Theoretical insights into interfacial stability and ionic transport of Li2OHBr solid electrolyte for all-solid-state batteries

Li-rich antiperovskite materials are promising candidates as inorganic solid electrolytes (ISEs) for all-solid-state Li-ion batteries (ASSLIBs). However, the material faces several pressing issues for its application, concerning the phase stability and electrochemical stability of the synthesized material and the Li-ion transport mechanism in it. Herein, we performed first-principles computational studies on the phase stability, interfacial stability, defect chemistry, and electronic/ionic transport properties of Li2OHBr material. The calculation results show that the Li2OHBr is thermodynamically metastable at 0 K and can be synthesized experimentally. This material exhibits a wider intrinsic electrochemical stability window (0.80–3.15 V) compared with sulfide solid electrolytes. Moreover, the Li2OHBr displays significant chemical stability when in contact with typical cathode materials (LiCoO2, LiMn2O4, LiFePO4) and moisture. The dominant defects of Li2OHBr are predicted to be VLi− and Lii+, corresponding to lower Li-ion migration barriers of 0.38 and 0.49 eV, respectively, while the replacement of some of the OH− by F− is shown to be effective in decreasing migration barriers in Li2OHBr. These findings provide a theoretical framework for further designing high performance ISEs.


Introduction
In recent years, inorganic solid electrolytes (ISEs) have received wide attention to replace organic liquid electrolytes currently used in commercial lithium-ion batteries. 1Unlike organic liquid electrolytes, ISEs are nonammable, nonvolatile, and have no liquid leakage problem, and are also expected to overcome the phenomenon of lithium dendrites, thus they have high safety performance. 2Moreover, ISEs have the potential to improve interfacial stability, which could enable the application of a high-voltage cathode and even lithium metal anode. 3In terms of Li-ion transport properties, several ISEs have been reported, such as the Li 10 GeP 2 S 12 , 4 Li 7 P 3 S 11 , 5 and lithium-rich anti-perovskites (LRAP), 6 with high Li + conductivities comparable to or even surpassing those of traditional liquid electrolytes.
One promising class of ISEs is antiperovskites Li 3−n OH n X (n = 0-1, X = Cl, Br) for ASSLIBs. 7For example, Zhao et al. rst experimental reported that Li 3 OCl and Li 3 O(Cl 0.5 Br 0.5 ) showed a high ion-conductivity (>10 −3 S cm −1 at 300 K) with low activation energies (0.18-0.26 eV). 8Subsequently, a good stability and low Li + vacancy migration barrier of Li 3 OX (X = Cl, Br) was veried by rst-principles calculations. 9Sugumar et al. reported the successful preparation of Li 2 OHBr by dry ball-milling of LiOH and LiBr at room temperature, which obtained high ion conductivity of 1.1 × 10 −6 S cm −1 with the activation energy of 0.54 eV. 10 Recently, Yamamoto et al. 11 reported that an ASSLIB composed of Li/Li 2 OHBr/Fe 2 (MoO 4 ) 3 were fabricated by pressing at room temperature, which exhibited good chargedischarge performance and excellent cycle stability.Zhao and co-workers 12 proposed the Li 2 OHBr as a protective layer for the Li 1.5 Al 0.5 Ge 1.5 (PO 4 ) 3 (LAGP) solid electrolyte to prevent the side reaction caused by direct contact between LAGP and Li metal anode.For practical applications, whether Li 2 OHBr material acts as a solid electrolyte or protective layer, it is crucial that the material shows good thermodynamic stability, electrochemical stability and fast Li-ion diffusion, which are the keys to ameliorating the electrochemical and rate performance of Li 2 -OHBr material.Moreover, Li 2 OHBr should possess the ability of moisture resistance and oxidation resistance, which will simplify the packaging of ASSLIBs in practice.However, indepth understanding of these important issues, has been hindered by the complicated synthesis and measurement conditions during the experiments.Therefore, it is critical that we explore the fundamental issues of the phase stability, electrochemical stability, chemical stability and electron/ion transport mechanism of Li 2 OHBr through reliable theoretical approaches to elucidating the main behind physics mechanism.
In this work, we employ rst-principles calculations to assess the phase stability, interfacial stability against electrode material, defect chemistry and electron/ion transport mechanism of anti-perovskites Li 2 OHBr.We predict a wide electrochemical window and low chemical reactivity for Li 2 OHBr, ensuring that this material is thermodynamically stable under high-voltage operation and in air.The analysis Li-ion transport mechanism shows the existence of low migration barriers involving charge carriers (V Li −, Li i + ) in Li 2 OHBr.We also study the effect of F − substitution of OH − on the Li + migration barriers in Li 2 OHBr.The computational approach in this work can be extended to the design of other ISEs system.

Computational methods
All calculations are performed based on density functional theory (DFT) by using the projector augmented wave method, as implemented in the Vienna ab initio Simulation Package (VASP). 13The generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) is applied to treat the electronic exchange-correlation interactions. 14The cutoff energy is set to 520 eV.The atomic force and energy convergence parameters are consistent with Materials Project (MP) 15 for all calculations.
Based on DFT ground-state energies in the MP database, the phase stability and interfacial stability (including electrochemical and chemical stability) of Li 2 OHBr are evaluated using the same scheme in the previous work. 16he phase stability of Li 2 OHBr is assessed by computing the energy above convex hull, corresponding the decomposition energy to the thermodynamic phase equilibria.The electrochemical window of Li 2 OHBr is calculated by using the Li grand potential phase diagram.In this method, the grand potential f of the Li 2 OHBr is dened as: where The defect formation energy E f (i, q) with a defect i at charge state q is calculated via the following equation: 18 where E tot (Li 2 OHBr, bulk) and E tot (i, q) are the DFT energies of Li 2 OHBr supercell without and with a defect, respectively.n is the number of Li or Li 2 O compound added (n > 0) or removed (n < 0) from the perfect supercell, and m i is the chemical potential of Li (bcc structure) or Li 2 O (fcc structure) compound.The Fermi level (3 F ) is dened relative to the valence-band maximum (E V ) of perfect Li 2 OHBr and varies with defect concentration.

Structural and electronic property
The Li 2 OHBr orthorhombic structure with space group Cmcm is constructed, as shown in Fig. 1(a).Table 1 lists the optimized lattice parameters of Li 2 OHBr obtained by DFT calculations, together with the data from Howard et al. 19 The lattice parameters are a = 8.015 Å, b = 8.152 Å, and c = 7.944 Å, which are agree with the experiment data (within 2% error).To obtain the electronic properties of Li 2 OHBr, the electronic band structure of Li 2 OHBr is evaluated.Since the GGA-PBE functional generally underestimate the band gap, the advanced SCAN meta-GGA functional is used to provide a rigorous result. 20Fig. 1(b) shows that the direct band gap of Li 2 OHBr is 4.79 eV, and its VBM and CBM are both located at the G point of the rst Brillouin zone.The large band gap indicates that Li 2 OHBr is electron insulator, which can effectively block electron leakage and prevent electrode corrosion.The band gap between the valence band maximum (VBM) and the conduction band minimum (CBM) provides an upper limit for the electrochemical window of solid electrolytes.When the chemical potential of the electrode/solid electrolyte is mismatched, i.e., thermodynamically unstable, a chemical reaction between the two materials will occur spontaneously upon contact.

Phase stability and interfacial stability
The feasibility and complexity level of the experimental synthesis of one given material could be evaluated by its phase stability.In general, for a particular component that does not have a stable phase, the corresponding system will decompose into a stable phase around its component coordinate points.The Li-H-O-Br quaternary phase diagram is constructed at 0 K by minimizing the formation energies of various compositions, as shown in Fig. 2(a).The phase diagram indicates that Li 2 OHBr is energetically unstable duo to positive formation energy with respect to that form the Li 4 H 3 BrO 3 and LiBr.However, the energy above hull (E hull ) of Li 2 OHBr is only 11.6 meV per atom, suggesting that Li 2 OHBr is likely to be metastable at 0 K against possible decomposition products, and therefore may be stabilized by external conditions (such as pressure, temperature, and entropy). 10For example, the Li 2 OHBr was synthesized from LiOH and LiBr starting materials by sintering method above 300 °C. 21n fact, successful synthesis of metastable phases has been widely reported for ISEs, such as Li 6 PS 5 Cl (21 meV per atom), 22 Li 10 -GeP 2 S 12 (25 meV per atom) 4 and Li 7 P 3 S 11 (27 meV per atom). 23or the practical application of ASSLIBs, the ISEs should satisfy the conditions of good interfacial stability, including electrochemical stability and chemical stability. 24Using eqn (1), the phase equilibrium of Li 2 OHBr for a series of lithiation/ delithiation reactions is predicted to obtain the electrochemical stability window.The detailed lithiation/delithiation reactions with m Li are listed in Table S1.† As shown in Fig. 2 2 shows that Li 2 OHBr has much wider electrochemical window than that of reported suldes and oxides solid electrolyte, such as Li 10 GeP 2 S 12 (1.71-2.14V), Li 7 P 3 S 11 (2.28-2.31V), Li 6 PS 5 Cl (1.71-2.01V), Li 2 PO 2 N (0.68-2.63 V) and Li 7 La 3 Zr 2 O 12 (0.05-2.91). 25However, it should be pointed out that the dissociation of ISEs depends on kinetic factors, suggesting that the dissociation of the phases may be slowed down or interrupted under certain circumstances, such as slow electron/ion transport in dissociated phases.The above calculations assume complete thermodynamic equilibrium and no kinetic constraints in the reactions.Therefore, ISEs are expected to withstand a wider range of voltages in use than calculated, as measured by cyclic voltammetry (CV) using Li/ Li 2 OHBr/Au cell, the electrochemical potential window of Li 2 -OHBr was 1.7-3.5 V. 11 The chemical stability between the Li 2 OHBr and various cathodes is calculated by using eqn (2).Three typical cathode  OHBr is in contact with high-voltage cathodes, which may result in the formation of unwanted interfacial byproducts, thereby reducing the rate capacity and electrochemical performance of ASSLIBs.Therefore, further experiment techniques are awaited to assess potential interfacial products, such as X-ray photoelectron spectroscopy (XPS), X-ray absorption spectroscopy (XAS), and electron microscopy (EM). 28he air stability of ISEs is another issue involved in electrolyte handling and battery assembly in the development of ASSLIBs, where the electrolyte will inevitably be exposed to air and undergo structural changes if it is not chemically stable. 29or example, using the rst-principles calculations, Zhang et al. 30 revealed the thermodynamic and kinetic mechanism in the reaction of Li 10 GeP 2 S 12 with H 2 O in air to produce H 2 S gas.Here, the stability of Li 2 OHBr toward air is also studied using reaction energies DE calculation for the reaction with moisture, the higher negative value indicates the material is strongly favorable to react with moisture.The estimation of driving force for Li 2 OHBr when exposed to air via following reaction:   The estimated value of DE is only −1 meV per atom when Li 2 OHBr reacts with H 2 O.While Li 4 (OH) 3 Br forms as a hydrolysis intermediate and subsequently reacts favorably with CO 2 to produce LiOH 2 Br, Li 2 CO 3 and H 2 O (DE = −118 meV per atom).Therefore, it is suggested that the Li 2 OHBr solid electrolyte is stable in dry air.To understand the degradation mechanism of ISEs exposed to air, some experimental techniques, such as in situ scanning/transmission electron microscopy, neutron ray diffraction depth analysis and synchrotron Xray imaging technologies, have been performed to track local nanoscale chemical evolution and structural information of interfacial phases. 313 Ionic transport mechanism 3.3.1.Defect structure and formation energy.Defects in ISEs have a remarkable effect on Li-ion diffusion, and the types of defects are determined by synthesis conditions (e.g., chemical potential) affecting their formation energies.32 To elucidate the ion transport mechanism, it is necessary to understand which defects favor the diffusion of lithium ions in Li 2 OHBr.Herein, four defect types in Li 2 OHBr are considered, including lithium vacancy as per our previous work. 33Among these defects, lithium Frenkel defect and Li 2 O Schottky defect pair in Li 2 OHBr are described as follows: Lithium Frenkel defect: Li 2 O Schottky defect: According to the symmetry of Li 2 OHBr, the possible defect congurations and formation energies are investigated to obtain the lowest energy conguration.The possible defect congurations include two different lithium vacancy defects ðV  3.By comparing the formation energies, it is found that the dominant defect conguration is V near , and the corresponding defect formation energies is 0.34 eV.In contrast, single V 0 Li and Li i show higher defect formation energies (3.93 eV and 1.29 eV), implying a lower concentration of lithium vacancy and lithium interstitial defect in neutral Li 2 OHBr.In addition, the defect formation energies of lithium vacancy and interstitial at different charge states q as a function of Fermi level are also calculated in Fig. 4 using CI-NEB method.Fig. 5 shows the diffusion path of a single lithium vacancy (V Li − ) along the ab-plane and c-axis in Li 2 OHBr, corresponding to the migration barriers are 0.38 and 0.57 eV, respectively.For the direct lithium interstitial (Li i + ) migration in Li 2 OHBr, migration process from an interstitial site to its adjacent interstitial site needs to cross an energy barrier of 0.49 eV, as shown in Fig. 6.The energy barriers of V Li − is slightly lower than that of Li i + , suggesting that V Li − and Li i + will be generated simultaneously when the migrating Li leaves the lattice site.Therefore, we can conclude that the charge carriers (V Li − and Li i + ) make main contribution to the ionic conductivity of Li 2 OHBr and that increasing the concentrations of V Li − and Li i + defects are crucial to obtain high Li-ion conductivity.Furthermore, the doping of Li 2 OHBr with halogen element (F or Cl) may be one of the key factors to enhance the ionic conductivity.In Fig. 7

Conclusions
In conclusion, the electronic properties, phase stability, interfacial stability, defect chemistry and Li-ions migration mechanisms of Li 2 OHBr have been systematically studied by the rstprinciples calculations.The calculations results indicate that Li 2 OHBr crystal structure is metastable by thermodynamics analysis.The electronic band structure shows that the Li 2 OHBr is an insulator with a wide direct band gap.The Li 2 OHBr has a wide electrochemical stability window that can be matched   with the cathode materials.Moreover, the Li 2 OHBr also exhibits good chemical stability with typical cathode materials and in air.By comparing the defect formation energies in neutral and charged states, it is shown that charged Li i + and V Li − are the most dominant defect types in Li 2 OHBr.The Li 2 OHBr show the low migration barriers by using the CI-NEB calculation, while Fdoped Li 2 OHBr has a lower migration barrier compared with pristine Li 2 OHBr.This work provides insights into the thermodynamic and kinetic process of Li 2 OHBr and demonstrates the potential of computational methods in the efficient design of future ISEs.

Fig. 1
Fig. 1 (a) Atomic structure and (b) electronic band structure of Li 2 OHBr.The ball colors green, dark red, red, and gray indicate Li, Br, O, and H sites, respectively.
(b), Li 2 OHBr is oxidized to form Li 4 H 3 BrO 3 and Br when the oxidation voltage is higher than 3.15 V.Meanwhile, Li 2 OHBr is reductively decomposed into LiH, LiBr and Li 2 O starting from 0.80 V.The calculated electrochemical stability window range of Li 2 OHBr are 0.80-3.15V vs. Li/Li + .Table

Fig. 2
Fig. 2 (a) Li-H-O-Br quaternary phase diagram.The metastable Li 2 OHBr is marked in red font.(b) The voltage profiles and phase equilibria of Li 2 OHBr at different potentials.The light yellow region indicates the electrochemical stability window range.

Fig. 3
Fig. 3 Predicted reaction energies DE between Li 2 OHBr and various cathode materials in both (a) fully-discharged and (b) half-charged states.The reaction energy DE min corresponds to the lowest mutual reaction energy at a ratio of x.

0O
Li -I and V 0 Li -IIÞ, one lithium interstitial defect ðLi i Þ, two lithium Frenkel defect pair (V near and V far ), and three Li 2 O Schottky defect pair (V adjacent , V separated-1 , and V separated-2 ) in the ESI of Fig.S1 and S2.† The formation energies of four defect types ðV Þ are calculated by eqn (3) in the neutral state, as listed in Table

Fig. 4
Fig. 4 Formation energies of lithium vacancy and interstitial at different charge states.
(a) and (b), we present the lithium vacancy migration barriers obtained using CI-NEB calculations for Fdoped Li 2 OHBr, namely Li 2 (OH) 0.875 F 0.125 Br.The results show that the migration barriers of Li 2 (OH) 0.875 F 0.125 Br is 0.37 and 0.33 eV along the ab-plane and c-axis, respectively, which is a lower value than that of pristine Li 2 OHBr.The main reason is that the substitution of F − for OH − increases the antiperovskite tolerance factor and favors a disordering of the OH − orientation for Li 2 OHBr, as previous reported by Li et al. 21Therefore, the Li 2 OHBr can be doped by the substitution of OH − by F − is benecial to reduce the migration barrier and improve the ionic conductivity.

Fig. 5
Fig. 5 Diffusion pathway and migration barriers of V Li − in Li 2 OHBr (a) along the ab-plane and (b) along the c-axis.

Fig. 6
Fig. 6 Diffusion pathway and migration barriers of Li i + in Li 2 OHBr along the c-axis.

Fig. 7
Fig. 7 Diffusion pathway and migration barriers of V Li − in F-doped Li 2 OHBr (a) along the ab-plane and (b) along the c-axis.

m
Li , n Li [c], and E[c] are the Li chemical potential, Li concentration and DFT energy of composition c, respectively.The chemical stability of Li 2 OHBr/cathode interfaces are determined by estimating the reaction between the Li 2 OHBr and cathode with the lowest reaction energy (DE), 17 namely: DEðc cathode ; c Li 2 OHBr Þ ¼ min

Table 1
Relaxed lattice parameters and atomic coordinates of Li 2 -OHBr in the orthorhombic

Table 2
Summary of electrochemical window (EW), equilibria phases at reduction and oxidation potentials of some typical solid-state electrolytes . The results show that the formation energies of Li i + and V Li − are lower than those of V , suggesting that the Li i + and V Li − may be the main defect types in Li 2 OHBr at room temperature.Therefore, charged defects (Li i + and V Li − ) should act as charge carriers in Li 2 OHBr and will be used to calculate the migration barriers in the next section.3.3.2.Li-ion migration via vacancy and interstitial mechanism.A high ionic conductivity at room temperature is one of most important indices for the practical application of ISEs in ASSBs.Herein, the Li-ion diffusion pathways and migration barriers of charge carriers (V Li − , Li i + ) in Li 2 OHBr are studied O

Table 3
Defect formation energies corresponding to various defect types and configurations in Li 2 OHBr 0 Li -I V 0 Li -II Li