Tracking Ions the Direct Way: Long-Range Li+ Dynamics in the Thio-LISICON Family Li4MCh4 (M = Sn, Ge; Ch = S, Se) as Probed by 7Li NMR Relaxometry and 7Li Spin-Alignment Echo NMR

Tracking Li atoms in real-time with ultra-fast NMR simulations

We present for the first time a multiscale machine learning approach to jointly simulate atomic structure and dynamics with the corresponding solid state Nuclear Magnetic Resonance (ssNMR) observables. We study the use-case of spin-alignment echo (SAE) NMR for exploring Li-ion diffusion within the solid state electrolyte material Li3PS4 (LPS) by calculating quadrupolar frequencies of 7Li. SAE NMR probes long-range dynamics down to microsecond-timescale hopping processes. Therefore only a few machine learning force field schemes are able to capture the time- and length scales required for accurate comparison with experimental results. By using a new class of machine learning interatomic potentials, known as ultra-fast potentials (UFPs), we are able to efficiently access timescales beyond the microsecond regime. In tandem, we have developed a machine learning model for predicting the full 7Li electric field gradient (EFG) tensors in LPS. By combining the long timescale trajectories from the UFP with our model for 7Li EFG tensors, we are able to extract the autocorrelation function (ACF) for 7Li quadrupolar frequencies during Li diffusion. We extract the decay constants from the ACF for both crystalline β-LPS and amorphous LPS, and find that the predicted Li hopping rates are on the same order of magnitude as those predicted from the Li dynamics. This demonstrates the potential for machine learning to finally make predictions on experimentally relevant timescales and temperatures, and opens a new avenue of NMR crystallography: using machine learning dynamical NMR simulations for accessing polycrystalline and glass ceramic materials.

Revealing the Local Structure and Dynamics of the Solid Li Ion Conductor Li3P5O14

The development of fast Li ion-conducting materials for use as solid electrolytes that provide sufficient electrochemical stability against electrode materials is paramount for the future of all-solid-state batteries. Advances on these fast ionic materials are dependent on building structure-ionic mobility-function relationships. Here, we exploit a series of multinuclear and multidimensional nuclear magnetic resonance (NMR) approaches, including 6Li and 31P magic angle spinning (MAS), in conjunction with density functional theory (DFT) to provide a detailed understanding of the local structure of the ultraphosphate Li3P5O14, a promising candidate for an oxide-based Li ion conductor that has been shown to be a highly conductive, energetically favorable, and electrochemically stable potential solid electrolyte. We have reported a comprehensive assignment of the ultraphosphate layer and layered Li6O16 26- chains through 31P and 6Li MAS NMR, respectively, in conjunction with DFT. The chemical shift anisotropy of the eight resonances with the lowest 31P chemical shift is significantly lower than that of the 12 remaining resonances, suggesting the phosphate bonding nature of these P sites being one that bridges to three other phosphate groups. We employed a number of complementary 6,7Li NMR techniques, including MAS variable-temperature line narrowing spectra, spin-alignment echo (SAE) NMR, and relaxometry, to quantify the lithium ion dynamics in Li3P5O14. Detailed analysis of the diffusion-induced spin-lattice relaxation data allowed for experimental verification of the three-dimensional Li diffusion previously proposed computationally. The 6Li NMR relaxation rates suggest sites Li1 and Li5 (the only five-coordinate Li site) are the most mobile and are adjacent to one another, both in the a-b plane (intralayer) and on the c-axis (interlayer). As shown in the 6Li-6Li exchange spectroscopy NMR spectra, sites Li1 and Li5 likely exchange with one another both between adjacent layered Li6O16 26- chains and through the center of the P12O36 12- rings forming the three-dimensional pathway. The understanding of the Li ion mobility pathways in high-performing solid electrolytes outlines a route for further development of such materials to improve their performance.

Correlating local structure and migration dynamics in Na/Li dual ion conductor Na5YSi4O12

Na5YSi4O12 (NYSO) is demonstrated as a promising electrolyte with high ionic conductivity and low activation energy for practical use in solid Na-ion batteries. Solid-state NMR was employed to identify the six types of coordination of Na+ ions and migration pathway, which is vital to master working mechanism and enhance performance. The assignment of each sodium site is clearly determined from high-quality 23Na NMR spectra by the aid of Density Functional Theory calculation. Well-resolved 23Na exchangespectroscopy and electrochemical tracer exchange spectra provide the first experimental evidence to show the existence of ionic exchange between sodium at Na5 and Na6 sites, revealing that Na transport route is possibly along three-dimensional chain of open channel-Na4-open channel. Variable-temperature NMR relaxometry is developed to evaluate Na jump rates and self-diffusion coefficient to probe the sodium-ion dynamics in NYSO. Furthermore, NYSO works well as a dual ion conductor in Na and Li metal batteries with Na3V2(PO4)3 and LiFePO4 as cathodes, respectively.

The glass phase in the grain boundary of Na3Zr2Si2PO12, created by gallium modulation

Na3Zr2Si2PO12 has been proven to be a promising electrolyte for solid-state sodium batteries. However, its poor conductivity prevents application, caused by the large ionic resistance created by the grain boundary. Herein, we propose an additional glass phase (Na-Ga-Si-P-O phase) to connect the grain boundary via Ga ion introduction, resulting in enhanced sodium-ion conduction and electrochemical performance. The optimized Na3Zr2Si2PO12-0.15Ga electrolyte exhibits Na+ conductivity of 1.65 mS cm-1 at room temperature and a low activation energy of 0.16 eV, with 20% newly formed glass phase enclosing the grain boundary. Temperature-dependent NMR line shapes and spin-lattice relaxation were used to estimate the Na self-diffusion and Na ion hopping. The dense glass-ceramic electrolyte design strategy and the structure-dynamics-property correlation from NMR, can be extended to the optimization of other materials.

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.

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'.

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'.

Independent component analysis combined with Laplace inversion of spectrally resolved spin-alignment echo/T 1 3D 7Li NMR of superionic Li10GeP2S12

The use of independent component analysis (ICA) for the analysis of two-dimensional (2D) spin-alignment echo–T 1 7Li NMR correlation data with transient echo detection as a third dimension is demonstrated for the superionic conductor Li10GeP2S12 (LGPS). ICA was combined with Laplace inversion, or discrete inverse Laplace transform (ILT), to obtain spectrally resolved 2D correlation maps. Robust results were obtained with the spectra as well as the vectorized correlation maps as independent components. It was also shown that the order of ICA and ILT steps can be swapped. While performing the ILT step before ICA provided better contrast, a substantial data compression can be achieved if ICA is executed first. Thereby the overall computation time could be reduced by one to two orders of magnitude, since the number of computationally expensive ILT steps is limited to the number of retained independent components. For LGPS, it was demonstrated that physically meaningful independent components and mixing matrices are obtained, which could be correlated with previously investigated material properties yet provided a clearer, better separation of features in the data. LGPS from two different batches was investigated, which showed substantial differences in their spectral and relaxation behavior. While in both cases this could be attributed to ionic mobility, the presented analysis may also clear the way for a more in-depth theoretical analysis based on numerical simulations. The presented method appears to be particularly suitable for samples with at least partially resolved static quadrupolar spectra, such as alkali metal ions in superionic conductors. The good stability of the ICA analysis makes this a prospect algorithm for preprocessing of data for a subsequent automatized analysis using machine learning concepts.

Different Chemical Environments of [Ge4Se10]4- in the Li+ Compounds [Li4(H2O)16][Ge4Se10]·4.33H2O, [{Li4(thf)12}Ge4Se10], and [Li2(H2O)8][MnGe4Se10], and Ionic Conductivity of Underlying "Li4Ge4Se10"

The crystalline selenido germanates [Li₄(H₂O)₁₆][Ge₄Se₁₀]·4.3H₂O (1), [{Li₄(thf)₁₂}Ge₄Se₁₀] (2), and [Li₂(H₂O)₈][MnGe₄Se₁₀] (3) (thf = THF = tetrahydrofuran) were obtained by an extraction of a glassy ternary phase of the nominal composition Li₄Ge₄Se₁₀ (=Li₂S·2GeSe₂) with water (1) or THF (2) and slow evaporation of the solvent or by being layered with MnBr₂ in H₂O/MeOH (3), respectively. The compounds contain known selenido germanate anions, however, for the first time with Li⁺ counterions. This is especially remarkable for the prominent _∞³{[MnGe₄Se₁₀]^2-} open-framework structure, which was reported to crystallize with (NMe₄)⁺, Cs⁺, Rb⁺, and K⁺ counterions, but it has not yet been realized with the smallest alkali metal cation. Impedance spectroscopic studies on Li₄Ge₄Se₁₀ classify the glassy solid as a moderate Li⁺ ion conductor.