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

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.

A Multi-Scale Study of Water Dynamics under Confinement, Exploiting Numerical Simulations in Relation to NMR Relaxometry, PGSE and NMR Micro-Imaging Experiments: An Application to the Clay/Water Interface

Water mobility within the porous network of dense clay sediments was investigated over a broad dynamical range by using 2H nuclear magnetic resonance spectroscopy. Multi-quanta 2H NMR spectroscopy and relaxation measurements were first performed to identify the contributions of the various relaxation mechanisms monitoring the time evolution of the nuclear magnetisation of the confined heavy water. Secondly, multi-quanta spin-locking NMR relaxation measurements were then performed over a broad frequency domain, probing the mobility of the confined water molecules on a time-scale varying between microseconds and milliseconds. Thirdly, 1H NMR pulsed-gradient spin-echo attenuation experiments were performed to quantify water mobility on a time-scale limited by the NMR transverse relaxation time of the confined NMR probe, typically a few milliseconds. Fourthly, the long living quantum state of the magnetisation of quadrupolar nuclei was exploited to probe a two-time correlation function at a time-scale reaching one second. Finally, magnetic resonance imaging measurements allow probing the same dynamical process on time-scales varying between seconds and several hours. In that context, multi-scale modelling is required to interpret these NMR measurements and extract information on the influences of the structural properties of the porous network on the apparent mobility of the diffusing water molecules. That dual experimental and numerical approach appears generalizable to a large variety of porous networks, including zeolites, micelles and synthetic or biological membranes.

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.

Submillimeter coils for stimulated-echo spectroscopy of a solid sodium ion conductor by nonselective excitation of MHz broad 23Na quadrupolar satellite spectra

In solids the detection of ionic motion covering the time range of milliseconds and longer is often accomplished using stimulated-echo spectroscopy. For spectral line widths much below or much above 1MHz nonselective or fully selective radio-frequency pulse excitation, respectively, is typically applied in such experiments. To enable the study of samples with quadrupolarly broadened satellite spectra featuring intermediate widths (in the lower MHz range) the present work exploits microcoils. Using such coils, stimulated-echo spectroscopy can be performed under conditions of nonselective excitation for instance with ²³Na as a nuclear probe. Nutation experiments carried out used to assess the coil performance. The impact of second-order quadrupolar interactions is studied using explicit density-matrix calculations. The applicability of the present approach is successfully tested for a sodium orthophosphate based solid ion conductor.

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

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.

Combining 7Li NMR field-cycling relaxometry and stimulated-echo experiments: a powerful approach to lithium ion dynamics in solid-state electrolytes

We use (7)Li NMR to study lithium ion dynamics in a (Li2S)-(P2S5) glass. In particular, it is shown that a combination of (7)Li field-cycling relaxometry and (7)Li stimulated-echo experiments allows us to cover a time window extending over 10 orders of magnitude without any gaps. While the (7)Li stimulated-echo method proved suitable to measure correlation functions F2(t) of lithium ion dynamics in solids in recent years, we establish the (7)Li field-cycling technique as a versatile tool to ascertain the spectral density J2(ω) of the lithium ionic motion in this contribution. It is found that the dynamic range of (7)Li field-cycling relaxometry is 10(-9)-10(-5)s and, hence, it complements in an ideal way that of (7)Li stimulated-echo experiments, which amounts to 10(-5)-10(1)s. Transformations between time and frequency domains reveal that the field-cycling and stimulated-echo approaches yield results for the translational motion of the lithium ions that are consistent both with each other and with findings for the motional narrowing of (7)Li NMR spectra of the studied (Li2S)-(P2S5) glass. In the (7)Li field-cycling studies of the (Li2S)-(P2S5) glass, we observe the translational ionic motion at higher temperatures and the nearly constant loss at lower temperatures. For the former motion, the frequency dependence of the measured spectral density is well described by a Cole-Davidson function. For the latter phenomenon, which was considered as an universal phenomenon of disordered solids in the literature, we find an exponential temperature dependence.

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.

Lithium ionic jump motion in the fast solid ion conductor Li(5)La(3)Nb(2)O(12)

Using (7)Li NMR line-shape analysis, spin-lattice relaxation measurements and stimulated-echo spectroscopy, we investigate the lithium ionic jump motion in the garnet Li(5)La(3)Nb(2)O(12). Results for two samples are compared, which were annealed at 850( composite function)C (GR-850) and at 900( composite function)C (GR-900), respectively. All (7)Li NMR data consistently show that two lithium species with distinguishable dynamical behaviors coexist in each of the samples. While the less mobile species is the majority component in GR-850, the more mobile species is the majority component in GR-900. (7)Li NMR stimulated-echo spectroscopy provides straightforward access to the correlation functions describing the jumps of the respective majority component in both samples. From the temperature-dependent correlation times, we obtain activation energies of 56 and 32kJmol(-1) for GR-850 and GR-900, respectively. For both samples, the correlation functions substantially deviate from simple exponential behavior, indicating a high complexity of the lithium ionic motion in Li(5)La(3)Nb(2)O(12).

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).