Anti-perovskites for solid-state batteries: recent developments, current challenges and future prospects

Current commercial batteries cannot meet the requirements of next-generation technologies, meaning that the creation of new high-performance batteries at low cost is essential for the electri ﬁ cation of transport and large-scale energy storage. Solid-state batteries are being widely anticipated to lead to a step improvement in the performance and safety of batteries and their success is heavily dependent on the discovery, design and optimisation of the solid electrolytes that they are based on. In recent years, Li-and Na-rich anti-perovskite solid electrolytes have risen to become highly promising candidate materials for solid-state batteries on the basis of their high ionic conductivity, wide electrochemical window, stability, low cost and structural diversity. This perspective highlights experimental and atomistic modelling progress currently being made for Li-and Na-rich anti-perovskite solid electrolytes. We focus on several critical areas of interest in these materials, including synthesisability, structure, ion transport mechanisms, anion rotation, interfaces and their compatibility with anti-perovskite cathodes for the possible formation of anti-perovskite electrolyte-and cathode-based solid-state batteries. The opportunities and challenges for the design and utilisation of these materials in state-of-the-art solid-state batteries are also discussed. As featured throughout this perspective, the versatility, diversity and performance of anti-perovskite solid electrolytes make them one of the most important materials families currently under consideration for solid-state batteries.


Theodosios
Famprikis is currently a postdoctoral researcher at Technical University of Del in the Netherlands in the group of Professor Wagemaker.He has been researching ionic conductors for batteries for over ve years under the direction of Professors Masquelier, Islam and Zeier.His expertise includes the synthesis and diverse physicochemical characterisation of inorganic materials with the goal of fundamentally understanding ion conduction in the solid state.He has recently received two thesis awards from the French Chemical Society, as well as a Ludo Frevel Crystallography Award from the ICDD for his PhD work on solid electrolytes.

Introduction
The pursuit of improved energy storage is currently one of the most important scientic challenges.][10][11] One such example architecture is the solid-state battery, 8,[12][13][14][15] which relies on solid electrolytes and the fast ion conduction they deliver.Solid-state batteries are oen touted as having two main advantages over conventional Li-ion batteries.5][26] Solidstate batteries have been described as the battery technology of the 2030s but the research challenge of the 2020s. 27nic conduction in the solid state is the key enabler of solidstate batteries and is delivered through the use of solid electrolytes that can exhibit ion conductivity at levels competitive with that of liquid electrolytes.7,28 These solid electrolytes can be inorganic, polymer based or hybrids of the two.][36][37][38] Oxides (e.g., b 00 -alumina and NASICONs) and sulphides (e.g., Na 3 PS 4 and Na 10 SnP 2 S 12 ) also dominate the most promising Nabased candidates for solid-state batteries, 13,[39][40][41][42][43] with recent compositions offering ion conductivities higher than even that of Li 10 GeP 2 S 12 , such as Na 2.88 Sb 0.88 W 0.12 S 4 . 449][60][61] Despite their importance in this burgeoning eld and the wealth of experimental and computational studies dedicated to their design and performance, to the best of our knowledge, anti-perovskite solid electrolytes for batteries have yet to be thoroughly reviewed in the literature.
In this perspective, we highlight the fundamental progress that has been made for anti-perovskite solid electrolytes in a number of exiting areas via the combined efforts of experimentalists and modellers.We also draw attention to potential future trends and opportunities for these versatile materials and the challenges they face for their application in solid-state batteries.The anti-perovskite structure and its compositional diversity, as well as a brief history of fast ion transport in antiperovskites, are rst presented.Synthesisability is a complex issue for anti-perovskite solid electrolytes and has resulted in signicant confusion within the battery community.We assess the synthesisability of these materials with a particular focus on the fundamental differences between dry and hydrated Li-and Na-rich anti-perovskites.The structures of these hydrated materials are also heavily debated and we seek to clarify some of the misconceptions in this area.We next consider the atomicscale mechanisms that govern ion transport in these materials and the factors that drive them.One such factor is anion rotation and its considerable inuence on ion diffusion in antiperovskites is addressed here.Finally, we review the microstructural properties of anti-perovskites and their compatibility with electrodes, including anti-perovskite cathodes for the potential design of a solid-state battery with both an antiperovskite electrolyte and cathode.

Fundamentals and history of antiperovskite solid electrolytes
3][64][65][66] In the conventional ABX 3 perovskite structure, the A and B sites are occupied by cations while the X site is an anion, with the archetypal example being CaTiO 3 , which was rst discovered in the Ural Mountains of Russia in 1839. 67In anti-perovskites, the cation and anion sublattices are inverted so that the A and B sites are now occupied by anions and the X site is a cation, as shown in Fig. 1.The B-site anion is octahedrally coordinated to six cations and the A-site anions are cuboctahedrally coordinated to 12 nearest-neighbour cations.The ideal (anti-)perovskite structure is cubic (Pm3m, no.221) but can also readily exhibit tetragonal, orthorhombic, rhombohedral and hexagonal phases, depending on temperature, pressure and the composition of the material. 68,69nti-perovskites can behave as metals, semiconductors, insulators and even superconductors, meaning they can exhibit a range of interesting (and sometimes unusual) physical properties, including giant magnetoresistance (e.g., Mn 3 GaC), 70 superconductivity (e.g., Ni 3 MgC), 65 zero thermal expansion (e.g., Mn 3 CuN), 71 piezomagnetism (e.g., Mn 3 GaN) 72 and electrocatalytic activity (e.g., Ni 3 CuN). 63Hence, they have the potential to be used in an array of applications.Whilst the research focus for anti-perovskites has mostly been on the vast array of synthesised compositions, naturally occurring variants are also common and represent important structural units in various minerals. 66n this perspective, we focus on Li-and Na-rich antiperovskites for solid-state battery applications, which have experienced a remarkable rise in interest in recent years.Before discussing recent developments in this area, here we provide a short historical overview of their discovery and development.The rst structural and conductivity analyses of Li-rich antiperovskites (Li 2 (OH)Br and Li 2 (OH)Cl) were reported by Hartwig et al. 73,74 in 1981 during their investigations of the phase equilibria of the quasi-binary systems of LiBr-LiOH and LiCl-LiOH.This work extended the much earlier phase-diagram investigations of lithium-hydroxide-lithium-halide systems. 75,76n the anti-perovskite structure of these two materials, two thirds of the X sites are occupied by Li ions while the rest are vacant.The A and B sites are fully occupied by hydroxyl and halide groups, respectively.Despite the high lithium vacancy concentration in Li 2 (OH)Br and Li 2 (OH)Cl, both materials showed unexpectedly low ionic conductivities of 5 Â 10 À5 and 3 Â 10 À5 S cm À1 at 473 K, respectively.A high activation energy of 0.97 eV was also reported for Li 2 (OH)Cl.In addition to this, both materials readily reacted with lithium metal. 73,74he dehydrated form of Li 2 (OH)Br (Li 3 OBr) was reportedly rst prepared and characterised by Wortmann et al. in 1989. 77 This material shares the same cubic structure as Li 2 (OH)Br but with all lithium sites now fully occupied.No information regarding its ionic conductivity was reported.A later study by Eilbracht et al. 78 examined the deuterated forms of these materials, as well as the related LiBr$D 2 O anti-perovskite using X-ray and neutron diffraction and NMR spectroscopy.They discovered that both Li 2 (OD)Cl and LiBr$D 2 O exhibited a rstorder transition from orthorhombic to cubic symmetry at 330 and 305 K, respectively.Solid-state 2 H NMR spectroscopy also indicated a dynamical orientational disordering of the OD À and D 2 O molecules in high-temperature cubic modications, indicative of free deuteron rotation.
Schwering et al. 79 extended this work by systematically investigating the phase transitions and Li-ion conductivity of Li 3Àn (OH n )A (0.83 # n # 2; A ¼ Cl or Br) using a range of experimental techniques.The authors conrmed the previous phase transitions observed by Eilbracht et al. 78 and showed that the OH À and H 2 O species in the non-cubic phases are static and block lithium ions, thereby suppressing the Li-ion conductivity (<10 À8 S cm À1 ) in these materials.In contrast, in the cubic phases, where the OH À and H 2 O species rotate freely, the number of accessible positions for the Li ions increases and the ionic conductivity ($10 À4 S cm À1 at 323 K for Li 2 (OH)Cl) is therefore enhanced.A wide range of activation energies for Liion conduction in the cubic materials were also reported, with values of $0.56-0.88 and $0.26-0.46eV from impedance and 7 Li NMR measurements, respectively.Generally, the Cl-based materials had the highest conductivities and lowest activation energies, while the opposite was true for Br-based systems.It is noteworthy that even a decade before the current interest in anti-perovskite solid electrolytes began, Schwering et al. 79 had noted the potential of these materials as ion conductors with tuneable properties.
The rst report of a Na-rich anti-perovskite was Na 3 NO 3 by Zintl and Morawietz 80 in 1938.In this material, the X sites are occupied by Na ions and the A and B sites are occupied by NO 2 À and oxide anions, respectively.This initial investigation of Na 3 NO 3 was then extended by Klemenc and Gutmann 81 and Jansen 82 in 1950 and 1977, respectively, with the latter utilising X-ray experiments on single crystals to determine that the NO 2 À anion is disordered, a feature we return to below.It was not until 50 years aer the discovery of Na 3 NO 3 that the synthesis of the rst alkali metal chalcogenide halides, Na 3 OCl and Na 3 OBr, was reported by Sabrowsky et al. 83 This work help to lay the foundation for the current renaissance in Na-rich antiperovskite solid electrolyte research.
The rst Na-ion conductivity studies of Na 3 OBr and Na 3 NO 3 , as well as another anti-perovskite Na 3 OCN, were led by Jansen et al. 84,85 in the early 1990s.The authors reported substantial increases in conductivity at specic temperatures for each of these three materials.In the case of Na 3 NO 3 and Na 3 OCN, 85 these increases were ascribed to either melting of the sodium sublattice or the rotational disorder of the NO 2 À and CN À anions at higher temperatures.The coupling between cation transport and the rotational motion of anions is known as the "paddlewheel" mechanism and is an important factor in enhancing the conductivity of many solid electrolytes, [86][87][88][89] including anti-perovskites, as discussed below.For example, in the case of Na 3 OCN, Jansen et al. 85 observed an increase in Naion conductivity of around three orders of magnitude from $10 À5 S cm À1 at 480 K to $10 À2 S cm À1 at 500 K.
Interest in anti-perovskite materials has risen dramatically recently due to the discovery of their potential as Li-and Nabased solid electrolytes for solid-state batteries.This surge in attention primarily arose from the work of Zhao and Daemen 45 in 2012, who reported superionic conductivity in the Li-rich anti-perovskites Li 3 OCl (rst reported a year before by Reckeweg et al. 90 ), Li 3 OBr and Li 3 OCl 0.5 Br 0.5 for the rst time.The authors reported Li-ion conductivities of >10 À3 S cm À1 at room temperature with low activation energies (0.2-0.3 eV), low electronic conductivity and favourable voltage and current operation windows for these materials.They also emphasised the benets of the anti-perovskite structure in terms of structural manipulation and electronic tailoring.However, as we discuss in subsequent sections, the structural determination in these studies is limited by the fact that they only use X-ray diffraction, which is not sensitive to lighter elements, such as lithium or hydrogen content, meaning that differentiation between dry and hydrated phases (e.g., Li 3 OCl vs. Li 2 OHCl) is not possible.
This discovery has led to a wealth of studies on the ion transport, stability and interfacial properties of Li-and Na-rich anti-perovskite solid electrolytes.While the main focus on these materials has been centred on the tuning and performance of cubic Li-and Na-based oxyhalides, recent developments, as detailed below, have seen the synthesis, modelling and characterisation of more diverse and exotic compositions, including mixed-halide, superhalide and mixed-chalcogenide and double and Ruddlesden-Popper anti-perovskite structures.The application of Li-rich and Na-based Ruddlesden-Popper antiperovskites as battery cathode materials has even been proposed in recent years, which raises the question of whether solid-state batteries with both anti-perovskite electrolytes and cathodes could be designed in the near future.

Synthesisability challenges for antiperovskite solid electrolytes
A crucial rst step when designing new (anti-)perovskite materials is an assessment of their stability.The stability of a given (anti-)perovskite can be estimated using the Goldschmidt tolerance factor, t, 68,91 which is a dimensionless parameter calculated from the ratio of the ionic radii of the constituent ions in the material: where r A , r B and r X are the radii of the A, B and X ions, respectively.A value of t ¼ 1 represents the perfect case for the formation of a cubic structure.For values of t ¼ 0.8-1, the perovskite structure can still form but it becomes distorted and the symmetry is lowered, resulting in deviations from the ideal cubic structure. 68,92ig. 2 presents a schematic summary of Li-and Na-antiperovskite compositions that have been successfully synthesised, attempted and predicted so far (see also Table 1).This representation makes it apparent that the tolerance factor is not an adequate descriptor of stability for anti-perovskite battery materials.The most successfully synthesised compositions lie in the range 0.75 < t < 0.9 and they contain a small selection of Bsite anions (O 2À , OH À or H À ; see diagonal ribbons in Fig. 2).Despite many predictions (see Table 1) and some attempts, [93][94][95] no successful synthesis of Li-or Na-anti-perovskites with S 2À on the B site has been reported; even when combined with a large Fig. 2 Synthesisability of anti-perovskite battery materials as a function of the A-site anion radius and the Goldschmidt tolerance factor.The thermochemical radii used for anions are taken from ref. 96 and 97 (as listed in Table 1).The radii for Li + and Na + are taken from ref. 98.
Table 1 Chemical flexibility of anionic framework formers in Li-and Na-rich anti-perovskites, Li 3 BA and Na 3 BA.Shape and size of possible anionic species occupying the 6-and 12-coordinate sites, respectively, with associated notable compositions discussed in the literature Anion Shape (point group) Shannon radius a,98 ( A) Thermochemical radius b ( A) 96,97 Notable compositions      B-site cation so that the tolerance factor falls in the above identied range, e.g., Na 3 SPF 6 .In this sense, the identity of the B-site anion is a better indicator of stability than the tolerance factor. 95Larger A-site cations and smaller B-site anions that push the tolerance factor closer to unity do not lead to synthesisable compositions, as highlighted by the examples of Na 3 OI and Na 3 FS, respectively.In addition to our own analysis presented above, a recent study has highlighted the limited performance of this factor in predicting the structures for regular perovskites with heavier halides, such as Cl, Br and I. 99 This is clearly a severe limiting factor for anti-perovskite solid electrolytes given that they generally contain halide ions.
It is feasible that some of the limitations associated with the tolerance factor could be linked directly to the specic values of the input parameters, i.e., the Shannon radii values typically used. 98For example, in the case of halide containing antiperovskites, the values used may not be an accurate or true representation of the cation/anion environment within the structure, e.g., the Shannon radii values reported for the halides are not representative of the 12-coordinate sites they occupy. 98imilarly, the values reported for Li and Na do not necessarily account for any mobility/motion exhibited by the ions in this specic structure, i.e., in reality, the effective radii are likely to be larger than those tabulated, in agreement with the large cation voids and thermal atomic displacements reported for anti-perovskite cathode materials. 100In addition, this issue is further exacerbated by the fact that the coordination of Li and Na is not binary but ternary (i.e., combined coordination with two anions) in these materials, leading to discrepancies in Li-O and Li-halide bonds, as discussed in Ahiavi et al. 95 Hence, for anti-perovskite battery materials, it is possible that using Shannon radii values not fully representative of the environment of the ion could be contributing to the inaccuracies exhibited by the Goldschmidt tolerance factor.][103] Similarly, it is difficult to utilise Shannon-type radii for calculations of the Goldschmidt tolerance factor for antiperovskites containing cluster ions (e.g., BH 4 À , BF 4 À , NO 2 À and so on).This is because there are no straightforward methods to approximate an equivalent spherical radius for a non-spherical molecular anion.In addition, such an equivalent spherical radius of a molecular anion would be effectively dependent on its orientation in a given structure, i.e., smaller for an ordered (immobile) instance of the polyanion and larger for a disordered (possibly mobile) instance of the same.A practical solution might be to switch to a method that can derive radii for atomic and cluster species self-consistently.One such approach is to utilise thermochemical radii, derived from thermodynamic calculations of the lattice energy of crystals. 96,97This approach is agnostic of the crystal structure, shape and orientation of cluster ions and treats all ions (atomic or molecular) as spherical, deriving an equivalent spherical radius.Table 1 shows a comparison of Shannon-type and thermochemical radii for atomic anions, as well as the thermochemical radii for common complex anions considered in anti-perovskite research.
Whilst there are challenges associated with predicting the stability of anti-perovskites, experimentally, their hygroscopic nature makes them challenging to synthesise and, as such, their preparation has been the subject of considerable debate in recent years. 47,51,73,79Numerous synthetic strategies have been attempted for some of the most commonly reported antiperovskites, including X 3 OA (X ¼ Li or Na; A ¼ Cl or Br) and Li 2 OHCl, a summary of which is given in Table 2.
In the case of Li 3 OCl, conventional solid-state methods have been proposed, with the starting reagents (typically Li 2 O or LiOH and LiCl) mixed in specic molar ratios and annealed at various temperatures for a variety of different times.The pressing of powders into pellets, mechanochemistry (i.e., ball milling) and the effects of different cooling strategies have all been explored to determine their inuence on both the structure and resulting physical properties.Similarly, hydrothermal-based methods and the preparation of thin lms via pulsed laser deposition (PLD) methods have all been investigated to establish their feasibility.
The favourable hydration of Li 3 OCl makes it particularly difficult to prepare truly H-free samples of Li 3 OCl.Zhao and Daemen 45 reported the apparent synthesis of Li 3 OCl via solidstate methods (albeit with very limited synthetic details).Since then, it has been suggested that the as-prepared samples presented were in fact the hydrated composition, Li 2 OHCl, owing to their propensity to take up moisture. 47,115,116A recurring issue in many studies of anti-perovskite materials, and particularly in the case of Li 3 OCl, is a lack of comprehensive structural characterisation and analysis.Typically, only the raw diffraction patterns are presented, with no corresponding Rietveld analysis performed, making it difficult to conrm the composition of the sample.As previously mentioned, determining whether samples are truly moisture free is challenging using solely X-ray diffraction and, as a result, it is also difficult to know whether the conductivities reported are accurate or enhanced due to the presence of protons/hydroxide anions. 45hang et al. 123 reportedly prepared samples of Li 3 OCl via the dehydration of Li 3 (OH) 2 Cl using high-pressure/temperature methods, whilst Braga et al., 48,124 reported the preparation of 'glassy' samples of Li 3 OCl using hydrothermal-based methods (Table 2).One notable feature of their synthesis was their intentional addition of deionised water to the precursor powder mixture, which is somewhat surprising given the widely reported hygroscopic nature of the target composition.Hanghofer et al. 116  Thin lms of Li 3 OCl were also reportedly fabricated via PLD methods using 'Li 3 OCl' targets. 125Room-temperature ionic conductivities were reported for both the lm (8.9 Â 10 À6 S cm À1 ) and source material for the target (5.8Â 10 À7 S cm À1 ).A subsequent study by the same research team explored PLD of Li 3 OCl lms on a composite target (Li 2 O : LiCl,     Wang et al. 108 1 : 1 molar ratio) with the use of a protective layer of ZnO on top of the Li 3 OCl lms to prevent any exposure to air or moisture during characterisation. 52It is suggested that using a composite target, without pre-formation of the desired Li 3 OCl, is efficient and the prepared target has a greater stability.An ionic conductivity of 2.0 Â 10 À4 S cm À1 was reported at room temperature, which is higher than in their initial study. 52,125The cyclability and compatibility of the Li 3 OCl lms prepared were also evaluated using symmetric Li/Li 3 OCl/Li cells.However, given the uncertainties surrounding the precise composition of the lms, these ndings should be treated with a degree of caution. 52,125n 2016, Li et al. 126 explored alternative solid-state routes for the synthesis of proton-free samples of Li 3 OCl, specically the use of Li metal and LiH as reducing reagents in the starting mixture to assist with the removal of any residual OH in the products formed.LiH was identied as an effective reducing agent, with the apparent formation of Li 3 OCl.However, the presence of residual starting reagents and/or the formation of hydrated phases could not be ruled out using these methods.Nevertheless, the authors showed that the presence of OH À in their samples could be tracked using FTIR when targeting a purely H-free product.
Based on our own ndings, as well as those of the community, we believe that the formation of Li 3 OCl is experimentally challenging, if not unfeasible, and, to date, has not been achieved or sufficiently proven via experiment.As such, we strongly believe that most, if not all, of the samples presented as 'Li 3 OCl' are in fact hydrated phases, most likely Li 2 OHCl or a similar composition along the LiOH-LiCl pseudo-binary phase diagram.This is in line with various computational studies in which Li 3 OCl is predicted to have a strongly exothermic hydration enthalpy 115 and a positive formation energy relative to a two-phase mixture of LiCl and Li 2 O. 60,127 Even when using 'dry' reagents, it is notoriously difficult to fully remove the presence of water, likely owing to the large O-H bond enthalpy.Based on the studies and nding presented, we recommend that all studies detailing the apparent synthesis of Li 3 OCl be treated with a degree of caution.Hence, the pursuit of obtaining H-and moisture-free samples of Li 3 OCl continues.
Interestingly, the signicant experimental challenges detailed above are not limited to solely Li 3 OCl, with reports that the synthesis of Li 3 OBr is equally as challenging.Again, computational studies have suggested the starting reagents, LiBr and Li 2 O, are more stable than the desired product. 128umerous synthetic strategies have been utilised to try and prepare samples of Li 3 OBr, as summarised in Table 2. Of these, the most notable are the studies of Li et al. 126 and Zhu et al., 128 where a combination of solid-state and ball milling methods was used to prepare samples of Li 3 OBr from Li 2 O and LiBr.Despite their 'phase pure' samples of Li 3 OBr containing small quantities of the starting reagents, this perhaps represents the most likely preparation of Li 3 OBr to date, as any potential source of water/hydroxide anions has been eliminated from the outset.
Our own studies of Li 3 OBr (unpublished) have suggested the presence of the related composition, Li 7 O 2 Br 3 , in addition to the staring reagents, again questioning the feasibility of preparing Li 3 OBr.Theoretical studies have suggested that both Li 3 OBr and Li 7 O 2 Br 3 are meta-stable relative to the starting reagents Li 2 O and LiBr. 128Hence, additional studies are needed to determine whether these anti-perovskite phases can actually be prepared.
As detailed above, hydrated Li-rich anti-perovskites can be (albeit oen inadvertently) prepared with considerable ease.In Li 2 OHA (A ¼ Cl or Br), two thirds of the available Li sites per unit cell are occupied. 78It is the presence of these vacancies that is believed to result in Li-ion diffusion and enhanced conductivities.Hence, similar to their non-hydrated counterparts, there is considerable interest in them as potential solid electrolytes and ion conductors.The potential inuence of the proton position and dynamics on the diffusion of the Li + ions is discussed in the following section.
The presence of OH À and halogens makes Li 2 OHA reactive and, as such, considerable care needs to be taken during synthesis to avoid any uncontrollable doping from occurring via unwanted reaction with the crucibles used, e.g., aluminium, nickel and silver. 45,51,79This is particularly important, as metal dopants can signicantly alter the physical properties, namely the ionic conductivity of the system.Similarly, it is vital that moisture is avoided, both during synthesis and subsequent characterisation by using a well-controlled, air-tight environment for both.Only then can it be said with both certainty and accuracy as to what the true composition of the sample is and how it relates to the physical properties observed.In contrast to Li 3 OA (A ¼ Cl or Br), where a synthetic strategy could not be agreed upon, there is general agreement that solidstate methods can be used to prepare samples of Li 2 OHA (A ¼ Cl or Br).Whilst the precise method can vary, i.e., different annealing times, with or without ball milling, fast versus slow cooling and so on, the same general strategy is adopted with LiCl and LiOH as the starting reagents.To date, numerous studies of Li 2 OHCl have been presented by a variety of different authors, including Schwering et al., 79 Hood et al., 51 Song et al., 58 Dawson et al., 115 Hanghofer et al. 116 and Wang et al., 117 as detailed in Table 2.
Hood et al. 51 explored the effects of different cooling rates on Li 2 OHCl where it was determined that, at elevated temperatures, 'fast cooled' samples of Li 2 OHCl exhibited the highest ionic conductivity.However, it is noted that no detailed explanation is given for the enhancement in conductivity and it is merely suggested that the increase is a result of defects in the crystal lattice.
Song et al. 58 recently prepared samples of Li 2 OHCl, Li 2+x -OH 1Àx Cl and Li 2 OHBr via a melt-casting method using an induction heater, graphite crucible and graphite mould.It has been suggested that rapid heating via induction heaters could enable materials to be synthesised quickly and in a scalable manner.Furthermore, the use of a graphite crucible and mould is an effective way of reducing unwanted side reactions and/or impurities.The authors noted the challenges associated with accurately identifying the presence of Li 2 OHCl by highlighting the numerous characterisation methods used when determining the composition of the sample.
Solid-state methods can also be used to prepare Li 2 OHBr (using LiBr and LiOH as the starting reagents). 47,58In contrast to Li 2 OHCl, the room-temperature structure of Li 2 OHBr is reported to be cubic and remains so as a function of temperature.However, it has been noted by Song et al. 58 that, as samples are heated, the irreversible formation of LiBr is observed.However, relatively speaking, Li 2 OHBr is a somewhat 'easier' system to study, both synthetically and structurally.
Numerous doping strategies have been suggested for improving the ionic conductivities of anti-perovskites, including halogen mixing (Li 3 OCl 0.5 Br 0.5 ), cationic doping (Li 3Àx Ca x/2 OCl) or a combination of the two (Li 3Àx Ca x/2 OCl 0.5 Br 0.5 ). 45,123,124owever, to date, few have been achieved experimentally, likely owing to the synthetic challenges associated with preparing Li 3 OA (A ¼ Cl or Br)-based compositions, as detailed above.Zhao and Daemen initially suggested the mixed halogen composition Li 3 OCl 0.5 Br 0.5 could be a promising ion conductor aer reportedly obtaining ionic conductivities of 1.94 Â 10 À3 and 6.05 Â 10 À3 S cm À1 at room temperature and 250 C, respectively. 45owever, these ndings have yet to be experimentally reproduced and validated.Other doping strategies have been reported, including those by Zhang et al. (Li 3Àx Ca x/2 OCl), 123 Braga et al. ((Li 3À2x M x OA), where M ¼ Mg, Ca or Ba, x ¼ 0.005 and A ¼ Cl À or I À ), 124 115 with varying degrees of success reported for each.
Like their Li counterparts, Na-based anti-perovskites have garnered considerable interest in recent years.Reports of superb ionic conductivities at room temperature for compositions such as Na 3 OBH 4 have added to the excitement surrounding these systems. 94Similar to Li 3 OA (A ¼ Cl or Br), the synthesis of the equivalent Na-based compositions via the direct reaction from sodium hydroxide and the respective halide by melting them together and removing the redundant water has not been reported, again likely owing to the difficulty of dehydrating NaOH.However, the successful synthesis of Na 3 OCl has been reported via the reaction of Na 2 O and NaCl (Table 2). 108,109imilar to the synthesis of Li-based compositions, trace amounts of the sodium halides are oen observed as impurity phases.It has been suggested that a signicant challenge associated with the synthesis of all Na-based anti-perovskites is the purity of the Na 2 O used during synthesis, with a particular emphasis on the importance of using high purity Na 2 O, which is rarely available commercially.Hence, to circumvent this, it is recommended that Na 2 O is made 'in house'.This presents an additional advantage when it is prepared from Na metal because Na metal is also an efficient scavenger for any residual hydroxyls in the system. 108hiavi et al. 95 recently demonstrated the use of mechanochemical methods (ball milling) for the efficient synthesis of numerous Na-rich anti-perovskites, Na 3 OA (A ¼ Cl, Br, I and/or BH 4 ).Using solely a planetary ball mill (i.e., no annealing) they were able to produce high-purity samples.Similar mechanochemical methods have also been used by Fan and co-workers to prepare other compositions, including Na 3 SO 4 F. 57 Similar to Li-based anti-perovskites, various doping strategies can be used to improve the ionic conductivities.Again, as for Li-rich anti-perovskites, divalent doping in the Na + sites will introduce more vacancies which are essential for high ionic conductivity and, at present, there are many possible doping strategies that still need to be evaluated to determine, not only their feasibility, but also their signicance and inuence.
It is noteworthy that, unlike their Li equivalents, there are currently no reports of any Na 2 OHA (A ¼ Cl or Br)-based compositions.As highlighted above, it is of particular note that Li 3 OA cannot be readily synthesised, whereas Na 3 OA can.Inversely, Li 2 OHA can be synthesised whereas Na 2 OHA cannot.Given that the effective radii of O 2À and OH À are practically identical, and the trends are reversed between Li and Na, these observations cannot be easily explained through ionic radii arguments and there must be other, more fundamental considerations that need to be taken into account.As this continues to be a topical area of interest, with various synthetic strategies and optimisations being proposed and explored for a variety of Li-and/or Na-based compositions, it is hoped that some of the outstanding challenges can be resolved and explained, as this will undoubtedly assist in driving the area forward and developing better ion conductors.

Structural elucidation complexities in anti-perovskite solid electrolytes
A crucial rst step in determining structure-property relationships is structural determination, i.e., the structure must be known if structure-property relationships are to be accurately identied and characterised.In the case of Li 2 OHCl, this is still the subject of considerable debate.It is widely accepted that Li 2 OHCl undergoes a phase transition to cubic symmetry (Pm3m) above $40 C and it is the existence of this phase that is reported to coincide with a substantial increase in ionic conductivity. 79,117It has been suggested by both theorists and experimentalists that a complex interplay exists between Li-ion migration and rotation of the OH À anions.Howard et al. 114 demonstrated that OH À bond orientations inuenced the Li + motion, whilst Song et al. 58 argued that there was correlated motion between OH À and Li + .Schwering et al. 79 also suggested that defect sites were formed within the structure by replacement of the Li ions with H, forming OH À or OH 2 units which 'freely' rotate in the high-temperature cubic phase of Li 2 OHCl.They also suggested there was a strong correlation between Li motion and OH À /OH 2 group rotation.
Experimentally, the existence of a complex relationship between the OH À groups and Li ions was veried by Dawson et al., 115 using a combination of 2 H magic-angle spinning (MAS) and 1 H and 7 Li pulsed-eld gradient (PFG) NMR spectroscopy.Here, the presence of long-range Li-ion mobility and limited H mobility in the high-temperature phase of Li 2 OHCl was conrmed, with the H identied as pointing towards Li vacancy sites and rotating around the O atoms.The presence of localised OH À groups was also later conrmed by Wang et al. 117 Using 2 H MAS NMR spectroscopy, Dawson et al. 115 conrmed the presence of two different OH À environments in the cubic phase of Li 2 OHCl, both static and locally rotating OH À groups.Early 2 H NMR studies by Eilbracht et al. 78 indicated dynamical orientational disordering of the hydroxide ions.Dynamic disorder of the OH À anion was also identied by Wang et al. 117 via maximum entropy method analysis of the neutron powder diffraction data obtained.As a result, the relative positions of the O and H could not be resolved.
In contrast, the room-temperature structure of Li 2 OHCl remains somewhat elusive.In recent years, numerous structures and space groups have been suggested, based on both experimental and/or computational studies, all of which are summarised in Table 3.However, to date, very few complete and accurate structural models have been presented.In addition, of those presented, none have, as yet, been reproduced or veried by the community, further highlighting the complexities associated with determining the room-temperature structure of this material.Early diffraction studies by both Barlage and Jacobs 131 and Eilbracht et al. 78 hinted at the signicant challenges  78 were able to identify weak superstructure reections and subtle orthorhombic splittings, but were unable to determine the structure, or even propose a space group from their neutron diffraction data.Since then, Schwering et al., 79 Hood et al., 51 Song et al., 58 Howard et al., 114,132 Hanghofer et al. 116 and Wang et al. 117 have all proposed different possible structures and/or space groups for the room-temperature phase of Li 2 OHCl, as summarised in Table 3. Whilst a comprehensive review of each structure/model is beyond the scope of this work, it is important to highlight the notable features of each study, as well as any discrepancies between studies, as outlined below.
Schwering et al. 79 suggested an orthorhombic structure, in space group Amm2.However, no corresponding structural model was presented, making it difficult for it to be evaluated.Hood et al. 51 explored the effects of post synthetic cooling strategies and their inuence on the phases of Li 2 OHCl formed.It was concluded that their 'fast cooled' samples exhibited a more complex crystal structure, with increased defects owing to the overcooling effect.Whilst the performance of their samples was discussed in detail, no Rietveld analysis was completed and only a comment regarding the presence of an orthorhombic phase at room temperature was made, without the suggestion of a space group.
Using a Pawley renement, Song and co-workers 58 suggested the room-temperature phase of Li 2 OHCl to be orthorhombic and, upon heating to 40 C, an orthorhombic (Pmmm) to tetragonal (P4mm) phase transition was reportedly observed.They highlight this phase transition as routinely being mistakenly treated as the widely reported orthorhombic to cubic phase transition.An additional phase transition was observed at 60 C, corresponding to the known cubic phase.Whilst schematic structural representations are given depicting the possible phase transitions, no structural models are provided. 58ombining the results of theoretical methods with experimental ndings for a series of 'slow cooled' samples, Howard and co-workers 114 proposed two potential structures of Li 2 OHCl: a tetragonal ground-state structure (P4mm) and a metastable state structure (Pmc2 1 ).The major difference between the two is the position of the OH À groups.In the ground-state structure, all of the OH À groups are oriented along the b axis, whereas in the metastable phase, the OH À groups are in opposite directions along the b axis.In a later study, also by Howard and Holzwarth, 132 an additional ground-state structure (Cmcm) was proposed for Li 2 OHCl.
Using neutron diffraction, Hanghofer et al. 116 explored a variety of different structural models for Li 2 OHCl and nally proposed an orthorhombic Pban structure.Most notably, similar to the structure proposed by Schwering et al., 79 a doubling of the unit cell was required to obtain the best t for the experimental data.The authors comment on the similarity of their renements using the Pban and Pmmm models.However, the Pban structure provided the best renement for the room-temperature neutron diffraction data.Full structural models, inclusive of H positions, are provided for both the Pban and Pmmm structures.The authors also highlight the possible presence of Li disordering. 116It is noted that the authors did not deuterate their samples for analysis via neutron diffraction, which is in contrast to many other neutron diffraction studies involving proton-containing samples. 117ang and co-workers 117 also recently investigated the roomtemperature structure of Li 2 OHCl using a combination of highresolution X-ray and neutron diffraction, quasi-elastic neutron scattering and conductivity measurements with ab initio molecular dynamics (AIMD) simulations.Combining the highresolution neutron diffraction data with AIMD calculations, an orthorhombic defective anti-perovskite model was identied in space group Pban, containing six separate Li positions and Hoccupied sites split into four possible positions.In addition, positional disordering was identied across the O, H and Li sites, which is in contrast to the earlier work of Hanghofer et al. 116 Interestingly, to accurately t the room-temperature Xray diffraction data obtained, three distinct, yet very similar, orthorhombic phases were needed, whereas a single phase was sufficient to t the neutron diffraction data.Again, this highlights the challenges associated with elucidating the roomtemperature phase of Li 2 OHCl.It has been proposed that different cooling strategies from the high-temperature cubic phase could be responsible for the structural discrepancies observed between the Hanghofer et al. 116 and Wang et al. 117 models.
The structural studies presented highlight the complexities associated with accurately determining the room-temperature structure of Li 2 OHCl, with the structure being considerably more complex than initially thought.For example, even the symmetry of the unit cell is still widely disputed, with both tetragonal and orthorhombic structures having been proposed.Several studies have also hinted at the presence of positional disordering, as well as possible microstructure effects based on sample preparation methods, all of which make structural elucidation considerably more challenging.Hence, at present, the room-temperature structure of Li 2 OHCl remains under investigation.

Li-and Na-ion transport mechanisms in anti-perovskite solid electrolytes
Given the central role ion transport plays in the performance, design and utilisation of solid electrolytes for solid-state batteries, it is not surprising that there is a vast collection of studies in the literature dedicated to increasing the ionic conductivity, lowering the activation energy and understanding the underlying mechanistic features of ion transport in fast ion conductors. 8,12,13,17,28,133The anti-perovskite family of solid electrolytes is no exception, as clearly illustrated in Table 4, which summarises the reported ionic conductivities and activation energies (both from experiment and modelling) for a vast array of anti-perovskites.With regards to modelling, signicant efforts have been committed to comprehending the atomistic features that control the motion of Li and Na ions in these materials.The rst computational study to investigate the ion transport mechanisms in Li 3 OCl, Li 3 OBr and Li 3 OCl 0.5 Br 0.5 was by Zhang et al. 134 in 2013.Using density functional theory (DFT) and AIMD simulations, the authors reported that Li vacancies and structural disorder are key to reducing the enthalpy barriers for Li-ion transport.The calculated Li-ion conductivities and activation energies from AIMD were in good agreement with the experimental work of Zhao and Daemen for Li 3 OCl and Li 3 OBr, 45 but the authors could not reproduce the enhanced Liion conductivity in the mixed Li 3 OCl 0.5 Br 0.5 phase.Alternatively, Emly et al. 60 carried out DFT calculations on the same materials and found a very low Li-ion migration barrier of $0.17 eV for all three systems via a three-ion hop mechanism involving Li interstitial dumbbells, as illustrated in Fig. 3(a).1][142] Nevertheless, despite this low energy pathway, the formation energies of Li interstitials in these materials were found to be high, meaning that it is unlikely that this is the mechanism responsible for the observed high conductivity.
Through the use of classical atomistic simulations, Mouta et al. 143 also investigated defect formation and Li-ion migration in Li 3 OCl.In agreement with earlier computational works, they reported low Li vacancy and high Li interstitial formation energies, with LiCl Schottky defects dominating the defect chemistry.Similar to Emly et al., 60 the authors found a larger vacancy migration enthalpy of 0.30 eV compared to a value of 0.13 eV for interstitial migration.However, given the predicted six orders of magnitude greater concentration of Li vacancies compared to Li interstitials, Li vacancies were deemed to be the major charge carriers and therefore vacancy migration the dominant transport mechanism.The same conclusion was also reached from combined DFT and larger scale classical molecular dynamics simulations of Li 3 OCl. 144In contrast, in a later study, Mouta et al. 145 reported that Li interstitials can become the dominant charge carriers in Li-rich anti-perovskites when they are sufficiently Li-halide decient with oxide ions occupying the vacant chloride sites.The conicting results from early theoretical studies have undoubtedly contributed to the confusion regarding the defect chemistry of these complicated materials.
Deng et al. 56 utilised DFT, AIMD and nudged elastic band (NEB) calculations in combination with a bond percolation model to optimise the conductivity in the Li 3 OCl 1Àx Br x series.They predicted that Li 3 OCl 0.75 Br 0.25 has a higher Li-ion conductivity than even Li 3 OCl 0.5 Br 0.5 based on low migration barriers for Li-rich channels with Br-rich end points.We also  This journal is © The Royal Society of Chemistry 2021 investigated both Li-and Na-based mixed halide antiperovskites (Li 3Àx Na x OCl 1Ày Br y ) using large-scale molecular dynamics. 136Our calculations revealed low formation energies for alkali-halide Schottky defects and that the Li-ion conductivity was signicantly higher than the Na-ion conductivity in these materials.In contrast to some earlier studies, our simulations suggested that the effect of Cl/Br mixing on ionic conductivity was small.We also considered ion transport in theoretical Li/Na mixed materials, e.g., Li 2 NaOCl and LiNa 2 OCl, but found their conductivities to be low and their activation energies high compared to Li 3 OCl and Na 3 OCl.Li-and Na-ion transport was shown to be proportional to the Li and Na vacancy concentration, respectively, while their activation energies were relatively insensitive to the vacancy concentration.These results were also found in a subsequent study that utilised deep potential molecular dynamics. 146s with other solid electrolytes, doping is critical to realising the full potential of anti-perovskite solid electrolytes and particularly for enhancing ion conduction.On this basis, we recently carried out defect and MD simulations to investigate the inuence of divalent cations (Mg 2+ , Ca 2+ , Sr 2+ and Ba 2+ ) and F À doping on ion conduction in Li 3 OCl. 147Whilst F-doped Li 3 OCl was revealed to be a poor conductor due to the high binding energies between dopant-Li vacancy pairs, Mg-doped Li 3 OCl was predicted to have high Li-ion conductivity and low migration barriers based on weaker dopant-vacancy binding energies.Our work therefore presented a viable doping strategy to improve the electrochemical performance of Li 3 OCl and potentially other anti-perovskites.
Kim and Siegel 55 systematically studied a series of 24 model Li-and Na-based anti-perovskite ion conductors using DFT calculations.By controlling the lattice distortion based on the Goldschmidt tolerance factor using isovalent composition variation of anti-perovskites, the authors were able to elucidate the relationships between the distortion and ion mobility and thermodynamic stability.They reported that highly distorted anti-perovskites tend to exhibit the lowest ion migration barriers through the widening of migration channels and the destabilisation of equilibrium congurations.Given that larger distortions inevitably correlate with reduced stability, a delicate balance must be struck between mobility and stability in these materials to realise their optimum performance.Na 3 SI was identied as an anti-perovskite that can potentially achieve such a balance.Although not considered explicitly, Wang et al. 148 hypothesised that the bcc packing of anions in the antiperovskite structure will be particularly favourable for ion conduction based on design principles for solid-state Li superionic conductors.
Zhu et al. 107 carried out the rst combined experimentalcomputational study of Na 3 OBr and the modied layered antiperovskite Na 4 OI 2 (rst reported by Sabrowsky et al. 83 in 1989).The authors reported a low Na migration energy of 0.34 eV for an occupied Na site to a neighbouring vacant site in Na 3 OBr based on DFT calculations.Three Na migration energies of 0.30, 0.45 and 1.10 eV were obtained for the anti-Ruddlesden-Popper phase Na 4 OI 2 based on the different Na sites present in the material.A DFT investigation by Yu et al. 139 extended this work to consider a series of stable anti-Ruddlesden-Popper phases with the general formula Na 4Àx Li x BA 4 (B ¼ O and/or S; A ¼ I and/or Cl).These materials were proposed to be excellent solid electrolytes for Na-based solid-state batteries.In particular, Na 3 LiS 0.5 O 0.5 I 2 was reported to have an extremely low activation energy for Na-ion transport (0.12 eV) and a high conductivity of 6.3 Â 10 À3 S cm À1 at room temperature.The Na-ion diffusion proles of Na 4 S 0.5 O 0.5 I 2 and Na 3 LiS 0.5 O 0.5 I 2 from this study are presented in Fig. 3(b).
Wan et al. 138 focused on Na 3 OCl and its alkaline earth doping using a combination of NEB and AIMD simulations.In analogy with Li 3 OCl, it was found that NaCl Schottky pairs are the dominant defects in Na 3 OCl and this results in Na-ion transport occurring through a vacancy hopping mechanism.Ca was identied as a promising dopant for this material on the basis that its incorporation results in charge compensating Na vacancies and because it exhibits the lowest binding energy with Na vacancies of the dopants (Mg, Ca, Sr and Ba) tested.
In addition to the substitution of halide ions, researchers have also considered the role of superhalogens/cluster ions in improving the performance of anti-perovskite solid electrolytes.Modelling work in this area has been particularly driven by Fang and Jena, who have proposed and predicted the performance of numerous anti-perovskite superionic conductors based on superhalogens. 53,111,122Fang et al. 53,122 used DFT and AIMD calculations to probe the stability, defects and migration barriers in Li 3 OBH 4 and Li 3 SBF 4 , as well as mixed phases of Li 3 OCl 0.5 (BH 4 ) 0.5 and Li 3 SCl 0.5 (BF 4 ) 0.5 .They found that these materials exhibit high Li-ion conductivities of between 10 À4 and 10 À1 S cm À1 at room temperature, resulting from Li vacancy migration, with activation energies of $0.18-0.30eV.The inuence of the superhalogens was also investigated and it was revealed that their translation and rotation are critical in enhancing the Li-ion migration in these systems (via a 'paddlewheel' effect).This behaviour is fundamental to ion conduction in many anti-perovskites and indeed other solid electrolytes and is discussed in more detail in the next section.
The same authors also extended their analysis in this area by providing guidelines for the rational design of Na-rich antiperovskite superionic conductors, again based on the use of superhalogens. 111Based on their guidelines, they proposed Na 3 S(BCl 4 ) and Na 3 S(BCl 4 ) 0.5 I 0.5 , which possessed Na-ion conductivities of >10 À3 S cm À1 with remarkably low activation energies of <0.20 eV.Na ion motion was found to be highly correlated in these materials and once again, the motion of the cluster ions was key to lowering the migration barriers, as hypothesised decades earlier by Jansen et al. 85 for Na 3 NO 3 (and also recently conrmed using DFT 121 ) and Na 3 OCN.
Inspired by these studies, the rst synthesis of Na 3 OBH 4 was reported in 2019 by Sun et al. 94 In addition to their experimental characterisation, the authors performed NEB and AIMD simulations to clarify the mechanism responsible for the excellent Na-ion transport in this material.They found that the Na migration barrier is 0.1 eV lower in Na 3 OBH 4 than Na 3 OBr and conrmed that the nearly free rotation of the BH 4 molecules is central to this reduction.However, in our own recent experimental-computational study of Na 3 OA (A ¼ Cl, Br, I and/ or BH 4 ), 95 we could not reproduce the high Na-ion conductivity reported by Sun et al. 94 despite also observing the same anion rotation.
As a result of its strongly hygroscopic nature, 115 there has been signicant confusion over the synthesis and characterisation of Li 3 OCl, with suggestions that previous as-prepared samples of Li 3 OCl were actually hydrated. 47,58,115Numerous studies have attempted to clarify some of the misconceptions regarding the synthesis of these materials and understand the inuence of protons on their overall ionic conductivity.The rst major study of this kind was conducted by Song et al., 58 who used a large combination of materials characterisation techniques and AIMD simulations to carefully identify the compositions of Li 2+x (OH 1Àx )Cl (0 # x < 0.7) and Li 2 (OH)Br and revealed an interesting Li-ion transport mechanism involving the creation of Li Frenkel defects resulting from OH À group rotation.This mechanism resulted in a signicant enhancement in the Li-ion conductivity of Li 2 (OH)Cl.In an integrated AIMD and 1 H, 2 H and 7 Li solid-state NMR study, 115 we also investigated the Li 3Àx (OH x )Cl system and discovered a strong relationship between Li-ion and proton dynamics based on Liion hopping and OH À rotation (see Fig. 4).We also ruled out the possibility of long-range proton transport in these materials based on the large separation between oxide ions of $4 A. Similar conclusions were also found by Song et al. 137 (see Fig. 3(c)) and Effat et al. 61 in later studies.
Howard et al. 114 used DFT to complete an in-depth study of the structural and ion transport properties of the different phases of Li 2 (OH)Cl.In addition to the known ordered orthorhombic and disordered cubic phases, the authors also considered a tetragonal ground state that is not observed experimentally.A large Haven ratio for the highly Li-ion conducting cubic phase was found, suggesting the existence of highly correlated Li-ion transport in this phase, in contrast to the low-temperature orthorhombic and tetragonal phases.The OH À groups were again found to strongly affect the Li-ion motion.Despite the many studies on the relationship between Li-ion and proton dynamics in anti-perovskites, interest in this area continues, with a recent experimental-computational study from Wang et al. 117 reaffirming earlier results regarding the increased OH À rotation in the cubic phase of Li 2 (OH)Cl and its enhancement of the Li-ion conductivity (paddlewheel effect).
As well as the intense research into Li-and Na-ion transport in anti-perovskites, there is also debate over the nature of oxideand halide-ion diffusion in the materials, particularly Li 3 OCl.The possibility of O and Cl diffusion in crystalline Li 3 OCl, Li 3 OBr and Li 3 OCl 0.5 Br 0.5 was actually considered by Zhang et al. 134 in the rst computational study of Li-ion transport in this material, but it was not observed with AIMD, even at 2000 K. Furthermore, they reported that the exchange of a Cl ion and an O ion was thermodynamically unfeasible and even when such an exchange was forced, the ions showed no tendency to return to their starting positions.However, when glassy Li 3 OCl was considered using classical molecular dynamics by Heenen et al., 135 signicant Cl-ion conductivity was observed, even at room temperature (2.5 Â 10 À4 S cm À1 ).Oxide ions were found to still be immobile in this glass material.In a very recent study, Serejo et al. 54 also predicted the existence of Cl and even O diffusion in Li 3 OCl using classical molecular dynamics simulations, albeit "sluggish" compared to Li-ion diffusion.
Using a materials genome approach based on DFT, Wang et al. 112 reported two new potential Li-ion conducting antiperovskites with compositions of Li 3 SI and Li 6 OSI 2 (a double anti-perovskite), as well as determining the stability and ion transport characteristics of a variety of other Li-based antiperovskites.The Li 6 OSI 2 double perovskite exhibited both energetic and dynamic stability, with a lower activation energy for Li interstitial transport (0.18 eV) compared to Li vacancy transport (0.26 eV).The same authors then extended their work to consider the Na analogue of this new material, i.e., Na 6 OSI 2 .Using AIMD simulations, they showed that moderate offstoichiometry in the material resulted in a low activation barrier for Na-ion transport of $0.16 eV and a very high conductivity of $10 À2 S cm À1 at room temperature.
In addition to the earlier work on the anti-Ruddlesden-Popper Na 4 OI 2 material, 107 recent computational studies have also considered fast Li-ion conduction and its mechanisms in low-dimensional (2D, 1D and 0D) Li-based anti-perovskites.Based on the archetypal Li 3 OCl, Lu et al. 149 used DFT and AIMD simulations to illustrate the potential for Li-ion conductivity of >10 À2 S cm À1 in 2D Li 4 OCl 2 (anti-Ruddlesden-Popper), 1D Li 5 OCl 3 and Li 6 OCl 4 .The authors reported increased conductivity with decreasing dimensionality as a result of decreased Li-ion migration bottlenecks and the soening of rotation modes of the octahedra in the structures.They also proposed that lowering the dimensionality of the primitive structural units in superionic conductors could be a new design principle for solid electrolytes.In a similar study, the migration mechanisms of alkali ions in Ruddlesden-Popper antiperovskites with the general formula X 4 OA 2 (X ¼ Li or Na; A ¼ Cl, Br or I) were investigated. 150Both vacancy and interstitial migration were simulated, with interstitials predicted to have lower migration barriers than vacancies and therefore play a signicant role in the ionic conduction of these materials.
The design of new ion conducting anti-perovskites has recently even led to the synthesis, characterisation and modelling of hydride-based systems with so anionic sublattices.Gao et al. 49 successfully synthesised M 3 HCh (M ¼ Li or Na; Ch ¼ S, Se or Te) anti-perovskites and despite the large variation in the ionic radii of these ions, all the materials were found to exhibit the ideal cubic structure, with the exception of Na 3 HS, which was orthorhombic.NEB calculations were used to estimate the cation migration barriers for vacancy and interstitial dumbbell hopping in these materials.As noted previously for Li 3 OCl and related anti-perovskites, the dumbbell migration mechanism was shown to be particularly favourable with low values of 0.05-0.14eV (compared to 0.15-0.32eV for vacancy migration).These low migration barriers and the high ionic conductivity observed experimentally were proposed to be the result of a so phonon mode associated with the rotational motion of HM 6 octahedra.
One of the greatest challenges in materials science is the ability to accurately determine the relationship between structure and dynamic properties.It is now widely accepted that, in order to gain a comprehensive structural understanding of a system, including the identication and characterisation of complex structure-property relationships, a combined experimental and computational approach is required.This is particularly true for anti-perovskites, where structural and/or compositional subtleties can lead to enhancements in both the functionality and performance.As detailed above, numerous computational studies currently exist for anti-perovskite solid electrolytes.In contrast, there are relatively few experimentally veried studies in which ion transport mechanisms have been identied and/or conrmed.This is not unique to anti-perovskites, or indeed battery-related materials, this is a signicant challenge faced by all classes of functional materials, i.e., verifying the means by which a material is classed as 'functional'.There are many reasons why probing conduction mechanisms via experimental methods is challenging.Ideally, to verify how an ion moves within a particular system, real time measurements are needed in which the movement of the mobile species is monitored in situ.At present, many of the characterisation methods typically used are limited in their ability to perform such in situ measurements, owing to factors such as hardware limitations or an inability to host systems requiring specialist environments, e.g., air sensitive systems.For example, in NMR spectroscopy it is possible to probe ion mobility; however, the temperature range over which this can be done is severely limited using conventional hardware.Furthermore, to carry out in situ experiments specialist, non-standard experimental setups and hardware are required that are oen costly.Experimental time can be applied for at national facilities, for example, using techniques such as muon spin relaxation spectroscopy to probe ion mobility.However, as time at such facilities becomes increasingly competitive, it can be difficult to secure experimental time.It is for these types of reasons that relatively few experimental studies currently exist for anti-perovskites in which the ion mobility mechanisms and conduction pathways have been experimentally veried.
Instead, various combined experimental and computational studies exist where, using experimental ndings, conduction pathways and mechanisms are proposed or hypothesised using theory.Ionic conductivities are routinely reported.However, oen these values are simply stated and not fully evidenced, i.e., the conduction pathway leading to such ionic conductivities is not detailed.Granted, this can be very challenging to do, particularly in the case of anti-perovskites given their hygroscopic nature.However, without an appreciation or understanding of how or why that conductivity is generated, it is difficult for it to be optimised further.Experimentally, techniques including impedance spectroscopy and variable-temperature solid-state NMR spectroscopy have been used to try and probe ion dynamics within anti-perovskites, alongside methods such as powder diffraction and microscopy.Typically, experimental data is collected for an array of samples and, from each dataset, an activation energy and conductivity are obtained.The challenge is then deciphering how and why there are variations across the datasets, and then being able to determine the correlation (if any) between each dataset.These are just some of the complexities and challenges associated with characterising functional materials and, in particular, ion conductors.
The Li-and Na-ion conduction mechanisms in antiperovskites remain a particularly topical area of interest.As established above, many conicting ideas have been proposed in recent years regarding the precise conduction pathways and mechanisms, the majority of which have been made via theoretical methods.Experimentally, pathways and mechanisms are oen merely inferred from the impedance data obtained, alongside a consideration of the crystal structure.Whilst the inferred mechanisms may be correct, it is important that they are experimentally veried.At present, the work of Dawson et al. 115 stands out as one of the very few experimental studies in which Li-ion diffusion and OH À rotation was conrmed via PFG NMR experiments and variable 2 H MAS NMR for the cubic phase of Li 2 OHCl (Fig. 4(c)).As previously discussed, determining whether alkali vacancies or interstitials are the dominant charge carriers has been the subject of much debate in recent years, with arguments for both being presented for a variety of different compositions.Experimentally, there are many factors that can inuence the ion conduction capabilities of a system, including composition, (dis)ordering, the thermal/ physical/electrochemical history of the sample, pressure, pellet texture and so on.These can all play a signicant role and, unfortunately, such factors are oen ignored during characterisation.This further highlights the complexities associated with experimentally validating the conduction pathways and ion transport mechanisms within a system.

Role of cluster ion rotation in antiperovskite solid electrolytes
The components of the archetypical oxyhalide composition (e.g., Li 3 OCl) can be replaced with atomic clusters (i.e., polyanions) with similar chemical function.The majority of such substitutions target the halide site (i.e., the larger anion site) in anti-perovskites.Polyanions with a net charge of À1, such as CN À , NO 3 À and BH 4 À , which can be referred to as superhalogens, have already been successfully substituted at the halide site of sodium anti-perovskites.
The effects that the inclusion of such cluster ions can have on solid electrolytes are multifold.For example, they can lead to an overall expansion of the lattice and, as such, an enlargement of the conduction bottlenecks, with positive effects on ionic conductivity.Although the largest usable halide is iodine, one can envisage using superhalogens larger than iodine to create antiperovskites with even larger lattice volumes.They can also affect the electrochemical stability of anti-perovskites, in particular oxidative stability, i.e., high-voltage stability in electrochemical applications, including batteries.The oxidative stability, to a rst approximation depends on the propensity of the anions (and particularly the halide in anti-perovskites) to release electrons.Certain cluster ions could actually have higher electron affinities than the atomic anions they replace and therefore be harder to oxidise, opening up routes to the design of solid electrolytes with greater stability at high voltages.Furthermore, as a result of covalent, intramolecular bonding, the electronic density of polyanions will be anisotropic, compared to an atomic anion, thereby effectively altering the potential energy landscape for mobile cations, such as Li + and Na + .This can have distinct implications on ion transport, especially considering that the inclusion of cluster ions can also result in unique coupling between anion and cation dynamics.Such effects have been considered for decades in the solid electrolyte literature 86 and such discussions have been reignited recently, in large part in connection to anti-perovskite ion conductors, as elaborated below.
Fang and Jena extended the concept of superhalogens to "superalkalis" in anti-perovskite solid electrolyte research, 53,111,122 i.e., cluster cations that behave chemically as alkali metal ions, such as Li 3 O + /Li 3 S + .Anti-perovskite compositions can then be thought of as equimolar pseudo-binary "supersalt" mixtures of superalkalis and superhalides, e.g., Na 3 O + and BH 4 À (in direct comparison with an equimolar mixture of alkali and halide, e.g., rocksalt NaCl).The smaller ionisation potentials of superalkalis compared to alkali metals in principle make them more mobile in the anti-perovskite structure.Na 3 O(NO 2 ) (or Na 3 NO 3 ) is likely the rst sodium antiperovskite discovered as early as 1938. 80,81Its Na-ion conduction characteristics were rst investigated by Jansen and co-workers 82,84,86,110 and they reported a link between the NO 2 À rotational disorder and ion conductivity.The room-temperature structure is already characterised by rotational disorder of the Vshaped NO 2 À exhibiting six different orientations. 82,120,121A clear transition is observed in the conductivity behaviour at $200 C without any clear structural implications (i.e., a change in symmetry), with the ionic conductivity increased by approximately two orders of magnitude and the activation energy approximately halved from 0.8 to 0.4 eV.This material has recently been reinvestigated by Zou and Zhao, 121 who showed that the transition corresponds to the activation of dynamic disorder (i.e., continuous reorientational motions) of the V-shaped NO 2 À anion that facilitates ion transport.In particular, they propose that the terminal oxygen anions of the nitrite ion interact with the Na + and effectively shuttle them between the available lattice sites.This mechanism is visualised in the consecutive simulation frames of Fig. 4(a).One of the terminal oxygen anions of the NO 2 À always points towards the migrating Na + .The correlated Na-ion hop/ NO 2 À is initiated by the NO 2 À rotating so that the terminal O previously coordinating the mobile Na + shis in a way that prepares it to coordinate the Na + in the initially vacant position.This rotation creates space, causing a momentary local expansion allowing for the Na + hop.In essence, the process can be conceptualised as the NO 2 À rotation "dragging" the Na + to its new position in the lattice.It is telling that when the authors of the study attempted the same model simulation but articially restraining the NO 2 À rotation, the result was an impressive suppression of Na + mobility.An analogous description might hold for Na 3 OCN featuring a linear CN À dipole and a similar thermally activated stepwise increase in ionic conductivity. 84,86 similar structure has been elucidated by X-ray 94,95 and neutron diffraction 94 for the recently discovered Na 3 OBH 4 , namely, featuring rotationally disordered BH 4 À tetrahedral anions in a cubic average structure.Although AIMD simulations demonstrate the dynamic nature of the BH 4 À rotation at high temperatures, the exact mechanistic inuence of said rotations on Na + diffusion remains to be investigated, although it is conceivable that a similar mechanism to Na 3 NO 3 takes place, where the terminal hydrogen anions of the rotating BH 4

À
cluster "drag" sodium ions to vacant sites.
We conclude the discussion of cluster anions in antiperovskite ion conductors with the best-studied case of Li 2 -OHCl, featuring a linear OH À dipole, 58,78,[114][115][116][117][118] this time on the B site in contrast to the previous examples.As discussed above, substitutions of molecular anions in the anti-perovskite structure can also be aliovalent with the protonation of Li 3 OCl to Li 2 OHCl, being a typical example.Protonation is concomitant with the removal of Li, i.e., the introduction of Li vacancies, since the added proton is much smaller than Li + and is covalently bonded to oxygen instead of occupying Li + sites.As such, hydration/protonation can be also considered as a strategy to increase ionic conductivity by generation of mobile defects.
Li 2 OHCl features a phase transition from an orthorhombic to a cubic phase close to room temperature ($35 C), 58,78,79,115,117 widely associated with the onset of rotational mobility of the OH À dipole, as discussed in detail above.We highlight that this feature of a crystallographic phase transition is unique in Li 2 -OHCl, in contrast to the other cluster-based anti-perovskites described in this section which remain in cubic average symmetry below the temperatures associated with the onset of mobility of their cluster anions (e.g., Na 3 NO 3 and Na 3 OCN).
2 H MAS NMR and 1 H and 7 Li PFG experiments and AIMD simulations converge to the combination of rotationally mobile (translationally xed) OH À dipoles and increased Li + mobility in the cubic phase, 115 which is further conrmed by impedance spectroscopy experiments. 79,116,117As noted above, the substitution of O 2À by OH À introduces vacant Li sites in Li 2 OHCl, as compared to the archetypal Li 3 OCl.It was shown through AIMD that the barycentre of the oxygen anion of OH À remains in the A site while the hydrogen cation (i.e., the positive end of the OH À dipole) is relatively mobile at a xed radius around the central oxygen; again in contrast to NO 2 À or CN À that rotate as a whole about the A site, as seen by the molecular simulation of Fig. 4(d).Locally, the hydrogen cation (i.e., the positive end of the OH À dipole) is always pointing to the vacant Li sites contributing to the electrostatic stabilisation of the structure, as shown in Fig. 4(b).Li migration to vacant sites is accompanied with rotation of the OH À group about the central oxygen so that the hydrogen cation points to the newly vacant site, as conrmed by both 2 H MAS NMR spectroscopy and 1 H and 7 Li PFG experiments and AIMD simulations. 115inally, we also mention the recent report of hydride-based M 3 HCh (M ¼ Li or Na; Ch ¼ S, Se or Te) anti-perovskites. 49hese do not formally contain covalently-bonded cluster polyanions and are "inverted" in the sense that the smaller B-site is occupied by the halogen-like hydride (H À , sp 2 ), while the larger A-site is occupied by large chalcogenides (e.g., S 2À or Se 2À ).Nevertheless, the authors propose the rotational motion of HM 6 tetrahedra as a key mechanistic peculiarity in these materials, which might bear some relation to the discussions of concerted migration touched on above.

Interfacial stability and resistance of anti-perovskite solid electrolyte
Combined experimental and computational efforts have led to an unprecedented understanding of solid electrolytes at the bulk scale.However, the performance of a solid-state battery is not simply a combination of the properties of the individual materials that it consists of and is instead heavily dependent on the interfaces that they form.These interfaces can be heterogeneous (e.g., electrode-electrolyte) or microstructural (e.g., grain boundaries), with both types having the potential to act as bottlenecks in the performance of solid-state batteries. 8,13As famously stated by Prof. Herbert Kroemer during his lecture for receiving the Nobel Prize in Physics 2000, "the interface is the device"; however, despite this statement being particularly relevant to solid-state batteries, the current understanding of the interfaces in solid electrolytes is still in its infancy compared to the bulk materials.
Nevertheless, there are a number of studies for antiperovskite solid electrolytes focused on the interfacial stability and microstructural characteristics of Li 3 OCl and its hydrated form.We begin by considering electrode-electrolyte interfaces.One prominent example is the work of Hood et al., 51 where the interface between Li 2 OHCl and Li metal was explicitly investigated.Through the use of a fast-cooling process, the authors found that Li 2 OHCl could form an extremely stable interface with the metallic Li anode.Li/Li 2 OHCl/Li cells cycled at high temperatures ($200 C) still showed stability between the solid electrolyte and molten Li anode upon solid electrolyte interphase (SEI) formation (see Fig. 5(a)), with minimal interfacial resistance.The SEI was found to have a high concentration of oxygen, supporting the formation of a lithium oxide layer that stabilises the interface without signicantly compromising the ionic conductivity.However, it should be noted that formation of such a lithium oxide layer implies the reduction of the hydroxide proton and the evolution of hydrogen gas, which might prove problematic in a practical setting.
Similar interfacial stability has also been proposed for Li 3 OCl on the basis of in-depth electrochemical testing and a variety of cell architectures. 52,125,151Beyond these more traditional approaches, signicant interest has arisen in recent years from the use of cation-doped Li 3 OCl and Na 3 OCl glass solid electrolytes in "glass" batteries, 48,152 as also discussed above.It was proposed that the anti-perovskite electrolytes in these glass batteries are not only wetted by the metallic anode but also have dielectric constants capable of creating large electric-doublelayer capacitance at the electrode/electrolyte interfaces.While the ability to reversibly plate/strip an alkali-metal anode from a solid electrolyte clearly has transformative potential for solidstate batteries and energy storage, these results have been met with considerable scepticism and have so far not been reproduced. 13,153st recently, Xiao et al. 50proposed a novel solid electrolyte melt inltration technique based on Li 1.9 OHCl 0.9 as a potential route to the scalable manufacturing of solid-state batteries.Benetting from its low melting point of $300 C, the solid electrolyte was inltrated into dense and thermally stable electrodes (LiNi 0.33 Mn 0.33 Co 0.33 O 2 as a cathode and Li 4 Ti 5 O 12 and graphite as anodes) as a liquid that then solidies during cooling.High-resolution SEM micrographs and EDS maps demonstrated a perfect wetting with sharp interfaces between the active materials and solid electrolyte, as illustrated in Fig. 5(b).This resulted in minimal interfacial resistance at the electrode-electrolyte interfaces, as conrmed by charge/ discharge tests.
Regarding Na-based anti-perovskites, Fan et al. 57 designed a solid-state battery based on a doped monoclinic Na 3 SO 4 F (Na 2.98 Mg 0.01 SO 4 F 0.95 Cl 0.05 ) anti-perovskite solid electrolyte, Prussian blue as a cathode and a Na metal anode.The rst discharge capacity for this solid-state cell was 83.3 mA h g À1 ; however, aer only ten cycles, the capacity was attenuated to 34.5 mA h g À1 because of the poor interfacial stability or wettability of the Na metal used.As a result, a Na-Sn alloy was used to replace the Na anode and this enabled a higher discharge capacity of 91.0 mA h g À1 for the rst cycle that was reasonably well maintained at 77.0 mA h g À1 aer 20 cycles with a coulombic efficiency of close to 100%.A decomposition voltage of 4.75 V was obtained from linear scan voltammetry, suggesting a wide electrochemical window for Na 2.98 Mg 0.01 SO 4 F 0.95 Cl 0.05 .
Given the challenges of explicitly modelling electrode-electrolyte interfaces, computational studies of electrode-antiperovskite electrolyte interfaces are also scarce.Nevertheless, Kim and Siegel 154 were able to probe the Li 3 OCl-Li metal anode interface at the atomic scale using DFT (see Fig. 5(c)).The authors calculated a variety of properties, including the interfacial energy, work of adhesion, wettability, band edge shis and electrochemical window, and found that the oxygenterminated interface is the most thermodynamically stable, with the potential for low interfacial resistance.However, this strong interfacial interaction signicantly reduced the electrochemical window of Li 3 OCl, implying a trade-off between strong interfacial bonding/wettability and electrochemical stability.Stegmaier et al. 155 also used DFT to model Li 3 OCl surfaces, but in this case, in contact with a nearly ideal metallic intercalation cathode model using a polarisable continuum model with a large dielectric constant.They predicted that very large Li vacancy concentrations will build up in a single layer of Li 3 OCl at the cathode interface to form a compact double layer.They also calculated a potential drop across the interface of $3 V for a nearly full concentration of vacancies at the surface, suggesting that nearly all the cathode potential drop in Li 3 OCl occurs at the Helmholtz plane rather than in a diffuse spacecharge region.
The interfacial stability of Li 3 OCl, Na 3 OBr and Na 4 OI 2 has also been considered implicitly using a combination of DFT and thermodynamic calculations.In one of the earliest computational studies of Li 3 OCl, Emly et al. 60 predicted the onset of oxidation of this material at 2.55 V (relative to metallic Li) with the formation of Li 2 O 2 and LiCl.Furthermore, Li 3 OCl was also considered in the seminal work of Richards et al., 156 where the interfacial stability and anodic and cathodic reactions of a wide variety of solid electrolytes were considered.In this study, oxidation was predicted to occur from 3.00 V (relative to metallic Li), with LiCl, LiClO 3 and ClO 3 as the products.Given that these decomposition products are electronic insulators, a passivated interphase can be expected to form at high voltages, which may prevent further oxidation of Li 3 OCl. 157he same methodology was also used to study Na-based solid electrolytes. 158The authors predicted an oxidation limit of 1.79 V (relative to metallic Na) for Na 3 OBr, with anodic reaction products of Na 2 O 2 and NaBr, similar to the Li and Cl equivalents suggested for Li 3 OCl by Emly et al. 60 A similar value of 1.66 V (relative to metallic Na) was obtained for Na 4 OI 2 and again with the formation of the corresponding metal halide (NaI) and metal halate (NaIO 3 ).The oxidation limits of these two Na-based anti-perovskites were found to be close to that of Na 2 O (1.67 V, relative to metallic Na), consistent with the presence of fully reduced anions in all of these structures.
We now turn our attention to the internal interfaces that exist within polycrystalline anti-perovskite solid electrolytes.The compositional or structural inhomogeneities present at nanometre to micrometre scales oen dominate the overall ionic conductivity of a material, either benecially 159,160 or detrimentally. 46,161,162Of these microstructural features, grain boundaries, which are surfaces of contact between crystallites of different orientation that oen differ extensively from the bulk crystal in terms of structure and composition, are the prime example.
It is oen challenging to separate the bulk and grain boundary contributions within an electrochemical impedance spectrum of a polycrystalline material.This is also the case for anti-perovskites, as typied by Schwering et al., 79 who attempted such a deconvolution for mixed-halide Li 2 OHA (A ¼ Cl and/or Br) compositions and was able to obtain estimated activation energies of $0.62-0.73 and $0.31-0.38 eV for the grain boundary and bulk conductivities, respectively.This signicant difference in activation energies suggests the presence of large grain boundary resistance in these materials, which is a typical feature for oxide-based solid electrolytes. 46,163In a later study, Lü et al. 52,125 synthesised Li 3 OCl thin lms with an activation energy of 0.35 eV, considerably lower than the value of 0.59 eV for the bulk material.This difference was explained by the larger grain size of the lms compared to the bulk material and, as a result, the reduced grain boundary resistance.Furthermore, impedance measurements have also conrmed large grain boundary resistances and lower conductivities for Li 3 OBr. 126,128More recently, the conductivity hysteresis in Li 2 OHCl has also been attributed to grain boundary resistance. 117It is noteworthy that the cation-doped Li 3 OCl and Na 3 OCl glass (and therefore free of grain boundaries) solid electrolytes developed by Braga et al. 48,152 were reported to have remarkably high conductivities of >10 À2 S cm À1 at room temperature.
Despite the fundamental impact of grain boundaries in solid electrolytes, they are far from being fully understood and grain boundary resistance is rarely quantied or characterised in detail, especially on the atomic scale.In light of this, we used Li 3 OCl as a model polycrystalline electrolyte and applied large-scale molecular dynamics simulations to analyse ionic transport at the grain boundaries of this anti-perovskite. 46We predicted high concentrations of grain boundaries and showed that Li-ion conductivity is severely hindered through them, thereby conrming the high grain boundary resistance in this material.Based on our results, we also proposed a polycrystalline model to quantify the impact of grain boundaries on conductivity as a function of grain size.Furthermore, the ndings from this study clearly illustrate the importance in directly considering grain boundary contributions to conductivity in solid electrolytes.This is particularly important in modelling, as the majority of rst-principles and classical simulations on antiperovskite solid electrolytes signicantly underestimate the activation energy for ion conduction, since they only consider the bulk material. 46This study has led to similar works that also focus on characterising grain boundaries in Li 3 OCl. 59,164 Anti-perovskite cathodes and their potential application in solid-state batteries Benetting from its ionic conduction properties, as well as a myriad of other functionalities, 62 the anti-perovskite structure has also recently been demonstrated as being able to support reversible redox reactions with lithium (de-)insertion.100 This is achieved through partial substitution of transition metals M (e.g., Fe) on the lithium site, resulting in disordering of Li and M on the same crystallographic site, similar to disordered rocksalt cathodes, 165 which are currently experiencing a surge in interest.In order to accommodate the increased formal charge on the cation site, large chalcogenides (e.g., S or Se) take the typical place of halides on the A site, resulting in bichalcogenide compositions, such as Li 2 FeOS. 100 Li 2 FeOS has been shown to accommodate reversible extraction and reinsertion of more than one Li ion per formula unit, corresponding to reversible Fe 2+ -Fe 3+ redox, as well as anionic redox of the sulphur anion for increased capacity (see Fig. 6), 166 similar to the so-called Li-rich compositions of layered cathodes.167,168 The lightweight framework of this material affords theoretical capacities directly competing those of commercial LiCoO 2 and NMC layered cathodes ($280 mA h g À1 for 1. 25 Li per formula unit for Li 2 FeSO).Most interestingly, high capacities have been demonstrated to be accessible at rather high rates, leading to very competitive power capability (e.g., >200 mA h g À1 at 1C for Li 2 FeSO, see Fig. 6(b)).The power capability is likely linked to the facile and isotropic Li-ion migration in the cubic anti-perovskite structure, as presented above, characterised by a low migration barrier of <0.35 eV.169 This combination of energy density, power capability and inexpensive reagents (e.g., Li 2 CO 3 , Fe and S in the case of Li 2 -FeOS) could make such anti-perovskite cathodes very serious contenders in the various battery application markets that are currently in ux.
0][171] Any transition metal with an accessible M 2+ -M 3+ redox pair is in principle usable, with Li 2 MnOS and Li 2 CoOS having already been synthesised 119 and the properties of the Cr, Cu, Mo, Ni and V analogues having been probed through DFT calculations. 169Careful optimisation of the composition is expected to allow for the tailoring of properties, including the average operating voltage, electronic conductivity and phase stability, 169 in close analogy with commercial NMC electrodes.For example, small amounts of Co incorporation were shown to dramatically increase the accessible capacity to >250 mA h g À1 . 171No reports of sodium equivalent versions (e.g., Na 2 FeOS) currently exist yet, with the exception of the recently discovered anti-Ruddlesden-Popper phase Na 2 Fe 2 OS 2 . 172oreover, anti-perovskite cathode materials possess certain intrinsic advantages with respect to their application in solidstate batteries.Firstly, similarities between the crystal structure and chemistry between electrode and electrolyte materials can be expected to lead to a compatible and unstrained interface.For example, the cubic lattice parameters of Li 2 FeSO and Li 2 OHCl are approximately equal ($3.91 A).Furthermore, antiperovskite cathodes have shown minimal and isotropic electrochemical expansion upon cycling; as lithium is reversibly (de)inserted, the cubic lattice parameter varies by less than 1%. 100,166,171This is especially relevant for solid-state batteries where mechanical degradation mechanisms (e.g., interface delamination, loss of contact and cracking) are exacerbated and directly linked to localised stresses generated by the large electrochemical expansion of the layered cathode materials typically used.Finally, although the utilisation of M 2+ -M 3+ redox pairs and the inclusion of sulphur tend to limit the operating voltage to $2.5 V vs. Li + /Li 0 , this can enable the use of solid electrolytes with limited electrochemical stability in oxidation.

Summary, remaining challenges and future directions
In this perspective, we have described and discussed the signicant progress made and the challenges faced in the synthesis, design, development and understanding of antiperovskite materials for solid-state batteries.In particular, we have highlighted how and why the Goldschmidt tolerance factor fails to accurately predict the synthesisability of antiperovskites, the challenges facing the synthesis of H-free samples, the issues of structural determination associated with hydrated phases, the underlying atomic-scale mechanisms that make anti-perovskites excellent ion conductors, the role of cluster ion rotation, the microstructural properties of antiperovskites and the interfaces they form with electrodes, and the recent development of anti-perovskite cathodes and their potential application in solid-state batteries.Despite recent progress and the fact that these materials have considerable potential as both battery materials and model systems for the understanding of solid electrolytes in general, a variety of challenges remain that continue to hinder their development.In this nal section, we highlight some of these challenges, as well as their relationship to general challenges currently facing battery materials development.We then also explore the exciting potential opportunities for the application of solid electrolyte battery materials and the future directions their development may take.
The Goldschmidt tolerance factor is an important tool for the design of perovskite materials, but in the case of Li-and Narich anti-perovskites, its predicative performance is severely limited.We have suggested a number of reasons for this, primarily based on the reliability of the input parameters (Shannon radii) used for anti-perovskites.Nevertheless, a number of new tolerance factors have been developed in recent years based on a variety of methods, including datadriven approaches, 99 kernel support vector machines, 173 gradient boosted decision trees 174 and a random forest of decision trees. 175These new descriptors are generally far more accurate than the Goldschmidt tolerance factor in predicting the stability of perovskites; however, they have yet to be fully assessed specically for Li-and Na-rich anti-perovskites.
The current literature for anti-perovskite solid electrolytes is dominated by Li 3 OA (A ¼ Cl or Br); however, it remains unclear whether these H-free materials can even be synthesised.Given the dramatic impact that protons have in these systems with regards to conductivity and structure, it is essential that great care is taken in both the synthesis and characterisation of these anti-perovskites to avoid further confusion and scepticism within the battery community.In addition, in the case of Li 2 -OHCl, even when the hydrated material is correctly determined, confusion remains over its room-temperature structure, with several different space groups having been proposed.These challenges clearly illustrate the need for state-of-the-art characterisation techniques when assessing the surprisingly complicated structures and properties of anti-perovskite solid electrolytes.Neutron-based techniques and NMR spectroscopy, uniquely sensitive to Li and H will be indispensable to gaining insight into the structural and dynamic subtleties of these materials.Another unexplained feature of these materials is the difference in the synthesisability of the Li-and Na-based compositions.For example, Li 3 OA cannot be readily synthesised, whereas Na 3 OA can.Inversely, Li 2 OHA can be synthesised whereas Na 2 OHA cannot.The underlying reasons for this discrepancy are not currently known and it is somewhat surprising that no computational study exists that assesses the hydration of Na 3 OA and the energetics of formation for Na 2 OHA.perspective has illustrated the power of computational modelling in regard to identifying the atomistic features and mechanisms that govern ion transport in solid electrolytes.However, the direct observation of such mechanisms with experiment remains highly challenging and this is certainly not only the case for anti-perovskites.Furthermore, another critical issue affecting the development of solid-state batteries in general is that our current understanding of interfaces in energy materials is far weaker than for the bulk materials, with antiperovskites being no exception.This is true for both experimental and modelling studies of interfaces, with each facing their own unique obstacles.In order to address the grand challenge of net-zero emissions by 2050, it is vital that new techniques are developed for the characterisation and explicit modelling of realistic interfaces in energy materials.The complementarity of experiment and modelling is essential to revolutionise the fundamental understanding of ion transport and interfaces in energy materials over different length scales and has been regularly highlighted throughout this Perspective.
Since the study of Zhao and Daemen 45 into superionic antiperovskites almost a decade ago, there has been a surge in interest in these materials for battery applications.While the majority of the studies in this area have centred on the application of Li-and Na-rich solid electrolytes in solid-state batteries, other diverse uses of these versatile materials have begun to emerge in recent years.For example, the electrolyte melt inltration reported by Xiao et al. 50based on Li 1.9 OHCl 0.9 holds potential for the low-cost and scalable manufacturing of inorganic solid-state batteries with high volumetric energy density.Fine-tuning of the ionic conductivity of the antiperovskite electrolyte (or indeed other electrolytes with low melting points) and its interfaces with the active materials will help to drive this new technology closer to large scales and improved cell performance.Guo et al. 176 proposed another alternative application for Li 2 OHCl, namely, as a lithium reservoir for the prelithiation of anodes in high energy density batteries on the basis of its large lithium storage capacity.
Li 3 OCl has also been considered as a "quasi-solid-state electrolyte" to potentially overcome both the safety problems associated with liquid electrolytes and the high interfacial resistance typically associated with solid electrolytes. 177A 500 nm-thick Li 3 OCl layer was used to protect a Li anode and resulted in a remarkable drop in its polarisation, as well as inhibiting the decomposition of the routine solvents typically found in liquid electrolytes at <4.5 V. Li 2 OHCl has also been recently proposed as a coating material for other solid electrolytes.Lai et al. 178 reported a simple aqueous method to prepare in situ Li 2 OHCl-coated garnet solid electrolytes and their method was shown to successfully reduce the sintering temperature of the garnet from 1200 to 350 C, as well as enhancing its ability to suppress lithium dendrite growth.
The recent use of high-pressure synthesis to stabilise M 3 HCh (M ¼ Li or Na; Ch ¼ S, Se or Te) 49 illustrates the potential of nonconventional syntheses in expanding the available phase space of anti-perovskite battery materials.Finally, in another recent study, Kim and Siegel 179 moved beyond Li-and Na-based antiperovskites to multivalent metal-ion-based anti-perovskites (Mg 3 NA, Ca 3 NA (where A ¼ P, As, Sb or Bi), Ca 3 PSb and Ca 3 -AsSb).Despite DFT calculations revealing their large formation energies for vacancies and interstitials, these materials do show some promise based on their predicted stability against Mg or Ca anodes and barriers for vacancy and interstitial migration of less than $500 and $200 meV, respectively.This is yet another illustration of the vast potential and versatility of these materials and a strong indication that research into anti-perovskite battery materials is only likely to increase in forthcoming years.

Karen
Johnston is an Assistant Professor of Inorganic Chemistry at Durham University.Her current work focuses on the design, development and characterisation of novel solid electrolytes for all-solid-state batteries using a combination of high-resolution multinuclear solid-state NMR spectroscopy with X-ray and neutron powder diffraction.Karen completed her PhD at the University of St Andrews in 2010 under the supervision of Professors Sharon Ashbrook and Philip Lightfoot.Aer postdoctoral work at the University of Windsor (Canada) she joined ALISTORE-ERI, working with Professor Clare Grey FRS.In 2019, she was awarded the NMRDG/ BRSG Prize for Excellent Contribution to Magnetic Resonance by an Early Career Researcher.

Fig. 1
Fig.1Schematic highlighting the structural and compositional versatility of anti-perovskite battery materials.

Li 3 125 Li 3 52 Li 3 52 Li 3
OCl (thin lm) Li 3 OCl target for pulsed laser deposition (PLD) prepared via annealing LiOH and LiCl under vacuum at 300 C for 48 h Li 3 OCl powders obtained described as containing 'some hydroxyl radicals' Lü et al.OCl lms deposited on substrate (LaAlO 3 , Ag or Li coated stainless steel) by PLD using KrF laser, 248 nm, 20 Hz, 4.0 J cm À2 , 175 C, 60 min under vacuum using the asprepared Li 3 OCl target Protective layer of TiO 2 deposited on top of Li 3 OCl lms deposited on LaAlO 3 Lü et al. 125 Composite target for PLD prepared from Li 2 O : LiCl (1 : 1 molar ratio), pressed into pellet (3000 psi) and annealed at 350 C in a controlled environment for 4 h Lü et al.OCl lms deposited on Li-coated silicon and polished stainless-steel substrates by PLD using KrF laser, 248 nm, 20 Hz, 4.0 J cm À2 , 175 C, 60 min under vacuum using the asprepared composite target Protective layer of ZnO deposited on top of Li 3 OCl lms Lü et al.OBr (bulk powder) Direct reaction of Li 2 (OH)Br and Li metal Method disputed by Friese et al.
LiCl and LiOH annealed at 350 C for 30 min inside a muffle furnace in a Ar-lled glovebox Dawson et al. 115 LiCl and LiOH pressed into pellets and annealed at 673 K, with or without a dwelling period of 30 min, aer which they were naturally cooled to room temperature Hanghofer et al. 116 LiCl and LiOH mixed in molar ratio of 1 : 1.05 and heated at 573 K (320 C) for 2 h before being poured into a Teon die and allowed to cool.Sample was then ball milled for 10 min Wang et al. 117 Na 3 OCl (bulk powder) Na 2 O and NaCl sintered in closed silver crucibles between 573 and 873 K in an Ar atmosphere (3 bar) Hippler et al. 109 Na 3 OCl and Na 3 OBr (bulk powder) NaOH and NaCl/Br are mixed before being paved onto Na metal.The resulting mixture is placed in a capped alumina crucible, sealed in a quartz tube and heated to 150 C (1.5 C min À1 ) then 350 C (10 C min À1 ) under vacuum.Aer annealing for 3 h samples are cooled naturally to room temperature.To improve sample purity, grinding and heating cycles are repeated three times Wang et al.

Fig. 3
Fig. 3 Ion transport mechanisms determined from DFT.(a) Low energy migration pathway for a Li interstitial dumbbell in Li 3 OCl.Reproduced with permission from ref. 60 Copyright (2013) American Chemical Society.(b) Projections of Na-ion diffusion trajectories for Na 4 S 0.5 O 0.5 I 2 (left) and Na 3 LiS 0.5 O 0.5 I 2 (right) over a AIMD simulation time of 90 ps at 800 K. Reproduced with permission from ref. 139 Copyright (2019) Royal Society of Chemistry.(c) Mechanisms of and correlations between Li and H dynamics in Li 2 OHCl.Reproduced with permission from ref. 137 Copyright (2020) Wiley.

Fig. 4
Fig. 4 Influence of cluster ion rotation on ion transport.(a) Na-ion conduction mechanism in Na 3 NO 3 demonstrated through successive frames of an atomic simulation at 485 K.The yellow and red arrows in the first frame indicate the correlated motion of the migrating Na + cation and rotation of the terminal oxygen anion of the NO 2 À group, respectively.Reproduced with permission from ref. 121 Copyright (2020) Royal Society of Chemistry.(b) Li-ion migration mechanism in Li 2 OHCl.(c) Variable-temperature 2 H MAS NMR spectra acquired for Li 2 ODCl at 19, 33, 63, 69, 95 and 110 C. (d) Density plots of trajectories for Li and H in blue and black respectively, from AIMD of Li 2 OHCl at 800 K. Oxygen atoms are shown in red and chlorine atoms omitted for clarity.Reproduced with permission from ref. 115 Copyright (2018) Royal Society of Chemistry.

Fig. 5
Fig. 5 Experimental and computational studies of electrode-anti-perovskite solid electrolyte interfaces.(a) SEM image of Li/Li 2 OHCl/Li symmetric cell after 160 charge/discharge cycles showing the cross section of the SEI.Reproduced with permission from ref. 51 Copyright (2016) American Chemical Society.(b) EDS mapping of melt-infiltrated NCM (top left), graphite (top right) and Li 4 Ti 5 O 12 electrodes (bottom left) and the cross-section of the all-solid-state battery cell, where purple represents combined Ni/Co/Mn, black represents C (graphite), red represents combined Ti/O (Li 4 Ti 5 O 12 ) and the green colour represents Cl from Li 1.9 OHCl 0.9 (SSE).Reproduced with permission from ref. 50 Copyright (2021) Springer Nature.(c) Relaxed structure of Cl-and O-terminated interfaces consisting of seven layers of Li 3 OCl (100) and bcc Li (100) planes.Reproduced with permission from ref. 154 Copyright (2019) American Chemical Society.

Fig. 6
Fig. 6 Anti-perovskite cathode materials.(a) Schematic representation of a graphitejLi 2 FeSO battery cell.Reproduced with permission from ref. 100 Copyright (2017) American Chemical Society.(b) Specific capacity, coulombic efficiency and inset voltage profiles of a Li 2 -FeSOjLi cell cycled at a 1C rate.Reproduced with permission from ref. 171 Copyright (2021) Frontiers. 58

Table 2
Summary of synthetic methods and conditions reported for the preparation of samples of Li 3 OCl, Li 3 OBr, Li 2 OHCl, Na 3 OCl and Na 3 OBr

Table 2 (
Contd. ) a Method also used for synthesis of Li 3 OBr using LiBr.

Table 3
Summary of structural models and parameters proposed for the room-temperature phase of Li 2 OHCl Sample deuterated associated with determining the structure of Li 2 OHCl.Barlage and Jacobs 131 initially suggested Li 2 OHCl was orthorhombic in space group Pmma.Eilbracht and co-workers Pmma Orthorhombic a ¼ 7.680 A, b ¼ 4.001 A, c ¼ 3.899 A No X-ray diffraction study Eilbracht et al.78 -Orthorhombic -No Neutron diffraction study.Weak superstructure reections and small orthorhombic splittings identied Schwering et al. 79 Amm2 Orthorhombic a ¼ 3.8220 A, b ¼ 7.9968 A, c ¼ 7.7394 A No X-ray diffraction study Song et al. 58 Pmmm Orthorhombic a ¼ 3.8945 A, b ¼ 3.9937 A, c ¼ 7.6634 A No In situ X-ray diffraction study.Structure observed at 26 C Song et al. 58 P4mm Tetragonal a ¼ b ¼ 3.9129 A, c ¼ 3.9188 A No In situ X-ray diffraction study.Structure observed at 40 C Howard et al. 114 P4mm Tetragonal a ¼ b ¼ 3.794 A, c ¼ 3.578 A Yes DFT predicted ground-state structure using non-standard coordinates Howard et al. 114 Pmc2 1 Orthorhombic a ¼ 3.831 A, b ¼ 3.617 A, c ¼ 7.985 A Yes DFT predicted metastable structure state Howard and Holzwarth 132 Cmcm Orthorhombic a ¼ 7.91 A, b ¼ 7.74 A, c ¼ 7.42 A Yes DFT predicted structure Hanghofer et al. 116 Pban Orthorhombic a ¼ 7.74574 A, b ¼ 7.99730 A, c ¼ 3.8229 A 117 Pban Orthorhombic a ¼ 7.7578 A, b ¼ 7.9963 A, c ¼ 3.8254 A No Combined synchrotron X-ray and neutron diffraction study.Three similar orthorhombic phases needed to t synchrotron X-ray diffraction data and only one needed to t neutron diffraction data (parameters shown).

Table 4
Summary of selected ionic conductivities and activation energies for typical anti-perovskite solid electrolytes