Lattice-geometry effects in garnet solid electrolytes: a lattice-gas Monte Carlo simulation study

Accurate Estimation of Diffusion Coefficients and their Uncertainties from Computer Simulation

Self-diffusion coefficients, D*, are routinely estimated from molecular dynamics simulations by fitting a linear model to the observed mean squared displacements (MSDs) of mobile species. MSDs derived from simulations exhibit statistical noise that causes uncertainty in the resulting estimate of D*. An optimal scheme for estimating D* minimizes this uncertainty, i.e., it will have high statistical efficiency, and also gives an accurate estimate of the uncertainty itself. We present a scheme for estimating D* from a single simulation trajectory with a high statistical efficiency and accurately estimating the uncertainty in the predicted value. The statistical distribution of MSDs observable from a given simulation is modeled as a multivariate normal distribution using an analytical covariance matrix for an equivalent system of freely diffusing particles, which we parametrize from the available simulation data. We use Bayesian regression to sample the distribution of linear models that are compatible with this multivariate normal distribution to obtain a statistically efficient estimate of D* and an accurate estimate of the associated statistical uncertainty.

On the Discrepancy between Local and Average Structure in the Fast Na+ Ionic Conductor Na2.9Sb0.9W0.1S4

Aliovalent substitution is a common strategy to improve the ionic conductivity of solid electrolytes for solid-state batteries. The substitution of SbS₄^3- by WS₄^2- in Na_2.9Sb_0.9W_0.1S₄ leads to a very high ionic conductivity of 41 mS cm^-1 at room temperature. While pristine Na₃SbS₄ crystallizes in a tetragonal structure, the substituted Na_2.9Sb_0.9W_0.1S₄ crystallizes in a cubic phase at room temperature based on its X-ray diffractogram. Here, we show by performing pair distribution function analyses and static single-pulse ¹²¹Sb NMR experiments that the short-range order of Na_2.9Sb_0.9W_0.1S₄ remains tetragonal despite the change in the Bragg diffraction pattern. Temperature-dependent Raman spectroscopy revealed that changed lattice dynamics due to the increased disorder in the Na⁺ substructure leads to dynamic sampling causing the discrepancy in local and average structure. While showing no differences in the local structure, compared to pristine Na₃SbS₄, quasi-elastic neutron scattering and solid-state ²³Na nuclear magnetic resonance measurements revealed drastically improved Na⁺ diffusivity and decreased activation energies for Na_2.9Sb_0.9W_0.1S₄. The obtained diffusion coefficients are in very good agreement with theoretical values and long-range transport measured by impedance spectroscopy. This work demonstrates the importance of studying the local structure of ionic conductors to fully understand their transport mechanisms, a prerequisite for the development of faster ionic conductors.

Pushing Forward Simulation Techniques of Ion Transport in Ion Conductors for Energy Materials

Simulation techniques are crucial to establish a firm link between phenomena occurring at the atomic scale and macroscopic observations of functional materials. Importantly, extensive sampling of space and time scales is paramount to ensure good convergence of physically relevant quantities to describe ion transport in energy materials. Here, a number of simulation methods to address ion transport in energy materials are discussed, with the pros and cons of each methodology put forward. Emphasis is given to the stochastic nature of results produced by kinetic Monte Carlo, which can adequately account for compositional disorder across multiple sublattices in solids.

Toward Understanding of the Li-Ion Migration Pathways in the Lithium Aluminum Sulfides Li3AlS3 and Li4.3AlS3.3Cl0.7 via 6,7Li Solid-State Nuclear Magnetic Resonance Spectroscopy

Li-containing materials providing fast ion transport pathways are fundamental in Li solid electrolytes and the future of all-solid-state batteries. Understanding these pathways, which usually benefit from structural disorder and cation/anion substitution, is paramount for further developments in next-generation Li solid electrolytes. Here, we exploit a range of variable temperature ⁶Li and ⁷Li nuclear magnetic resonance approaches to determine Li-ion mobility pathways, quantify Li-ion jump rates, and subsequently identify the limiting factors for Li-ion diffusion in Li₃AlS₃ and chlorine-doped analogue Li_4.3AlS_3.3Cl_0.7. Static ⁷Li NMR line narrowing spectra of Li₃AlS₃ show the existence of both mobile and immobile Li ions, with the latter limiting long-range translational ion diffusion, while in Li_4.3AlS_3.3Cl_0.7, a single type of fast-moving ion is present and responsible for the higher conductivity of this phase. ⁶Li-⁶Li exchange spectroscopy spectra of Li₃AlS₃ reveal that the slower moving ions hop between non-equivalent Li positions in different structural layers. The absence of the immobile ions in Li_4.3AlS_3.3Cl_0.7, as revealed from ⁷Li line narrowing experiments, suggests an increased rate of ion exchange between the layers in this phase compared with Li₃AlS₃. Detailed analysis of spin-lattice relaxation data allows extraction of Li-ion jump rates that are significantly increased for the doped material and identify Li mobility pathways in both materials to be three-dimensional. The identification of factors limiting long-range translational Li diffusion and understanding the effects of structural modification (such as anion substitution) on Li-ion mobility provide a framework for the further development of more highly conductive Li solid electrolytes.

Fundamental investigations on the sodium-ion transport properties of mixed polyanion solid-state battery electrolytes

Lithium and sodium (Na) mixed polyanion solid electrolytes for all-solid-state batteries display some of the highest ionic conductivities reported to date. However, the effect of polyanion mixing on the ion-transport properties is still not fully understood. Here, we focus on Na1+xZr2SixP3-xO12 (0 ≤ x ≤ 3) NASICON electrolyte to elucidate the role of polyanion mixing on the Na-ion transport properties. Although NASICON is a widely investigated system, transport properties derived from experiments or theory vary by orders of magnitude. We use more than 2000 distinct ab initio-based kinetic Monte Carlo simulations to map the compositional space of NASICON over various time ranges, spatial resolutions and temperatures. Via electrochemical impedance spectroscopy measurements on samples with different sodium content, we find that the highest ionic conductivity (i.e., about 0.165 S cm-1 at 473 K) is experimentally achieved in Na3.4Zr2Si2.4P0.6O12, in line with simulations (i.e., about 0.170 S cm-1 at 473 K). The theoretical studies indicate that doped NASICON compounds (especially those with a silicon content x ≥ 2.4) can improve the Na-ion mobility compared to undoped NASICON compositions.

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'.

Impacts of vacancy-induced polarization and distortion on diffusion in solid electrolyte Li3OCl

Lithium-rich oxychloride antiperovskites are promising solid electrolytes for enabling next-generation batteries. Here, we report a comprehensive study varying Li⁺ concentrations in [Formula: see text] using ab initio molecular dynamics simulations. The simulations accurately capture the complex interactions between Li⁺ vacancies ([Formula: see text]), the dominant mobile species in [Formula: see text]. The [Formula: see text] polarize and distort the host lattice, inducing additional non-vacancy-mediated diffusion mechanisms and correlated diffusion events that reduce the activation energy barrier at concentrations as low as 1.5% [Formula: see text]. Our analyses of discretized diffusion events in both space and time illustrate the critical interplay between correlated dynamics, polarization and local distortion in promoting ionic conductivity in [Formula: see text]. 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'.

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.

Measurements of the size and correlations between ions using an electrolytic point contact

The size of an ion affects everything from the structure of water to life itself. In this report, to gauge their size, ions dissolved in water are forced electrically through a sub-nanometer-diameter pore spanning a thin membrane and the current is measured. The measurements reveal an ion-selective conductance that vanishes in pores <0.24 nm in diameter-the size of a water molecule-indicating that permeating ions have a grossly distorted hydration shell. Analysis of the current noise power spectral density exposes a threshold, below which the noise is independent of current, and beyond which it increases quadratically. This dependence proves that the spectral density, which is uncorrelated below threshold, becomes correlated above it. The onset of correlations for Li+, Mg2+, Na+ and K+-ions extrapolates to pore diameters of 0.13 ± 0.11 nm, 0.16 ± 0.11 nm, 0.22 ± 0.11 nm and 0.25 ± 0.11 nm, respectively-consonant with diameters at which the conductance vanishes and consistent with ions moving through the sub-nanopore with distorted hydration shells in a correlated way.

Inducing High Ionic Conductivity in the Lithium Superionic Argyrodites Li6+ xP1- xGe xS5I for All-Solid-State Batteries

Solid-state batteries with inorganic solid electrolytes are currently being discussed as a more reliable and safer future alternative to the current lithium-ion battery technology. To compete with state-of-the-art lithium-ion batteries, solid electrolytes with higher ionic conductivities are needed, especially if thick electrode configurations are to be used. In the search for optimized ionic conductors, the lithium argyrodites have attracted a lot of interest. Here, we systematically explore the influence of aliovalent substitution in Li_{6+ x}P_{1- x}Ge _xS₅I using a combination of X-ray and neutron diffraction, as well as impedance spectroscopy and nuclear magnetic resonance. With increasing Ge content, an anion site disorder is induced and the activation barrier for ionic motion drops significantly, leading to the fastest lithium argyrodite so far with 5.4 ± 0.8 mS cm^-1 in a cold-pressed state and 18.4 ± 2.7 mS cm^-1 upon sintering. These high ionic conductivities allow for successful implementation within a thick-electrode solid-state battery that shows negligible capacity fade over 150 cycles. The observed changes in the activation barrier and changing site disorder provide an additional approach toward designing better performing solid electrolytes.

Ustinov A, Sergienko VI. Effect of Hf-doping on electrochemical performance of anatase TiO2 as an anode material for lithium storage

Hafnium-doped titania (Hf/Ti = 0.01; 0.03; 0.05) had been facilely synthesized via a template sol-gel method on carbon fibre. Physico-chemical properties of the as-synthesized materials were characterized by X-ray diffraction, Raman spectroscopy, scanning electron microscopy, energy-dispersive X-ray analysis, scanning transmission electron microscopy, X-ray photoelectron spectroscopy, thermogravimetry analysis and Brunauer-Emmett-Teller measurements. It was confirmed that Hf4+ substitute in the Ti4+ sites, forming Ti1-x Hf x O2 (x = 0.01; 0.03; 0.05) solid solutions with an anatase crystal structure. The Ti1-x Hf x O2 materials are hollow microtubes (length of 10-100 µm, outer diameter of 1-5 µm) composed of nanoparticles (average size of 15-20 nm) with a surface area of 80-90 m2 g-1 and pore volume of 0.294-0.372 cm3 g-1. The effect of Hf ion incorporation on the electrochemical behaviour of anatase TiO2 in the Li-ion battery anode was investigated by galvanostatic charge/discharge and electrochemical impedance spectroscopy. It was established that Ti0.95Hf0.05O2 shows significantly higher reversibility (154.2 mAh g-1) after 35-fold cycling at a C/10 rate in comparison with undoped titania (55.9 mAh g-1). The better performance offered by Hf4+ substitution of the Ti4+ into anatase TiO2 mainly results from a more open crystal structure, which has been achieved via the difference in ionic radius values of Ti4+ (0.604 Å) and Hf4+ (0.71 Å). The obtained results are in good accord with those for anatase TiO2 doped with Zr4+ (0.72 Å), published earlier. Furthermore, improved electrical conductivity of Hf-doped anatase TiO2 materials owing to charge redistribution in the lattice and enhanced interfacial lithium storage owing to increased surface area directly depending on the Hf/Ti atomic ratio have a beneficial effect on electrochemical properties.