Superionic Diffusion through Frustrated Energy Landscape

Machine Learning Prediction Models for Solid Electrolytes Based on Lattice Dynamics Properties

Recently, machine-learning approaches have accelerated computational materials design and the search for advanced solid electrolytes. However, the predictors are currently limited to static structural parameters, which may not fully account for the dynamic nature of ionic transport. In this study, we meticulously curated features considering dynamic properties and developed machine-learning models to predict the ionic conductivity, σ, of solid electrolytes. We compiled 14 phonon-related descriptors from first-principles phonon calculations along with 16 descriptors related to the structure and electronic properties. Our logistic regression classifiers exhibit an accuracy of 93%, while the random forest regression model yields a root-mean-square error for log(σ) of 1.179 S/cm and R2 of 0.710. Notably, phonon-related features are essential for estimating the ionic conductivities in both models. Furthermore, we applied our prediction model to screen 264 Li-containing materials and identified 11 promising candidates as potential superionic conductors.

Kam R, Ceder G. The nonexistence of a paddlewheel effect in superionic conductors

Since the 1980s, the paddlewheel effect has been suggested as a mechanism to boost lithium-ion diffusion in inorganic materials via the rotation of rotor-like anion groups. However, it remains unclear whether the paddlewheel effect, defined as large-angle anion group rotations assisting Li hopping, indeed exists; furthermore, the physical mechanism by which the anion-group dynamics affect lithium-ion diffusion has not yet been established. In this work, we differentiate various types of rotational motions of anion groups and develop quaternion-based algorithms to detect, quantify, and relate them to lithium-ion motion in ab initio molecular dynamics simulations. Our analysis demonstrates that, in fact, the paddlewheel effect, where an anion group makes a large angle rotation to assist a lithium-ion hop, does not exist and thus is not responsible for the fast lithium-ion diffusion in superionic conductors, as historically claimed. Instead, we find that materials with topologically isolated anion groups can enhance lithium-ion diffusivity via a more classic nondynamic soft-cradle mechanism, where the anion groups tilt to provide optimal coordination to a lithium ion throughout the hopping process to lower the migration barrier. This anion-group disorder is static in nature, rather than dynamic and can explain most of the experimental observations. Our work substantiates the nonexistence of the long-debated paddlewheel effect and clarifies any correlation that may exist between anion-group rotations and fast ionic diffusion in inorganic materials.

Halide Superionic Conductors with Non-Close-Packed Anion Frameworks

Halide superionic conductors (SICs) are drawing significant research attention for their potential applications in all-solid-state batteries. A key challenge in developing such SICs is to explore and design halide structural frameworks that enable rapid ion movement. In this work, we show that the close-packed anion frameworks shared by traditional halide ionic conductors face intrinsic limitations in fast ion conduction, regardless of structural regulation. Beyond the close-packed anion frameworks, we identify that the non-close-packed anion frameworks have great potential to achieve superionic conductivity. Notably, we unravel that the non-close-packed UCl3-type framework exhibit superionic conductivity for a diverse range of carrier ions, including Li+, Na+, K+, and Ag+, which are validated through both ab initio molecular dynamics simulations and experimental measurements. We elucidate that the remarkable ionic conductivity observed in the UCl3-type framework structure stems from its significantly more distorted site and larger diffusion channel than its close-packed counterparts. By employing the non-close-packed anion framework as the key feature for high-throughput computational screening, we also identify LiGaCl3 as a promising candidate for halide SICs. These discoveries provide crucial insights for the exploration and design of novel halide SICs.

Dynamic Monkey Bar Mechanism of Superionic Li-ion Transport in LiTaCl6

The LiTaCl6 solid electrolyte has the lowest activation energy of ionic conduction at ambient conditions (0.165 eV), with a record high ionic conductivity for a ternary compound (11 mS cm-1 ). However, the mechanism has been unclear. We train machine-learning force fields (MLFF) on ab initio molecular dynamics (AIMD) data on-the-fly and perform MLFF MD simulations of AIMD quality up to the nanosecond scale at the experimental temperatures, which allows us to predict accurate activation energy for Li-ion diffusion (at 0.164 eV). Detailed analyses of trajectories and vibrational density of states show that the large-amplitude vibrations of Cl- ions in TaCl6 - enable the fast Li-ion transport by allowing dynamic breaking and reforming of Li-Cl bonds across the space in between the TaCl6 - octahedra. We term this process the dynamic-monkey-bar mechanism of superionic Li+ transport which could aid the development of new solid electrolytes for all-solid-state lithium batteries.

Understanding the role of aliovalent cation substitution on the li-ion diffusion mechanism in Li6+xP1-xSixS5Br argyrodites

Due to their high ionic conductivity, lithium-ion conducting argyrodites show promise as solid electrolytes for solid-state batteries. Aliovalent substitution is an effective technique to enhance the transport properties of Li6PS5Br, where aliovalent Si substitution triples ionic conductivity. However, the origin of this experimentally observed increase is not fully understood. Our density functional theory (DFT) study reveals that Si4+ substitution increases Li diffusion by activating Li occupancy in the T4 sites. Redistribution of Li-ions within the lattice results in a more uniform distribution of Li around the T4 and neighboring T5 sites, flattening the energy landscape for diffusion. Since the T4 site is positioned in the intercage jump pathway, an increase in the intercage jump rate is found, which is directly related to the macroscopic diffusion and bulk conductivity. Analysis of neutron diffraction experiments confirms partial T4 site occupancy, in agreement with the computational findings. Understanding the aliovalent substitution effect on interstitials is crucial for improving solid electrolyte ionic conductivity and advancing solid-state battery performance.

Entropy and Isokinetic Temperature in Fast Ion Transport

Ion transport in crystalline solids is an essential process for many electrochemical energy converters such as solid-state batteries and fuel cells. Empirical data have shown that ion transport in crystal lattices obeys the Meyer-Neldel Rule (MNR). For similar, closely related materials, when the material properties are changed by doping or by strain, the measured ionic conductivities showing different activation energies intersect on the Arrhenius plot, at an isokinetic temperature. Therefore, the isokinetic temperature is a critical parameter for improving the ionic conductivity. However, a comprehensive understanding of the fundamental mechanism of MNR in ion transport is lacking. Here the physical significance and applicability of MNR is discussed, that is, of activation entropy-enthalpy compensation, in crystalline fast ionic conductors, and the methods for determining the isokinetic temperature. Lattice vibrations provide the excitation energy for the ions to overcome the activation barrier. The multi-excitation entropy model suggests that isokinetic temperature can be tuned by modulating the excitation phonon frequency. The relationship between isokinetic temperature and isokinetic prefactor can provide information concerning conductivity mechanisms. The need to effectively determine the isokinetic temperature for accelerating the design of new fast ionic conductors with high conductivity is highlighted.

Design principles for sodium superionic conductors

Motivated by the high-performance solid-state lithium batteries enabled by lithium superionic conductors, sodium superionic conductor materials have great potential to empower sodium batteries with high energy, low cost, and sustainability. A critical challenge lies in designing and discovering sodium superionic conductors with high ionic conductivities to enable the development of solid-state sodium batteries. Here, by studying the structures and diffusion mechanisms of Li-ion versus Na-ion conducting solids, we reveal the structural feature of face-sharing high-coordination sites for fast sodium-ion conductors. By applying this feature as a design principle, we discover a number of Na-ion conductors in oxides, sulfides, and halides. Notably, we discover a chloride-based family of Na-ion conductors NaxMyCl6 (M = La-Sm) with UCl3-type structure and experimentally validate with the highest reported ionic conductivity. Our findings not only pave the way for the future development of sodium-ion conductors for sodium batteries, but also consolidate design principles of fast ion-conducting materials for a variety of energy applications.

Solid electrolytes redefine ion conduction

A mechanism of ion transport in solid electrolytes can guide the design of lithium batteries.

Dynamic Lone Pairs and Fluoride-Ion Disorder in Cubic-BaSnF4

Introducing compositional or structural disorder within crystalline solid electrolytes is a common strategy for increasing their ionic conductivity. (M,Sn)F2 fluorites have previously been proposed to exhibit two forms of disorder within their cationic host frameworks: occupational disorder from randomly distributed M and Sn cations and orientational disorder from Sn(II) stereoactive lone pairs. Here, we characterize the structure and fluoride-ion dynamics of cubic BaSnF4, using a combination of experimental and computational techniques. Rietveld refinement of the X-ray diffraction (XRD) data confirms an average fluorite structure with {Ba,Sn} cation disorder, and the 119Sn Mössbauer spectrum demonstrates the presence of stereoactive Sn(II) lone pairs. X-ray total-scattering PDF analysis and ab initio molecular dynamics simulations reveal a complex local structure with a high degree of intrinsic fluoride-ion disorder, where 1/3 of fluoride ions occupy octahedral "interstitial" sites: this fluoride-ion disorder is a consequence of repulsion between Sn lone pairs and fluoride ions that destabilizes Sn-coordinated tetrahedral fluoride-ion sites. Variable-temperature 19F NMR experiments and analysis of our molecular dynamics simulations reveal highly inhomogeneous fluoride-ion dynamics, with fluoride ions in Sn-rich local environments significantly more mobile than those in Ba-rich environments. Our simulations also reveal dynamical reorientation of the Sn lone pairs that is biased by the local cation configuration and coupled to the local fluoride-ion dynamics. We end by discussing the effect of host-framework disorder on long-range diffusion pathways in cubic BaSnF4.

Bimetallic Anionic Organic Frameworks with Solid-State Cation Conduction for Charge Storage Applications

A new phosphonate-based anionic bimetallic organic framework, with the general formula of A4 -Zn-DOBDP (wherein A is Li+ or Na+ , and DOBDP6- is the 2,5-dioxido-1,4-benzenediphosphate ligand) is prepared and characterized for energy storage applications. With four alkali cations per formula unit, the A4 -Zn-DOBDP MOF is found to be the first example of non-solvated cation conducting MOF with measured conductivities of 5.4×10-8  S cm-1 and 3.4×10-8  S cm-1 for Li4 - and Na4 - phases, indicating phase and composition effects of Li+ and Na+ shuttling through the channels. Three orders of magnitude increase in ionic conductivity is further attained upon solvation with propylene carbonate, placing this system among the best MOF ionic conductors at room temperature. As positive electrode material, Li4 -Zn-DOBDP delivers a specific capacity of 140 mAh g-1 at a high average discharge potential of 3.2 V (vs. Li+ /Li) with 90 % of capacity retention over 100 cycles. The significance of this research extends from the development of a new family of electroactive phosphonate-based MOFs with inherent ionic conductivity and reversible cation storage, to providing elementary insights into the development of highly sought yet still evasive MOFs with mixed-ion and electron conduction for energy storage applications.

Liquid-Like Li-Ion Conduction in Oxides Enabling Anomalously Stable Charge Transport across the Li/Electrolyte Interface in All-Solid-State Batteries

The softness of sulfur sublattice and rotational PS4 tetrahedra in thiophosphates result in liquid-like ionic conduction, leading to enhanced ionic conductivities and stable electrode/thiophosphate interfacial ionic transport. However, the existence of liquid-like ionic conduction in rigid oxides remains unclear, and modifications are deemed necessary to achieve stable Li/oxide solid electrolyte interfacial charge transport. In this study, by combining the neutron diffraction survey, geometrical analysis, bond valence site energy analysis, and ab initio molecular dynamics simulation, 1D liquid-like Li-ion conduction is discovered in LiTa2 PO8 and its derivatives, wherein Li-ion migration channels are connected by four- or five-fold oxygen-coordinated interstitial sites. This conduction features a low activation energy (0.2 eV) and short mean residence time (<1 ps) of Li ions on the interstitial sites, originating from the Li-O polyhedral distortion and Li-ion correlation, which are controlled by doping strategies. The liquid-like conduction enables a high ionic conductivity (1.2 mS cm-1 at 30 °C), and a 700 h anomalously stable cycling under 0.2 mA cm-2 for Li/LiTa2 PO8 /Li cells without interfacial modifications. These findings provide principles for the future discovery and design of improved solid electrolytes that do not require modifications to the Li/solid electrolyte interface to achieve stable ionic transport.

Recent progress and strategic perspectives of inorganic solid electrolytes: fundamentals, modifications, and applications in sodium metal batteries

Solid-state electrolytes (SEs) have attracted overwhelming attention as a promising alternative to traditional organic liquid electrolytes (OLEs) for high-energy-density sodium-metal batteries (SMBs), owing to their intrinsic incombustibility, wider electrochemical stability window (ESW), and better thermal stability. Among various kinds of SEs, inorganic solid-state electrolytes (ISEs) stand out because of their high ionic conductivity, excellent oxidative stability, and good mechanical strength, rendering potential utilization in safe and dendrite-free SMBs at room temperature. However, the development of Na-ion ISEs still remains challenging, that a perfect solution has yet to be achieved. Herein, we provide a comprehensive and in-depth inspection of the state-of-the-art ISEs, aiming at revealing the underlying Na⁺ conduction mechanisms at different length scales, and interpreting their compatibility with the Na metal anode from multiple aspects. A thorough material screening will include nearly all ISEs developed to date, i.e., oxides, chalcogenides, halides, antiperovskites, and borohydrides, followed by an overview of the modification strategies for enhancing their ionic conductivity and interfacial compatibility with Na metal, including synthesis, doping and interfacial engineering. By discussing the remaining challenges in ISE research, we propose rational and strategic perspectives that can serve as guidelines for future development of desirable ISEs and practical implementation of high-performance SMBs.

Correlated factors for Li-ion migration in ionic conductors with the fcc anion sublattice

The development of solid-state electrolytes (SSEs) with high lithium ionic conductivities is critical for the realization of all-solid-state Li-ion batteries. Crystal structure distortions, Li polyhedron volumes, and anion charges in SSEs are reported to affect the energy landscapes, and it is paramount to investigate their correlations. Our works uncover the cooperative effect of lithium site distortions, anion charges, and lattice volumes on Li-ion migration energy barrier in superionic conductors of LiMS2 (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) and Li2MO3 (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni). Combined with the Least Absolute Shrinkage and Selection Operator analyses, the volume and Continuous symmetrical methods (CSMs) of Li tetrahedral (Tet) sites appear to have a larger effect on the manipulation of Ea for Li migration, compared to that of Li octahedral (Oct) sites, which is further confirmed by the results from the face-centered cubic (fcc) anion lattice model. For the Tet-Oct-Tet Li migration path, the CSM (the volume of Li site) has a negative (positive) correlation with Ea, while for the Oct-Tet-Oct Li migration paths, opposite correlations have been observed. The understanding of the correlation between site preference, anion charge, lattice volume, and structural distortion as well as the prediction model of Ea in terms of these three factors, namely, C-V-D model, could be useful for the design of solid-state electrolytes with lower activation energy.

Frustration in Super-Ionic Conductors Unraveled by the Density of Atomistic States

The frustration in super-ionic conductors enables their exceptionally high ionic conductivities, which are desired for many technological applications including batteries and fuel cells. A key challenge in the study of frustration is the difficulties in analyzing a large number of disordered atomistic configurations. Using lithium super-ionic conductors as model systems, we propose and demonstrate the density of atomistic states (DOAS) analytics to quantitatively characterize the onset and degree of disordering, reveal the energetics of local disorder, and elucidate how the frustration enhances diffusion through the broadening and overlapping of the energy levels of atomistic states. Furthermore, material design strategies aided by the DOAS are devised and demonstrated for new super-ionic conductors. The DOAS is generally applicable analytics for unraveling fundamental mechanisms in complex atomistic systems and guiding material design.

High-entropy mechanism to boost ionic conductivity

Advances in solid-state batteries have primarily been driven by the discovery of superionic conducting structural frameworks that function as solid electrolytes. We demonstrate the ability of high-entropy metal cation mixes to improve ionic conductivity in a compound, which leads to less reliance on specific chemistries and enhanced synthesizability. The local distortions introduced into high-entropy materials give rise to an overlapping distribution of site energies for the alkali ions so that they can percolate with low activation energy. Experiments verify that high entropy leads to orders-of-magnitude higher ionic conductivities in lithium (Li)-sodium (Na) superionic conductor (Li-NASICON), sodium NASICON (Na-NASICON), and Li-garnet structures, even at fixed alkali content. We provide insight into selecting the optimal distortion and designing high-entropy superionic conductors across the vast compositional space.

Anharmonic Cation-Anion Coupling Dynamics Assisted Lithium-Ion Diffusion in Sulfide Solid Electrolytes

Sulfide-based lithium superionic conductors often show higher Li-ion conductivity than other types of electrolyte materials. This work unveils a unique Li-ion conductive behavior in these materials through the perspective of anharmonic coupling assisted Li-ion diffusion. Li hopping events can happen simultaneously with various types of lattice dynamics, while only a statistically important synchronization of motions may indicate coupling. This method enables a direct evaluation of the coupling strength between these motions, which more fundamentally decides if a specific type of lattice motion is really anharmonically coupled to the Li hopping event and whether the coupling can facilitate the Li diffusion. By a new ab initio computational approach, this work unveils a unique phenomenon in prototype sulfide electrolytes in comparison with typical halide ones, that Li-ion conduction can be boosted by the anharmonic coupling of low-frequency Li phonon modes with high-frequency anion stretching or flexing phonon modes, rather than the low-frequency rotational modes. The coupling pushes Li ions toward the diffusion channels for reduced diffusion barriers. The result from the lower temperature range (≈0-300 K) of simulation can also be more relevant to the application of solid-state batteries.

Ion Hopping: Design Principles for Strategies to Improve Ionic Conductivity for Inorganic Solid Electrolytes

Solid electrolytes are considered as an ideal substitution of liquid electrolytes, avoiding the potential hazards of volatilization, flammability, and explosion for liquid electrolyte-based rechargeable batteries. However, there are significant performance gaps to be bridged between solid electrolytes and liquid electrolytes; one with a particular importance is the ionic conductivity which is highly dependent on the material types and structures. In this review, the general physical image of ion hopping in the crystalline structure is revisited, by highlighting two main kernels that impact ion migration: ion hopping pathways and skeletons interaction. The universal strategies to effectively improve ionic conductivity of inorganic solid electrolytes are then systematically summarized: constructing rapid diffusion pathways for mobile ions; and reducing resistance of the surrounding potential field. The scoped strategies offer an exclusive view on the working principle of ion movement regardless of the ion species, thus providing a comprehensive guidance for the future exploitation of solid electrolytes.

Lithium superionic conductors with corner-sharing frameworks

Superionic lithium conductivity has only been discovered in a few classes of materials, mostly found in thiophosphates and rarely in oxides. Herein, we reveal that corner-sharing connectivity of the oxide crystal structure framework promotes superionic conductivity, which we rationalize from the distorted lithium environment and reduced interaction between lithium and non-lithium cations. By performing a high-throughput search for materials with this feature, we discover ten new oxide frameworks predicted to exhibit superionic conductivity-from which we experimentally demonstrate LiGa(SeO₃)₂ with a bulk ionic conductivity of 0.11 mS cm^-1 and an activation energy of 0.17 eV. Our findings provide insight into the factors that govern fast lithium mobility in oxide materials and will accelerate the development of new oxide electrolytes for all-solid-state batteries.

Anharmonic Lattice Dynamics in Sodium Ion Conductors

We employ terahertz-range temperature-dependent Raman spectroscopy and first-principles lattice dynamical calculations to show that the undoped sodium ion conductors Na₃PS₄ and isostructural Na₃PSe₄ both exhibit anharmonic lattice dynamics. The anharmonic effects in the compounds involve coupled host lattice-Na⁺ ion dynamics that drive the tetragonal-to-cubic phase transition in both cases, but with a qualitative difference in the anharmonic character of the transition. Na₃PSe₄ shows an almost purely displacive character with the soft modes disappearing in the cubic phase as the change in symmetry shifts these modes to the Raman-inactive Brillouin zone boundary. Na₃PS₄ instead shows an order-disorder character in the cubic phase, with the soft modes persisting through the phase transition and remaining Raman active in the cubic phase, violating Raman selection rules for that phase. Our findings highlight the important role of coupled host lattice-mobile ion dynamics in vibrational instabilities that are coincident with the exceptional conductivity of these Na⁺ ion conductors.

Ionic Conductivity of Nanocrystalline and Amorphous Li10GeP2S12: The Detrimental Impact of Local Disorder on Ion Transport

Solids with extraordinarily high Li⁺ dynamics are key for high performance all-solid-state batteries. The thiophosphate Li₁₀GeP₂S₁₂ (LGPS) belongs to the best Li-ion conductors with an ionic conductivity exceeding 10 mS cm^–1 at ambient temperature. Recent molecular dynamics simulations performed by Dawson and Islam predict that the ionic conductivity of LGPS can be further enhanced by a factor of 3 if local disorder is introduced. As yet, no experimental evidence exists supporting this fascinating prediction. Here, we synthesized nanocrystalline LGPS by high-energy ball-milling and probed the Li⁺ ion transport parameters. Broadband conductivity spectroscopy in combination with electric modulus measurements allowed us to precisely follow the changes in Li⁺ dynamics. Surprisingly and against the behavior of other electrolytes, bulk ionic conductivity turned out to decrease with increasing milling time, finally leading to a reduction of σ_20°C by a factor of 10. ³¹P, ⁶Li NMR, and X-ray diffraction showed that ball-milling forms a structurally heterogeneous sample with nm-sized LGPS crystallites and amorphous material. At −135 °C, electrical relaxation in the amorphous regions is by 2 to 3 orders of magnitude slower. Careful separation of the amorphous and (nano)crystalline contributions to overall ion transport revealed that in both regions, Li⁺ ion dynamics is slowed down compared to untreated LGPS. Hence, introducing defects into the LGPS bulk structure via ball-milling has a negative impact on ionic transport. We postulate that such a kind of structural disorder is detrimental to fast ion transport in materials whose transport properties rely on crystallographically well-defined diffusion pathways.

Ionic Conductivity of LiSiON and the Effect of Amorphization/Heterovalent Doping on Li+ Diffusion

The search for and design of suitable superior lithium ion conductors is a key process for developing solid state batteries. In order to realize a large range of applications, we researched the ionic conductivity of LiSiON, an example oxynitride mainly composed of elements with high abundance and a similar mixed anion size. Both its amorphous and heterovalent-doped phases were studied through density functional theory simulations. The Li+ ion diffusion behaviors and related properties are discussed. These elements are abundant in nature, and we found that amorphization or doping with P obviously enhanced the ionic conductivity of the system. General strategies to improve the kinetic properties of a candidate structure are presented, to help in the design of solid state electrolytes for lithium batteries.

Opening Diffusion Pathways through Site Disorder: The Interplay of Local Structure and Ion Dynamics in the Solid Electrolyte Li6+xP1–xGexS5I as Probed by Neutron Diffraction and NMR

Solid electrolytes are at the heart of future energy storage systems. Li-bearing argyrodites are frontrunners in terms of Li⁺ ion conductivity. Although many studies have investigated the effect of elemental substitution on ionic conductivity, we still do not fully understand the various origins leading to improved ion dynamics. Here, Li_6+xP_1–xGe_xS₅I served as an application-oriented model system to study the effect of cation substitution (P⁵⁺ vs Ge⁴⁺) on Li⁺ ion dynamics. While Li₆PS₅I is a rather poor ionic conductor (10^–6 S cm^–1, 298 K), the Ge-containing samples show specific conductivities on the order of 10^–2 S cm^–1 (330 K). Replacing P⁵⁺ with Ge⁴⁺ not only causes S^2–/I^– anion site disorder but also reveals via neutron diffraction that the Li⁺ ions do occupy several originally empty sites between the Li rich cages in the argyrodite framework. Here, we used ⁷Li and ³¹P NMR to show that this Li⁺ site disorder has a tremendous effect on both local ion dynamics and long-range Li⁺ transport. For the Ge-rich samples, NMR revealed several new Li⁺ exchange processes, which are to be characterized by rather low activation barriers (0.1–0.3 eV). Consequently, in samples with high Ge-contents, the Li⁺ ions have access to an interconnected network of pathways allowing for rapid exchange processes between the Li cages. By (i) relating the changes of the crystal structure and (ii) measuring the dynamic features as a function of length scale, we were able to rationalize the microscopic origins of fast, long-range ion transport in this class of electrolytes.

Paradigms of frustration in superionic solid electrolytes

Superionic solid electrolytes have widespread use in energy devices, but the fundamental motivations for fast ion conduction are often elusive. In this Perspective, we draw upon atomistic simulations of a wide range of superionic conductors to illustrate some ways frustration can lower diffusion cation barriers in solids. Based on our studies of halides, oxides, sulfides and hydroborates and a survey of published reports, we classify three types of frustration that create competition between different local atomic preferences, thereby flattening the diffusive energy landscape. These include chemical frustration, which derives from competing factors in the anion-cation interaction; structural frustration, which arises from lattice arrangements that induce site distortion or prevent cation ordering; and dynamical frustration, which is associated with temporary fluctuations in the energy landscape due to anion reorientation or cation reconfiguration. For each class of frustration, we provide detailed simulation analyses of various materials to show how ion mobility is facilitated, resulting in stabilizing factors that are both entropic and enthalpic in origin. We propose the use of these categories as a general construct for classifying frustration in superionic conductors and discuss implications for future development of suitable descriptors and improvement strategies. This article is part of the Theo Murphy meeting issue 'Understanding fast-ion conduction in solid electrolytes'.

Paradigms of frustration in superionic solid electrolytes

Superionic solid electrolytes have widespread use in energy devices, but the fundamental motivations for fast ion conduction are often elusive. In this Perspective, we draw upon atomistic simulations of a wide range of superionic conductors to illustrate some ways frustration can lower diffusion cation barriers in solids. Based on our studies of halides, oxides, sulfides and hydroborates and a survey of published reports, we classify three types of frustration that create competition between different local atomic preferences, thereby flattening the diffusive energy landscape. These include chemical frustration, which derives from competing factors in the anion-cation interaction; structural frustration, which arises from lattice arrangements that induce site distortion or prevent cation ordering; and dynamical frustration, which is associated with temporary fluctuations in the energy landscape due to anion reorientation or cation reconfiguration. For each class of frustration, we provide detailed simulation analyses of various materials to show how ion mobility is facilitated, resulting in stabilizing factors that are both entropic and enthalpic in origin. We propose the use of these categories as a general construct for classifying frustration in superionic conductors and discuss implications for future development of suitable descriptors and improvement strategies. This article is part of the Theo Murphy meeting issue 'Understanding fast-ion conduction in solid electrolytes'.

Understanding fast-ion conduction in solid electrolytes

The ability of some solid materials to exhibit exceptionally high ionic conductivities has been known since the observations of Michael Faraday in the nineteenth century (Faraday M. 1838 Phil. Trans. R. Soc. 90), yet a detailed understanding of the atomic-scale physics that gives rise to this behaviour remains an open scientific question. This theme issue collects articles from researchers working on this question of understanding fast-ion conduction in solid electrolytes. The issue opens with two perspectives, both of which discuss concepts that have been proposed as schema for understanding fast-ion conduction. The first perspective presents an overview of a series of experimental NMR studies, and uses this to frame discussion of the roles of ion-ion interactions, crystallographic disorder, low-dimensionality of crystal structures, and fast interfacial diffusion in nanocomposite materials. The second perspective reviews computational studies of halides, oxides, sulfides and hydroborates, focussing on the concept of frustration and how this can manifest in different forms in various fast-ion conductors. The issue also includes five primary research articles, each of which presents a detailed analysis of the factors that affect microscopic ion-diffusion in specific fast-ion conducting solid electrolytes, including oxide-ion conductors [Formula: see text] and [Formula: see text], lithium-ion conductors [Formula: see text] and [Formula: see text], and the prototypical fluoride-ion conductor [Formula: see text]-[Formula: see text]. This article is part of the Theo Murphy meeting issue 'Understanding fast-ion conduction in solid electrolytes'.

Fuzzy logic: about the origins of fast ion dynamics in crystalline solids

Nuclear magnetic resonance offers a wide range of tools to analyse ionic jump processes in crystalline and amorphous solids. Both high-resolution and time-domain [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] NMR helps throw light on the origins of rapid self-diffusion in materials being relevant for energy storage. It is well accepted that [Formula: see text] ions are subjected to extremely slow exchange processes in compounds with strong site preferences. The loss of this site preference may lead to rapid cation diffusion, as is also well known for glassy materials. Further examples that benefit from this effect include, e.g. cation-mixed, high-entropy fluorides [Formula: see text], Li-bearing garnets ([Formula: see text]) and thiophosphates such as [Formula: see text]. In non-equilibrium phases site disorder, polyhedra distortions, strain and the various types of defects will affect both the activation energy and the corresponding attempt frequencies. Whereas in [Formula: see text] ([Formula: see text]) cation mixing influences F anion dynamics, in [Formula: see text] ([Formula: see text]) the potential landscape can be manipulated by anion site disorder. On the other hand, in the mixed conductor [Formula: see text] cation-cation repulsions immediately lead to a boost in [Formula: see text] diffusivity at the early stages of chemical lithiation. Finally, rapid diffusion is also expected for materials that are able to guide the ions along (macroscopic) pathways with confined (or low-dimensional) dimensions, as is the case in layer-structured [Formula: see text] or [Formula: see text]. Diffusion on fractal systems complements this type of diffusion. This article is part of the Theo Murphy meeting issue 'Understanding fast-ion conduction in solid electrolytes'.

Prospects of Integrated Photovoltaic-Fuel Cell Systems in a Hydrogen Economy: A Comprehensive Review

Integrated photovoltaic-fuel cell (IPVFC) systems, amongst other integrated energy generation methodologies are renewable and clean energy technologies that have received diverse research and development attentions over the last few decades due to their potential applications in a hydrogen economy. This article systematically updates the state-of-the-art of IPVFC systems and provides critical insights into the research and development gaps needed to be filled/addressed to advance these systems towards full commercialization. Design methodologies, renewable energy-based microgrid and off-grid applications, energy management strategies, optimizations and the prospects as self-sustaining power sources were covered. IPVFC systems could play an important role in the upcoming hydrogen economy since they depend on solar hydrogen which has almost zero emissions during operation. Highlighted herein are the advances as well as the technical challenges to be surmounted to realize numerous potential applications of IPVFC systems in unmanned aerial vehicles, hybrid electric vehicles, agricultural applications, telecommunications, desalination, synthesis of ammonia, boats, buildings, and distributed microgrid applications.

Garnet to hydrogarnet: effect of post synthesis treatment on cation substituted LLZO solid electrolyte and its effect on Li ion conductivity

We investigated why commercial Li₇La₃Zr₂O₁₂ (LLZO) with Nb- and Ta substitution shows very low mobility on a local scale, as observed with temperature-dependent NMR techniques, compared to Al and W substituted samples, although impedance spectroscopy on sintered pellets suggests something else: conductivity values do not show a strong dependence on the type of substituting cation. We observed that mechanical treatment of these materials causes a symmetry reduction from garnet to hydrogarnet structure. To understand the impact of this lower symmetric structure in detail and its effect on the Li ion conductivity, neutron powder diffraction and ⁶Li NMR were utilized. Despite the finding that, in some materials, disorder can be beneficial with respect to ionic conductivity, pulsed-field gradient NMR measurements of the long-range transport indicate a higher Li⁺ diffusion barrier in the lower symmetric hydrogarnet structure. The symmetry reduction can be reversed back to the higher symmetric garnet structure by annealing at 1100 °C. This unintended phase transition and thus a reduction in conductivity is crucial for the processing of LLZO materials in the fabrication of all-solid state batteries.

Investigation of commercial Li₇La₃Zr₂O₁₂ (LLZO) with various substituents. Although impedance spectroscopy suggests something else: the ion conductivity does not show a strong dependence on the substituting cation, but rather on the sample treatment.

Structure motif-centric learning framework for inorganic crystalline systems

Incorporation of physical principles in a machine learning (ML) architecture is a fundamental step toward the continued development of artificial intelligence for inorganic materials. As inspired by the Pauling's rule, we propose that structure motifs in inorganic crystals can serve as a central input to a machine learning framework. We demonstrated that the presence of structure motifs and their connections in a large set of crystalline compounds can be converted into unique vector representations using an unsupervised learning algorithm. To demonstrate the use of structure motif information, a motif-centric learning framework is created by combining motif information with the atom-based graph neural networks to form an atom-motif dual graph network (AMDNet), which is more accurate in predicting the electronic structures of metal oxides such as bandgaps. The work illustrates the route toward fundamental design of graph neural network learning architecture for complex materials by incorporating beyond-atom physical principles.

Mechanistic Origin of Superionic Lithium Diffusion in Anion-Disordered Li6PS5 X Argyrodites

The rational development of fast-ion-conducting solid electrolytes for all-solid-state lithium-ion batteries requires understanding the key structural and chemical principles that give some materials their exceptional ionic conductivities. For the lithium argyrodites Li6PS5X (X = Cl, Br, or I), the choice of the halide, X, strongly affects the ionic conductivity, giving room-temperature ionic conductivities for X = {Cl,Br} that are ×103 higher than for X = I. This variation has been attributed to differing degrees of S/X anion disorder. For X = {Cl,Br}, the S/X anions are substitutionally disordered, while for X = I, the anion substructure is fully ordered. To better understand the role of substitutional anion disorder in enabling fast lithium-ion transport, we have performed a first-principles molecular dynamics study of Li6PS5I and Li6PS5Cl with varying amounts of S/X anion-site disorder. By considering the S/X anions as a tetrahedrally close-packed substructure, we identify three partially occupied lithium sites that define a contiguous three-dimensional network of face-sharing tetrahedra. The active lithium-ion diffusion pathways within this network are found to depend on the S/X anion configuration. For anion-disordered systems, the active site-site pathways give a percolating three-dimensional diffusion network; whereas for anion-ordered systems, critical site-site pathways are inactive, giving a disconnected diffusion network with lithium motion restricted to local orbits around S positions. Analysis of the lithium substructure and dynamics in terms of the lithium coordination around each sulfur site highlights a mechanistic link between substitutional anion disorder and lithium disorder. In anion-ordered systems, the lithium ions are pseudo-ordered, with preferential 6-fold coordination of sulfur sites. Long-ranged lithium diffusion would disrupt this SLi6 pseudo-ordering, and is, therefore, disfavored. In anion-disordered systems, the pseudo-ordered 6-fold S-Li coordination is frustrated because of Li-Li Coulombic repulsion. Lithium positions become disordered, giving a range of S-Li coordination environments. Long-ranged lithium diffusion is now possible with no net change in S-Li coordination numbers. This gives rise to superionic lithium transport in the anion-disordered systems, effected by a concerted string-like diffusion mechanism.

Hydride-based antiperovskites with soft anionic sublattices as fast alkali ionic conductors

Most solid-state materials are composed of p-block anions, only in recent years the introduction of hydride anions (1s²) in oxides (e.g., SrVO₂H, BaTi(O,H)₃) has allowed the discovery of various interesting properties. Here we exploit the large polarizability of hydride anions (H^-) together with chalcogenide (Ch^2-) anions to construct a family of antiperovskites with soft anionic sublattices. The M₃HCh antiperovskites (M = Li, Na) adopt the ideal cubic structure except orthorhombic Na₃HS, despite the large variation in sizes of M and Ch. This unconventional robustness of cubic phase mainly originates from the large size-flexibility of the H^- anion. Theoretical and experimental studies reveal low migration barriers for Li⁺/Na⁺ transport and high ionic conductivity, possibly promoted by a soft phonon mode associated with the rotational motion of HM₆ octahedra in their cubic forms. Aliovalent substitution to create vacancies has further enhanced ionic conductivities of this series of antiperovskites, resulting in Na_2.9H(Se_0.9I_0.1) achieving a high conductivity of ~1 × 10^-4 S/cm (100 °C).

Designing disorder into crystalline materials

Crystals are a state of matter characterized by periodic order. Yet, crystalline materials can harbour disorder in many guises, such as non-repeating variations in composition, atom displacements, bonding arrangements, molecular orientations, conformations, charge states, orbital occupancies or magnetic structure. Disorder can sometimes be random but, more usually, it is correlated. Frontier research into disordered crystals now seeks to control and exploit the unusual patterns that persist within these correlated disordered states in order to access functional responses inaccessible to conventional crystals. In this Review, we survey the core design principles that guide targeted control over correlated disorder. We show how these principles - often informed by long-studied statistical mechanical models - can be applied across an unexpectedly broad range of materials, including organics, supramolecular assemblies, oxide ceramics and metal-organic frameworks. We conclude with a forward-looking discussion of the exciting link between disorder and function in responsive media, thermoelectrics and topological phases.

Rapid Low-Dimensional Li+ Ion Hopping Processes in Synthetic Hectorite-Type Li0.5[Mg2.5Li0.5]Si4O10F2

Understanding the origins of fast ion transport in solids is important to develop new ionic conductors for batteries and sensors. Nature offers a rich assortment of rather inspiring structures to elucidate these origins. In particular, layer-structured materials are prone to show facile Li+ transport along their inner surfaces. Here, synthetic hectorite-type Li0.5[Mg2.5Li0.5]Si4O10F2, being a phyllosilicate, served as a model substance to investigate Li+ translational ion dynamics by both broadband conductivity spectroscopy and diffusion-induced 7Li nuclear magnetic resonance (NMR) spin-lattice relaxation experiments. It turned out that conductivity spectroscopy, electric modulus data, and NMR are indeed able to detect a rapid 2D Li+ exchange process governed by an activation energy as low as 0.35 eV. At room temperature, the bulk conductivity turned out to be in the order of 0.1 mS cm-1. Thus, the silicate represents a promising starting point for further improvements by crystal chemical engineering. To the best of our knowledge, such a high Li+ ionic conductivity has not been observed for any silicate yet.

Li diffusion in Si and LiSi: Nuclear quantum effects and anharmonicity

The diffusion of Li in bulk Si and crystalline LiSi is investigated over a wide range of temperatures employing first-principles calculations based on density functional theory, transition state theory, and the kinetic Monte Carlo method. Nuclear quantum effects are incorporated by computing the vibrational spectrum and its effect on the effective energy barrier. The Li diffusion coefficient in bulk Si calculated with such quantum effects is ∼33% lower than the classical limit near room temperature due to higher effective energy barrier and tends to the classical limit at a high temperature (>1000 K). The presence of anharmonicity, estimated by the quasiharmonic approximation and the cBΩ model, increases the diffusion coefficient by ∼60%. For Li diffusion in LiSi with multiple vacancy jumps, we obtain an effective diffusion barrier of 0.27 eV ± 0.01 eV. In the Li-Si system, the quantum mechanical effects are only marginally significant at room temperature.

Finding the Right Blend: Interplay Between Structure and Sodium Ion Conductivity in the System Na5AlS4-Na4SiS4

The rational design of high performance sodium solid electrolytes is one of the key challenges in modern battery research. In this work, we identify new sodium ion conductors in the substitution series Na_5-xAl_1-xSi_xS4 (0 ≤ x ≤ 1), which are entirely based on earth-abundant elements. These compounds exhibit conductivities ranging from 1.64 · 10⁻⁷ for Na₄SiS₄ to 2.04 · 10⁻⁵ for Na_8.5(AlS₄)_0.5(SiS₄)_1.5 (x = 0.75). We determined the crystal structures of the Na⁺-ion conductors Na₄SiS₄ as well as hitherto unknown Na₅AlS₄ and Na₉(AlS₄)(SiS₄). Na⁺-ion conduction pathways were calculated by bond valence energy landscape (BVEL) calculations for all new structures highlighting the influence of the local coordination symmetry of sodium ions on the energy landscape within this family. Our findings show that the interplay of charge carrier concentration and low site symmetry of sodium ions can enhance the conductivity by several orders of magnitude.

Li-Ion Cooperative Migration and Oxy-Sulfide Synergistic Effect in Li14 P2 Ge2 S16-6 x Ox Solid-State-Electrolyte Enables Extraordinary Conductivity and High Stability

Critical to the development of all-solid-state lithium-ion batteries technology are novel solid-state electrolytes with high ionic conductivity and robust stability under inorganic solid-electrolyte operating conditions. Herein, by using density functional theory and molecular dynamics, a mixed oxygen-sulfur-based Li-superionic conductor is screened out from the local chemical structure of β-Li₃ PS₄ to discover novel Li₁₄ P₂ Ge₂ S₈ O₈ (LPGSO) with high ionic conductivity and high stability under thermal, moist, and electrochemical conditions, which causes oxygenation at specific sites to improve the stability and selective sulfuration to provide an O-S mixed path by Li-S/O structure units with coordination number between 3 and 4 for fast Li-cooperative conduction. Furthermore, LPGSO exhibits a quasi-isotropic 3D Li-ion cooperative diffusion with a lesser migration barrier (≈0.19 eV) compared to its sulfide-analog Li₁₄ P₂ Ge₂ S₁₆ . The theoretical ionic conductivity of this conductor at room temperature is as high as ≈30.0 mS cm^-1 , which is among the best in current solid-state electrolytes. Such an oxy-sulfide synergistic effect and Li-ion cooperative migration mechanism would enable the engineering of next-generation electrolyte materials with desirable safety and high ionic conductivity, for possible application in the near future.

Anharmonic lattice dynamics and superionic transition in AgCrSe2

Intrinsically low lattice thermal conductivity ([Formula: see text]) in superionic conductors is of great interest for energy conversion applications in thermoelectrics. Yet, the complex atomic dynamics leading to superionicity and ultralow thermal conductivity remain poorly understood. Here, we report a comprehensive study of the lattice dynamics and superionic diffusion in [Formula: see text] from energy- and momentum-resolved neutron and X-ray scattering techniques, combined with first-principles calculations. Our results settle unresolved questions about the lattice dynamics and thermal conduction mechanism in [Formula: see text] We find that the heat-carrying long-wavelength transverse acoustic (TA) phonons coexist with the ultrafast diffusion of Ag ions in the superionic phase, while the short-wavelength nondispersive TA phonons break down. Strong scattering of phonon quasiparticles by anharmonicity and Ag disorder are the origin of intrinsically low [Formula: see text] The breakdown of short-wavelength TA phonons is directly related to the Ag diffusion, with the vibrational spectral weight associated to Ag oscillations evolving into stochastic decaying fluctuations. Furthermore, the origin of fast ionic diffusion is shown to arise from extended flat basins in the energy landscape and collective hopping behavior facilitated by strong repulsion between Ag ions. These results provide fundamental insights into the complex atomic dynamics of superionic conductors.