Rational Composition Optimization of the Lithium-Rich Li3OCl1−xBrxAnti-Perovskite Superionic ConductorsZhi Deng, Balachandran Radhakrishnan, and Shyue Ping Ong*

Department of NanoEngineering, University of California San Diego, 9500 Gilman Drive, Mail Code 0448, La Jolla, California92093-0448, United States

*S Supporting Information

ABSTRACT: The newly discovered lithium-rich antiperov-skite (LRAP) superionic conductors are an extremelyinteresting class of materials with potential applications assolid electrolytes in Li-ion batteries. In this work, we present arational composition optimization strategy for maximizing theLi+ conductivity in the LRAP guided by a combination of first-principles calculations and percolation theory. Using nudgedelastic band (NEB) calculations, we show that a Cl-richchannel with Br-rich end points configuration leads to lowvacancy migration barriers in the LRAP structure. Byincorporating the halide-environment-dependent NEB barriersin a bond percolation model, we predict that there are potentially higher conductivity Li3OCl1−xBrx structures near 0.235 ≤ x ≤0.395. This prediction is confirmed by AIMD simulation that finds Li3OCl0.75Br0.25 to have a higher Li+ conductivity thanLi3OCl0.5Br0.5, the highest conductivity LRAP identified experimentally thus far. These results highlight that there is scope forfurther enhancing the conductivity in the LRAP chemistry. The general approach developed can potentially be extended to otherion-conducting systems, such as the structurally similar perovskite oxygen-ion conductors of interest in solid-oxide fuel cells aswell as other superionic conductors.

■ INTRODUCTION

In recent years, ceramic or glass-ceramic superionic conductorsolid electrolytes have garnered increasing interest as potentialreplacements for the widely used organic liquid electrolytes incommercial lithium-ion batteries.1−4 Unlike organic solvents,ceramic superionic conductors are nonflammable and exhibitmuch better safety. Furthermore, ceramic superionic con-ductors have the potential for improved electrochemicalstability, which can enable the application of high-voltagecathodes and perhaps even lithium metal anodes.5,6 In terms oftransport properties, several recently discovered materials, suchas the Li10MP2S12 family (M = Ge, Sn, Si)7−11 and Li7P3S11

12,13

sulfides and the lithium-rich antiperovskites,14−19 have Li+

conductivities comparable to or even exceeding those oftraditional liquid electrolytes.In particular, the lithium-rich antiperovskites (LRAPs) with

formula Li3OX, where X = Cl, Br, or a mixture of both halogens(shown in Figure 1), reported by Zhao et al.14 present aninteresting class of superionic conductors with the potential infurther composition optimization to increase the ionicconductivity. Zhao et al. reported that the Li3OCl end memberhas a room-temperature ionic conductivity of 0.85 mS/cm, andthe mixed halide Li3OCl0.5Br0.5 has a significantly higherconductivity of 1.94 mS/cm.14 However, Li3OBr shows muchpoorer conductivity compared with Li3OCl and Li3OCl0.5Br0.5(though no actual conductivity value was reported). Theauthors postulated that the presence of smaller Cl− creates

larger channel for Li+ diffusion, whereas partial Br substitutionprevents octahedral tilting from shrinking the channel size.To date, there have been several theoretical works on

understanding the transport mechanisms in the LRAPs. Usingab initio molecular dynamics (AIMD) simulations, Zhang etal.15 demonstrated that Li vacancies and structural disorderpromote the diffusion of Li+ in LRAP. Later, Emly et al.16

proposed a migration mechanism involving Li interstitialdumbbells, where the barrier is calculated to be around 50%lower than that for vacancy driven migration. However, the

Received: March 16, 2015Revised: April 29, 2015

Figure 1. Unit cell of the Li3OCl antiperovskite. O2− occupies the

body-centered site. Li+ occupy faced-centered sites forming a Li6Ooctahedron with O2−. Cl− occupies the corner sites.

Article

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© XXXX American Chemical Society A DOI: 10.1021/acs.chemmater.5b00988Chem. Mater. XXXX, XXX, XXX−XXX

authors also pointed out that this mechanism cannot explainthe superionic conductivity of LRAP due to the high formationenergy of Li interstitial defects. A recent work by Mouta et al.19

also showed that the formation energy of Li Frenkel defect ismuch higher than other intrinsic charge neutral defects inLi3OCl. Although these theoretical works have shed usefulinsights into the phase stability and ionic conductivity in theLRAP superionic conductors, they stop short of providing aconcrete optimization strategy for further enhancing theirperformance.In this paper, we present a comprehensive analysis of the

phase stability and ionic conduction mechanisms in the LRAPsusing a combination of first-principles calculations andpercolation theory. Consistent with previous theoretical work,we find relatively low halide mixing energies in the LRAPs,indicating that the mixed halide Li3OCl1−xBrx is likely to bedisordered at room temperature. Using nudged elastic band(NEB) calculations, we elucidate the effect of the halide localenvironment on vacancy migration barriers. We then outline arational composition optimization strategy for further enhanc-ing the ionic conductivity of the LRAP chemistry byincorporating the computed migration barriers into a bondpercolation model. Finally, we provide supporting evidencefrom ab initio molecular dynamics (AIMD) simulations thatthere exist potential compositions that yield even higher Li+

conductivities than Li3OCl0.5Br0.5, the highest conductivitycomposition in the LRAP chemistry identified experimentallythus far. The approach developed in this work has applicationsbeyond the LRAP chemistry, and can potentially be extendedto other perovskite/cubic ion-conducting systems such as theperovskite oxygen-ion conductors of interest in solid-oxide fuelcells.20

■ METHODSAll density functional theory (DFT) calculations in this work wereperformed using the Vienna Ab initio Simulation Package (VASP)21

within the projector augmented wave approach.22 The Perdew−Burke−Ernzerhof (PBE) generalized-gradient approximation (GGA)23

was adopted for all calculations. Because of the vastly differingrequirements (in terms of force/energy convergence, etc.), we havecarefully selected parameters to achieve an optimal balance of accuracyand computational cost for each type of calculation in this work, asoutlined in subsequent subsections. All analyses, including phasediagram construction, computation of diffusivities and conductivities,and plot generation, were performed using the Python MaterialsGenomics (pymatgen) software library.24

Energy Calculations. For all total energy calculations, a k-pointdensity of at least 1000/(number of atoms in unit cell) was used, withan energy cutoff of 520 eV. All calculations were spin-polarized. Forintermediate compositions of Li3OCl1−xBrx, we enumerated allsymmetrically distinct Cl and Br orderings at three compositions (x= 0.25, 0.5 and 0.75) in a 2 × 2 × 2 supercell using the algorithm ofHart et al.25

Nudged Elastic Band Calculations. Nudged elastic band (NEB)calculations were performed using 2 × 2 × 2 supercells ofLi3OCl1−xBrx with one negatively charged Li+ vacancy, with overallcharge neutrality preserved via a compensating background charge.Convergence tests with larger supercell sizes of Li3OCl found that 2 ×2 × 2 supercell is sufficient to obtain reasonably well-convergedmigration barrier. The migration pathway was constructed using fivelinearly interpolated images between fully relaxed initial and finalpoints. Because our conclusions are predicated only on relativemigration barrier differences, we did not perform any corrections forthe interactions between periodic images of the charged vacancy;because the charges and structures are similar in all instances, thecorrections would amount to approximately the same additive term.

To exclude the effect of the energy difference between the initialand final states, we calculated the the kinetically resolved activation(KRA) barrier26 for vacancy migration, ΔEKRA, as follows

Δ = − +E E E E12

( )KRA max init final (1)

where Emax is the saddle point energy along the pathway, Einit and Efinalare the energy of the initial and final points, respectively. With hoppingdirections considered, the activation barrier is calculated as thefollowing equation

Δ = −E E Ef(b) max init(final) (2)

where ΔEf is the activation barrier for the hop from the initial to thefinal point, and ΔEb is the other way round.

Ab Initio Molecular Dynamics Simulations. We investigatedthe Li+ diffusivity and conductivity in antiperovskite using ab initiomolecular dynamics (AIMD) simulations. To keep the computationalcost at a reasonable level, we used a smaller plane wave energy cutoffof 400 eV, and a minimal Γ-centered 1 × 1 × 1 k-point grid. All AIMDsimulations were also non-spin-polarized.

Similar to the setup in previous work by Zhang et al.,15 we carriedout the AIMD simulations using a constant volume (NVT) ensembleon 2 × 2 × 2 supercells of Li3OCl1−xBrx with a single Li+ vacancy. Toensure charge balance, a compensating background charge was applied.The volume and atomic positions of the unit cell were fully relaxedprior to the simulations. The integration of Newton’s equation is basedon the Verlet algorithm27 implemented in VASP, and the time step ofmolecular dynamics was chosen to be 2 fs. At the start of the MDsimulations, the samples were assigned an initial temperature of 300 Kaccording to a Boltzmann distribution, then heated up to the desiredtemperature (900−2100 K) by velocity scaling and equilibrated at thedesired temperature for 50000 time steps (100 ps) with a Nose−Hoover thermostat.28,29 Although the MD simulations were performedat relatively high temperatures to ensure sufficient diffusion events andconvergence of the diffusivity, no lattice melting was observed. TheMD simulations then continued for approximately 300 ps until thediffusion coefficient was converged. Given the substantial number ofAIMD simulations performed (∼10 structures × 5 temperatures each),we developed an in-house workflow software to automate theperformance of multiday AIMD simulations using pymatgen and theFireWorks workflow software.30

The diffusivity of Li+ can be calculated from the mean squaredisplacement (MSD) as described by Einstein relation

= ⟨ ⟩Ddt

tr1

2[ ( )]2

(3)

where t is the time and d is the dimension of the lattice in whichdiffusion takes place (d = 3 in this particular structure). The MSD⟨[r(t)]2 ⟩is calculated as

∑⟨ ⟩ = ⟨ + − ⟩tN

t t tr r r[ ( )]1

[ ( ) ( )]i

i i t2

0 02

0(4)

where N is the total number of Li+ ions and ri(t) is the position of thei-th Li+ at time t.

The MSD is an average over all Li+ ions and also an ensembleaverage over time t0. Therefore, the calculated diffusion coefficient D isthe self-diffusion of Li+ ions rather than the combined diffusion of thecenter of the mass of all Li+ ions. It is known that these two definitionsof diffusion coefficients become equivalent if there is no crosscorrelation between displacement of different particles at differenttimes.31 The value of D is obtained by performing a linear fitting to therelationship of MSD versus 2dt.

The conductivity of Li+ is calculated as

ρΛ = −Δ⎛

⎝⎜⎞⎠⎟

z FRT

DE

kTexp

2 2

0a

(5)

where ρ is the molar density of Li+ ions, z is the charge of Li+ (z = +1),F is the Faraday constant, R is the gas constant, k is the Boltzmann

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constant, T is the temperature and ΔEa is the overall activation energy.D0 and ΔEa can be computed by fitting an Arrhenius curve betweendiffusivities and temperatures, and the room-temperature diffusivitiesand conductivities are then extrapolated from the derived parameters.

■ RESULTS

Halide Ordering and Crystal Structures. To investigatethe phase stability of the mixed halide Li3OCl1−xBrx, wecalculated the energies of all symmetrically distinct orderings atx = 0.25, 0.5, and 0.75 in a 2 × 2 × 2 supercell (which resultedin 3, 6, and 3 unique structures, respectively) and the two endmembers Li3OCl and Li3OBr as well. The resulting Li3OCl−Li3OBr pseudobinary phase diagram is shown in Figure 2a. Theformation energies of all intermediate compositions arepredicted to be small, positive values, suggesting solid solutionbehavior will likely prevail at room temperature. This isconsistent with the fact that the Li3OCl0.5Br0.5 compound hasalready been synthesized experimentally.14 The narrow range ofthe formation energies at each composition further suggeststhat there is no single strongly preferred ordering of halide ions,indicating that the halide ion sublattice is likely to be disorderedat temperatures of interest. These results are consistent with theearlier results reported by Emly et al.16

The final relaxed lattice parameters of all calculatedLi3OCl1−xBrx are plotted in Figure 2b. As all the final relaxedlattices have a pseudocubic structure with very minordifferences in the lattice parameters in the a, b, and c directions,we report only the averaged cubic lattice parameter for eachstructure. The calculated lattice parameters of the end membersLi3OCl and Li3OBr are 3.89 and 3.99 Å, respectively, in goodagreement with the experimental lattice parameters andprevious DFT calculations.14−16 We find that the changes inlattice parameter with composition generally follow Vegard’slaw. Further details on the computed lattice parameters of allstructures are provided in the Supporting Information.Effect of Halide Local Environment on Vacancy

Migration Barriers. Figure 3 shows a schematic of a vacancymigration in the LRAP structure. In LRAP, each Li+ iscoordinated by two O2− and four halide ions X−. Nearestneighbor Li+ share three coordinated anions (one O2− and twoX−). During a vacancy hop, the vacancy migrates from a Li+ siteto a nearest Li+ site via a triangular channel comprising thethree shared anions. We can then label such a hop using aXiaXib−XcaXcb−XfaXfb scheme, where XiaXib denotes the nearestneighbor halide ions to the initial site that are not shared with

the final site, XcaXcb denotes the halide ions in the channelshared between the initial and final sites, and XfaXfb denotes thenearest neighbor halide ions to the final site that are not sharedwith the initial site. The letters i, c, and f represent “initial”,“channel”, and “final”, respectively. The oxygen is not relevantfor the labeling scheme because it is common to all hops. Forexample, the pathway in Figure 3 is labeled as BB−CC−BC(only the first letter for the halogen is used for brevity). Itshould be noted that the specific order of the halide ions withineach group is ignored, and we have excluded the effect of theenergy differences between the initial and final sites by usingthe kinetically resolved activation (KRA) barrier.26 In otherwords, the BB−CC−CB, BC−CC−BB, and CB−CC−BB hopsare considered equivalent to the BB−CC−BC hop. In general,we find that the effect of hopping direction on the barriers isnegligible, which justifies the use of the KRA. Please see theSupporting Information for more details.On the basis of the above labeling scheme, there are 18

distinct vacancy migration pathways in the mixed Li3OCl1−xBrxantiperovskites. The majority of these pathways (12) can befound in at least one of the six distinct 2 × 2 × 2 Li3OCl0.5Br0.5supercells, whereas the remaining (pathways containing a largenumber of halide ions of a particular type) can be found in theLi3OCl0.25Br0.75 and Li3OCl0.75Br0.25 structures. To exclude theeffect of lattice parameter differences on the barrier, weminimized the number of different compositions used toperform the NEB calculations, though it was generally foundthat the minor variations in lattice parameters with compositionhave a relatively small effect on computed barriers.Figure 4 shows the computed KRA barriers for all 18 distinct

vacancy migration pathways. We note that the barriers obtainedfor the pure Li3OCl and Li3OBr (328 and 361 meVrespectively) are consistently lower than those previously

Figure 2. (a) Computational Li3OCl-Li3OBr pseudobinary phase diagram; (b) calculated pseudocubic lattice parameter of Li3OCl1−xBrx. The valuesin both figures are normalized to one formula unit of Li3OCl1−xBrx.

Figure 3. Schematic of BB-CC-BC pathway.

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calculated by Zhang et al.15 by about 40 meV, which is likelydue to slight differences in calculation parameters. We maymake a few key observations:

• The halide species in the channel have a large effect onthe migration barrier. The migration barriers aresignificantly lower when the channel comprise onlysmaller Cl− ions. The more Br− ions in the channel, thehigher the migration barrier.

• The reverse trend is seen for the halide species that arenot in the channel. Among pathways with a commonchannel XX, the CC−XX−CC pathway always has thehighest migration barrier, whereas increasing Br− in theinitial and final sites decreases the migration barrier.

We performed a multiple linear regression analysis to quantifythe relationship between the vacancy migration barrier and thenumber of Br− in the channel and end point (nonchannel)sites. The relationship is given by the following equation

Δ = − +E n n42.5 13.4 334.1a cBr

eBr

(6)

where ncBr and ne

Br are the number of Br− at channel and endpoint sites respectively, and ΔEa is the migration barrier inmeV. We find that each Br− in the channel sites increases themigration barrier by 43 meV, whereas each Br− in the end pointsites decreases the migration barrier by 13 meV.It should be noted that Emly et al. performed a similar, but

more limited analysis of the migration barrier in Li3OCl0.5Br0.5on the basis of their proposed Li interstitial dumbbellmechanism.16 Translating their results to our labeling scheme,they find that the relative migration barriers for three differentdumbbell migration pathways are BC−CC−BC < BC−BC−BC< CC−BB−CC, which is qualitatively similar to our result thatCl− in the channel leads to lower migration barriers. This is animportant observation as it implies that the conclusion from thebond percolation analysis in the next section holds regardless ofthe specific diffusion mechanism.Bond Percolation Model for Macroscopic Conductiv-

ity. On the basis of the results in the two preceding sections,we can conclude that (i) the mixed Li3OCl1−xBrx antiper-ovskites are likely to exhibit disorder on the halide sublattice attemperatures of interest, and (ii) Cl− in the channel and Br− inthe end points result in low energy migration pathways.However, these insights do not yet provide a concrete strategyfor optimizing the conductivity in Li3OCl1−xBrx. From purelythe channel perspective, the Li3OCl end member is already an“ideal” structure because all channels comprise Cl− by

definition; it is unclear what level of Br− incorporation, ifany, would result in a structure with increased conductivity.Any Br− present would certainly increase the migration barriersof some pathways, while lowering the barriers of adjacentpathways. For macroscopically facile diffusion, a material musthave low barrier paths that percolate through the entire crystal.To derive an optimal Br− concentration, we developed a

bond percolation model for vacancy migration based on thehalide-environment-dependent barriers from the NEB calcu-lations. In this analysis, we define an “open bond” as amigration pathway whose energy barrier is less than a certainenergy cutoff value. From the NEB calculations (Figure 4 andeq 6), we note that the pure Cl− channels generally result in thelowest migration barriers. We will therefore limit our analysis tothe bonds with the pure Cl− channels, and the barrier cutoffscan then be naturally selected based on the number of Br− inthe end points (ne

Br in eq 6). It should, however, be noted thatthe BB−BC−BB bond is predicted to have a lower barrier thanthe CC−CC−CC bond, though this type of bond only existswith significant probability at higher overall Br− concentrations.A key result from bond percolation theory is that there is a

critical probability of open bonds, pc, below which the networknever percolates, and above which it does. Using the algorithmdeveloped by Newman et al.,32 we estimate the bondpercolation threshold of the lithium sublattice in the LRAPstructure to be 0.186, i.e., percolation is achieved when theprobability of “open bonds” exceeds 0.186 in the LRAP (see theSupporting Information for details). We note that thisthreshold value is fairly close to that of the bcc structure(0.18),33 which is consistent with the observation that in theLRAP, each Li+ is similarly coordinated by 8 other Li+ ions.Using a random sampling technique, we calculate the

probability of open bonds in Li3OCl1−xBrx at various Br−

concentrations with different barrier cutoffs. As shown inFigure 5, when the barrier cutoff is set at 302 meV, only two

types of bonds (BB−CC−BB and BB−CC−BC) areconsidered “open” and a percolating network of open bondscannot be achieved at any concentration. When the cutoff isincreased to 314 meV (bonds having at least 2 Br− in the endpoints designated as open), percolation is achieved only withina narrow concentration range of 0.344 ≤ x ≤ 0.449. Theconcentration range is further extended to 0.054 ≤ x ≤ 0.558when the cutoff is further increased to 323 meV. Finally, whenthe pure Cl− halide environment (CC−CC−CC) is included asan open bond, percolation occurs from 0 ≤ x ≤ 0.565, with the

Figure 4. Vacancy migration barriers of different pathways from NEBcalculations. The chart is divided into three regions according to thehalide species in the channel.

Figure 5. Probability of open bonds in Li3OCl1−xBrx at various Br−

concentrations. Each curve corresponds to a particular barrier cutoff.neBr denotes the number of Br− in the end points. The antiperovskitebond percolation threshold is indicated by the black dashed line.

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Li3OCl having the highest probability (1.0) of having openbonds.The proportion of open bonds for ne

Br ≥ 2 and 1 reaches amaximum of 0.191 and 0.388 at x = 0.395 and 0.235respectively. The percolation analysis therefore suggests thatthere are potential compositions near 0.235 ≤ x ≤ 0.395 thatmay yield conductivities higher than that of the Li3OCl0.5Br0.5,the highest conductivity composition reported experimentallyand theoretically thus far.Higher Conductivity Composition Confirmed by Ab

Initio Molecular Dynamics Simulations. To validate thepredictions from our percolation model, we performed AIMDsimulations for various halide orderings at x = 0, 0.25, 0.5, 0.75,1. Figure 6 shows the ionic conductivities and activation

energies associated with the highest Li+ conductivity at roomtemperature achieved at each composition. Both values comefrom the same structure as the ionic conductivity wasextrapolated from the Arrhenius equation. The overall trendin activation energies is similar to the NEB calculations. Theextrapolated room temperature Li+ conductivities from ourAIMD simulations are generally 2 orders of magnitude lowerthan those reported in the original experiments by Zhao et al.,14

but are consistent with the values reported in a recent work byLu et al.18 Lu attributed the higher conductivities reported inthe original experiments as possibly due to the formation of adepleted antiperovskite Li3−δOCl1−δ or Al3+ doping. Never-theless, the relevant observation here is the trend ofconductivities with composition. Comparing the Li+ con-ductivities of x = 0,0.5,1, the trend in conductivity isLi3OCl0.5Br0.5 > Li3OCl > Li3OBr, in agreement with previousexperimental and theoretical results.14,15 We also find that themaximum conductivity achieved by a Li3OCl0.75Br0.25 is about30% higher than that of Li3OCl0.5Br0.5 composition, consistentwith the predictions of our percolation model.

■ DISCUSSIONComposition tuning is a frequently used and effective strategyfor further enhancing ionic conductivity, particularly in lithiumsuperionic conductors.1,2,34 However, such tuning is typicallycarried out in a trial-and-error fashion, with only chemicalintuition guiding the selection of dopants and doping levels.For instance, while previous experimental work found theLi3OCl0.5Br0.5 lithium-rich antiperovskite (LRAP) to have ahigher Li+ conductivity than the Li3OCl and Li3OBr endmembers, there was no indication, either from experiments or

theory, on whether higher conductivity compositions existwithin the Li3OCl-Li3OBr pseudobinary system.Using a combination of first-principles calculations and

percolation theory, we have outlined a rational strategy to tunethe disordered LRAP composition to maximize the Li+

conductivity. We demonstrate that a Cl-rich channel with Br-rich end points leads to low vacancy migration barriers. Byincorporating the computed local-environment-dependentmigration barriers in a bond percolation model, we show thatthere are potentially higher conductivity Li3OCl1−xBrxstructures near 0.235 ≤ x ≤ 0.395. This prediction is furtherconfirmed by AIMD simulations, which predict a higherconductivity for Li3OCl0.75Br0.25 compared to Li3OCl0.5Br0.5. Itis our hope that this prediction will be verified experimentallysubsequently.The bond percolation model is key to the development of

the composition optimization strategy. Although the NEBcalculations can provide insights into the local atomistic factorsgoverning migration barriers, the bond percolation analysisextends that information to incorporate the compositionaltrade-offs at the macroscopic level. Low levels of Brincorporation would increase the proportion of fast migrationpaths in the LRAP structure, but an excess of Br incorporationwould lead to “choking” in the channels and decreasedconductivity. Our percolation analysis is similar in spirit torecent work by Urban et al., who used a site percolation modelto provide a unifying theory to explain the lithium exchangecapacity of rocksalt-like structures.35,36 In this work, we havechosen to use a bond percolation analysis as it is moreintuitively related to the facile pathways determined from NEBcalculations. We also note that the specifics of the migrationmechanism (vacancy or the earlier proposed interstitialdumbbell16) is largely irrelevant to the results from the bondpercolation model; the only relevant factor is the relativemigration barriers for different halide local environments, andthis is similar for both mechanisms.Finally, we wish to highlight that the approach and the

percolation model outlined in this work are surprisingly generaland have applications beyond just Li+ conduction in the LRAPsystem. For instance, O2− conductivity in ABO3 perovskites,such as LaGaO3, is extremely important in fuel cellapplications.37 A common strategy to boost the O2−

conductivity is to dope the A and B cation sites, such as Srfor La doping in the case of LaGaO3. The LRAP structures areisostructural with the ABO3 perovskites, except that the sitesoccupied by the cations and anions are reversed. Hence, O2−

conduction in regular perovskites is equivalent to Li+

conduction in the antiperovskite, and is governed by thesame network topology and local environmental factors.Indeed, the optimal O2− conductivity achieved in Sr-dopedLaGaO3 thus far is at around 20% Sr doping level,20 which isfairly close to the optimal Br doping level obtained in ourmodel. Beyond the perovskite structure and topology, themodel can also be trivially extended to study other diffusionnetwork topologies.

■ CONCLUSIONIn this paper, we present a rational composition optimizationstrategy for maximizing the Li+ conductivity in the lithium-richantiperovskites (LRAPs) guided by a combination of first-principles calculations and percolation theory. The low mixingenergies in the Li3OCl-Li3OBr pseudobinary system indicatethat halide disorder is likely at room temperature. Nudged

Figure 6. Overall activation energy, Ea and Li+ conductivity at roomtemperature as a function of x in Li3OCl1−xBrx.

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elastic band (NEB) calculations find that a Cl-rich channel withBr-rich end points leads to low vacancy migration barriers inthe LRAP structure. By incorporating the computed NEBbarriers in a bond percolation model, we show that there arepotentially higher conductivity Li3OCl1−xBrx structures near0.235 ≤ x ≤ 0.395. We then confirm this prediction usingAIMD simulations, which predict a higher conductivity forLi3OCl0.75Br0.25 compared to Li3OCl0.5Br0.5, the highestconductivity composition in the antiperovskite chemistryidentified experimentally thus far. The approach developed inthis work has applications beyond the LRAP chemistry, and canpotentially be extended to other perovskite/cubic ion-conducting systems such as the perovskite oxygen-ionconductors of interest in solid-oxide fuel cells.

■ ASSOCIATED CONTENT*S Supporting InformationOrdered Li3OCl1−xBrx (x = 0.25, 0.5, and 0.75) 2 × 2 × 2supercells, calculated lattice parameters, complete results ofNEB calculations, and bond percolation threshold for LRAPstructure. The Supporting Information is available free ofcharge on the ACS Publications website at DOI: 10.1021/acs.chemmater.5b00988.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: ongsp@eng.ucsd.edu.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was supported by the U.S. Department of Energy,Office of Science, Basic Energy Sciences under Award DE-SC0012118. A portion of the computations performed in thiswork also used the Extreme Science and Engineering DiscoveryEnvironment (XSEDE), which is supported by NationalScience Foundation grant number ACI-1053575.

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