Theoretical Design of Defects as a Driving Force for Ion Transport in Li3OBr Solid Electrolyte

Due to ever‐increasing concerns about safety issues in using Li ionic batteries, solid electrolytes have extensively explored. The Li‐rich anti‐perovskite Li3OBr has been considered as a promising solid electrolyte candidate, but it still suffers challenges to achieve a high ionic conductivity owing to the high intrinsic symmetry of the crystal lattice. Herein, we presented a design strategy that introduces various point defects and grain boundaries to break the high lattice symmetry of Li3OBr crystal, and their effect and microscopic mechanism of promoting the migration of Li‐ion were explored theoretically. It has been found that Lii· are the dominant defects responsible for the fast Li‐ion diffusion in bulk Li3OBr and its surface, but they are easily trapped by the grain boundaries, leading to the annihilating of the Frenkel defect pair VLi′+Lii· and thus limits the VLi′ diffusion at the grain boundaries. The VBr· defect near the grain boundaries can effectively drive VLi′ across the grain boundary, thereby converting the carrier of Li+ migration from Lii· in the bulk and surface to VLi′ at the grain boundary, and thus improving the ionic conductivity in the whole Li3OBr crystal. This work provides a comprehensive insight into the Li+ transport and conduction mechanism in the Li3OBr electrolyte. It opens a new way of improving the conductivity for all‐solid‐state Li electrolyte material through the defect design.


Introduction
[3][4][5] Until now, many important inorganic SSEs families such as perovskite Li 3x La 2/3-x TiO 3 (LLTO) and its derivatives, [6,7] Li 10 GeP 2 S 12 (LGPS), [8,9] LiPON, [10] and garnet solid electrolyte Li 7 La 3 Zr 2 O 12 (LLZO) [11] as superionic conductors have been intensively investigated.Unfortunately, challenges such as insufficient ionic conductivity, [10] and narrow electrochemical stability windows, existing with conventional electrolytes still need to be overcome.Some become unstable by contact with high reductive lithium metal anode due to the high valence metal ions (such as Ti 4+ in LLTO), [6,7] deteriorating the interface between the electrolyte and electrode.These weaknesses reduce the specific energy and power capacity of the electrolytes and thus limit the power density and/or cycle life of Li ion batteries.Therefore, it is still essential to develop novel solid electrolytes with high ionic conductivity that work well with metallic lithium anodes at high voltage to apply all-solid-state Li-metal batteries (ASS-LMBs).
Recently, inspired by the high-temperature superionic conductor in fluorine-rich perovskite NaMgF 3 , [12] a series of Li-rich anti-perovskite materials, charge-inverted isostructural forms of fluorine-rich perovskites including Li 3 OX (X = Cl, Br), have been designed and synthesized as a new type of Li + superionic conductor for applications in Li-ion batteries. [13][15][16][17][18] However, scattered Li + conductivity from 10 −3 to 10 −1 mS cm −1 for Li 3 OX at room temperature has been reported. [13,19,20]][21] At the same time, it was found that the pristine Li 3 OX bulk material is not a good superionic conductor because Li + ions are bound and locally vibrate around their lattice positions due to the high crystal symmetry. [22,23]In recent years, through many theoretical studies, the ultrafast Li + ionic conductivity of these materials has been attributed to intrinsic defects formed in the crystals.Currently, the origin and mechanism of Li + migration of Li 3 OX materials are controversial.Few studies suggested that Li + vacancies are the main mobile charge carriers, [22,24] and the Schottky defect Li 3 OCl are the most important point defects responsible for the fast diffusion of Li. [25] Other studies proposed that interstitial Li + is the major carrier at the surface, [26] and the diffusion of interstitial dumbbell Li-ions with a three-atom cooperative hopping induces high Li + conductivity. [27]In addition, some studies anticipated that the grain boundaries (GBs) in the Li 3 OX solid electrolytes could also inhibit ion migration. [16,20,21]Therefore, there is a profound interest in understanding the discrepancy of activation energies and the migration mechanisms in Li 3 OX SSEs.Li 3 OBr was first selected as a representative in this investigation to systemically examine the effect of different intrinsic point defects and defect pairs on the migration of Li-ion by using the first-principle The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/eem2.12627.DOI: 10.1002/eem2.12627Due to ever-increasing concerns about safety issues in using Li ionic batteries, solid electrolytes have extensively explored.The Li-rich antiperovskite Li 3 OBr has been considered as a promising solid electrolyte candidate, but it still suffers challenges to achieve a high ionic conductivity owing to the high intrinsic symmetry of the crystal lattice.Herein, we presented a design strategy that introduces various point defects and grain boundaries to break the high lattice symmetry of Li 3 OBr crystal, and their effect and microscopic mechanism of promoting the migration of Li-ion were explored theoretically.It has been found that Li Á i are the dominant defects responsible for the fast Li-ion diffusion in bulk Li 3 OBr and its surface, but they are easily trapped by the grain boundaries, leading to the annihilating of the Frenkel defect pair V 0 Li + Li Á i and thus limits the V 0 Li diffusion at the grain boundaries.The V Á Br defect near the grain boundaries can effectively drive V 0 Li across the grain boundary, thereby converting the carrier of Li + migration from Li Á i in the bulk and surface to V 0 Li at the grain boundary, and thus improving the ionic conductivity in the whole Li 3 OBr crystal.This work provides a comprehensive insight into the Li + transport and conduction mechanism in the Li 3 OBr electrolyte.It opens a new way of improving the conductivity for all-solid-state Li electrolyte material through the defect design.
calculations.Then, different mechanisms for Li-ion migration were explored in the bulk Li 3 OBr material and its surface.From the calculations, Li Á i were identified as the main ion migration sources in bulk Li 3 OBr and its surface.Further studies illustrate that many GB structures could be formed in the Li 3 OBr crystal, which greatly hinders Li + migration and is the key reason for reducing the conductivity of Li 3 OBr SSE.Therefore, the microscopic migration mechanism of Li-ion at the GB was studied further, and a strategy has been proposed to change the Li + migration path and significantly reduce the barrier effect of GB on Li + migration mediated by Br vacancy.It is anticipated that the outcomes from this study provide deep insight into the mechanism of Li + conduction in the anti-perovskite Li 3 OX materials and develop a defectcontrolling method to improve the conductivity of Li + for future applications as solid-state Li-ion electrolytes.

Structures and Electronic Properties of Bulk Li 3 OBr and Its Surface
Li 3 OBr belongs to the cubic crystal system with Pm3m space group.The relaxed structure of Li 3 OBr is shown in Figure 1a, where Br − ions are located at the corners, Li + at the face centers, and O 2− at the body center site.Two types of coordination environments exist for Li + in the lattice: Li 12 Br cuboctahedron and LiO 2 Br 4 octahedron, which provide strong binding interaction to Li + and lead to a complex Li + migration pathway and mechanism.This structure is the origin of the intrinsically low ionic conductivity of the Li 3 OBr crystal.As an outstanding solid electrolyte, Li 3 OBr should possesses a wide electrochemical window, ensuring it can resist the breaking down by the high voltage.In addition, it presents complete ionic transport and negligible electronic components, ensuring minimum self-discharge for a long shelf-life.Most of these basic properties are related to the material's electronic structure, such as band structure.For example, the band gap can provide an upper limit for the region of electrochemical stability, and the solid electrolyte is not considered broken down with a band gap larger than 5 eV.As shown in Figure S1a, Supporting Information, Li 3 OBr has a weak indirect band gap of 5.89 eV, and the conduction band minimum (CBM) and valence band maximum (VBM) are located at the Г and M points of the first Brillouin zone, respectively.Based on the large indirect band gap, Li 3 OBr can be considered an insulator with excellent electrochemical stability and low electrical conductivity.The stability of Li ions at their lattice sites can be further analyzed by AIMD simulation.AIMD simulation was performed at 500 K (just below the melting temperatures of Li 3 OX, 550-600 K [13] ) and 1200 K (superionic conduction usually occurs at high temperature accompanied by an order-disorder transition of the ion sub-lattice [22] ), and the phonon spectrum of Li 3 OBr was calculated to verify its thermodynamic and dynamic stabilities (Figure S1b,c, Supporting Information).The Li + probability density function for the bulk Li 3 OBr is shown in Figure 1b.The selfpart G s (t, r) and distinct-part G d (t, r) of the van Hove function (at 500 and 1200 K) exhibit correlated or cooperative ion motion, as shown in Figure 1c-f, respectively.The plots of G s (t, r) describe the diffusion probability of the Li-ion away from its original site by a distance of r after time t.The plots of G d (t, r) correspond to the probability of finding other Li ions by a distance of r after time t when the Li-ion is away from its original position.They are defined as follows: Here, δ is the one-dimensional Dirac delta function, the angular bracket stands for the ensemble average over the initial time t 0 .r i (t) denotes the position of the ith particle at time t.N d and r are the number of diffusing ions in the unit cell and radial distance, respectively.ρ serves as the normalization factor.It is observed that Li + ions tend to vibrate around their lattice positions locally at 500 or 1200 K. G s (t, r) maintains <1 Å with the extension of time (as shown in Figure 1c,e), indicating that Li + ions move in a short r value ~1 Å.These results confirm that highly symmetric lattices firmly bind Li + ions, and the bulk Li 3 OBr is not a fast ionic superconductor.The G d (t, r) results present a significantly high probability at the proximity of r = 2.8 Å at 500 or 1200 K (as shown in Figure 1d,f).Due to the high crystal symmetry of Li 3 OBr anti-perovskites, only two independent paths exist for direct Li hopping: along the edge of the Li 6 O octahedron and the other is between the vertices of two adjacent Li 6 O octahedrons. [22]Because the distance between two adjacent Li ions in Li 6 O octahedrons is 2.87 Å, Li ions have a high probability of moving along the edge of a Li 6 O octahedron.G d (t, r) also shows a high probability of Li hopping above 4 Å, corresponding to the distance between adjacent Li 6 O octahedral vertices (4.07 Å).However, the probability of Li hopping along the vertices of the octahedrons is much lower than along the edge of the Li 6 O octahedron.This agrees well with the previously reported high Li + ion migration barrier along the vertices of two neighboring octahedrons. [22]ecause surface properties play key role in the application of antiperovskite Li 3 OBr as the SSEs candidate, three low exponential surface models ((100), (110), and (111) surfaces) were conducted to investigate the migration of Li + ion at the surfaces.As shown in Figure S2a, Supporting Information, Li 3 OBr(100) surface has two kinds of termination surfaces: one containing Li and Br atoms with Li:Br = 1:1 is abbreviated as LB(100), and the other containing Li and O atoms with Li:O = 2:1 is abbreviated as LO(100).Therefore, three Li 3 OBr(100) surface models can be constructed, namely, nonstoichiometric LB (100) and LO(100) surfaces (both sides of surface models are the same) as well as stoichiometric Li 3 OBr(100) surface (one side is LB (100), and the other side is LO(100), abbreviated as LBLO(100)).Similarly, three Li 3 OBr(110) surface models are present: nonstoichiometric LOB(110) and L(110) surfaces, as well as the stoichiometric LOBL(110) surface.Also, three Li 3 OBr(111) surface models exist: nonstoichiometric LB(111) and O(111) surfaces, as well as stoichiometric LBO(111) surface.The surface energy valuates the relative stability of these surfaces.The number of layers was tested for different surface configurations to ensure that the calculations converged well.The surface energy of the stoichiometric surface can be calculated using the following Equation ( 3).
where E slab and E bulk represent the total energies of a slab surface structure and the bulk Li 3 OBr unit cell, respectively.n is the number of bulk Li 3 OBr unit cells in the slab surface structure, μ compd is the chemical potential of the remaining compound in the slab surface structure after removing the maximized stoichiometric fraction, and S is the surface area.
The calculated surface energies of different surface configurations are shown in Figure S2b, Supporting Information.It can be observed that the LB(100) slab surface with seven layers is the most stable surface structure with the lowest surface energy of 0.032 J m −2 .As shown in Figure 2a, through the average atomic displacements calculations of the LB(100) surface along the z-axis, only Li (Li 1 and Li 2 ) and Br (Br 1 and Br 2 ) atoms at the surface layer slightly relax.In contrast, atoms in the inner layers do not move.AIMD simulation at 500 K and calculated phonon spectrum (Figure S2c,d, Supporting Information) verify the thermodynamic and dynamic stability of the LB(100) surface.It can be seen from Figure 2b that the charge distribution at the LB(100) surface is almost the same as the bulk Li 3 OBr.The valence bands near the Fermi level are composed of O 2p and Br 4p states, and the conduction bands are mainly from the Li 2p states.Li atoms on the LiBr terminal surface are completely ionized into Li + ions, and Br 4p orbitals are almost filled with electrons transferred from Li.Therefore, the probability density function of Li + at the top-two layers of the LB(100) surface (Figure 2c) is different from the bulk Li 3 OBr; three-dimensional mesh channels are formed on the surface and sub-surface.In contrast, the Li + probability density function of the inner layer maintains the characteristics in the bulk Li 3 OBr, indicating that the surface is more conducive to Li + migration than the bulk.

Point Defects in the Bulk Li 3 OBr and (100) Surface
Normally, fast ionic conductor with high Li conductivity exhibits substantial disordered structure or high vacancy concentration due to the incomplete filling of particular crystallographic sites. [28,29]Li 3 OBr is highly ordered, and intrinsic vacancies enhance its Li + ion conductivity. [23]To understand the type of vacancy defects and their contribution to the high ionic conductivity of Li 3 OBr, the possible vacancy defects in the bulk Li 3 OBr and at the LB(100) surface, and the Li migration mechanism mediated by the vacancy defects were systematically investigated.Here, defect symbols are marked by Kröger-Vink notations to reflect the valence state of different defects, negative status, null status and positive status are marked 0 , ×, and Á.The point defects, including oxygen vacancy (V Ö), bromine vacancy (V Á Br ), lithium vacancy (V 0 Li ), and lithium interstitial (Li Á i ), as well as the V 0 Li þ Li Á i Frankel defect pair and V 0 Li þ V Á Br Schottky defect pair were investigated in both the bulk Li 3 OBr and its surface (Figures S3 and S6, Supporting Information).The defect formation energy (E f ) was calculated using Equation ( 5).
where E def and E perf are the total energies of the structures with and without defects, n i indicates the number of type i atoms added to (n i > 0) or removed from (n i < 0) the defect-free structure when the defects are created, μ i is the corresponding chemical potential of the species i.The most stable defect configuration was noted for the defect pairs by changing the single defect position and their relative distance.In this, the total energy of the most stable structure was set as 0, and the energy difference between the other structure and the most stable one was calculated.The location-dependent formation energies of a single defect and the distance-dependent formation energies of defect pairs are compared for the bulk Li 3 OBr, and LB(100) surface (Tables S1-S6, Supporting Information), and the most stable ones for each type of defect are summarized in Table 1.The formation energies of V Ö are extremely high both in the bulk Li 3 OBr and at the LB(100) surface, thus, the formation of V Ö in Li 3 OBr was not considered.Li Á i defect is more stable than the V Á Br and V 0 Li defects both in bulk and at the surface, indicating the dominant defect of Li Á i in Li 3 OBr.It should be noticed that although V Á Br and V 0 Li are not the most stable defects in all the considered point defects, the formation energies completely decreased after forming the defect pairs ).This illustrates that the single V Á Br and V 0 Li defect can only exist in a small amount in the crystal, and most of them tend to aggregate to form a defect pair that influence Li migration in the crystal.Meanwhile, the formation energies of all the defects at the LB(100) surface are lower than in the bulk Li 3 OBr, indicating that the surface is not the barrier to the defect formation and subsequent migration.

Li-Ion Migration in the Bulk Li 3 OBr
The mean square displacement (MSD) of the ionic positions and the diffusion coefficient for Li + transport may give macroscopic information on Li + diffusion behavior.Since the MSD could hardly be measured in Li 3 OBr below 750 K, [22] we thus chose 1200 K to explore the ion diffusion characteristics by calculating the MSD via the below equation MSD is average over all Li + ion, r i !t ð Þ is the displacement of the ith Li + ion at time t, and N is the total number of Li + ions in the whole system.The diffusion coefficient is defined as where d is the dimension of the lattice on which ion hooping takes place.The calculated MSDs of Li as a function of time at 1200 K and diffusion coefficients (D) for perfect bulk Li 3 OBr, as well as Li 3 OBr with Br defects are shown in Figure 3.The calculated MSD for the perfect Li 3 OBr is too small to be observed, verifying that the perfect Li 3 OBr is not superionic conductors since the high intrinsic symmetric lattice does not provide pathway for Li + ion transport.The MSDs of Li 3 OBr with defects are significantly higher than that of the perfect Li 3 OBr, and they are linear increase with the simulation time at heating temperature, indicating these defects accelerate the Li + migration significantly.Meanwhile, MSD and diffusion coefficient show that Li Á i and V 0 Li þ V Á Br are the main defects responsible for the ionic conductivity, while V 0 Li þ Li Á i has little effect on ionic conductivity.Superionic transport can be understood as fast ion hopping through favorable pathways in a structural framework, the available ion transport pathways are critical to ionic conductivity.Therefore, the effect of defects on the Li + migration path and energy barrier in Li 3 OBr was then systematically investigated by a more microscopic nudged elastic band (NEB) algorithm.In Figure 4a,b, the Li migration paths and energy barriers are given through V 0 Li and Li Á i .The migration of Li Á i (V 0 Li ) in the V 0 Li þ Li Á i Frankel defect pair was investigated by fixing the position of V 0 Li (Li Á i ).The previous study indicated that the halogen vacancies are non-diffusive even at high temperatures, [22] therefore, the position of V Á Br was fixed to optimize Li + migration paths for the V 0 Li þ V Á Br Schottky defect pair.As confirmed by earlier reports, Li + ions  were observed to have a relatively low energy barrier migrating along the edge of the Li 6 O octahedron. [22,24,27]Therefore, for V 0 Li in the bulk Li 3 OBr, only two migration paths along the edge of the Li 6 O octahedron are displayed in Figure 4a.Path 1 is a direct jump from V 0 Li to the nearest Li + .In contrast, another nearest Li + jumps to V 0 Li simultaneously for path 2. It is seen that the migration barriers of V 0 Li in both paths are 0.33 eV.The migration barrier of Li Á i along path 1 (0.16 eV) is only a quarter of path 2 (0.65 eV) and is almost a half of the V Li migration barrier.This illustrates that the single Li Á i is easy to migrate as interstitial dumbbell Li-ions with a three-atom cooperative hopping in the bulk Li 3 OBr.Combined with the formation energies of single V 0 Li and Li Á i (Table 1), we found that V 0 Li are difficult to be formed at high concentration, and thus, Li Á i are responsible for the high ionic conductivity of Li 3 OBr.This is consistent with the calculation results of MSD.In addition, the effect of valence state of point defects on their ionic migration has also been considered by comparing the migration paths and energy barriers of V 0 Li and V Â Li as well as Li Á i and Li i × , as shown in Figure S4, Supporting Information.It was found that the vacancy diffusion barriers of neutral (V Â Li ) and charged (V 0 Li ) in bulk Li 3 OBr are both 0.33 eV, while the interstitial diffusion barriers of neutral (Li Á i ) and charged (Li i × ) are both 0.16 eV.Meanwhile, their migration paths are not influenced by the valence state of point defects.Therefore, the effect of defect valence state on the migration behaviors can be neglected in Li 3 OBr.
The V 0 Li and Li Á i defects could form V 0 Li þ Li Á i Frenkel defect pair that influences the migration of Li + ions.Because the V 0 Li and Li Á i defects have the possibility to combine with each other, we first investigated the thermodynamic stability of V 0 Li þ Li Á i Frenkel defect pair by AIMD simulations at 500 K.As shown in Figure S5, Supporting Information, when V 0 Li and Li Á i are closest neighbors, Li Á i quickly (<1 ps) fills V 0 Li , leading to the obvious reduction of energy (Figure S5a, Supporting Information).When the distance between V 0 Li and Li Á i is far, they will not recombine with each other, keeping a good thermodynamic stability (Figure S5b, Supporting Information).However, increasing the distance between V 0 Li and Li Á i may make the isolated V 0 Li and Li Á i act as the migration carriers in the Li 3 OBr.Therefore, the V 0 Li þ Li Á i defect pair is not the dominant factor contributing to the ionic conductivity of Li 3 OBr due to the recombination during the cycle.This is consistent with the extremely low MSD and diffusion coefficient of V 0 Li þ Li Á i defect pair in Figure 3.
Since the V 0 Li þ Li Á i Frenkel defect pair contains two Li carriers, the migration of V 0 Li and Li Á i was investigated separately.For V 0 Li migration, a possible low energy pathway between two nearby interstitial Li-Li dumbbells was generated, as shown in Figure 4c.It is seen that the Li Á i defect environment does not promote V 0 Li migration because of a similar V 0 Li migration energy barrier with and without Li Á i defect environment.For Li Á i migration, Li Á i moves along the edge of the distorted polyhedron by repelling the corner Li atom to migrate further along the edge of the polyhedron.The V 0 Li defect environment had no significantly effect on the Li Á i migration energy barrier.The barrier remained as low as 0.16 eV (Figure 4d), indicating that Li Á i could promote the ionic conduction of the bulk Li 3 OBr.This result consistent with Li 3 OCl that Li Á i is more conducive to migration in the V 0 Li þ Li Á i Frenkel defect pair. [25]Besides, as shown in Figure 4e, the migration path and energy barrier of V 0 Li do not change owing to the weak binding ability of V Á Br to V 0 Li .Through the above analysis, it could be concluded that Li Á i is the dominant defect contributing to the conductivity of Li + in bulk Li 3 OBr, and V 0 Li þ V Á Br with low formation energy is also a possible type of carrier for the fast Li + ion conductivity in the bulk Li 3 OBr.

Li-Ion Migration at the Li 3 OBr (100) Surface
The migration of Li + ions at the surface shows a different mechanism than in the bulk Li 3 OBr.For the V 0 Li migration at the LB(100) surface, as shown in Figure 5a, two possible migration paths for a single V 0 Li have been investigated: path 1 represents V 0 Li directly moving to the adjacent Li site at the surface.Path 2 indicates the cooperative transition path of the adjacent Li atoms at the surface and subsurface layers, namely, V 0 Li at the surface moves to the adjacent subsurface Li site, and V 0 Li at the subsurface moves to the nearest Li site at the surface.Besides, another path (path 3) which refers to the separate V 0 Li migration between the sub-surface and surface Li sites.Because the formation energy of the sub-surface V 0 Li is 0.21 eV higher than the surface V 0 Li (Table S3, Supporting Information), the path 3 is not considered.The diatomic cooperation at the surface and subsurface significantly lower the V 0 Li migration barrier from 0.58 to 0.17 eV, indicating a fast Li + migration at the LB(100) surface (Figure 5a).The V 0 Li migration in the V 0 Li þ Li Á i defect pair shows a similar migration energy barrier and migration path (Figure 5b), indicating that Li i has a little influence on the migration of V 0 Li at the surface.A similar investigation has also been performed for the V 0 Li migration modulated by V Á Br via calculating the migration characteristics of V 0 Li along path 1 and path 2 (consistent with path 1 and path 2 in Figure 5a).The migration barriers of V 0 Li are extremely high in both paths, even higher than in the bulk Li 3 OBr, indicating that V Á Br hinders V 0 Li migration at the surface and thus has a little effect on improving the ionic conductivity of material surface (Figure 5c).
For Li i , the most stable location at the LB(100) surface was first examined.By calculating the minimum configuration energies (Table S4, Supporting Information) for five possible locations at the surface (Figure S6d, Supporting Information), it has been found that Li Á i could stably adsorb on the surface instead of intercalating into the sublayer and the inner surface (labeled as Li i-ad ).According to their stable location, three migration paths were considered (Figure 5d).Path 1 and path 2 represent Li i-ad at the surface layer directly moving to the adjacent Li site along the direction of Br and Li atoms, respectively.Path 3 indicates the cooperative transition path of Li i-ad and adjacent Li atoms at the surface.It is to be noted that the migration energy barrier of Li i-ad along path 1 (0.02 eV) is much lower than those along path 2 (0.21 eV) and path 3 (0.53 eV), and also lower than in bulk (0.17 eV).This implies that the interaction with Br atoms easily mediates Li Á i migration at the LB(100) surface.The preferable migration path illustrates that Li Á i migration at the surface is conducive to long-distance migration and is also beneficial for the fast ionic conductivity of Li + .Also, the Li Á i in the V 0 Li þ Li Á i Frenkel defect pair in the bulk may migrate to the surface before recombination to supply an abundant Li Á i source for the fast ionic conductivity of Li + at the surface.The V 0 Li defect environment leads to enormous local strain on the surrounding surface of Br atoms, changing the Li i-ad migration path from the straight line of path 1 (Figure 5d) to the zigzag path 1 (Figure 5e).Even then, Li i-ad migration energy barrier in the V 0 Li þ Li Á i Frenkel defect is as low as 0.08 eV, signifying that the V 0 Li defect environment has negligible influence on the migration of Li Á i at the surface.Therefore, Li Á i is the dominant Li migration carrier at the surface contributing to the fast ionic conductivity of Li 3 OBr.
One of the most prominent advantages of solid-electrolyte is the good compatibility with Li metal anode without the Li dendrite problem that commonly encountered in liquidelectrolyte.AIMD simulation provides an indepth analysis of the mechanism of avoiding the formation of Li-dendrites between the Li 3 OBr electrolyte and Li anodes, as shown in Figure S7, Supporting Information.In the calculations, both the perfect Li 3 OBr and that with Li Á i and V 0 Li defects are in contact with the Li anode.It is seen that both the total energy and temperature of Li 3 OBr with point defects only oscillate within small ranges, and there is no significant structure distortion at an elevated temperature of 500 K, proving the defective Li 3 OBr solid electrolytes are thermodynamically stable at an elevated temperature of 500 K.Although the Li anode distorts greatly, the Li + in the Li 3 OBr do not diffuse into the Li electrolyte.Meanwhile, the Li atoms in the anode do not diffuse into the perfect Li 3 OBr electrolyte and the electrolyte with V 0 Li far away from the interface (Figure S7a,d, Supporting Information).When V 0 Li locates at the surface of Li 3 OBr, the Li atom in the Li electrode diffuses to fill the V 0 Li , but the Li does not diffuse into the Li 3 OBr electrolyte again (Figures S7c, Supporting Information).These results illustrate that there are no sufficient sources of Li at the interface to form Li-dendrites.On the other hand, the calculated difference charge densities for the V 0 Li defect in the bulk Li 3 OBr and its surface showed that the charges accumulate at the neighboring O and Br atoms for the V 0 Li , while the nearest-neighboring Li atoms do not participate in the charge transfer process (Figure S8, Supporting Information).This demonstrates that the reduction process of Li + to Li 0 is not preferable.The experiments also revealed that the interfacial contact between Li and isologue Li 3 OBr (i.e.Li 3 OCl) is relatively smooth and compatible without observing Li-dendrites. [16,21]Therefore, the formation of Lidendrites is not the dominant factor that reduces the stability of Li 3 OBr during the electrochemical cycles.

Structure of the Grain Boundary and the Li-Ion Migration Across the Grain Boundary
It has been reported that the GBs could hinder Li ion migration in Li 3 OX materials; [16,20,21] hence, the microscopic mechanism of Li + migration through the GBs of Li 3 OBr was further investigated.The Σ5 GB is recognized as a typical GB consisting of the most important i Frenkel defect pair, and e) V 0 Li in the V 0 Li + V Á Br Schottky defect pair in the bulk Li 3 OBr.The connected green and black spheres correspond to the migration paths of V 0 Li and Li Á i , respectively.The dark blue sphere represents V Á Br .The connected orange spheres simultaneously represent mobile V 0 Li or Li Á i .
features of GBs, which has already been widely observed in other materials. [30]Thus, two kinds of Σ5 GBs for Li 3 OBr, Σ5(210) and Σ5(310) were constructed, as shown in Figure 6a,b, respectively.The x direction is perpendicular to the GB plane, whereas the y and z directions represent the GBs plane.The GB energy (γ GB ) [31] is calculated by following Equation (8).
where E tot GB ð Þ and E tot bulk ð Þ are the total energies of a pristine GB supercell and a bulk lattice with the same number of atoms.S is the area of the GB interface.The outcome of calculations show that the GB energies of Li 3 OBr Σ5(210) and Σ5 (310) are lower than Li 3 OCl [32] and other perovskite oxides, [33] confirming that the GBs can be easily formed in the Li 3 OBr crystals.Because Σ5(210) GB has a lower GB energy than Σ5(310) GB, the electronic structures of Σ5(210) GB of Li 3 OBr were explored.It is found that the dangling bonds at the GBs introduce interface levels into the band gap, and the GB states are mainly contributed by the O 2p and Li 2s states (Figure 6c), indicating that Li + migration through the GB may be influenced by the interaction between Li and O atoms at the GBs.It is also seen from Figure 6d that the space charge distributions of both VBM and GB states are around GBs, further verifying the inhibition of electron and ion migration by the GBs.The formation of GB states in the band gap could reduce the electrochemical stability of Li 3 OBr compared to the bulk area.However, GB leads to an obvious anisotropy of the macroscopic electrostatic potentials.As shown in Figure 6e, the macroscopic electrostatic potential along the x direction, perpendicular to the GB plane, significantly increases in the GB area, illustrating a blocking effect on the electron transport and can effectively reduce the self-discharge rate of Li 3 OBr SSE.The macroscopic electrostatic potentials along the y and z directions, parallel to the GB plane, remain level, indicating that GB could block the electrical conductivity only through the GB instead of along the GBs.
On the other hand, GB proves to possess atom segregation feature that significantly influences material properties. [34,35]Hence, the segregation tendency of Li atoms towards the Σ5(210) GB of Li 3 OBr was investigated by calculating the segregation energy (γ seg ) based on the following Equation ( 9). [36]seg ¼ E GB ÀE bulk (9)   where E GB and E bulk are the formation energies of segregation atoms in the Σ5(210) GB and bulk, respectively.E GB and E bulk can be calculated using the following Equations ( 10) and (11), respectively.
where E GB-im and E bulk-im are the total energies of GB or bulk with n impurity atoms, and E GB and E bulk represent the total energies of GB and bulk without impurity.μ i is the chemical potential of the i Schottky defect pair at the LB(100) surface.The connected green and black spheres correspond to the migration paths of V 0 Li and Li Á i , respectively.The dark blue sphere represents V Á Br .The connected orange spheres simultaneously represent mobile V 0 Li or Li Á i .
impurity atom.A negative value of γ seg indicates the preference of segregation towards GB from the bulk environment.γ seg of Li near the Σ5(210) GB is much smaller than those far away from the GB (Figure S9a and Table S7, Supporting Information), indicating that GB prefers to trap Li atoms, thereby making Li migration through the GB becomes quite difficult.Based on this, the migration of Li across the GB can only be in the form of V 0 Li , rather than Li Á i , which is easily segregated.The calculated defect formation energies of V Li (Table S8 and Figure S9b, Supporting Information) denote that V 0 Li is more likely to generate near the GB than in bulk and at the surface.Therefore, the migration mechanism of V 0 Li through the GB was focused on finding a strategy to promote the migration of V 0 Li by regulating the defects.
Three V 0 Li migration paths perpendicular to the GB were considered, and only path 1 with the lowest energy barrier is shown in Figure 7a (path 2 and path 3 can be seen in Figure S10, Supporting Information).It is observed that V 0 Li migrates across the perfect GB through path 1 (initial → 1 → 2 → final) has a relatively low barrier (0.28 eV), which is lower than in bulk (0.33 eV), indicating that the GB could not limit V 0 Li diffusion in the whole Li 3 OBr SSE.However, when the GB segregates a few Li atoms, V 0 Li migration is hindered to some extent.As shown in Figure 7b, Li 1 is the most easily segregated location, which can repel Li atoms in the normal site into the deep GB (gray path).When V 0 Li moves from initial to position 1, the Li 1 diffuses to position 1 with a low diffusion barrier of 0.15 eV, leading to the annihilation of V 0 Li and Li Á i , thereby blocking subsequent Li migration.When Li Á i locates at the less stable site (Li 2 in Figure 7c), Li 2 in the GB increases V 0 Li migration barriers of 1 → 2 and 2 → final, which is not beneficial for V 0 Li migration across the GB.Therefore, it is necessary to find a microstructure that can greatly reduce the migration energy barrier of V 0 Li at the GB, so that V 0 Li can have a greater advantage to cross the GB, rather than being bound or annihilated by the Li atoms at the GB.
Halide ions inside the transfer path channel were greatly affected by the energy barrier of Li migration in Li 3 OCl 1-x Br x .The energy became higher in the presence of more Br ions. [37]As V Br is one of the possible point defects in Li 3 OBr, the influence of V Á Br on the migration of V 0 Li across the GB was investigated.As shown in Figure S11a, Supporting Information, the formation energies of V Br in Σ5(210) GB are lower than in the bulk Li 3 OBr and LB(100) surface, indicating that V Á Br formation in the Σ5(210) GB is easy.Meanwhile, the calculation results show that the formation energy of a single V Á Br could be further decreased by forming double, triple and quintuple V Á Br complexes in the GB (Figure S11b-d, Supporting Information).With increase in the concentration of V Á Br defect, the distribution of V Á Br tends to extend from inside the GB to the outside until it leaves the GB region.Hence, the impact of V Á Br being inside and outside GB on V 0 Li migration across the GB was considered (Figure 7d,e).The calculated V 0 Li migration barriers exhibit that V Á Br inside the GB cannot promote V 0 Li migration across the GB by significantly increasing the energy barriers of 1 → 2 and 2 → final (Figure 7d) due to the induced large lattice distortion in the GB structure by the inside V Á Br (Figure S12, Supporting Information).On the contrary, V Á Br outside the GB significantly reduces V 0 Li migration energy barriers of each step along the initial→1 → 2 → final path (Figure 7e), demonstrating that the presence of V Á Br outside the GB could greatly overcome the undesirable hindrance arising from the GB to V 0 Li migration across the GB.In this case, the migration path of Li ions in the whole Li 3 OBr crystal is opened, which is conducive to improving the ultrafast Li ionic conductivity performance of the Li 3 OBr crystal as a solid-state electrolyte material.It should be noticed that the V Br will not cause the dimerization of adjacent O atoms and release of O 2 (with the O-O distances >3.9 Å, much larger than the bond length of 1.227 Å in O 2 molecule), as shown in Figure S13, Supporting Information, and therefore, the formation of V Br will not damage the structural stability of Li 3 OBr and cause the secondary reaction.

Conclusion
In summary, the defect chemistry in Li 3 OBr has been systematically investigated.The effect of point defects on the migration of Li-ion in the bulk Li 3 OBr, at the LB (100) surface and Σ5(210) GBs were explored using the first-principles calculations.The calculations verify that the perfect bulk Li 3 OBr is not a fast ionic conductor.It has been noted that the driving force of Li-ion migration in the bulk, surface and GB structures is strongly dependent on the defect types.Li Á i contribute significantly to the ionic conductivity of bulk Li 3 OBr and the (100) surface.However, Li Á i are very easily separated by the GB, making them difficult to migrate across the GB.The calculation results illustrate that V 0 Li could act as the dominant carrier for the migration of Li across the GB.Single V 0 Li is difficult to cross the interface between the perfect lattice and the GB because of the relatively high migration energy barrier and the annihilation effect of Li atoms at the GB.However, by introducing V Á Br outside the GB, the energy barrier of Energy Environ.Mater.2024, 7, e12627

Figure 1 .
Figure 1.a) Crystal structure of the bulk Li 3 OBr with Li 6 O octahedrons, and the coordination environments of Li 12 Br cuboctahedron and LiO 2 Br 4 octahedron.b) Li + probability density distribution in the bulk Li 3 OBr obtained from AIMD simulation at 500 K. Self-part G s (t, r) and distinct-part G d (t, r) of the van Hoff correlation functions at c, d) 500 K and e, f) 1200 K.

Figure 2 .
Figure 2. a) Crystal structures of the LB(100) surface and the corresponding atomic displacement along the z-axis.b) Partial density of states (PDOSs) of the bulk Li 3 OBr, LB(100) surface and the exposed layers of LB(100) surface.c) Probability density distribution of Li + at the LB(100) surface from AIMD simulation at 500 K.

Figure 3 .
Figure 3. Mean square displacement (MSD) of Li as a function of time at 1200 K for perfect bulk Li 3 OBr, as well as Li 3 OBr withV 0 Li , Li Á i , V 0 Li þ Li Á i ,and V 0Li + V Á Br defects.The illustration shows the diffusion coefficient (D) of each defect.

Figure 4 .
Figure 4. Migration pathways and energy barriers of single a) V 0 Li , b) Li Á i , c) V 0 Li in the V 0 Li þ Li Á i Frenkel defect pair, d) Li Á i in the V 0 Li þ Li Ái Frenkel defect pair, and e) V 0 Li in the V 0 Li + V Á Br Schottky defect pair in the bulk Li 3 OBr.The connected green and black spheres correspond to the migration paths of V 0Li and Li Á i , respectively.The dark blue sphere represents V Á Br .The connected orange spheres simultaneously represent mobile V 0 Li or Li Á i .

Figure 5 .
Figure 5. Migration pathways and energy barriers of a) singleV 0 Li , b) V 0 Li in the V 0 Li þ Li Á i Schottky defect pair, c) V 0 Li in the V 0 Li þ V Á Br Frenkel defect pair, d) Li Á i , and e) Li Á i in the V 0 Li þ Li Ái Schottky defect pair at the LB(100) surface.The connected green and black spheres correspond to the migration paths of V 0Li and Li Á i , respectively.The dark blue sphere represents V Á Br .The connected orange spheres simultaneously represent mobile V 0 Li or Li Á i .

Figure 6 .
Figure 6.a, b) Grain boundary structures and energies of Σ5(210) and Σ5(310) in Li 3 OBr, respectively.c) Band structure and spin density of states of Li 3 OBr Σ5(210) grain boundary.d) Space charge distributions of the GB states and VBM of Li 3 OBr Σ5(210) grain boundary.e) Potential distributions of the Li 3 OBr Σ5(210) grain boundary along different directions.

Figure 7 .
Figure 7. Migration pathways and energy barriers of a) singleV 0 Li , V 0 Li in the V 0 Li þ Li Á i Frenkel defect pair with b, c) different Li Á i locations, and V 0 Li in the V 0 Li þ V Á Br Schottky defect pair with d, e) different V ÁBr locations in the Li 3 OBr Σ5(210) GB.The black and yellow spheres correspond to Li Á i and V Á Br , respectively.Connected orange, purple, and green spheres correspond to the migration paths of V 0Li .

Table 1 .
Defect formation energies of different defects in the bulk Li 3 OBr and LB(100) surface.