Simple modeling of dipolar coupled 7Li spins and stimulated-echo spectroscopy of single-crystalline beta-eucryptite

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

Solid electrolytes are key elements for next-generation energy storage systems. To design powerful electrolytes with high ionic conductivity, we need to improve our understanding of the mechanisms that are at the heart of the rapid ion exchange processes in solids. Such an understanding also requires evaluation and testing of methods not routinely used to characterize ion conductors. Here, the ternary Li₄MCh₄ system (M = Ge, Sn; Ch = Se, S) provides model compounds to study the applicability of ⁷Li nuclear magnetic resonance (NMR) spin-alignment echo (SAE) spectroscopy to probe slow Li⁺ exchange processes. Whereas the exact interpretation of conventional spin-lattice relaxation data depends on models, SAE NMR offers a model-independent, direct access to motional correlation rates. Indeed, the jump rates and activation energies deduced from time-domain relaxometry data perfectly agree with results from ⁷Li SAE NMR. In particular, long-range Li⁺ diffusion in polycrystalline Li₄SnS₄ as seen by NMR in a dynamic range covering 6 orders of magnitude is determined by an activation energy of E _a = 0.55 eV and a pre-exponential factor of 3 × 10¹³ s^-1. The variation in E _a and 1/τ₀ is related to the LiCh₄ volume that changes within the four Li₄MCh₄ compounds studied. The corresponding volume of Li₄SnS₄ seems to be close to optimum for Li⁺ diffusivity.

Lithium ion dynamics in LiZr2(PO4)3 and Li1.4Ca0.2Zr1.8(PO4)3

High ionic conductivity, electrochemical stability and small interfacial resistances against Li metal anodes are the main requirements to be fulfilled in powerful, next-generation all-solid-state batteries. Understanding ion transport in materials with sufficiently high chemical and electrochemical stability, such as rhombohedral LiZr2(PO4)3, is important to further improve their properties with respect to translational Li ion dynamics. Here, we used broadband impedance spectroscopy to analyze the electrical responses of LiZr2(PO4)3 and Ca-stabilized Li1.4Ca0.2Zr1.8(PO4)3 that were prepared following a solid-state synthesis route. We investigated the influence of the starting materials, either ZrO2 and Zr(CH3COO)4, on the final properties of the products and studied Li ion dynamics in the crystalline grains and across grain boundary (g.b.) regions. The Ca2+ content has only little effect on bulk properties (4.2 × 10-5 S cm-1 at 298 K, 0.41 eV), but, fortunately, the g.b. resistance decreased by 2 orders of magnitude. Whereas, 7Li spin-alignment echo nuclear magnetic resonance (NMR) confirmed long-range ion transport as seen by conductivity spectroscopy, 7Li NMR spin-lattice relaxation revealed much smaller activation energies (0.18 eV) and points to rapid localized Li jump processes. The diffusion-induced rate peak, appearing at T = 282 K, shows Li+ exchange processes with rates of ca. 109 s-1 corresponding, formally, to ionic conductivities in the order of 10-3 S cm-1 to 10-2 S cm-1.

Experimental evidence for the relaxation coupling of all longitudinal 7Li magnetization orders in the superionic conductor Li10GeP2S12

This contribution addresses the experimental proof of the relaxation coupling of the ⁷Li (I = 3/2) longitudinal magnetization orders in the solid-state electrolyte Li₁₀GeP₂S₁₂ (LGPS). This effect was theoretically described by Korb and Petit in 1988 but has not yet been shown experimentally. In a 2D-T₁/spin-alignment echo (SAE) experiment, the inverse Laplace transformation of the spectral component over two time dimensions revealed the asymmetric course of the spin-lattice relaxation following from the coupling of all longitudinal orders. These observations were supported by Multi-quantum-filter experiments and by simulations of the 2D-T₁/SAE experiment with a lithium spin system. Since the asymmetric relaxation effects are directly dependent on the velocities and degrees of freedom of ion motion they could be used especially in fast Li-ion conductors as a separation tool for environments with different mobility processes.

Investigation of the Li-ion conduction behavior in the Li10GeP2S12 solid electrolyte by two-dimensional T1-spin alignment echo correlation NMR

Li₁₀GeP₂S₁₂ (LGPS) is the fastest known Li-ion conductor to date due to the formation of one-dimensional channels with a very high Li mobility. A knowledge-based optimization of such materials for use, for example, as solid electrolyte in all-solid-state batteries requires, however, a more comprehensive understanding of Li ion conduction that considers mobility in all three dimensions, mobility between crystallites and different phases, as well as their distributions within the material. The spin alignment echo (SAE) nuclear magnetic resonance (NMR) technique is suitable to directly probe slow Li ion hops with correlation times down to about 10^-5 s, but distinction between hopping time constants and relaxation processes may be ambiguous. This contribution presents the correlation of the ⁷Li spin lattice relaxation (SLR) time constants (T₁) with the SAE decay time constant τ_c to distinguish between hopping time constants and signal decay limited by relaxation in the τ_c distribution. A pulse sequence was employed with two independently varied mixing times. The obtained multidimensional time domain data was processed with an algorithm for discrete Laplace inversion that does not use a non-negativity constraint to deliver 2D SLR-SAE correlation maps. Using the full echo transient, it was also possible to estimate the NMR spectrum of the Li ions responsible for each point in the correlation map. The signal components were assigned to different environments in the LGPS structure.

Four-time 7Li stimulated-echo spectroscopy for the study of dynamic heterogeneities: Application to lithium borate glass

To study the nature of the nonexponential ionic hopping in solids a pulse sequence was developed that yields four-time stimulated-echo functions of previously inaccessible spin-3/2-nuclei such as ⁷Li. It exploits combined Zeeman and octupolar order as longitudinal carrier state. Higher-order correlation functions were successfully generated for natural-abundance and isotopically-enriched lithium diborate glasses. Four-time ⁷Li measurements are presented and compared with two-time correlation functions. The results are discussed with reference to approaches devised to quantify the degree of nonexponentiality in glass forming systems and evidence for the occurrence of dynamic heterogeneities and dynamic exchange were found. Additional experiments using the ⁶Li species illustrate the challenge posed by subensemble selection when the dipolar interactions are not very much smaller than the quadrupolar ones.

Nanostructured Ceramics: Ionic Transport and Electrochemical Activity

Ceramics with nm-sized dimensions are widely used in various applications such as batteries, fuel cells or sensors. Their oftentimes superior electrochemical properties as well as their capabilities to easily conduct ions are, however, not completely understood. Depending on the method chosen to prepare the materials, nanostructured ceramics may be equipped with a large area fraction of interfacial regions that exhibit structural disorder. Elucidating the relationship between microscopic disorder and ion dynamics as well as electrochemical performance is necessary to develop new functionalized materials. Here, we highlight some of the very recent studies on ion transport and electrochemical properties of nanostructured ceramics. Emphasis is put on TiO

Observing different modes of mobility in lithium titanate spinel by nuclear magnetic resonance

Using a newly developed analysis method for SAE NMR andab initiocalculations we show the formation of localized high-mobility domains in lithium titanate that influence its global ion mobility.

Quadrupolar transients, cosine correlation functions, and two-dimensional exchange spectra of non-selectively excited spin-3/2 nuclei: A (7)Li NMR study of the superionic conductor lithium indium phosphate

Cos-cos stimulated echoes of non-selectively excited spin-3/2 nuclei were not exploited in studies of slow motional processes in solids and solid-like samples, so far. Based on a theoretical analysis of the quadrupolar transients which hitherto obviously precluded the application of such echoes, their utility is demonstrated for the example of (7)Li NMR on the polycrystalline fast ion conductor lithium indium phosphate. Quadrupolar transients can adversely affect the shape of two- and three-pulse echo spectra and strategies are successfully tested that mitigate their impact. Furthermore, by means of suitably adapted cos-cos echo sequences an effective suppression of central-line contributions to the NMR spectra is achieved. By combining cos-cos and sin-sin datasets static two-dimensional exchange spectra were recorded that display quadrupolarly modulated off-diagonal intensity indicative of ionic motion.

Second-order quadrupole interaction based detection of ultra-slow motions: Tensor operator framework for central-transition spectroscopy and the dynamics in hexagonal ice as an experimental example

The second-order quadrupolar broadening of the central transition of nuclear probes with half-integer spins I is demonstrated to be useful to detect ultraslow molecular motions. On the basis of density matrix calculations explicit expressions are derived for quadrupolarly modulated sin-sin and cos-cos signals of selectively excited nuclei with I=3/2, 5/2, 7/2, and 9/2. These correlation functions are suitable for implementation in two-dimensional exchange spectroscopy as well as for stimulated-echo experiments. As an application, ¹⁷O measurements of the reorientational correlation function of water molecules in hexagonal ice are presented.

Local-field approximation of homonuclear dipolar interactions in ⁷Li-NMR: density-matrix calculations and random-walk simulations tested by echo experiments on borate glasses

NMR echo techniques have proven to be important to study dynamics in ion conductors and other solid materials. Using the spin-3/2 nucleus (7)Li as a probe, both the quadrupolar and the often neglected homonuclear dipolar interactions modulate the NMR frequency as the ion performs jump processes. Retaining only the local-field term of the many-body Hamiltonian, the impact of the dipolar interaction on various echo experiments was studied using spin dynamics calculations yielding products of dipolar and quadrupolar correlation functions. Using a simple stochastic model these functions were simulated with particular emphasis on the impact of ionic motions and on the conditions under which the dipolar and quadrupolar contributions factorize. The results of the computations and of the random-walk simulations are compared with experimental data obtained for various lithium borate and lithium borophosphate glasses. It is concluded that the local-field approximation is a useful means of treating the Li-Li dipole interactions and that the simple model that we introduce is capable of describing many experimentally observed features. Furthermore, because the dipolar and quadrupolar contributions essentially factorize, a selective determination of the corresponding correlation functions becomes possible.

Extremely slow Li ion dynamics in monoclinic Li2TiO3--probing macroscopic jump diffusion via 7Li NMR stimulated echoes

A thorough understanding of ion dynamics in solids, which is a vital topic in modern materials and energy research, requires the investigation of diffusion properties on a preferably large dynamic range by complementary techniques. Here, a polycrystalline sample of Li(2)TiO(3) was used as a model substance to study Li motion by both (7)Li spin-alignment echo (SAE) nuclear magnetic resonance (NMR) and ac-conductivity measurements. Although the two methods do probe Li dynamics in quite different ways, good agreement was found so that the Li diffusion parameters, such as jump rates and the activation energy, could be precisely determined over a dynamic range of approximately eleven decades. For example, Li solid-state diffusion coefficients D(σ) deduced from impedance spectroscopy range from 10(-23) m(2) s(-1) to 10(-12) m(2) s(-1) (240-835 K). These values are in perfect agreement with the coefficients D(SAE) deduced from SAE NMR spectroscopy. As an example, D(SAE) = 2 × 10(-17) m(2) s(-1) at 433 K and the corresponding activation energy determined by NMR amounts to 0.77(2) eV (400-600 K). At room temperature D(σ) takes a value of 3 × 10(-21) m(2) s(-1).

Studying Li Dynamics in a Gas-Phase Synthesized Amorphous Oxide by NMR and Impedance Spectroscopy

Li diffusion parameters of a structurally disordered Li-Al-Si-oxide prepared by gas-phase synthesis were complementarily investigated by both time-domain NMR techniques and impedance spectroscopy. The first include 7Li NMR spin-lattice relaxation (SLR) measurements in the laboratory as well as in the rotating frame of reference. An analysis of variable-temperature NMR line widths point to an activation energy Ea of approximately 0.6 eV. The value is confirmed by rotating-frame SLR NMR data recorded at approximately 11 kHz. Above room temperature the low-temperature flank of a diffusion-induced rate peak shows up which can be approximated by an Arrhenius law yielding Ea=0.56(1) eV. This is in very good agreement with the result obtained from 7Li spin-alignment echo (SAE) NMR being sensitive to even slower Li dynamics. For comparison, dc-conductivity measurements, probing long-range motions, yield Ea=0.8 eV. Interestingly, low-temperature SAE NMR decay rates point to localized Li motions being characterized with a very small activation energy of only 0.09 eV.

Spin-alignment echo NMR: probing Li+ hopping motion in the solid electrolyte Li7La3Zr2O12 with garnet-type tetragonal structure

(7)Li spin-alignment echo (SAE) nuclear magnetic resonance (NMR) spectroscopy has been used to measure single-spin hopping correlation functions of polycrystalline Li(7)La(3)Zr(2)O(12). Damping of the echo amplitude S(2)(t(m),t(p)), recorded at variable mixing time t(m) but fixed preparation time t(p), turns out to be solely controlled by slow Li jump processes taking place in the garnet-like structure. The decay rates τ(SAE)(-1) directly obtained by parametrizing the curves S(2)(t(m),t(p)) with stretched exponential functions show Arrhenius behaviour pointing to an activation energy of approximately 0.5 eV. This value, probed by employing an atomic-scale NMR method, is in very good agreement with that deduced from impedance spectroscopy used to measure macroscopic Li transport parameters. Most likely, the two methods are sensitive to the same hopping correlation function although Li dynamics are probed in a quite different manner.

Ultra-slow Li ion dynamics in Li(2)C(2)--on the similarities of results from (7)Li spin-alignment echo NMR and impedance spectroscopy

Li diffusion and transport parameters of binary lithium carbide Li(2)C(2) were complementarily investigated by (7)Li (nuclear magnetic resonance) NMR and impedance spectroscopy. Long-range Li diffusion parameters were measured by using mixing-time-dependent and temperature-variable stimulated echo NMR spectroscopy. The method is sensitive to ultra-slow Li hopping processes which were probed from an atomic-scale point of view. Two-time phase correlation functions S(2) obtained can be parameterized by stretched exponentials only. The corresponding echo decay rates τ(-1), which were recorded at a resonance frequency of e.g. 155.5 MHz, show Arrhenius behaviour revealing an activation energy of 0.80(2) eV. This value is in very good agreement with that deduced from dc conductivity measurements (0.79(2) eV) probing Li transport processes on a macroscopic length scale. The comparison of impedance data with the measured NMR echo decay functions showed that both methods reflect diffusion processes being characterized by very similar motional correlation functions.

Mistimed stimulated echoes and distorted spin-alignment spectra of powdered solids

It is commonplace that NMR echo maxima appear at times for which the dephasing and the rephasing periods of a pulse sequence are equally long. However, for stimulated echoes a significant time shift from this naively expected echo position can be observed if the dephasing times are smaller than the inverse line width of the NMR spectrum. This effect, which will be observable for any line shape, is evaluated quantitatively for Gaussian and for Pake-like patterns. Comparison of the calculations is made with experimental results from (6)Li- and from (2)H-NMR and excellent agreement is found. In the simultaneous presence of broad and narrow lines, the apparent time shift can give rise to characteristic distortions in spin-alignment spectra. This explains some features previously observed using (7)Li-NMR.

Microscopic Access to Long-Range Diffusion Parameters of the Fast Lithium Ion Conductor Li7BiO6 by Solid State 7Li Stimulated Echo NMR

Li self-diffusion in rhombohedral Li7BiO6, being a promising basic material for cathodes of rechargeable ion batteries, is studied by means of 7Li stimulated echo NMR. Using the pulse sequence introduced by Jeener and Broekaert, a spin-alignment echo is created whose amplitude decay is recorded as a function of mixing time. The so-obtained two-time correlation functions follow stretched exponential behavior and lead to decay rates which can be identified directly with microscopic Li motional correlation rates (tau(-1)). Using a jump distance of about 0.2 nm, this results in a diffusion coefficient (D) of about 0.5 x 10(-16) m(2) s(-1) at 294 K. The activation energy turned out to be 0.53(3) eV which is in very good agreement with recently obtained results by means of dc-conductivity measurements probing long-range diffusion parameters. This shows that stimulated echo NMR, due to its inherent time scale, gives microscopic access to long-range transport. The prefactor tau(0)(-1) of the corresponding Arrhenius law lies in the typical range of phonon frequencies, tau(0)(-1) = 3 x 10(12) s(-1).

Spin relaxation and ultra-slow Li motion in an aluminosilicate glass ceramic

The ion dynamics in a lithium aluminosilicate glass ceramic was studied using stimulated-echo 7Li-NMR. For temperatures 300 K<T<450 K the hopping correlation times, tau(C), were determined from the decay of the quadrupolar spin-alignment amplitude. The decay times were thermally activated with an energy barrier of 0.61 eV, in agreement with conductivity measurements. For T<300 K the temperature dependence of the decay times, now corresponding to T1Q, was much weaker. The T1Q times followed the same trend as the independently measured spin-lattice relaxation times, T1, but were a factor of about three shorter than those. The theoretical ratio of T1/T1Q is shown to be 25/8 in the slow-motion regime if quadrupolar spin relaxation prevails. This result explains the present observation and similar ones made for several Li ion conductors. The relaxation of the octupolar spin-alignment order is discussed.

Ultraslow Li diffusion in spinel-type structured Li4Ti5O12 - a comparison of results from solid state NMR and impedance spectroscopy

The cubic spinel oxides Li(1+x)Ti(2-x)O(4) (0 < or =x< or = 1/3) are promising anode materials for lithium-ion rechargeable batteries. The end member of the Li-Ti-O series, Li(4)Ti(5)O(12), can accommodate Li ions up to the composition Li(7)Ti(5)O(12). Whereas a number of studies focus on the electrochemical behaviour of Li insertion into and Li diffusion in the Li intercalated material, only few investigations about low-temperature Li dynamics in the non-intercalated host material Li(4)Ti(5)O(12) have been reported so far. In the present paper, Li diffusion in pure-phase microcrystalline Li(4)Ti(5)O(12) with an average particle size in the microm range was probed by (7)Li solid state NMR spectroscopy using spin-alignment echo (SAE) and spin-lattice relaxation (SLR) measurements. Between T = 295 K and 400 K extremely slow Li jump rates tau(-1) ranging from 1 s(-1) to about 2200 s(-1) were directly measured by recording the decay of spin-alignment echoes as a function of mixing time and constant evolution time. The results point out the slow Li diffusion in non-intercalated Li(4)Ti(5)O(12) x tau(-1) (1/T) follows Arrhenius behaviour with an activation energy E(ASAE) of about 0.86 eV. Interestingly, E(ASAE) is comparable to activation energies deduced from conductivity measurements (0.94(1) eV) and from SLR measurements in the rotating frame (0.74(2) eV) rather than from those performed in the laboratory frame, E(A)(low-T) = 0.26(1) eV at low T.

Ultraslow Diffusion in Polycrystalline h-LiTiS2 Studied by 7Li Spin-Alignment Echo NMR Spectroscopy

Multiple-time spin-alignment echo (SAE) NMR spectroscopy of spin- 3 2 nuclei is used to study ultraslow diffusion in the hexagonal layered Li ion conductor LixTiS2 (x 1). Two-time correlation functions were monitored by recording (Jeener-Broekaert) echo amplitudes for constant evolution and variable mixing times. Echo decay rates t