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[Halimah Harfah](https://orcid.org/0000-0002-7268-3758), [Yoshitaka Tateyama](https://orcid.org/0000-0002-5532-6134), [Kazunori Takada](https://orcid.org/0000-0001-7568-1806), [Randy Jalem](https://orcid.org/0000-0001-9505-771X)

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[Lithium superionic behavior and defect robustness in LiNbOCl                    <sub>4</sub>                    : a first-principles molecular dynamics study](https://mdr.nims.go.jp/datasets/0f6e4882-157c-40c1-8445-64177e8f35b5)

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Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics studyJournal ofMaterials Chemistry APAPERPublished on 06 March 2026Licensed under CC-BY-NC 4.0Lithium superionaResearch Center for Energy and Environmenfor Materials Science (NIMS), 1-1 Namiki, TJALEM.Randy@nims.go.jpbLaboratory for Chemistry and Life Science,of Science Tokyo, 4259 Nagatsuta-cho, MidJapanCite this: J. Mater. Chem. A, 2026, 14,17385Received 7th July 2025Accepted 23rd February 2026DOI: 10.1039/d5ta05478hrsc.li/materials-aThis journal is © The Royal Society oic behavior and defect robustnessin LiNbOCl4: a first-principles molecular dynamicsstudyHalimah Harfah, a Yoshitaka Tateyama, ab Kazunori Takada aand Randy Jalem *aLithium-ion conductors that exhibit high ionic conductivity, thermal robustness, and mechanicalcompliance are essential for advancing all-solid-state battery technologies. In this study, wesystematically investigate Li-ion transport in pristine and LiCl Schottky-defected LiNbOCl4 using densityfunctional theory molecular dynamics (AIMD). Pristine LiNbOCl4 demonstrates robust superionicbehavior with low activation energy (0.236 eV) and high room-temperature conductivity (9.57 ×10−3 S cm−1), facilitated by a rigid Nb–O–Cl framework and a disordered Li sublattice. Introducing LiClSchottky defects slightly increases the activation energy to 0.241 eV and slightly reduces conductivity to8.20 × 10−3 S cm−1. While defects preserve global percolation networks and mechanical softness, theyintroduce localized structural disruptions at vacancy-adjacent polyhedra. Notably, the dynamic gatingmechanism where coherent anion rotations transiently expand diffusion bottlenecks is impaired. Unlikethe classical paddle-wheel mechanism involving rotating polyanion clusters, this mechanism describesa distinct mode of transient bottleneck expansion driven by coordinated motion of individual halide andoxide anions within an oxyhalide lattice. The disruption of this mechanism is reflected in the emergenceof rotational incoherence, rapid bond angle decorrelation, attenuation of high-frequency O-basedphonon modes (∼80 meV), and a strong reduction and spatial localization of anion reorientation eventsthat are associated with enhanced Li-ion motion, as identified by event-triggered ensemble. Together,these effects suppress bottleneck breathing, limiting the transient widening of diffusion pathways andeffectively increasing the migration barrier. Li space–time correlation analysis further reveals diminishedtemporal coherence and transport cooperativity in the defected structure. These findings underscore theimportance of cooperative lattice dynamics in enabling low-barrier Li-ion transport and demonstratethat LiNbOCl4 retains high conductivity even under defect-induced perturbations, establishing it asa defect-tolerant candidate for next-generation solid electrolytes.1. IntroductionAll-solid-state batteries (ASSBs) are attracting considerableattention as a promising alternative to conventional lithium-ionbatteries (LIBs), primarily due to their enhanced safety, higherenergy density, and suitability for advanced applications such aselectric vehicles and portable electronics.1 In contrast to tradi-tional LIBs, which rely on ammable liquid electrolytes, ASSBsemploy solid electrolytes (SEs) to facilitate lithium-ion (Li-ion)transport between the anode and cathode. The use of SEs elim-inates the risks associated with liquid electrolyte leakage andtal Materials (GREEN), National Institutesukuba, Ibaraki 305-0044, Japan. E-mail:Institute of Integrated Research, Instituteori-ku, Yokohama, Kanagawa 226-8501,f Chemistry 2026ammability, thereby signicantly improving the thermal andmechanical stability of batteries for large-scale applications.1,2An ideal SE must possess high Li-ion conductivity, chemicalstability, and interfacial compatibility with both the cathode andanode materials. Generally, SEs can be classied into three maincategories: oxides, suldes, and halides, each offering uniqueadvantages and challenges. Oxide-based SEs are recognized fortheir excellent chemical and electrochemical stability but oenexhibit relatively low Li-ion conductivity.3,4 Sulde-based SEs,conversely, demonstrate high ionic conductivity but suffer frompoor chemical and electrochemical stability, rendering themvulnerable to degradation under operating conditions.5–7 Halide-based SEs offer a balance between these extremes, combiningmoderate to high ionic conductivity with good chemical andoxidative stability.8 However, their relatively low reductive stabilitymay limit their applicability in certain battery architectures.9Lithium (Li) oxyhalides have emerged as a new class of SEs thatpotentially integrate the favorable properties of both oxides andJ. Mater. Chem. A, 2026, 14, 17385–17401 | 17385http://crossmark.crossref.org/dialog/?doi=10.1039/d5ta05478h&domain=pdf&date_stamp=2026-05-06http://orcid.org/0000-0002-7268-3758http://orcid.org/0000-0002-5532-6134http://orcid.org/0000-0001-7568-1806http://orcid.org/0000-0001-9505-771Xhttps://creativecommons.org/licenses/by-nc/4.0/Journal of Materials Chemistry A Paperhalides. By introducing oxygen into the halide lattice, oxyhalidesare expected to retain high ionic conductivity akin to halides whileenhancing chemical and electrochemical stability similar tooxides.10–13 In particular, oxyhalide-type LiNbOCl4 has been thefocus of recent studies; it exhibits an ionic conductivity of about 10mS cm−1 at room temperature.10,13 Structurally, LiNbOCl4 has beendescribed as a framework of corner-O-sharing NbO2Cl4 octahedraforming parallel chains, sometimes written as (NbCl4O2/2)N,where O2/2 indicates two bridging O atoms each shared by two Nbcenters (i.e., 12O per Nb).10,13 These chains create loosely packedregions that host disordered Li-ions; the Li sublattice does notform distinct layers but instead occupies partially lled interstitialsites.10 This structural motif differs from classical layeredcompounds like LiCoO2, where well-dened alternating CoO6 andLiO6 octahedral layers exist.14 Instead, in LiNbOCl4, the layerednature arises from the anisotropic connectivity of the rigid Nb-based octahedral network, while Li mobility is facilitated withinand between these slabs due to structural openness and ionicdisorder.10 In addition to its promising ionic conductivity,LiNbOCl4 exhibits a low elastic stiffness which is critical formaintaining good interfacial contact and thus, a good structuralintegrity during battery operation.10,13 These combined attributesplace LiNbOCl4 in direct competition with established SEs such asgarnet-type Li7La3Zr2O12 (LLZO)15 and sulde-based materials.16–18To date, a comprehensive understanding of the Li-ion migrationmechanism within the LiNbOCl4 structure remains under activeinvestigation. Computational approaches, particularly those basedon density functional theory (DFT), have proven invaluable forprobing ion dynamics, defect chemistry, and thermodynamicstability in SE materials.10,13,19,20 By integrating theoretical insightswith experimental observations, it becomes possible to ne-tunematerial properties and guide the discovery of new electrolytecompositions with enhanced performance.In this study, we systematically explore the fundamental prop-erties of LiNbOCl4 SE using DFT calculations. Combined withmolecular dynamics (MD) simulations, we investigate Li-iontransport in both pristine and LiCl Schottky-defected structures.The initial part of this work focuses on establishing a computa-tional framework by benchmarking various van der Waals (vdW)correction schemes within DFT to accurately model LiNbOCl4'sstructural and Li-ion transport properties. Structural and thermo-dynamic stabilities are assessed via convex hull analysis. We furtheranalyze Li-ion dynamics through temperature-dependent meansquare displacement (MSD) analysis, extract diffusion coefficients,and quantify ionic conductivity using the Nernst–Einstein relation.Activation energies for Li migration are derived from Arrheniusbehavior, allowing a direct comparison between pristine anddefected systems, as well as available experimental data. Our resultsprovide useful insights for the design of high-conductivity andpractical SEs for ASSBs.2. Computational methods2.1 Initial structure and atomic model generationThe initial structural model for LiNbOCl4 is based on experi-mental crystallographic data reported for the tetragonal phase(space group I4/m).10 The lattice parameters are set to a = b =17386 | J. Mater. Chem. A, 2026, 14, 17385–174018.9109 Å and c = 3.9542 Å, with angles a = b = g = 90°. Theatomic site coordinates and occupancies are summarized inTable S1 (in the SI). Li atoms occupy three partially lled 8hWyckoff positions (Li(1), Li(2), and Li(3)) with partial occupan-cies of 0.04, 0.17, and 0.04, respectively, reecting experimen-tally observed Li disorder.To capture the intrinsic disorder brought upon by the Lipartial occupancy sites, a 2 × 2 × 3 supercell is constructed and1000 distinct Li congurations are generated by randomsampling of Li sites. This procedure preserves the experimen-tally observed site occupancy ratios. The atomic structure isillustrated in Fig. 1, where Cl, Nb, O, and Li atoms are depictedwith distinct colors to highlight the spatial distribution ofpartially occupied Li sites.Ewald energy calculations are performed on each congu-ration using the pymatgen library21 to evaluate electrostaticstability. Based on this Ewald energy screening step, the 10congurations with the lowest electrostatic energies areselected for subsequent full DFT relaxation. This approachensures a representative sampling of low-energy Li distributionsconsistent with experimental ndings.To introduce the Schottky-type LiCl defect, one Li and one Clatom are removed from each 168-atom LiNbOCl4 supercell(Fig. 2), corresponding to a vacancy concentration of ∼1.1 at%.To systematically assess the defect energetics, 1000 distinct Li–Cl vacancy arrangements are generated in the same relaxedsupercell. For each conguration, (i) the Ewald electrostaticenergy and (ii) the minimum periodic separation between the Liand Cl vacancies, dVLi–VClare evaluated. When the congurationsare ordered based on ascending Ewald energy, short vacancyseparations (dVLi–VCl( 3 Å) populate the low-energy region,whereas structures with dVLi–VClT 5 Å occur predominantly athigher Ewald energies (Fig. S2). Because the Ewald sum isolatesthe long-range coulombic contribution at a xed compositionand volume, this trend indicates that compact Li–Cl vacancypairs are electrostatically preferred. The lowest-energy, short-separation conguration is therefore selected as the represen-tative LiCl-Schottky model and it is relaxed fully using the sameconvergence criteria as for the pristine supercell, enablinga direct comparison of the relaxed geometries. The resultinglattice response is modest: aer full relaxation; the a latticeparameter increases from 18.8488 Å (pristine) to 18.9803 Å(+0.70%), and b from 18.8935 Å to 19.1622 Å (+1.42%), while cremains essentially unchanged atz12.04 Å (−0.002%). The off-diagonal elements of the cell matrix are #∼0.02 Å, indicatingnegligible shear distortions. These values, taken directly fromthe relaxed cell matrices, show that the LiCl Schottky defectinduces only a small, nearly isotropic in-plane expansion andleaves the c axis essentially intact. This relaxed lowest-energyconguration is used in all subsequent AIMD simulations.2.2 DFT calculation conditionsTo ensure an accurate and reliable structural and transportproperty analysis of LiNbOCl4, a systematic benchmarking ofvdW correction schemes is carried out within the framework ofDFT. All calculations are performed using the Vienna Ab initioThis journal is © The Royal Society of Chemistry 2026Fig. 1 Atomic structure representation of LiNbOCl4, highlighting atomic configurations and Li occupancy distributions across crystallographicsites. Chlorine (Cl) atoms are depicted in green, niobium (Nb) atoms in blue, oxygen (O) atoms in red, and lithium (Li) atoms with partialoccupancy in magenta. This visualization illustrates the atomic arrangement within the LiNbOCl4 crystal lattice, with Li disorder emphasizedaccording to occupancy variations, guided by symmetry considerations.Paper Journal of Materials Chemistry ASimulation Package (VASP)22 with the projector augmented-wave method.23 Exchange–correlation effects are treated usingthe generalized gradient approximation as parametrized byPerdew, Burke, and Ernzerhof (PBE).24 Various vdW correctionsare evaluated, including DFT-D2,25 DFT-D3,26 DFT-D3(BJ),27optB88,28 optPBE,28 optB86b,28 DF,29 and DF2,30 to assess theirperformance in reproducing experimental structuralparameters.All structural optimizations are conducted on a 2 × 2 × 3supercell (168 atoms), with a plane-wave cutoff energy of 520 eVand a k-point grid spacing of 0.3–0.5 Å−1. Electronic energyconvergence is set to 1 × 10−5 eV, and ionic force convergenceto 0.01 eV Å−1, ensuring precise and stable relaxation.2.3 Thermodynamic stability evaluationThe thermodynamic stability of pristine and Schottky-defectedLiNbOCl4 systems is evaluated through convex hull analysisbased on formation energy calculations.31 Formation energiesare derived from fully geometry-optimized structures obtainedvia DFT calculations and post-processed with the Pymatgenlibrary.21The energy above the convex hull (Ed) at 0 K is used asa measure of thermodynamic (meta)stability; it is computed foreach structure using eqn (1):Fig. 2 Structural representation of the Schottky-defected LiNbOCl4 supeLeft: three-dimensional perspective showing the global arrangement of ac-axis, emphasizing the local structural distortions induced by vacanciesVacancies are indicated by red circles and arrows, illustrating how locapotentially affects ion transport pathways.This journal is © The Royal Society of Chemistry 2026Ed = Ephase − Ehull (1)where Ephase is the formation energy per atom of the phase ofinterest and Ehull is the convex hull energy per atom at the samecomposition. The convex hull is constructed by identifying theset of phases with the lowest energies at each composition.Phases with Ed = 0 lie on the convex hull and are thermody-namically stable at 0 K, whereas non-ground-state phases withEd > 0 are located above the hull.I n this case, Ed represents thedecomposition energy, i.e., the energy difference between thephase and the closest linear combination of stable phases at thesame composition.Physically, Ed quanties the thermodynamic driving force fordecomposition: a zero Ed means the phase is stable, whilea small positive Ed indicates a metastable phase that is stillpotentially synthesizable if the kinetic barriers to decomposi-tion are high. Full derivation and implementation details forthe convex hull construction are provided in the SI (Section S3).2.4 Mechanical property evaluation via pressure–volumettingThe mechanical compressibility of LiNbOCl4 is evaluatedthrough direct pressure–volume (P–V) tting based on DFT-calculated structures.32 External hydrostatic pressures of 0, 2,4, 6, 8, and 10 kbar are applied to the fully optimized supercell.rcell highlighting the introduction of Li (VLi) and chlorine (VCl) vacancies.toms and the position of vacancy pairs. Right: top-down view along the. Nb atoms are shown in blue, Cl in green, O in red, and Li in magenta.lized removal of Li and Cl atoms perturbs the surrounding lattice andJ. Mater. Chem. A, 2026, 14, 17385–17401 | 17387Journal of Materials Chemistry A PaperAt each pressure step, full structural relaxation is performed,allowing simultaneous optimization of both atomic positionsand lattice vectors. This procedure enables a direct simulationof the material's volumetric response under hydrostatic stress.The bulk modulus (B) is determined from the linear rela-tionship between pressure and volume according to eqn (2):B ¼ �V dPdV(2)where V is the equilibrium volume at zero pressure and dP/dV isthe slope obtained from linear tting of the P–V data. This directtting method provides an alternative to the commonly usedBirch–Murnaghan equation of state33 and is particularly well-suited for mechanically so ionic materials such as LiNbOCl4.2.5 Thermal expansion analysisThe thermal expansion behavior of LiNbOCl4 is investigatedusing constant-pressure AIMD simulations performed with theVASP in the isothermal–isobaric (NPT) ensemble with a ther-mostat damping parameter (g) of 10 ps−1. Temperature controlis achieved using the Langevin thermostat,34 with simulations atxed temperatures of 600 K, 800 K, 1000 K, 1200 K, and 1400 K.Each simulation is run for 10 ps with a time step of 1 fs. Thenal 5000 steps of each trajectory are used to extract the averagecell volume corresponding to each temperature.The volumetric thermal expansion coefficient (aV) is deter-mined by linearly tting the temperature dependence of theequilibrium volumes. It is calculated according to eqn (3):aV ¼ 1V0dVdT(3)where V0 is the average volume at 600 K and dV/dT is the slope ofthe linear t. This approach provides a direct assessment of thelattice's thermal response under conditions relevant to batteryoperation.2.6 Li-ion transport analysisFollowing thermal expansion analysis, AIMD simulations areperformed to investigate Li-ion transport properties. Initialequilibration is conducted in the NPT ensemble using theLangevin thermostat for 10 ps to determine equilibriumvolumes at each temperature. Fixed-volume supercells derivedfrom this equilibration step are then used for productionsimulations in the canonical (NVT) ensemble, employing theNosé–Hoover thermostat35,36 with an integration time step of 1fs. Each production run spanned 100 ps (100 000 steps) at targettemperatures of 600, 800, 1000, 1200, and 1400 K.Li-ion diffusivity is determined from the mean squareddisplacement (MSD) curves. The diffusion coefficients (DLi) arecalculated from the linear regime of the MSD using the Einsteinrelation, expressed as eqn (4):DLi ¼ limt/N16tDjriðtÞ � rið0Þj2E(4)where hjri(t) − ri(0)j2i denotes the ensemble-averaged MSD of Liions.17388 | J. Mater. Chem. A, 2026, 14, 17385–17401The Li-ion conductivity (sLi) is estimated using the Nernst–Einstein relation (eqn (5)):sLi ¼ nq2DLikBT(5)where n is the number density of Li ions, q is the elementarycharge, kB is the Boltzmann constant, and T is the simulationtemperature.Activation energies (Ea) for Li diffusion are extracted byperforming Arrhenius ts to the temperature dependence of thediffusion coefficients and ionic conductivities according toeqn (6):DLi ¼ D0e� EakBT (6)where D0 is the pre-exponential factor. Linear regressions of DLiand ln sLi versus 1/T were used to obtain Ea from the slope.Trajectory density maps and structural snapshots were furtheranalyzed to visualize Li-ion percolation networks and localdiffusion pathways across different temperatures.3. Results and discussion3.1 Validation of structural models via van der WaalsbenchmarkingThe benchmarking of dispersion-corrected density functionalsis performed, and the results are summarized in Table 1. Allvalues in Table 1 are obtained from geometry optimizationscarried out in this work using identical initial structures andcomputational parameters; only the dispersion (vdW) treatmentis varied across functionals. The performance of each func-tional is evaluated based on the deviations of lattice parameters,unit cell volume, and Nb–Cl bond lengths relative to experi-mental values. In the absence of vdW correction, the structureexhibits signicant overestimations in both lattice constantsand bond lengths, with a total deviation exceeding 6.8%.Among the tested functionals, DFT-D3(BJ), DFT-D2, and optB88demonstrate the best agreement with experimental data.Notably, DFT-D3(BJ) produces the lowest total deviation(1.35%), with the a and c lattice parameters deviating by only0.92% and 0.24%, respectively, and the unit cell volume within0.04% of the reference value. The average Nb–Cl bond length isalso consistent with experimental observations for relatedcompounds, such as TlNbOCl4 (2.38–2.41 Å).10,13These results conrm that explicit inclusion of vdW inter-actions is critical for accurately reproducing the lattice param-eters and Nb–Cl bond lengths vs. the experiment. Based on thisbenchmarking, the DFT-D3(BJ) functional was selected for allsubsequent static and dynamic simulations, including struc-tural relaxations, AIMD simulations, and defect calculations.3.2 Thermodynamic stabilityThe thermodynamic stability of pristine and Schottky-defectedLiNbOCl4 structures is evaluated through Ehull analysis, basedon formation energies calculated from fully relaxed DFTgeometries. The pristine LiNbOCl4 compound exhibitsa formation energy of−2.101 eV per atom and lies 0.0211 eV perThis journal is © The Royal Society of Chemistry 2026Table 1 Comparison of vdW functional performance in predicting lattice parameters and Nb–Cl bond length. This table summarizes thecalculated lattice parameters (a and c), unit cell volume, and average Nb–Cl bond length for various vdW functionals applied to the LiNbOCl4system. Percentage differences relative to the reference values13 are provided for the bond length, lattice parameters, and volume to assess theaccuracy of each functional. The average is the combined percentage difference for all metrics, providing an overall measure of deviationvdW functionalLatticeparameterVolume (Å3)Average Nb–Clbond length (Å)Percentage difference to ref. 13 (%)a (Å) c (Å)Nb–Clbond length a c Volume AverageExperiment7 8.911 3.954 313.98 2.32 0.0 0.0 0.0 0.0 0.0Without vdW (this work) 9.471 4.012 360.994 2.426 4.573 6.291 1.467 14.974 6.826Df (this work) 9.227 4.042 345.391 2.454 5.784 3.543 2.227 10.004 5.39df2 (this work) 9.042 4.02 332.811 2.472 6.56 1.47 1.659 5.997 3.922dd2 (this work) 8.881 3.965 317.641 2.418 4.203 0.34 0.263 1.166 1.493dd3 (this work) 8.903 3.978 319.747 2.422 4.401 0.084 0.595 1.837 1.729dd3-bj (this work) 8.829 3.964 313.85 2.418 4.216 0.918 0.243 0.041 1.354optb88 (this work) 8.831 3.952 312.708 2.428 4.634 0.056 0.405 0.893 1.497Optpbe (this work) 9.006 3.987 325.767 2.436 5.009 1.068 0.836 3.754 2.666optb86b (this work) 8.803 3.947 311.183 2.419 4.263 1.213 0.178 0.891 1.636r2SCAN-D4 (this work) 9.521 4.013 362.859 2.426 4.569 6.844 1.483 15.568 7.116Paper Journal of Materials Chemistry Aatom above the convex hull, indicating metastability. TheSchottky-defected structure, generated by removing one Li andone Cl atom per supercell (Li23Nb24Cl95O24), shows a marginallymore-negative formation energy of −2.104 eV per atom anda reduced hull distance of 0.0185 eV per atom.Both Ehull values fall within the commonly accepted meta-stability threshold (<50 meV per atom), suggesting that pristineand defected LiNbOCl4 are potentially synthesizable underappropriate experimental conditions. Decomposition pathwayanalysis identied NbCl3O and LiCl as the dominant competingphases, with relative phase fractions of∼71% and∼29% for thepristine structure, and 72% and 28% for the defected structure,respectively.The slight reduction in Ehull with LiCl-Schottky defectsindicates that the introduction of Li–Cl vacancy pairs does notsignicantly destabilize the host lattice and may even promotea degree of stabilization. This result supports the synthesiz-ability of Schottky-defected LiNbOCl4 which is also consistentwith the dynamic stability observed during AIMD simulations(see the later section).3.3 Mechanical property evaluationFig. S6 (see SI S6) presents the pressure–volume (P–V) relation-ships for pristine and LiCl Schottky-defected LiNbOCl4 as ob-tained from DFT simulations. Both systems exhibit a lineardecrease in volume under increasing hydrostatic pressure,allowing direct determination of the bulk modulus via linearregression of the P–V data.For pristine LiNbOCl4, the bulk modulus is determined to be15.98 GPa, with a standard error of 0.78 GPa, corresponding toa 95% condence interval of 14.45–17.51 GPa. In the Schottky-defected structure, the bulk modulus is calculated to be15.91 GPa, with a standard error of 0.47 GPa and a 95% con-dence interval of 14.98–16.84 GPa. The overlap in these intervalsindicates no statistically signicant difference in compress-ibility between the two structures.This journal is © The Royal Society of Chemistry 2026This relatively low bulkmodulus, signicantly lower than the∼70 GPa obtained via Birch–Murnaghan EOS33 tting, alignswith values reported for other mechanically so solid electro-lytes such as Li3PS4, Li6PS5Cl, and Na3PS4 of 15–25 GPa.6,37,38This mechanical soness, arising from the intrinsic latticeexibility and structural anharmonicity of these materials, isknown to facilitate dynamic bottleneck expansion and locallattice uctuations that enable rapid Li-ion transport.39,40Consequently, the comparable bulk moduli observed in bothpristine and defected LiNbOCl4 structures emphasize theinherent mechanical compliance of the Nb–O–Cl framework,supporting its applicability as a robust solid electrolyte underpractical conditions.3.4 Thermal expansion analysisThe temperature dependence of the equilibrium cell volume,extracted from NPT-MD simulations in the range of 600–1400 K,is depicted in Fig. S7 (see SI S7) for both pristine and LiClSchottky-defected LiNbOCl4. The data reveal a linear increase involume with temperature in both systems.Both pristine and Schottky-defected LiNbOCl4 exhibit volu-metric thermal expansion coefficients (aV) that fall within therange reported for known superionic conductors. Specically,aV values of 1.03 × 10−4 K−1 for the pristine system and 8.44 ×10−5 K−1 for the Schottky-defected system are obtained fromlinear ts to temperature-dependent volume data. For refer-ence, the sulde-based electrolyte Li10GeP2S12 (LGPS) has beencomputationally reported to have a linear thermal expansioncoefficient of aL z 3.2 × 10−5 K−1 at 300 K, corresponding to aVz 9.6 × 10−5 K−1 assuming isotropic expansion.41 Experi-mental XRD studies on LGPS also show near-linear latticeexpansion trends below its decomposition point (∼700 K), withminor anisotropy between a and c lattice parameters.41In contrast, oxide-based solid electrolytes such as cubic Al-stabilized Li7La3Zr2O12 (LLZO) exhibit lower expansion coeffi-cients. Synchrotron XRD measurements report aL z 15.5 ×J. Mater. Chem. A, 2026, 14, 17385–17401 | 17389Journal of Materials Chemistry A Paper10−6 K−1 for LLZO in the temperature range of 25 °C to 700 °C,corresponding to a volumetric coefficient aV z 4.65 × 10−5K−1.42 When compared directly, the aV values for both pristineand defected LiNbOCl4 are higher than that of LLZO andcomparable to those of LGPS, placing LiNbOCl4 within theupper range of thermal expansivity observed in SEs. The abso-lute difference in aV between the pristine and Schottky-defectedLiNbOCl4 systems (1.03 × 10−4 vs. 8.44 × 10−5 K−1) is smallerthan the full range of aV values reported across sulde andoxide electrolyte families, indicating that the introduction ofSchottky defects leads to a moderate change in thermalexpansion behavior.To elucidate the local structural behavior underlying thesemacroscopic thermal responses, temperature-dependent Vor-onoi volume distributions and nearest-neighbor (NN) bondlengths are quantitatively analyzed (see the SI). In pristineLiNbOCl4, the average Li-site Voronoi volume increases from18.8 Å3 at 600 K to 21.5 Å3 at 1400 K. In the Schottky-defectedstructure, the Li-site Voronoi volume expands more substan-tially, from 19.8 Å3 to 22.7 Å3 over the same temperature range,providing direct evidence of enhanced local structural exibilityaround Li sites. However, analysis of the NN bond lengthsreveals only marginal changes (∼0.03 Å at 1400 K) in the Nb–Oand Nb–Cl backbone, consistent with the comparable bulkmoduli observed for both systems.Quantitative analysis of temperature-dependent Voronoivolumes and bulk moduli reveals a decoupling between localstructural exibility and macroscopic thermal expansionFig. 3 Mean squared displacement (MSD) profiles of Li ions in LiNbOtemperature-dependent MSD curves for the pristine and LiCl Schottky-(orange), 1200 K (red), and 1400 K (purple). Panels (c) and (d) present asystems, respectively. In both cases, Li ions (blue solid line) exhibit subscontributors to long-range transport. Nb atoms (yellow dashed line)remaining close to their crystallographic positions and highlighting the rhigher displacement than Nb andO, especially in the defected system, reflof vacancies.17390 | J. Mater. Chem. A, 2026, 14, 17385–17401behavior in LiNbOCl4. Specically, although Schottky defectsinduce localized volumetric expansion around Li sites, as evi-denced by increased Li-site Voronoi volumes, the overallthermal expansion coefficient is slightly reduced in the defectedsystem. This reduction occurs despite the enhanced local ex-ibility, suggesting that the global thermal response is predom-inantly governed by the comparatively rigid Nb–O–Clframework. Such hierarchical mechanical behavior, whereinlocal dynamic environments coexist with a robust structuralbackbone, is a dening characteristic of LiNbOCl4 asa mechanically so SE, highlighting its potential for main-taining mechanical integrity under thermal cycling.3.5. Analysis of Li-ion dynamics and diffusion behaviorThe Li-ion dynamics in pristine and Schottky-defectedLiNbOCl4 are systematically investigated through meansquared displacement (MSD) analysis using 100 ps NVT-MDtrajectories. The temperature-dependent MSD proles are pre-sented in Fig. 3a (pristine) and Fig. 3b (Schottky-defected). At600 K, Li-ion motion in both systems is characterized by inter-site Li jumps (from 1st–3rd NN Li sites), with contributionsfrom intra-site vibrational and back-and-forth jump dynamics.The MSD curves exhibit an initial ballistic regime within ∼1–2ps, marked by a steep, near-quadratic rise due to inertialmotion. This is followed by a vibrational plateau lasting up to∼25–30 ps, reecting connement within local coordinationenvironments. Aer ∼30 ps, a slight upward trend emerges,indicating the onset of the linear diffusive regime. The presenceCl4 from 100 ps NVT-MD simulations. Panels (a) and (b) show thedefected systems, respectively, at 600 K (blue), 800 K (green), 1000 Ktomic species-resolved MSDs at 1200 K for the pristine and defectedtantial diffusion indicative of high ionic mobility, forming the primaryand O atoms (green dash-dotted line) show minimal displacement,obustness of the host lattice. Cl atoms (red dotted line) exhibit slightlyectingmoderate thermal vibrations that are enhanced by the presenceThis journal is © The Royal Society of Chemistry 2026Paper Journal of Materials Chemistry Aof Schottky defects introduces local structural distortions butdoes not signicantly improve diffusion, conrming that thethermal energy at 600 K is insufficient to overcome migrationbarriers in either system.As the temperature increases to 800–1400 K, a clearprogression from vibrationally conned motion to long-rangediffusion is observed. The MSD curves increasingly displaylinear behavior, indicating thermally activated hopping andeventually robust superionic conduction. The pristine systemmaintains slightly higher MSD slopes across the temperaturerange, suggesting more efficient long-range transport pathways.Meanwhile, the defected system shows comparable diffusionbehavior at high temperatures but may experience mild locali-zation effects due to structural distortion near vacancies.Despite these variations, both systems exhibit sustained Li-ionmobility at elevated temperatures, conrming the dynamicstability of LiNbOCl4 even under defect perturbation.3.6 Estimation of Li-ion conductivity and activation energy3.6.1 Diffusion coefficients and the Nernst–Einstein rela-tion. Li-ion diffusion coefficients (DLi) are calculated from thelinear regime of the mean square displacement (MSD) prolesaccording to eqn (5). The corresponding ionic conductivities(sLi) are then derived using the Nernst–Einstein relation:sLi ¼ cðzFÞ2DLiRT(7)where c is the Li-ion carrier density, z= 1 is the ionic charge, F isthe Faraday constant, R is the ideal gas constant (8.314 J mol−1K−1), and T is the absolute temperature. The carrier concen-tration c is computed based on the number of mobile Li ions inthe simulation supercell and the equilibrium volume at eachtemperature, determined from NPT-MD simulations.The extracted diffusion coefficients for both pristine andSchottky-defected LiNbOCl4 are summarized in Fig. 4. We notethat the diffusion coefficient extracted from the COM-correctedMSD (e.g. at 1000 K, D z 1.5 × 10−4 cm2 s−1) lies within therange commonly reported by AIMD studies of Li superionicFig. 4 Arrhenius plots of temperature-dependent ionic conductivity(log(sT)) for pristine and Schottky-defected LiNbOCl4, compared withpreviously reported FF-MD, AIMD and experimental results. Activationenergies are annotated alongside linear fits.This journal is © The Royal Society of Chemistry 2026conductors at comparable temperatures (10−5–10−3 cm2s−1).19,20,43 The temperature dependence of DLi (see Table S6 inthe SI) clearly captures the enhancement of Li-ion mobility withincreasing thermal excitation. Notably, the pristine LiNbOCl4consistently displays higher DLi values across the studiedtemperature range, as compared to the Schottky-defectedstructure. Although LiCl Schottky defects introduce vacancysites that could potentially serve as transient migration path-ways, our simulations indicate a net hindrance to long-rangediffusion. To clarify the origin of this reduction in conduc-tivity, analyses are performed on local anion rotationalbehavior, dynamic bottleneck narrowing, and attenuation ofhigh-frequency vibrational modes (see the later section).3.6.2 Temperature dependence and Arrhenius behavior.The temperature dependence of sLiT for both pristine andSchottky-defected LiNbOCl4 is analyzed using the Arrheniusformalism:logðsTÞ ¼ logðs0Þ � Ea2:303R�1T�(8)where s0 is the conductivity prefactor, Ea is the activation energyfor Li-ion migration, and R is the gas constant.The Arrhenius plots from MD simulations are shown inFig. 4. Linear regression of the simulated data yielded activationenergies of 0.236 eV for the pristine structure and 0.241 eV forthe Schottky-defected variant. Extrapolated to room tempera-ture (300 K), the corresponding ionic conductivities are esti-mated to be 9.57 × 10−3 S cm−1 and 8.20 × 10−3 S cm−1,respectively.These simulation-derived values are in close agreement withexperimental measurements. Tanaka et al. reported an activationenergy of 0.24 eV and room-temperature ionic conductivity of10.7 mS cm−1 for cold-pressed LiNbOCl4 pellets.10 Similarly, Jeonet al. achieved an experimental conductivity of 8.4 mS cm−1 at 25°C using a hydrochloric acid-free synthesis route and measuredan activation energy consistent with values between ∼0.20 and0.25 eV, depending on synthesis conditions.113.7 Trajectory density analysisTrajectory density maps obtained from 100 ps NVT-MD simu-lations provide detailed insights into the dynamic behavior ofeach atomic species in pristine and Schottky-defected LiNbOCl4(Fig. 5). These visualizations elucidate both the vibrationalstability of the lattice framework and the emergence of Li-iontransport pathways under thermal excitation.For both pristine and defected systems, Nb atoms exhibitminimal spatial displacement across the temperature rangewith trajectory densities sharply localized near their crystallo-graphic positions. Here, “average spatial displacement” refersto the time-averaged root-mean-square (RMS) displacement ofspecies b dened as rRMSbðTÞ ¼ h ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiMSDbðDt; TÞp iDt over the 0–100 ps trajectory at each temperature. Quantitative analysisshows that the average spatial displacements of Nb atomsremain below 1.7 Å up to 1400 K in the pristine structure,increasing modestly to ∼1.5 Å in the defected system at 1200 Kand 1.49 Å at 1400 K (Table S2-1). These consistently low valuesJ. Mater. Chem. A, 2026, 14, 17385–17401 | 17391Fig. 5 Trajectory density maps in the c-directions of all atoms and individual atomic species, Li (magenta), Nb (blue), O (red), and Cl (cyan) inLiNbOCl4, obtained from 100 ps NVT-MD simulations. Panels (a) and (c) correspond to the pristine structure at 600 K and 1200 K, respectively,while (b) and (d) show the LiCl Schottky-defected structure at the same temperatures. Li ions exhibit pronounced delocalization, formingcontinuous three-dimensional diffusion networks. In contrast, Nb and O atoms remain near their equilibrium positions, reflecting a stable andrigid crystal framework. Cl atoms showmoderate vibrational broadening that becomesmore pronounced with increasing temperature and in thepresence of vacancies.Journal of Materials Chemistry A Paperhighlight the mechanical rigidity of the Nb–O–Cl frameworkand conrm the structural stability of the host lattice.O atoms display similarly restricted mobility in bothsystems, with time-averaged RMS displacements below 1.7 Å upto 1200 K, underscoring the robust backbone connectivityprovided by the oxygen sublattice.Cl atoms, in contrast, exhibit progressively enhancedthermal vibrations with increasing temperature, particularly inthe Schottky-defected system. In pristine LiNbOCl4, Cl time-averaged RMS displacements increase from ∼0.8 Å at 600 K to∼3.4 Å at 1200 K. In the defected structure, Cl displacementsincrease signicantly from ∼1.2 Å at 600 K to ∼3.5 Å at 1200 K.This increase is attributed to the additional accessible volumecreated by Cl vacancies, which enhances the vibrationalfreedom of neighboring Cl sites.The rotational behavior of rst-nearest-neighbor (1NN) Cland O atoms around the Nb polyhedron of the (potential)vacancy site is analyzed using spherical coordinates (r, q, f) overthe nal 5 ps of MD simulations at 600 K (Fig. 6). Here, r denotesthe instantaneous Nb–X distance (X = Cl, O); q is the polar (tilt)angle measured from the crystallographic c axis; and f is theazimuthal angle between the projection of the Nb–X vector ontothe ab plane and the a axis. In the pristine system (Fig. 6a–c), theCl neighbors, Cl-near (closest to the potential vacancy site) andCl-far (second closest), exhibit moderate and coherent17392 | J. Mater. Chem. A, 2026, 14, 17385–17401reorientation. The Cl-near atom has r uctuating within 2.2–2.6Å and q and f conned to ∼80–120° and ∼100°, respectively.The Cl-far atom displays similar r variations but with fextending down to ∼−100°, suggesting slightly more exiblemotion. The oxygen neighbor displays pronounced azimuthalreorientation (f excursions approaching ±100°) at nearlyconstant, modest tilt (q ∼ 5–25°) and limited Nb–O bond-lengthuctuation (r ∼ 1.7–2.1 Å). Thus, O predominantly precessesabout c within a small tilt cone, while the octahedral geometryremains intact.In the Schottky-defected system, the local structural envi-ronment around Nb transitions from octahedral to a ve-foldpyramidal coordination, typical of Nb centers lacking oneanionic ligand. The Cl neighbors (Cl-near and Cl-far) in thisenvironment display signicantly larger and more erratic rota-tional dynamics, with r oscillating up to 2.8 Å, q extending to∼120°, and f spanning nearly 180°. These pronounced andunsynchronized rotational motions highlight the disruption ofcollective coherence within the polyhedral framework due to thevacancy-provided volume. O neighbors in the defected structurealso exhibit enhanced rotational exibility compared to pris-tine, with r extending from 1.8–2.4 Å, q reaching ∼50°, and fdisplaying broad rotations of ±120°. While the amplitude ofangular motion increases in the defect (broader jfj, wider qcone, and larger r uctuations), the reorientation rate is lowerThis journal is © The Royal Society of Chemistry 2026Fig. 6 Spherical coordinate representation of anion rotational dynamics around vacancy-adjacent Nb polyhedra. Time evolution of sphericalcoordinate components r, q, and f for first-nearest-neighbor anions, Cl-near (blue), Cl-far (orange), and O (green), surrounding the Nb center inpristine (a–c) and Schottky-defected (d–f) LiNbOCl4, tracked over the final 5 ps of the MD simulation at 600 K. The local coordinate frame andstructural reference are shown in panel (g), where the spherical system is centered on Nb; q is the polar (tilt) angle from the crystallographic c axis;f is the azimuth about c; the Cl vacancy lies at q = 90°, f = 0°, oriented along the crystallographic a-axis. In the pristine structure, O shows largeazimuthal excursions (f up to ±100°) at modest, nearly constant tilt (q ∼ 5–25°) and narrow Nb–O distance fluctuations (r ∼ 1.7–2.1 Å), i.e.,precession about c within a small tilt cone. In contrast, the Schottky-defected system displays larger-amplitude, erratic, and spatially uncor-related rotations (shown by red arrows), particularly in f, with abrupt shifts and excursions approaching ±180° (shown by the red circle). Thesebehaviors highlight the loss of rotational synchrony and emergence of anharmonic distortions in the vacancy-adjacent environment, consistentwith disrupted local lattice dynamics.Fig. 7 Representative AIMD snapshot at 600 K (50–70 ps). Themagenta trace marks a diffusing Li-ion ion in the bc-plane, while thesurrounding framework atoms, Cl (teal), Nb (blue), and O (red),undergo cooperative displacements. This highlights a dynamiccoupling between Li-ion migration and local octahedral distortionswithin the NbO2Cl4 framework. This visualization approach is consis-tent with prior studies of framework–ion interactions in similarPaper Journal of Materials Chemistry A(longer dwell between bursts; see Section S9 in the SI). At 1000K, the overlapping (sliding-window) azimuthal switchingfrequency (1 ps window; 0.1 ps stride) averages hnfioverlapz 1.78ps−1 in the pristine cell and z1.47 ps−1 in the Schottky cell.Together, these observations indicate that the enhanced localvibrational/rotational freedom in the defected system is lesstemporally synchronized, reecting a loss of collective coher-ence within the polyhedral network.To directly link these local anion dynamics to Li-ion trans-port, we next examine a representative long-range migrationevent. As illustrated in Fig. 7, the Li-ion ion exhibits long-rangemigration across the bc plane, accompanied by coordinateddisplacement of surrounding Cl atoms within the NbO2Cl4framework. These results conrm that Li-ion diffusion occurs inconcert with the dynamic framework response. The Cl atomsundergo signicant angular distortions and cooperative motionduring Li-ion jumps, indicating a so vibrational environ-ment.44,45 This behavior is consistent with previous simulationsthat reported pronounced angular uctuations in the Cl–Nb–Clbonds and overlapping Li–Cl vibrational modes in the low-energy phonon region.44,45 While Cl− ions do not move trans-lationally, their local dynamical motion contributes to transientbottleneck widening during Li-ion migration.Trajectory density maps and average spatial displacementsdemonstrate that Li-ion delocalization in both pristine and LiCl-Schottky-defected LiNbOCl4 evolves signicantly withThis journal is © The Royal Society of Chemistry 2026temperature. Following the observed enhancement in Cl and Orotational amplitudes, particularly in the defected structure,where polyhedral coherence is locally diminished, the Li sub-lattice exhibits correspondingly increased dynamic behavior. Inthe pristine system, Li-ion motion increases steadily, with time-averaged RMS displacements increasing from 8.64 Å at 600 K to22.54 Å at 1200 K, and further to 27.46 Å at 1400 K. This trendreects the development of extended diffusion pathways,systems.45J. Mater. Chem. A, 2026, 14, 17385–17401 | 17393Journal of Materials Chemistry A Paperconsistent with the emergence of three-dimensional networkconnectivity observed in trajectory maps along the c-direction(Fig. 5). Similarly, in the Schottky-defected system, Li-ion time-averaged RMS displacements increases from 8.80 Å at 600 K to27.69 Å at 1200 K, suggesting comparable long-range mobility atelevated temperatures. Although the trajectory density distribu-tion in the defected system appears less uniform at lowertemperatures, it becomes increasingly connected with increasingtemperature. Nonetheless, both systems show extensive thermaldelocalization above 1000 K, conrming that defect introductiondoes not signicantly hinder global Li-ion transport under high-temperature conditions.3.8 Factors governing the conductivity reduction inSchottky-defected LiNbOCl4The ionic conductivity of SEs is typically expressed through theArrhenius relationship, where the conductivity prefactor s0encapsulates critical microscopic descriptors of ion transport.According to eqn (9),s0 ¼ nzðZeÞ2ða0Þ2n0kBexp�DSmkB�(9)where n is the Li-ion concentration, z is related to the diffusiongeometry and correlation, Ze is the ionic charge, a0 is the jumpdistance, n0 is the vibrational attempt frequency, kB is theBoltzmann constant and DSm is the migration entropy. Theprefactor thus integrates both geometric and entropic contri-butions to ion migration: the product (a0)2n0 reects theintrinsic hopping dynamics, while the exponential termexp�DSmkB�captures the entropic gain from the availability andaccessibility of diffusion pathways. Here, a detailed analysis ofs0 is essential for understanding the fundamental origin oftransport suppression in Schottky-defected LiNbOCl4; it alsoenables us to disentangle geometric advantages from entropicand dynamical penalties.Despite structural indicators suggesting improved diffusionaccessibility in the Schottky-defected LiNbOCl4, namely, anenlarged average bottleneck radius (1.9 Å vs. 1.5 Å in the pristinephase; see Section S8 in the SI) and a marginally increased Li-site Voronoi volume, it still shows a slightly higher activationenergy (EaSchottky = 0.241 eV vs. EaPristine = 0.236 eV). Meanwhile, theextrapolated prefactor is noted to increase from 2.60 × 104 to2.72 × 104 S cm−1 K, but this minor gain is offset by the expo-nential penalty imposed by the higher barrier. The calculatedBoltzmann factor ratio at 300 K, exp(−EaSchottky/kBT)/exp(−EaPristine/kBT)z 0.818, conrms that the conductivity reduction is largelyowed to the increased activation energy.To probe the microscopic origin of the increased activationenergy observed in the Schottky-defected system, we examinethe rotational dynamics of the anionic sublattice and its inu-ence on Li-ion mobility. The Bond Angle Correlation Function(BACF) further probes host lattice dynamics by evaluatingangular stability of anion bonds around the Nb polyhedron ofthe potential vacancy site. Dened as17394 | J. Mater. Chem. A, 2026, 14, 17385–17401BACF(s) = hv̂(t)$v̂(t + s)i (10)where v̂ is the normalized bond vector at time t, this functionmeasures the temporal persistence of anion orientations. TheBACFs of Nb–O and Nb–Cl coordination environments reveala distinct divergence in angular stability between pristine anddefected phases. As shown in Fig. 8, the BACF for Nb–Cl in theSchottky-defected structure decays rapidly, reaching zero andsubsequently negative values within ∼9 ps. The appearance ofnegative correlations (minimum z−0.4) indicates bond vectorinversion and loss of coherent rotational behavior, suggestingdynamic instability in the local anion environment. In contrast,the pristine phase maintains a high degree of rotational order,with BACF values remaining above 0.9 throughout the entire 80ps simulation window. This persistent angular correlationreects stable, cage-like oscillations of the anion frameworkaround Nb polyhedra, consistent with quasi-harmonicbehavior. The disrupted anion reorientation in the Schottky-defected structure likely contributes to increased Li-ionhopping barriers by narrowing diffusion bottlenecks, therebyproviding a mechanistic basis for the elevated activation energy.These disruptions are further supported by qualitativeinsights from spherical trajectory analysis of Cl and O neigh-bors around Nb centers, as previously described (Fig. 6). In thepristine structure, anion rotations remain relatively con-strained, with angular uctuations exhibiting smooth andconned patterns indicative of coherent polyhedral breathing.In contrast, the Schottky-defected system displays irregular andspatially uncorrelated angular motions, particularly in theazimuthal component f, with abrupt directional changes andexcursions across a broader angular space. This loss ofsynchronicity reects enhanced rotational disorder within thelocal coordination shells, consistent with the rapid BACF decayand inversion of bond vectors. These results signify a transitionfrom harmonic to anharmonic rotation, where weakened localcoordination leads to irregular anion dynamics. Importantly,such incoherent behavior does not translate into transport-effective dynamic gating: irregular, locally conned rotationsare less efficient in generating the transient bottleneck open-ings required for Li migration.46–48 Unlike the classical paddle-wheel mechanism involving rotating polyanion clusters, thedynamic gating mechanism introduced in this work describesa distinct mode of transient bottleneck expansion driven bycoordinated motion of individual halide and oxide anionswithin an oxyhalide lattice (see SI S8), as quantied moreexplicitly by the event-triggered ensemble (ETE) analysis inFig. 9.To directly test whether local anion reorientation acts asa dynamic gate for Li motion, we applied a time-aligned, event-triggered ensemble (ETE) analysis to the spherical-coordinatedescriptors {r, q, f} introduced above. Around a tracked NbX6polyhedron, chosen adjacent to the LiCl vacancy in the Schottkycase and at the same crystallographic site in the pristine cellprior to vacancy introduction, we construct several transport-relevant rotation/geometry descriptors (details in Section S10):an azimuthal switching rate n4(t), which counts abrupt 4 re-orientation events per picosecond via unwrapping, median-This journal is © The Royal Society of Chemistry 2026Fig. 8 Bond orientation correlation of Cl and O anions in pristine and Schottky-defected LiNbOCl4. Bond angle correlation functions (BACFs) offirst-nearest-neighbor anions, Cl-near (blue), Cl-far (orange), and O (green), coordinated to Nb in pristine (a) and Schottky-defected (b)LiNbOCl4, evaluated over an 80 ps MD trajectory at 600 K. In the pristine system, BACF values remain near unity across all anions, indicatingstable and long-lived angular orientation around the Nb polyhedron. In contrast, the defected system shows rapid decay in Nb–Cl BACF values,reaching minima near −0.4, reflecting inversion of bond vectors and breakdown of angular coherence. O atoms exhibit slightly damped butmore persistent correlations. These trends confirm enhanced rotational disorder and lattice anharmonicity in the presence of Schottky defects.Paper Journal of Materials Chemistry Acentering, and a Schmitt trigger with hysteresis; a tilt-weightedazimuthal activity A1(t) = jd4/dtjsin q, which emphasizes rota-tions that tilt the ligands toward the diffusion passage; a time-dependent bottleneck half-gap a(t), dened for a chosen anionpair that frames a local neck (larger a corresponds to a widergate); and a normalized composite “gate” score G(t) thatcombines bond stretching and tilting through r and q.In the ETE framework, we rst identify discrete anion-framework events around each NbX6 octahedron, for whichhere we focus on azimuthal “f-switch” events as the elementaryanion-framework events. This procedure yields a reproduciblelist of timestamps {ti} at which candidate transport-enablingopenings occur, where the Schmitt state s(t) of the trackedNbX6 octahedron ips sign, indicating an abrupt azimuthalreorientation (see SI S10). For each event time ti we thencompute the Li MSD relative to the conguration at the event,hDr2(s)i = hjr(ti + s) − r(ti)j2i,as a function of delay s, with s = 0 marking the anion event. Toresolve the spatial structure, Li ions are partitioned at eachevent into a “near” ensemble (within 4.5 Å of the tracked NbX6octahedron at ti) and a complementary “far” ensemble. The farions thus provide an internal reference for the background,system-wide motion away from the active octahedron. Aver-aging hDr2(s)i over all events yields near and far ETE–MSDcurves, Dr2(s)near and Dr2(s)far (Fig. 9). By construction, bothcurves vanish at s = 0, because displacements are measuredrelative to the event conguration, so all ETE curves exhibit a V-shaped minimum at s = 0. For s < 0, the curves describe how Licongurations approach the event from earlier times; for s > 0,they quantify how rapidly Li positions decorrelate aer theanion reorientation. Since events are selected based on a direc-tional criterion on f(t) (via the Schmitt trigger) rather thanbased on a symmetric oscillation about a reference angle, thereis no requirement for the ETE curves to be mirror-symmetricabout s = 0. The physically relevant information lies in howThis journal is © The Royal Society of Chemistry 2026the near and far branches differ on the pre-event (s < 0) andpost-event (s > 0) sides.This analysis reveals a clear contrast between pristine andLiCl-Schottky LiNbOCl4 (Fig. 9). Over the 100 ps window at 600K, the pristine cell exhibits several hundred f-switch eventsaround the reference octahedron, whereas the Schottky cellshows only a few tens of such events, indicating that dynami-cally active anion reorientation is strongly suppressed by thedefect. In the pristine system, the near and far ETE–MSD curvesare almost indistinguishable over jsj ( 0.5 ps. Both ensemblesdisplay very similar growth of hDr2(s)i on the s < 0 and s >0 sides, with only minor deviations. This similarity indicatesthat reorientation events of the reference NbX6 octahedron areembedded in a collectively responding anion–Li network: whenthe octahedron reorients, the associated Li displacements arespatially delocalized, and the local environment of the trackedoctahedron does not stand out as a special region of enhancedmobility.By contrast, in the LiCl-Schottky phase, f-switch events arerarer, and when they occur, far-eld Li consistently exhibitslarger MSD than vacancy-adjacent Li, both before and aer theevent (near < far for s < 0 and s > 0). This behavior can benaturally decomposed into a background contribution and anevent-triggered contribution: the background describes thepersistent difference in mobility between near and far Li thatwould exist even in the absence of a specic event, whereas theevent-triggered part captures the additional change in MSDinduced by the f-switch itself. At the background level, thepersistent inequality near < far on both sides of s= 0 reects thefact that Li adjacent to the vacancy reside in a structurally anddynamically constrained environment with intrinsically lowmobility, whereas Li in less distorted regions of the frameworksample a soer network with a higher underlying MSD. Super-imposed on this background, the f-switch produces a dynamicmodulation of the local motion: for the near ensemble, the post-event branch hDr2(s > 0)inear lies systematically above the pre-event branch hDr2(s < 0)inear, showing that anion reorientationJ. Mater. Chem. A, 2026, 14, 17385–17401 | 17395Fig. 9 Event-triggered ensemble (ETE) Li-ion mean-squareddisplacement (MSD) in pristine and LiCl-Schottky-defected LiNbOCl4at 600 K. For each azimuthal reorientation (“4-switch”) event at time tiof the tracked NbX6 polyhedron, the Li MSD is evaluated as hDr2(s)i =hjr(ti + s) − r(ti)j2i and averaged over all events, with the delay s =0 marking the anion event (vertical dashed line). Li ions within 4.5 Å ofthe active polyhedron at ti are classified as “near” (blue), and allremaining Li ions as “far” (orange). (a) In pristine LiNbOCl4, near and farETE–MSD curves are nearly indistinguishable for jsj ( 0.5 ps, indi-cating that anion reorientation events are embedded in a coherentlyresponding network that drives spatially delocalized Li motion. (b) Inthe Schottky system, Li-ions in the vacancy-adjacent environmentremain more localized than the far-field population (near < far bothbefore and after s = 0), consistent with stronger caging around thedefect and with the reduced long-timeMSD slope and diffusivity of theSchottky-defected phase.Fig. 10 Phonon density of states (DOS) of (a) pristine and (b) LiClSchottky-defected LiNbOCl4 at 600 K derived from MD simulations.The total DOS is shown in black, with atomic contributions from Li(blue), Nb (orange), Cl (green), and O (red). The pristine system exhibitsa sharper high-frequency peak (∼80 meV) primarily arising from Ovibrations, which is significantly attenuated in the defected system.Additionally, all atomic species show redshifts in vibrational bandJournal of Materials Chemistry A Paperslightly loosens the local cage and promotes additional decor-relation of vacancy-adjacent Li aer the event. However, thenear curve never catches up to the far curve over the jsj# 0.5 pswindow, indicating that even with this event-triggered “kick”, Liin the vacancy-adjacent region remain less mobile overall thanLi in the far eld.In the present context, the ETE results thus provide a direct,time-resolved view of the dynamic gating mechanism. Here,“dynamic gating” refers to Li transport being controlled bytransient openings of local bottlenecks formed by surroundinganions: rotations and vibrations of the NbX6 octahedratemporarily widen or reorient these bottlenecks, allowing Li tomove more easily before the gate recloses. In the ETE frame-work, each f-switch is treated as a discrete anion reorientationevent, and the near/far, s-resolved MSD tracks how Li motionresponds to that local gate dynamics in space and time. Inpristine LiNbOCl4, anion reorientations around the referenceoctahedron are frequent and elicit a delocalized Li response17396 | J. Mater. Chem. A, 2026, 14, 17385–17401(nearz far), which together underpin the larger long-time MSDslope and higher diffusivity. In the LiCl-Schottky phase,comparable events around the vacancy-adjacent octahedron areboth less frequent and less effective at mobilizing nearby Li(near < far), so their contribution to forming extended perco-lation pathways is limited, consistent with the reduced long-time MSD slope and lower computed diffusivity. These time-resolved observations show that the Schottky defect does notmerely modify static bottleneck dimensions, but alters thefrequency, coherence, and spatial reach of dynamically activeanion reorientation, a change that, as we show below, is alsoreected in the underlying vibrational spectrum (phonondensity-of-states analysis).The phonon density of states (DOS) at 600 K (Fig. 10)provides a complementary, frequency-domain view of thesedynamical differences. In the defected system, all atomicspecies exhibit redshis in their vibrational band centers, Li(32.66 / 31.14 meV), Nb (26.26 / 25.26 meV), Cl (20.48 /20.14 meV), and O (57.74 / 56.17 meV), consistent with locallattice soening. Notably, a high-frequency peak at ∼80 meV,primarily arising from O vibrations and linked to fast vibra-tional modulation of Li-ion pathways, is signicantly attenu-ated relative to the pristine structure. This suppression impliesdiminished access to thermally activated bottleneck widening,which in turn can increase the effective energy barrier.1centers in the defected phase, consistent with local lattice softening.This journal is © The Royal Society of Chemistry 2026Paper Journal of Materials Chemistry AThe partial phonon density of states (PDOS) in Fig. 10 revealsthat Cl atoms contribute signicantly to the low-energy vibra-tional modes below ∼18 meV, with a computed band center ataround 20.14 meV. This value is in close agreement withpreviously reported results for LiNbOCl4, where the Cl phononband center was found near 19 meV.45 Additionally, we observea strong spectral overlap between the Cl and Li components inthis low-frequency range, suggesting a substantial degree ofvibrational coupling. These ndings support the interpretationthat Li-ion transport is dynamically facilitated by frameworkuctuations, particularly involving the Cl sublattice. Thisframework-uctuation picture is further supported, albeitindirectly, by experiments: Raman spectroscopy on LiNbOCl4shows distinct low-frequency bands assigned to Nb–Cl modesand reveals orientational disorder and dynamic rotationalexibility within the NbO2Cl4 units.44 Taken together, thesecomputational and experimental observations indicate that Li-ion migration proceeds in a so, dynamically uctuatingNbO2Cl4 framework dominated by low-energy Cl motions.To quantify how this framework-mediated dynamics isencoded in the macroscopic transport coefficients, we nextexamine the Arrhenius parameters, with particular emphasis onthe conductivity prefactor s0. While the elevated activationenergy clearly governs the conductivity suppression in theSchottky-defected phase, a more detailed decomposition of theconductivity prefactor s0 offers insight into how microscopictransport descriptors respond to defect-induced changes.Building on eqn (9), we evaluated the relative contributions ofthe effective jump distance a0, attempt frequency n0, carrierdensity n, and correlation factor z, where the latter is taken to beapproximately equivalent across both systems due to theirnearly identical local environments. At 600 K, the Schottky-defected system exhibits a slightly shorter average jumpdistance (a0 = 2.63 Å) than the pristine counterpart (a0 = 2.78Å), which would normally act to suppress the prefactor.However, this is compensated for by an ∼15.6% increase in theattempt frequency n0, from 3.98 × 1012 s−1 (pristine) to 4.52 ×1012 s−1 (Schottky). The carrier density n is marginally reducedin the Schottky-defected structure due to Li vacancies, but thiseffect remains under 5%. On the other hand, the ratio ofcorrelation factors z between the two systems is expected to beclose to unity and should also have a negligible contribution tothe overall prefactor variation (see discussion below related tovan Hove analysis).When combining the different geometric and dynamicalcontributions, the overall increase in the conductivity prefactors0 for the Schottky system remains under 5%. However, theextrapolated prefactor obtained from Arrhenius analysis showsa more noticeable enhancement. This discrepancy indicates anadditional contribution from migration entropy. From theprefactor ratio and known parameters, we estimate that theentropic term exp(DSm/kB) increases by approximately 12% inthe Schottky-defected system. While this reects a slightbroadening of the diffusion pathway landscape due to localstructural disorder, the contribution remains modest and ulti-mately insufficient to overcome the conductivity suppressioncaused by the elevated migration barrier. These resultsThis journal is © The Royal Society of Chemistry 2026highlight that, in this case, the noted entropic gain is insuffi-cient to overcome the defect-related energetic penalty for Li ionmigration in Schottky-defected LiNbOCl4.We further analyze the ion dynamics in pristine andSchottky-defected LiNbOCl4 using the van Hove correlationfunction, G(r, t), derived from MD trajectories at 600 K (Fig. 11).This function quanties the time-dependent probability ofnding a particle at a position r at time t, given that another (orthe same) particle was at the origin at time t = 0. It is mathe-matically dened as:Gðr; tÞ¼ 1N*XNi¼1dðrþ rið0Þ � riðtÞÞ+þ 1N*XNisjd�rþ rjð0Þ � riðtÞ�+(11)where the rst term corresponds to the self-part, Gs(r, t), and thesecond to the distinct-part, Gd(r, t). The Dirac delta function d($)ensures positional matching, and h$i denotes the ensembleaverage over all ions.The self-part, Gs(r, t), captures the probability that a Li-ionhas moved a distance r over time t, reecting the extent ofindividual ion displacement. In the pristine system (as shown inFig. 11), the Gs(r, t), distribution exhibits long-tailed proleswith nonzero probabilities persisting beyond r > 6 Å, indicativeof long-range, percolative Li-ion diffusion. By contrast, thedefected system showsmore localized Gs(r, t) distributions, withpeak intensities centered near r = 2 Å, persistent bands aroundr = 1 Å and rapidly decaying tails, consistent with connedmotion, reduced jump distances, and increased back-jumpingprobability, hallmarks of restricted ionic mobility.The distinct-part, Gd(r, t), evaluates the likelihood of ndinga second Li-ion at distance r from the initial position ofa reference Li-ion aer time t, thereby characterizing pairwisecorrelations and cooperative motion. Our analysis reveals thatboth pristine and Schottky-defected LiNbOCl4 exhibit discon-tinuous and temporally uctuating peak intensities at 600 Knear r z 0–2 Å. These peaks do not persistently build up overtime but rather appear and vanish intermittently, signalingweak ion–ion correlations. This behavior is slightly differentfrom the persistent Gd(r, t) band in the same r range that is seenin other fast superionic conductors such as Na3SbS4.49 Suchbehavior in the latter is indicative of relatively sustained jumpcorrelations among Na+ ions, where consecutive ions rapidlyoccupy neighboring vacant sites, facilitating collective motion.In the LiNbOCl4 system, however, these peaks emerge inter-mittently and decay without persistent growth, suggestinga reduced degree of correlation. Nevertheless, the non-zerointensities around r = 0 across multiple time frames indicatethat the dynamics are not entirely random. Rather than purelyBrownian, the Li-ion transport exhibits a mixture of correlatedand uncorrelated jumps, where temporal coherence in motionmay still exist but is weakened. This intermediate regimereects partially cooperative behavior, which may still supportefficient diffusion pathways without manifesting as fullyconcerted motion.However, a closer comparison between pristine and defectedLiNbOCl4 reveals subtle but signicant differences in their Gd(r,J. Mater. Chem. A, 2026, 14, 17385–17401 | 17397Fig. 11 van Hove self and distinct correlation functions for Li-ion dynamics in pristine and Schottky-defected LiNbOCl4. Two-dimensional vanHove correlation function heatmaps for Li-ion motion in pristine (left) and Schottky-defected (right) LiNbOCl4 at 600 K over a 100 ps MDtrajectory. The self-part Gs(r, t) (top) quantifies the probability of a Li-ion moving a distance r after time t, revealing long-range delocalization inthe pristine phase and confined motion in the defected phase. The distinct-part Gd(r, t) (bottom) reflects pairwise spatial correlations between Liions. In both systems, discontinuous and temporally fluctuating peaks near r z 0–2 Å are observed, indicating uncorrelated, non-concertedhopping behavior. The defected system exhibits even more intermittent features, implying further disruption of spatial correlation and lowertransport cooperativity.Journal of Materials Chemistry A Papert) proles. The pristine system shows relatively denser andearlier-emerging intensity near r = 0 Å across time, indicatinga modest degree of temporally correlated motion. In contrast,the defected system exhibits fainter, more sporadic featureswith delayed onset and weaker central intensities, pointing todiminished temporal coherence in Li-ion movement. Thiscontrast implies that while both systems operate withina partially cooperative transport regime, the presence ofSchottky defects disrupts ion–ion correlations, weakening thetransiently collective behavior. Such disruptions may arise fromlocal site distortions or the loss of rotational coherence (aspreviously mentioned) in surrounding anion polyhedra, ulti-mately contributing to the observed reduction in conductivityand increased activation barrier.These ndings related to Gs(r, t) and Gd(r, t) indicate that theconductivity suppression in the Schottky-defected system stemsnot from a loss of collective motion per se, but from thedisruption of local structural dynamics that facilitate suchbehavior. Although the static bottleneck geometry appearsslightly more open in the defected system, this potentialadvantage is negated by incoherent anion rotations anda breakdown of synchrony within the surrounding polyhedralframework. This loss of rotational coherence weakens thedynamic gating mechanism, an essential contributor to tran-sient bottleneck expansion, which in turn reduces the effectivehopping volume accessible to Li-ions. Consequently, even17398 | J. Mater. Chem. A, 2026, 14, 17385–17401within a regime of cooperative transport, the defect-induceddisturbance in local lattice dynamics imposes a higher energycost for migration, ultimately manifesting as an increasedactivation barrier and diminished ionic conductivity.In summary, although the Schottky-defected LiNbOCl4system retains similar global elastic properties and diffusiontopology to its pristine counterpart, its conductivity is reduceddue to a localized increase in activation energy driven by di-srupted anion rotational dynamics, and suppression of keyphonon modes. These results highlight the critical role ofcooperative anion motion in modulating the dynamic energylandscape of fast-ion conductors and provide insight into thedefect tolerance limits of oxyhalide-based solid electrolytes.4. ConclusionIn this work, we used AIMD to elucidate Li-ion transport inpristine and LiCl Schottky-defected LiNbOCl4. PristineLiNbOCl4 exhibits robust Li mobility over 600–1400 K, with anactivation energy of 0.236 eV and an extrapolated room-temperature ionic conductivity of 9.57 × 10−3 S cm−1, in closeagreement with the experiment. The rigid Nb–O–Cl frameworkprovides mechanical stability, while the disordered Li sublatticesupports percolating diffusion pathways, consistently capturedby MSD, trajectory-density, and van Hove analyses.This journal is © The Royal Society of Chemistry 2026Paper Journal of Materials Chemistry AIntroducing LiCl Schottky defects preserves the globaldiffusion topology, mechanical soness, and metastability, butslightly increases the activation energy to 0.241 eV and lowersthe room-temperature conductivity to 8.20 × 10−3 S cm−1.Although static descriptors (e.g., a larger bottleneck radius andincreased local free volume) suggest more accessible migrationchannels, dynamic analyses show the opposite trend: thedefects induce pronounced anion rotational disorder andweaken coherent “gate-opening” uctuations. Event-triggeredensemble analysis reveals that transport-enabling anionevents become rarer and more spatially localized, limiting theirability to promote delocalized Li motion. Consistently, phononDOS shows overall redshis and a strong attenuation of the O-dominated mode near ∼80 meV associated with dynamicbottleneck modulation. Changes in the conductivity prefactorare modest (#5% net increase, plus ∼12% from migrationentropy) and cannot compensate for the exponential penaltyfrom the slightly higher barrier; van Hove functions furtherindicate reduced temporal coherence and weaker Li–Li corre-lations in the defected phase.Overall, our results demonstrate that LiNbOCl4 possessesa highly defect-tolerant, mechanically compliant frameworkthat maintains superionic Li conductivity even under LiClSchottky perturbations. The slight conductivity reduction in thedefected phase arises not from a loss of global percolation orcatastrophic structural instability, but from a subtler reshapingof the dynamic energy landscape: rotational incoherence,attenuation of key phonon modes, and spatially localized gate-opening events collectively increase the effective migrationbarrier. These insights highlight the central role of cooperativeanionmotion and dynamic bottleneck modulation in governingion transport, and they provide concrete design guidelines forengineering oxyhalide-based solid electrolytes with tailoreddefect chemistry and lattice dynamics.Author contributionsHalimah Harfah: methodology, soware, investigation, formalanalysis, visualization, writing – original dra. YoshitakaTateyama: supervision, writing – review & editing. KazunoriTakada: supervision, writing – review & editing. Randy Jalem:conceptualization, supervision, project administration, fundingacquisition, writing – review & editing, resources.Conflicts of interestThere are no conicts to declare.Data availabilityThe data supporting this study are available from the corre-sponding author upon reasonable request.Supplementary information (SI): Ewald and total energyscreening of Li congurations and LiCl Schottky-defect struc-tures, defect formation energies and convex hull stability anal-ysis, DFT and AIMD computational details, average spatialdisplacements, Voronoi volumes, and nearest-neighbor bond-This journal is © The Royal Society of Chemistry 2026length distributions, mechanical properties, bulk modulus, andthermal expansion, Li-ion diffusion coefficients, static anddynamic bottleneck analyses, angle analysis, azimuthalswitching frequencies, and transport-relevant gate descriptors.See DOI: https://doi.org/10.1039/d5ta05478h.AcknowledgementsThis work was nancially supported in part by JST throughGreen Technologies of Excellence (GteX) grant numberJPMJGX23S2, by JSPS KAKENHI grant number JP21K14729,MEXT as Materials Processing Science project (“Materealize”)grant number JPMXP0219207397 and the “Program forPromoting Research on the Supercomputer Fugaku” grantnumber JPMXP1020230325. 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A, 2026, 14, 17385–17401 | 17401https://doi.org/10.1038/s43246-024-00550-zhttps://doi.org/10.1038/s43246-024-00550-z Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study Lithium superionic behavior and defect robustness in LiNbOCl4: a first-principles molecular dynamics study