the GB formation energy, time average mean squared displacement, and defect formation energy have been described in the supplementary information.