Triggering dynamically disordered lithium sublattice in superionic conductors

Abstract

The design of superionic conductors has been largely focused on static structural features, with the dynamic ion transport mechanism less explored. Here, we explore a paradigm that harnesses the polyanion rotations to trigger the dynamically disordered Li sublattice as well as the liquid-like cation diffusion for superior ionic conductivity in crystals. A descriptor called rotation tolerance factor was proposed as a predictive metric for identifying the potential fast-rotating anion clusters with the low mass and reduced valence charge for given structural frameworks. Guided by this factor, halides with rotational polyanions, namely Li₃Y(SH)₆, Li₃Y(NH₂)₆, Li₂Zr(NH₂)₆, and an oxide (Li_6.5La₃Zr₂O_11.5(NH₂)_0.5) have been designed with synergistic polyanion rotation and Li⁺ sublattice disorder, which lead to enhanced Li ionic conductivities at room temperature compared to the counterparts without polyanions. The experimentally synthesized NH₂^- incorporated Li₂ZrCl_5.92(NH₂)_0.08 demonstrates a four-fold higher conductivity over Li₂ZrCl₆ control, enabling all-solid-state Li-In | |LiCoO₂ and Li-In | |LiNi_0.88Co_0.09Mn_0.03O₂ cells with 96.5% and 97.4% capacity retention after 190 cycles at 140 and 200 mA g^-1, respectively. This work provides an insight that flexible anion rotations could promote the dynamically disordered lithium sublattice distribution as well as the ionic conductivity.

Superionic conductors are typically engineered from static crystal structures. Here, authors present how flexible polyanion rotations induce dynamic disorder in lithium sublattice, enabling liquid-like ion diffusion and enhanced ionic conductivity.

Introduction

Superionic conductors (SICs), recognized for their anomalously high ion mobility in the solid state, have gained great research interest for their high ionic conductivities in all-solid-state batteries^1,2 and low thermal conductivities in thermoelectric devices³. Over the past decades, many lithium (Li) SICs, including Li₇La₃Zr₂O₁₂⁴, Li₁₀GeP₂S₁₂⁵, and Li₃MX₆ (M = Y, Sc, In, Er, etc., X = Cl, Br)⁶, are discovered as solid-state electrolytes (SSEs) with high room-temperature Li ionic conductivities on the order of 1–10 mS/cm. Though the distinct migration paths have been reported to constitute the Li diffusion channels for many Li SICs, the liquid-like dynamics of Li is a rare and poorly understood phenomenon^7,8. For the SSEs with face-centred cubic (Li₃YBr₆, Li₃ScI₆ and Li₂CuPS₄, etc.)⁹ and hexagonal-close-packed (Li₃YCl₆, Li₂ZrCl₆, etc.)¹⁰ anion frameworks, face-sharing tetrahedron (T) and octahedron (O) form the cation diffusion channels, denoted as the T-O-T, O-T-O and O-O paths. In the Li₁₀GeP₂S₁₂ and Li₇P₃S₁₁ sulfides with body-centred cubic anion frameworks, Li ions migrate along the T-T path with obvious directionality^11–13, which is different from the liquid-like diffusion behavior^7,8,14,15. Therefore, promoting the liquid-like diffusion of Li ions is desirable and worth pursuing from both experimental and theoretical perspectives to further improve the Li ionic conductivities.

The liquid-like ion dynamics, characterized by low-frequency vibrational modes following a linear dispersion rather than typical Debye quadratic law¹⁵, may be correlated with the highly disordered sublattice of mobile ions. As demonstrated by the most classic SIC, AgI, the superionic transition occurs from beta phase to alpha phase at the temperature above 420 K (Fig. 1a)¹⁶. The liquid-like Ag⁺ diffusion in the alpha phase is attributed to the highly disordered sublattice, namely 42 crystallographic positions (12 d tetrahedral, 24 h trigonal and 6b octahedral positions) for Ag⁺ random occupation in conventional unit cell¹⁷. The large number of available cation sites, together with their partial occupation, so called the disordered cation distribution is also discussed as the origin of high ionic conductivities and low activation energies observed in argyrodites (Li⁺, Cu⁺, Ag⁺)^18–20, which exhibit the liquid-like dynamics of mobile ions. In addition to temperature effect, doping or high-entropy strategy could be also applied to distort the local polyhedra and adjust the mobile ion distribution by reducing the site energy difference and then flattening the energy landscape^21–24. While high-temperature and high-entropy strategies both promote disordered Li distribution, the former is challenging at ambient conditions, and the latter is limited to specific SIC classes or dopants. In this work, we combined the density functional theory calculations and experiments to explore the feasibility of incorporating rotation dynamics to promote the disordered sublattice distribution for mobile ions as well as the frustrated energy landscape for fast ion transport.

Fig. 1. Schematic illustration of constructing disordered sublattice in the SICs.

a Crystal structure and radial distribution function (RDF) of superionic α-AgI phase with highly disordered sublattice compared to ordered β-AgI phase. The grey and purple spheres represent the Ag and I atoms, respectively. b Schematic of strengthening the disorder degree of cation sublattice through high-entropy and rotation dynamics of polyanions or anion clusters to reduce the activation energy. Notably, the representation of the high-entropy configuration is simplified, with different polyhedron colors representing different elements. RDF of high-entropy Li₂Se_0.5Te_0.25S_0.25O₄ without rotation and low-entropy Li₂SeO₄ with rotation.

Figure 1b illustrates our hypothesis of how rotation dynamics of polyanions or anion clusters could reduce the activation energy for Li transport. For the structure with stationary polyanion arrangements, the cation will hop along distinct lattice sites with a highly symmetrical energy landscape (a single energy profile between Site1 and Site2 in solid black line). Activating rotational dynamics will create more meta-stable lattice sites for cations along the hopping path (dynamically disordered sublattice distribution), causing a frustration of energy landscape (multiple energy profiles in green solid lines). Consequently, ion hopping between adjacent sites is facilitated by abundant shorter pathways with reduced energy barriers. This strategy may present a more disordered migrating cation sublattice than that of high-entropy effect. As shown in the lower panel of Fig. 1b, Li₂SeO₄ with anion rotation exhibits a flatter radial distribution function (RDF) profile compared to its high-entropy counterpart without anion rotation, Li₂Se_0.5Te_0.25S_0.25O₄. Detailed discussions are provided on rotation and high-entropy effects for the Li₂SeO₄ and Na_2.25Y_0.25Zr_0.75Cl₆ in Supplementary Fig. 1. This motivates studying how rotational motions frustrate the energy landscape, and trigger dynamically disordered or even liquid-like Li-sublattice. Crucially, how the rotational propensity of anion clusters and its correlation with the dynamical disorders of Li sublattice can be quantified for a crystal structure?

Results and discussion

For a specific type of Li solid-state electrolytes (Fig. 2a), the disorder degree of Li sublattice at 1100 K demonstrates a negative correlation with activation energy (E_a), while the former is characterized by the two-body excess entropy (S₂) of Li from Ab initio molecular dynamics (AIMD) simulations²⁵:

$$S_2=-2\pi \rho k_B{\int }_0^{\infty }\left[g\left(r\right)\log \left(g\left(r\right)\right)-g\left(r\right)+1\right]r^{2}dr.$$ 1

Fig. 2. Dynamical disorder and rotation dynamics analysis of SICs.

a Relationships between activation energy and disorder degree (two-body excess entropy, S₂) of Li sublattice at 1100 K in representative solid-state electrolytes with detailed activation energies, S₂ and space group information shown in Supplementary Table 1. b Phase map showing representative lithium-containing materials of oxides (yellow region), sulfides (blue region) and structures with flexible polyanions rotational dynamics (green region) as a function of disorder degree and decay constant (α) of angular autocorrelation function (Ct) calculated at 1100 K (Supplementary Table 2 and Supplementary Data 1). c Structures and polyanion trajectories during AIMD simulations (green lines) at 1100 K of Li₃PS₄. The pink, yellow spheres represent Li and S atoms, the light green polyhedra represent PS₄ polyhedra. d Structures and polyanion trajectories during AIMD simulations (green lines) at 1100 K of Li₃PO₄. The red spheres represent O atoms and the light green polyhedra represent PO₄ polyhedra. e 2D angular probability density distribution for four S atoms of PS₄ tetrahedron in the Li₃PS₄ at 1100 K. f 2D angular probability density for four O atoms of PO₄ tetrahedron in the Li₃PO₄ at 1100 K.

Here $\rho$ is the number density of Li, $g\left(r\right)$ and $r$ represent the radial distribution function and radial distance of Li ions, and k_B is the Boltzmann constant. Figure 2b shows that the oxide electrolytes with negligible anion rotation (yellow region) display more ordered Li sublattices with the more negative S₂ values. The more disordered Li sublattice in the sulfides with negligible anion rotation (such as Li₃PS₄, Li₁₀Ge(PS₆)₂ and Li₄GeS₄) show the less negative S₂ and the higher ionic conductivities than the oxygen counterparts (Li₃PO₄, Li₁₀Ge(PO₆)₂ and Li₄GeO₄) (Fig. 2a), due to the softer anion framework of sulfides. This drives our interests to explore effective strategy to activate the disordered Li sublattice for specific structural frameworks.

Interestingly, flexible rotation dynamics turns out to effectively frustrate the local potential surface and promote the dynamic disorder degree of Li sublattice as well as its diffusion. As displayed in Fig. 2b, the materials (green region) with obvious rotation dynamics (revealed by the larger decay constant of the reorientation correlation function Ct determined from AIMD simulations at 1100 K, see method, Supplementary Fig. 2 and Supplementary Data 1) demonstrate S₂ values comparable to sulfides yet exceeding those of oxides. As an example, Li₃PS₄ (space group: Pnma) exhibits a highly disordered Li sublattice with an S₂ value of −0.22, which is higher than that of the Li₃PO₄ (S₂ = −1.47) with the same crystal structure (Fig. 2c, d). According to the trajectory analysis, this order (Li₃PO₄)-disorder (Li₃PS₄) transition for Li sublattice may be attributed to the dynamics of polyanions, as Li₃PS₄ has a higher rotation freedom for polyanion (lower Ct). The S atoms in PS₄ tetrahedra move around the central P atom with a relatively large displacement, while the PO₄ tetrahedra only liberate around the lattice position. Thus, the PS₄ shows more flexible rotation motions in Li₃PS₄ (Fig. 2e) than PO₄ in Li₃PO₄ (Fig. 2f), as evidenced by the large angular change of the PS₄ polyanions (detailed definition of angle could be found in Supplementary Fig. 3). The rotation motions of polyanions in other structures in Fig. 2b are shown in Supplementary Fig. 4. For a given structure, introducing flexible polyanion rotational dynamics seems to enhance the dynamic Li-sublattice disorder degree more effectively than simply raising the temperature (Supplementary Fig. 5).

To further explore the contribution of anions’ rotation on the disorder degree of Li sublattice, we employed the machine learning molecular dynamics (see Methods) based on the moment tensor potential (MTP)²⁶ for Li₃BrSO₄ (see Fig. 3a and Supplementary Fig. 6), which was predicted by the combined density function theory (DFT) and crystal structure prediction in the previous work²⁷. The DFT lattice constant and AIMD dynamic properties of Li₃BrSO₄ are well reproduced with the molecular dynamics (MD) simulations based on MTP (MD-MTP), as displayed in Supplementary Fig. 7 and the corresponding crystal structures are provided in Supplementary Data 1. Therefore, this trained machine learning potential was adopted to reveal large-angle rotation of anions at low temperature, which cannot be visualized by the low-temperature AIMD simulations due to the inherent timescale limitations in capturing slow dynamic processes.

Fig. 3. Rotation-driven Li sublattice disorder and corresponding rotational structural descriptor.

a Comparing the MTP energies to the DFT energies and forces of the training and testing dataset in Li₃BrSO₄. b Diffusion coefficient, reorientation correlation function Ct and c RDF for Li₃BrSO₄ calculated at 100–500 K by the molecular dynamics simulations with the MTP (MD-MTP). Error bars represent the standard deviation from n = 4 independent simulations for Ct, while those for diffusivity represent the standard deviation from multiple independent simulations split from a long molecular dynamical trajectory, see the Methods section for details. d Probability density distribution (P) for the stable and metastable Li sites in the Li₃BrSO₄ during MD simulations at 200 and 300 K with P = 0.0004 a₀⁻³ (a₀ is the Bohr radius). The brown, red and green spheres represent the Br, O and Li atoms. e Linear and quadratic fits of the low-frequency vibrational density of states (VDOS) of Li₃BrSO₄ at 200 and 300 K. f Angular autocorrelation function (Ct) calculated by AIMD at 1100 K versus rotation tolerance factor (RTF) for systems in Supplementary Table 3. The red line was plotted only for guiding eyes.

Figure 3b shows the diffusion coefficient (D) of Li atoms in Li₃BrSO₄ from 100 to 500 K calculated by the MD-MTP, mean-square displacement (MSD) curves are shown in Supplementary Fig. 8a. A sharp increase of D is observed when the temperature rises from 200 to 300 K. By visualizing the trajectories of polyanions during MD simulations, this superionic transition in Li₃BrSO₄ can be contributed by the activation of large-angle rotation of polyanions (SO₄). As demonstrated by the 2D projected probability distribution ρ(θ, φ) (Supplementary Fig. 9), the polyanions exhibit negligible rotational motions at 200 K with a large Ct value of 0.98, showing the localized O ligands of SO₄. While at 300 K, the more dispersive distribution of angles (θ, φ) suggest the activated rotational motions of the polyanions (Ct = 0.78, Supplementary Fig. 8b), which is highly synergistic with the superionic transition character. Moreover, this superionic transition is further corroborated by the RDF of Li-Li pairs, as shown in Fig. 3c. Below the rotation-activated temperature (T_RA ≈ 300 K), the RDF exhibits distinct sharp peaks, which progressively broaden as the temperature increases. A significant attenuation of the primary peak intensities and their disappearance above T_RA suggest the large change of Li sublattice from order (S₂ = −2.91 at 200 K) to disorder (S₂ = −0.56 at 300 K) upon the activation of polyanion rotation (as further demonstrated by the trajectory analysis in Supplementary Fig. 10). This is in agreement with the result of density of atomistic states (DOAS, Supplementary Fig. 11), more Li-occupiable sites are activated with smaller energy differences by the polyanion rotation. As visualized in Fig. 3d, the continuous distribution of Li-occupiable sites connects the diffusion channels, showing abundant shorter pathways for Li hopping. These stable or meta-stable Li-occupiable sites construct the dynamically disordered Li sublattice.

Besides, the Li vibrational density of states (VDOS) at finite temperatures were calculated through the Fourier transform of the velocity autocorrelation function (Supplementary Fig. 12), indicating a prominent broadband phonon scattering with a loss of Li spectral weight. This phenomenon also implies the order-disorder transition of Li sublattice. Sharp vibrational peaks exist in the low-temperature Li power spectra, which undergo obviously broadening from 200 to 300 K, associated with the activation of SO₄ rotation and the superionic transition. Upon the rotation activation, the vibrational peaks of Li in Li₃BrSO₄ become broad and almost disappear, showing the liquid-like phonon character similar to liquid-like Cu ions in superionic Cu₃SbSe₄²⁸. As shown in the Fig. 3e, the VDOS of Li₃BrSO₄ at 200 K exhibited a conventional Debye-like quadratic DOS at low frequency. However, at 300 K (rotation-activated temperature), a linear dispersion of low-frequency Li phonon mode emerges. This phenomenon is consistent well with the definition of liquid-like dynamics reported by Olivier et al.¹⁵. Notably, a similar phenomenon is observed in high-temperature (HT) Li₂SO₄ (Supplementary Fig. 13), where the VDOS at 500 and 600 K exhibit conventional Debye-like quadratic DOS at low frequency. At 700 K, where rotational behavior activates, spectral intensity increases linearly with frequency. These results demonstrate that the liquid-like dynamics of Li ions is strongly correlated with the rotation dynamics.

This insight about activating the superionic transition through anion rotation could be applied for exploring and designing the SSEs or other conductors with higher ionic conductivities. One critical problem still remains, which anion cluster or polyanion can exhibit flexible rotation dynamics in a specific lattice framework. Herein, we designed a descriptor to describe the rotation freedom, namely rotation tolerance factor (RTF) to describe the rotation freedom:

$$\mathrm{RTF}=\frac{d_{center-Li}-d_{center-edge}}{qm},$$ 2

where the $d_{center-Li}$ and $d_{center-edge}$ represent the distance from the central atom of polyanion to the neighboring Li atoms and the edged atoms of the polyanion, respectively. $q$ is the total valence of polyanion and neighboring cations, and $m$ is the mass of polyanion. By plotting angular autocorrelation function Ct versus RTF for systems with rotational or rigid polyanions (Fig. 3f, details in Supplementary Table 3), the inverse correlation between Ct and RTF indicates that RTF effectively assesses anion rotational freedom in crystal structures. Generally, a larger RTF of a crystal structure indicates the higher possibility of anion rotation.

According to the RTF, the anion clusters with light mass and low charge have a high rotational possibility in a specific crystal framework. Thus, to further confirm the generality to utilize anion rotation for dynamically disordered Li sublattice and hence increased ionic conductivity, the halide, oxide and sulfide electrolytes with light anion clusters (SH⁻, NH₂⁻) were further studied. By substituting anions with SH⁻ and NH₂⁻ in typical electrolyte frameworks including Li₃YCl₆ (C2/c), Li₂ZrCl₆ (C2/m, $P\overline{3}m1$), Li₇La₃Zr₂O₁₂ (cubic phase, Ia−3d), Li₁₀GeP₂S₁₂ (P1), the anion cluster-based structures were constructed and relaxed (optimized crystal structures are shown in Supplementary Fig. 14 and Supplementary Tables 4–6). Thermodynamic stabilities were evaluated based on the energy above hulls (E_hull, Fig. 4a), also regarded as an indicator for the synthesizability. The cluster-based halides (Li₃Y(SH)₆, Li₃Y(NH₂)₆, Li₂Zr(SH)₆ and Li₂Zr(NH₂)₆) and oxides (such as Li_6.5La₃Zr₂O_11.5(NH₂)_0.5, LLZONH, and Li_6.5La₃Zr₂O_11.5(SH)_0.5, LLZOSH) are metastable with E_hull less than 100 meV/atom, while the cluster-based sulfides, Li_9.5GeP₂S_11.5(SH)_0.5 and Li_9.5GeP₂S_11.5(NH₂)_0.5, are thermodynamically unstable with the large E_hull of 269 and 273 meV/atom. The theoretical room-temperature ionic conductivities of these metastable cluster-based structures were further extrapolated based on the high-temperature AIMD simulations.

Fig. 4. Cluster-based halides and their Li diffusion and sublattice disorder.

a Energy above hulls for predicted cluster-based SSEs. b Temperature dependence of the lithium diffusion coefficient. Error bars of diffusivity represent the standard deviation from multiple independent simulations split from a long molecular dynamical trajectory, see the Methods section for details. c Comparison of disorder degree (S₂) of Li sublattice in pure halides and cluster-based halides at 1100 K, the S₂ values of Li₂ZrCl₆ (C2/m) and Li₂Zr(NH₂)₆ (C2/m) were calculated at 1000 K. d Shapley Additive exPlanations (SHAP) feature importance based on the linear regression model for the disorder degree of Li sublattice in systems with anion rotation dynamics.

As displayed in Fig. 4b, the Arrhenius relationships suggest the activation energies (E_a) of Li₃Y(SH)₆ (0.177 eV), Li₃Y(NH₂)₆ (0.18 eV), $P\overline{3}m1$-Li₂Zr(NH₂)₆ (0.155 eV) are significantly lower than that of Li₃YCl₆ (C2/c, 0.316 eV) and $P\overline{3}m1$-Li₂ZrCl₆ (0.306 eV), whose corresponding theoretical RT ionic conductivities are 54.1, 49.65 and 84.6 mS/cm, respectively. And the C2/m-Li₂Zr(NH₂)₆ (E_a = 0.21 eV) also exhibits the improved ionic conductivity than that of the C2/m-Li₂ZrCl₆ (E_a = 0.51 eV). Furthermore, these SH/NH₂-based structures show the expected low Ct values according to RTF (Fig. 3f). Notably, the lattice frameworks of Li₂Zr(SH)₆ exhibits the low dynamic stability evidenced by the MSD curves (Supplementary Fig. 15), the ionic conductivity of which is not considered in this work. The calculated activation energies of Li₃YCl₆ and $P\overline{3}m1$-Li₂ZrCl₆ agree well with the reported values (0.32 eV²⁹ and 0.3 eV³⁰, respectively), which implies the accuracy of our theoretical results. Besides, the anion rotation and disordered Li sublattice in these cluster-based halides are verified by AIMD simulations at 1100 K (Supplementary Figs. 16, 17 display the RDF and Ct curves of these halides). In detail, the disorder degrees of Li (S₂) in Li₃YCl₆, $P\overline{3}m1$-Li₂ZrCl₆ and C2/m-Li₂ZrCl₆ are −0.62, −0.51 and −0.56, respectively. By incorporating the rotating clusters, the disorder degrees or S₂ increased significantly to −0.23, −0.18 and −0.25 for Li₃Y(SH)₆, $P\overline{3}m1$-Li₂Zr(NH₂)₆ and C2/m-Li₂Zr(NH₂)₆ (Fig. 4c), which relates with the higher ionic conductivities and lower activation energies. Furthermore, these designed structures with rotation dynamics exhibit the behavior of liquid-like dynamics, whereas their non-rotating counterparts do not show this phenomenon, as verified by the VDOS shown in Supplementary Fig. 18. Also, the introduction of rotational NH₂⁻ in LLZO (namely LLZONH with Ct = 0.34 as shown in Fig. 3f) reduces the activation energy and enhances the disordered degree of Li sublattice compared to LLZO (Supplementary Fig. 19).

To further validate our hypothesis that anion rotation could promote the dynamic disorder of the Li sublattice, thereby enhancing ionic conductivity, we conducted additional experimental investigations. Because of the non-zero E_hull of above cluster-based structures, the halide with low concentration of NH₂⁻ was designed for synthesis (Li₂ZrCl_5.92(NH₂)_0.08, LZCNH, with E_hull = 0 meV/atom shown in Fig. 4a and the DFT optimized structure shown in Supplementary Fig. 20). In this work, the high-energy ball milling was used for preparing electrolyte samples (see Methods). The X-ray diffraction (XRD) patterns of Li₂ZrCl₆ and LZCNH are displayed in Fig. 5a. The Bragg reflections of our synthesized Li₂ZrCl₆ are identical to those of Li₃YCl₆ with the $P\overline{3}m1$ symmetry, which is consistent well with the previous works³¹. However, the XRD pattern of LZCNH matches well with Li₃lnCl₆ (C2/m), showing a different crystal structure from $P\overline{3}m1$-Li₂ZrCl₆, thus the C2/m-Li₂ZrCl₆ was synthesized by annealing at 350 °C for comparison (Fig. 5a). Then the Scanning Electron Microscopy (SEM) Energy Dispersive Spectroscopy (EDS) mapping images show a homogeneous distribution of N throughout the particles corroborates the substitution of NH₂^- (Fig. 5b). Then the Raman spectra of LZCNH, Li₂ZrCl₆ and LiNH₂, were measured to further confirm the successful doping of NH₂^-. The NH₂^- internal characteristic stretching modes are localized in the 3200–3300 cm⁻¹ region, which can be identified easily and unambiguously. As displayed in Fig. 5c, the existences of NH₂⁻ stretching modes in the LZCNH sample and LiNH₂ compound provide evidence that the NH₂⁻ is successfully doped into the halide electrolyte. Finally, according to results of electrochemical impedance spectroscopy (EIS) measurements (Fig. 5d and Supplementary Fig. 21), the RT ionic conductivity of NH₂⁻ substituted Li halide is 1 mS/cm, which is ~4 times higher than that of $P\overline{3}m1$-Li₂ZrCl₆ (0.26 mS/cm) and far larger than C2/m-Li₂ZrCl₆ (low-conductivity phase, as reported by Ma et al.³²). Besides, based on the Rietveld refinement results (Supplementary Table 7–9, corresponding refined XRD profiles are shown in Supplementary Fig. 22), the reduced occupancy of Li2 site from unity (C2/m-Li₂ZrCl₆) to ~0.89 (LZCNH) indicate the increased disorder of Li sublattice. The disorder also can be characterized by the ⁷Li nuclear magnetic resonance (NMR) spectra (Supplementary Fig. 23), the LZCNH ⁷Li NMR line shape is broader and less symmetrical than that of the C2/m-Li₂ZrCl₆, suggesting the overlapping signals due to the distribution of Li environments in the LZCNH. In general, these results strengthen our insight that rotation dynamics of NH₂ could increase the disorder of Li sublattice and improve the ionic conductivity.

Fig. 5. Synthesis and characterization of NH₂-substituted halides.

a XRD patterns of the as-milled Li₂ZrCl₆ ($P\overline{3}m1$), 350 °C-annealed Li₂ZrCl₆ (C2/m) and Li₂Zr_5.92(NH₂)_0.08 (LZCNH). b SEM-EDS mapping of the element distribution in the NH₂-halide. c Raman spectra of LZCNH, Li₂ZrCl₆ and LiNH₂ in the 2800–3800 cm⁻¹ region. The yellow region indicates the frequency range where the NH₂⁻ Raman peak appears. d EIS plots of as-synthesized LZCNH and Li₂ZrCl₆ at RT.

We further assessed the application of the synthesized LZCNH in all-solid-state batteries (ASSBs) with LiCoO₂ (LCO) or single-crystal LiNi_0.88Co_0.09Mn_0.03O₂ (NCM) positive electrode and a Li-In negative electrode. A protective interlayer of Li₆PS₅Cl was applied to prevent the reaction between the LZCNH and negative electrode. When cycled at specific current of 14 mA g⁻¹ (140 mA g⁻¹ = 1 C for LCO positive electrode) between 2.2 and 3.6 V, the ASSBs with LCO positive electrode (Li-In||LCO) exhibits a discharge capacity of over 137 mAh/g and an initial Coulombic efficiency of 98.2% (Fig. 6a). The great rate performance of the Li-In||LCO cell is displayed in Fig. 6c. The average capacities of 130, 124, and 116 mAh/g are achieved at 28, 70, and 140 mA g⁻¹, respectively. Even at 280 and 560 mA g⁻¹, averaged capacities of 102 and 72 mAh/g are still retained. The cycling stability was further investigated (Fig. 6d), after 190 cycles at 140 mA g⁻¹, the cell shows long-term cycling longevity with a Coulombic efficiency of 99.9% and a discharge capacity of 113 mAh/g. When LCO was replaced by NCM in ASSBs (Li-In||NCM), comparable electrochemical performances were observed. Being cycled at 20 mA g⁻¹ (200 mA g⁻¹ = 1C for NCM positive electrode), the Li-In||NCM shows an initial Coulombic efficiency of 89.8% and a discharge capacity of 208 mAh/g (Fig. 6b). The corresponding averaged discharge capacities at 40, 100, 200, 400, and 800 mA g⁻¹ are 198, 183, 166, 136, and 93 mAh/g, respectively (Fig. 6c). Figure 6e displays the long-term cycling data of Li-In||NCM cell, which indicates a Coulombic efficiency of 99.9% and a discharge capacity of 153 mAh/g after 190 cycles at 200 mA g⁻¹. Besides, the rate performance and cycling stability of Li-In||NCM cell are also better than that of the Li-In|Li₂ZrCl₆|NCM cell (Supplementary Fig. 24).

Fig. 6. All-solid-state batteries performance of Li₂Zr_5.92(NH₂)_0.08 (LZCNH) electrolyte.

a Charge-discharge curves at 14 mA g⁻¹ of LiCoO₂ (LCO) positive electrode SE cell for the first (1st) and second (2nd) cycles. b Charge-discharge curves at 20 mA g⁻¹ of LiNi_0.88Co_0.09Mn_0.03O₂ (NCM) positive electrode SE cell for the first (1st) and second (2nd) cycles. c Rate capability at 0.1, 0.2, 0.5, 1, 2 and 4 C (1C = 140 mA g⁻¹ for LCO and 1C = 200 mA g⁻¹ for NCM). d Long-term cycling performance of Li-In||LCO cell at 140 mA g⁻¹. e Long-term cycling performance of Li-In||NCM cell at 200 mA g⁻¹.

Notably, for the systems with rotation dynamics, Fig. 2b demonstrates a lack of consistent correlation between the disorder degree (S₂) and decay constant (α) across the material classes shown, which suggests that the Li site disorder is multi-faceted and not solely determined by rotational flexibility. To confirm the contribution of potential factors on the S₂ values, the SHapley Additive exPlanations (SHAP) is used to analyze the linear regression model results for the systems with anion rotation dynamics (Supplementary Table 11 displays the selected features and the involved systems can refer to green region in Fig. 2b). As shown in Fig. 4d, besides the decay constant of polyanion (DC), other factors, such as the decreased ICOBI (integrated crystal orbital bond index), more negative ICOHP (integrated crystal orbital hamilton population), increased VPA (volume per atom) and decreased LDFC (local difference frequency center), also contribute to the higher S₂ values. In detail, for the systems with anion rotation dynamics, the most important feature related to the S₂ is the decay constant and then is the interaction between Li ions and neighboring anions (ICOBI and ICOHP). Thus, triggering dynamic disorder of Li sublattice via polyanion rotation requires two prerequisites: sufficient anion rotational freedom and strong Li-polyanion interactions to drive Li⁺ migrations during polyanion rotational motions. If anions only rotate freely but interact weakly with Li ions, rotations cannot effectively activate dynamic disorder of lithium sublattice. Other potential factors influencing Li site disorder (such as local distortions, volume per atom) warrant further investigation but do not diminish the significance of the identified reorientation mechanism, triggering dynamically disordered lithium sublattice.

To substantiate the connection between the type of polyhedral rotation and Li site disorder, we further analyzed the MD trajectories in terms of rotation angles, Li probability density, Li MSD and Li site disorders, using HT-Li₂SO₄ and Li₃BrSO₄ as representatives. The time-dependent rotational angles for specific polyhedra have been determined by using CorrelationAnalyzer python package³¹ (see Supplementary Fig. 25 and details in Supplementary information). Therefore, to characterize the rotational behavior of all polyanions in HT‑Li₂SO₄, the time-dependent rotation angles were extracted, and four distinct 15‑ps time windows (Region 1–4) were identified (Supplementary Fig. 26). Specifically, in Region 1 the polyanions undergo a large average rotation angle of 44.38° with some polyhedron displaying reorientation as large as 180°, whereas in Region 2 they exhibit only small‑angle librations (14.47°). Consistent with this distinction, the dynamic Li‑site disorder degree is higher in Region 1 (S₂ = −0.73) than in Region 2 (S₂ = −1.13), indicating that large‑angle polyhedron rotations correlate with more meta‑stable Li‑occupiable sites and increased Li‑sublattice disorder (Supplementary Fig. 27). A similar trend is observed in Li₃BrSO₄: Region 1, with a larger average rotation angle (26.75°), shows a higher disorder degree (S₂ = −0.43) compared to Region 2 (19.01°, S₂ = −0.50). Overall, Li‑site disorder is positively correlated with the average rotation angle across different time windows in both materials (Supplementary Fig. 26c, d), and this relationship also persists at elevated temperatures (Supplementary Fig. 28).

To further probe how rotational dynamics influence the local Li⁺ sublattice, we distinguished polyanion rotational events as minor reorientations (rotation angles <30°) and major reorientations (rotation angles ≥30°) within the same time window. Li⁺ ions near the SO₄ undergoing major reorientations exhibit higher MSD in HT-Li₂SO₄ than those near the SO₄ with minor reorientations (Supplementary Fig. 29b and details in Supplementary information). Besides, the specific SO₄ (index 14) polyanion with major reorientations is also surrounded by Li⁺ ions with a larger MSD than the SO₄ (index 15) with minor reorientations (Supplementary Fig. 29). And more Li-occupiable sites exist around the SO₄ (14) than that around the SO₄ (15) (Supplementary Fig. 29f). These results highlight that major polyhedral reorientations—compared to minor ones—may play a more critical role in dynamically reshaping the Li⁺ energy landscape, increasing the number of Li-occupiable sites and thus amplifying the local dynamic disorder of the Li sublattice. Furthermore, these observations were also verified in the Li₃BrSO₄ system (Supplementary Fig. 30).

Our current work has identified a correlation between large-angle rotations and increased Li-site disorder. However, how the specific rotational motion characteristics (such as variations in the dynamic angular momentum of polyhedra, or the evolution of their principal rotational axes) contribute to cation disordering still awaits exploration. Deciphering these specific linkages to explore quantitative and mechanistic relationships between rotational descriptors and cation dynamics thus represents a vital and exciting frontier. Our present findings offer a foundation for this endeavor.

In summary, this study proposes a strategy for superionic conductor design by triggering the dynamically disordered Li sublattice through polyanion rotational dynamics, which shifts the paradigm from static structural optimization to dynamic modulation of ion transport. The rotational motion of anion clusters is found as a viable pathway to promote the dynamically disordered Li sublattice distribution as well as the liquid-like ionic diffusion in superionic conductors. This dynamically disordered Li sublattice effectively frustrates the energy landscape for lithium migration, thereby simultaneously reducing activation energy barriers. The rotation tolerance factor (RTF) is further proposed to reveal the insight that anion clusters with light mass and low charge have a high rotational possibility in a specific crystal framework. Therefore, the cluster-based halides (Li₃Y(SH)₆, Li₃Y(NH₂)₆ and Li₂Zr(NH₂)₆) and oxide (Li_6.5La₃Zr₂O_11.5(NH₂)_0.5) were designed following this strategy to introduce rotational dynamics as well as the more disordered Li sublattice. The three halides exhibit high theoretical RT ionic conductivities of 54.1, 49.65 and 84.6 mS/cm, respectively. Experimentally, the synthesized NH₂-halide (LZCNH) achieves a fourfold enhancement in ionic conductivity over Li₂ZrCl₆ control. The all-solid-state batteries (ASSBs) made of LZCNH with LCO or NCM positive electrode and a Li-In negative electrode show good Coulombic efficiency after 190 cycles. This work explores a general framework for engineering superionic conductors via polyanion rotation-driven sublattice disorder, unlocking pathways to high-performance solid electrolytes through dynamic anion engineering.

Methods

DFT calculation

The structural optimizations for the properties in this work were conducted by the vienna ab-initio simulation package (VASP) based on the projector augmented wave (PAW) method³³. The exchange-correlation potential for the overall lattice optimization are described by the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximant (GGA)³⁴ and the dispersion correction is considered for the anion cluster-based structures by the Grimme’s semi-empirical schemes. The energy cutoff is 520 eV for the plane wave expansion and the energy and force convergences are set to 10⁻⁶eV and 0.01 eV/Å, respectively. Ab initio molecular dynamics (AIMD), initialized from the lowest-energy atomic configurations, was used to investigate the ionic conductivity and radial distribution function (RDF). AIMD simulations for calculating ionic conductivity are performed in an NVT ensemble with a timestep of 2 fs and using a Nosé−Hoover thermostat³⁵ for a period of 100 ps (50,000 time steps). While for calculating the RDFs, the AIMD calculations were performed for a period of 30 ps. Importantly, for the systems with H element, the timestep of 1 fs was used. In addition, the smaller plane wave energy cutoff of 400 eV was used to keep the computational cost at a reasonable level. A minimal Γ-point-only k-point grid was used with no spin-polarized calculations. All the data were fitted assuming Arrhenius behavior to obtain the activation energies and ionic conductivities at 300 K. The mean-square displacement (MSD) of the Li ions was estimated from³⁶

$$\mathrm{MSD}\left(t\right)=\frac{1}{N}\sum _{i=1}^N{\mid r_i\left(t+t_0\right)-r_i\left(t_0\right)\mid }^2.$$ 3

According to the MSD, the self-diffusion coefficient was estimated using

$$D_{Li}=\frac{\mathrm{MSD}}{6t}=D_{Li}^0\exp \left(-\frac{E_a}{K_{B}T}\right),$$ 4

where $D_{Li}^0$ is a pre-factor, $k_B$ is the Boltzmann’s constant, T is the simulation temperatures, and $E_a$ is the activation energy. Following, the temperature-dependent ionic conductivity, ${\sigma }_{Li}\left(T\right)$, was estimated from the Nernst–Einstein relation³⁷ as

$${\sigma }_{Li}\left(T\right)=\frac{{\left(Z_{Li}e\right)}^{2}N{D}_{Li}}{V{k}_{B}T},$$ 5

where $Z_{Li}$ is the integer charge of a Li ion and $V$ is the volume of the simulation box. The MSD and the pair radial distribution function was calculated by pymatgen diffusion package³⁸. To assess the statistical uncertainty of the diffusivity D obtained from AIMD simulations, we performed the following analysis: a long molecular dynamics trajectory was split into multiple non‑overlapping shorter segments, each treated as an independent simulation. The variance of D was then quantified over this ensemble of segments. The standard deviation of D (S_D) was calculated from the set of fitted D values³⁹.

Rotational angles were calculated by using CorrelationAnalyzer python package which are well suited to study rotational trajectories³¹. The rotation angle diagram illustrates the rotational state of a single polyanion. This diagram illustrates the temporal correlation between the orientations of an anion group at time t₀ and t₀+dt with dt ranging from 0 to 5 ps. Color intensity quantifies the angular rotation angles required to realign the anion group from its orientation at the later time (y-axis) to its initial orientation at t₀. Then, the rotation angles at intervals of dt = 5 ps were extracted for each polyanion to characterize the all polyanion rotational behaviors in the structure. And four distinct 15-ps temporal regions or time windows (Region 1, 2, 3, and 4) were defined according to the time-dependent rotation angles. So averaged rotation angle is defined as the average angle of all rotational events within each region. Besides, we distinguish polyanion rotational events as minor reorientations (rotation angles <30°) and major reorientations (rotation angles ≥30°), and the MSD of Li atoms nearby the SO₄ groups (specifically, those within the first coordination shell as identified from the S-Li RDF) with minor or major reorientations were then calculated and analyzed separately. It shall be noted that such a choice of 30° is only for the convenience of analyses.

The reorientation correlation function was calculated to analyze the timescales of anions reorientation of the studied cluster-based SSEs:

$$\mathrm{Ct}=⟨\mathit{u}\left(t\right)\mathrm{\cdot }\mathit{u}\left(t+t^{\prime }\right)⟩,$$ 6

where $\mathit{u}\left(t\right)$ is a unit vector from the center atom of polyanion to its anion ligand at time $t$. The rate at which this function decays to zero reflects the reorientation rate of that species. We fitted the time correlation Ct function with an exponential model Ct=exp(-$\alpha t$), α is a decay constant that can probe the decay rate of rotation. The correlation time $t^{\prime }$ is 0–5 ps in this work.

Machine learning molecular dynamics simulation

The machine learning interatomic potential, Moment Tensor Potential (MTP), was trained based on the AIMD results with the NVT ensemble at different temperatures (300, 500, 700, 900, 1100 K) and three strains (0, +0.05 and −0.05), similar to the Shyue’s work⁴⁰. Firstly, the system was heated from 0 K to targeted temperature and equilibrated for 40 ps with the timestep of 2 fs. Then the snapshots of different temperatures or strains were extracted from the last 20 ps at 0.1 ps intervals. Therefore, a total of 3000 training structures (200$\times$15) were generated. Finally, we performed static calculations on these structures for accurate energies and forces, preparing for the MTP training. A k-point density of at least 100/ų was employed to ensure computational convergence. To enhance the accuracy of the machine learning potential, the hyperparameter nbasis was systematically optimized over a range of values (8, 10, 12, 14, 16, 18, 20). Considering the mean absolute errors of both energies and forces, nbasis = 14 was ultimately selected as the optimal parameter, as this setting yielded relatively low prediction errors on the test set. During the MTP training, we assigned the weights of 100:1 for energy and force data. All training and MD simulations in this work are based on the Python Materials Genomics (pymatgen) library, Machine Learning Interatomic Potentials (MLIP), and LAMMPS. The low-temperature molecular dynamics simulations for Li₃BrSO₄ (3$\times$3$\times$3, 243 atoms) were conducted based on the fitted MTP model at 100, 200, 300, 400, 500 K. The simulation time was 800 ns with a 1 fs time step in the NVT ensemble (Nosé-Hoover thermostat) for 100 and 200 K, 200 ns for 300 K, and 100 ns for 400 and 500 K.

The density of atomistic states (DOAS) was calculated as follows. A total of 1000 snapshots of atomistic structures were sampled from the MD simulations at constant time intervals over the entire duration. For each snapshot, a static relaxation was performed using the conjugate gradient algorithm with the energy and force convergence of 1 × 10⁻¹⁰eV/atom and 1 × 10⁻⁸eV/Å, respectively, LAMMPS by trained MTP models to eliminate the thermal vibration at the finite temperatures. After structural relaxation, the atomistic energy of each atom was directly outputted by the MTP model. The energy levels were referenced to the lowest energy among all Li configurations. The Li DOAS was calculated as a histogram of the atomistic energies of each Li atom.

Preparation of materials

The solid electrolyte used in this work were synthesized by a mechanochemical method using high-energy ball milling. All preparations and sample treatments were carried out under an Ar atmosphere (O₂ < 0.1 ppm, H₂O < 0.1 ppm). For the preparation of Li₂ZrCl_6-x(NH₂)_x (x = 0, 0.08), a stoichiometric mixture of LiCl (99.99%, Sigma Aldrich), ZrCl₄ (99.99%, Aladdin), and LiNH₂ (95%, Alfa) with a total mass of ~1 g was ball-milled at 600 rpm for 10 h (using a cycle of 5 min milling followed by 2 min rest) in a ZrO₂ vial with ZrO₂ balls (Retsch Emax). The ratio of grinding media to powder was 40:1 (5 mm in diameter). For comparison, pristine $P\overline{3}m1$ Li₂ZrCl₆ powder was also mechanochemically synthesized under identical milling conditions (rotation speed, duration, cycling mode, ball-to-powder ratio, and milling media) from a stoichiometric mixture of LiCl and ZrCl₄. The C2/m Li₂ZrCl₆ powder was obtained by sealing the aforementioned $P\overline{3}m1$ Li₂ZrCl₆ powder in a quartz tube under an argon atmosphere, followed by annealing in a muffle furnace at 350 °C for 5 h with a heating rate of 2 °C/min and subsequent natural cooling to room temperature. Then, the powder was taken out in a glove box and manually ground in a mortar for collection and future use.

Measurements of ionic conductivities

To evaluate the ionic conductivity of the as-prepared solid electrolytes (SEs), Electrochemical Impedance Spectroscopy (EIS) measurements were conducted using a two-electrode configuration with stainless steel rods as blocking electrodes. Specifically, 100–120 mg of SE powder was precisely weighed and subsequently uniaxially cold-pressed at 300 MPa to form dense pellets, each measuring 10 mm in diameter and 0.06–0.07 cm in thickness, and this pressure was maintained during the measurement as well. EIS measurements were performed at 25 °C under potentiostatic mode using a Metrohm Autolab PGSTAT302N electrochemical workstation. The impedance spectra were collected over a frequency range from 1 Hz to 1 MHz with an AC amplitude of 20 mV, acquiring a total of 60 data points. Prior to each measurement, a steady-state potential of 0 V was applied for 5 s to ensure open-circuit conditions. Throughout the experiments, the temperature was maintained constant using a controlled environmental chamber. DC polarization measurements were carried out using an identical cell configuration. A constant polarization voltage of 0.2 V was applied, and the resulting current response was recorded over a duration of 30 min.

Assembly and electrochemical characterizations of ASSBs

The solid-state batteries were assembled in a PEEK mold with a diameter of 10 mm following a sequential fabrication procedure. First, a buffer layer was formed by cold-pressing 40 mg of Li₆PS₅Cl under 0.5 tons (t), thickness around 260 μm. Subsequently, two types of solid electrolyte (SE) materials (Li₂ZrCl_6-x(NH₂)_x, Li₂ZrCl₆) were each compacted using 40 mg of powder under a pressure of 1.5 t for 2 min to obtain electrolyte pellets (thickness around 280 μm). For the cathode preparation, a positive electrode mixture was obtained by manually grinding the active material (NCM88/LCO) with the SE in a 7:3 weight ratio. Approximately 10 mg (8.9 mg/cm²) of this homogenized composite was then uniformly deposited onto the surface of the electrolyte layer and pressed at 4 t for 5 min (thickness around 55 μm) to complete the cell assembly. NCM88 (LiNi_0.88Co_0.09Mn_0.03O₂, supplied by China Automotive Battery Research Institute Co., Ltd.) incorporated 3 wt.% vapor-grown carbon fiber (VGCF), while pristine LCO (LiCoO₂, Aladdin) was used without modification. An In foil (10 mm diameter, thickness around 30 μm, Sino Santech Co., Ltd.) and Li foil (8 mm diameter, thickness around 20 μm, China energy Lithium Co., Ltd.) were sequentially laminated onto the Li₆PS₅Cl (LPSC) electrolyte side, with the entire assembly consolidated at 2 t to ensure robust interfacial contact. The batters were operated under a pressure of 2 t using a custom-designed, airtight cell with stainless steel electrodes. All procedures were conducted in an Ar-filled glove box (<0.1 ppm H₂O/O₂). Electrochemical evaluations were performed using Neware and Land test systems, with 1C-rates defined as 200 mA g⁻¹ for NCM88 and 140 mA g⁻¹ for LCO, and voltage windows set at 2.2–3.7 V (vs. LiIn/Li⁺) for NCM88 and 2.2-3.6 V (vs. LiIn/Li⁺) for LCO, respectively. The temperature during the cycling tests was maintained using an incubator (Tianjin Hongnuo Instrument, SPX-250B, temperature accuracy ±1 °C). All cells were stabilized for 2 h at 25 °C prior to cycling.

Characterization methods

The X-ray diffraction peak patterns measurement was conducted on a Bruker D8 Advance diffractometer equipped with Cu Kα radiation (λ = 1.5406 Å), using a scanning step of 0.02° and scanning speed of 2° min⁻¹. The microstructure and elemental distribution analyses of the samples were characterized by a scanning electron microscope (SEM, JEOL, JSM6510) coupled with energy dispersive X-ray spectroscopy (EDXS, Oxford Instruments) and transmission electron microscopy (TEM, JEM2100F). The SEM was operated at an accelerating voltage of 15 kV. Raman spectroscopy and the in situ Raman measurement were performed on a Jobin-Yvon Lab RAM HR-800 spectrometer with a laser excitation wavelength of 532 nm. ⁷Li MAS solid-state NMR measurements were performed on a AVANCE NEO spectrometer using a 3.2 mm MAS probe (B₀ = 14.09 T, Larmor frequency ω₀ = 600 and 233.24 MHz for ⁷Li).

Author contributions

C.G., H.Z. conceived the project and designed the simulations and experiments. J.Z, J.L. and Y.Z. conducted the experiments. C.G. carried out DFT simulations and data analysis. R.O. assisted with the analyses. C.G. wrote the manuscript. F.H. and H.Z. supervised the project. All authors contributed to the review and editing of the manuscript.

Peer review

Peer review information

Nature Communications thanks Shumin Zhang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The data generated in this study are provided in the Supplementary Information/Source Data file. Source data provided with this paper. Source data are provided with this paper.

Code availability

The machine learning molecular dynamics simulations were performed using open-source software packages, including LAMMPS, MLIP, Pymatgen and MAML, available at https://www.lammps.org, https://instadeepai.github.io/mlip/http://pymatgen.org and https://github.com/materialyzeai/maml. Additional scripts, structures, and relevant details are available at 10.5281/zenodo.18802601.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-71304-3.