Stimulated-echo NMR spectroscopy of 9Be and 7Li in solids: method and application to ion conductors

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.

Solid-state Be-9 NMR of beryllium compounds

Despite the favorable NMR-spectroscopic features of the 9Be isotope, the exploration of solid Beryllium compounds by this method has been very limited, owing to safety concerns regarding their preparation and handling. The present review aims to be the first comprehensive one on this topic, summarizing the classical and modern methodologies available for determining the relevant 9Be NMR observables in the solid state. Results on molecular crystals, oxidic materials, and intermetallic systems will be discussed in terms of their informational content in relation to atomic and electronic structure and dynamics, leading to suggestions for future paths of investigation.

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.

Solid-State NMR Spectroscopy Study of Cation Dynamics in Layered Na2Ti3O7 and Li2Ti3O7

Ti-based materials exhibit suitable properties for usage in secondary Li- and Na-ion batteries and were in the focus of several electrochemical and ion conductivity studies. A material of such interest is layer-structured, monoclinic Na2Ti3O7. Additionally, the sodium in Na2Ti3O7 can be replaced completely with lithium to achieve monoclinic Li2Ti3O7, whose electrochemical properties were already investigated as well. Both materials exhibit interesting properties such as zero-strain behavior upon intercalation and high cycling stability. However, there is still a lack of fundamental understanding of the ion diffusivity of both Na and Li in the corresponding host structure. Solid-state nuclear magnetic resonance (NMR) spectroscopy is used here for the first time to reveal the cation dynamics in layered Na2Ti3O7 and Li2Ti3O7. This includes activation energies for the ionic motion and jump rates on the microscopic scale from NMR spin-lattice relaxation (SLR), spin-alignment echo (SAE), and 2D NMR exchange techniques. Moreover, the dimensionality of the ionic motion is investigated by frequency-dependent NMR SLR. Structural details are studied using magic-angle spinning (MAS) NMR spectroscopy. Results for the electric field gradient at the Na and Li site, respectively, are compared with those from theoretical calculations performed within this study. The dynamics are similar for both cations, and the frequency-dependence of the 7Li NMR SLR rate indicates Li motion confined to two dimensions. Thus, these two materials may be regarded a model system for low-dimensional diffusion of two different cations.

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.

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.

Two-dimensional diffusion in Li0.7NbS2 as directly probed by frequency-dependent 7Li NMR

Li ion diffusion in layer-structured Li0.7NbS2 has been complementary investigated by nuclear magnetic resonance (NMR) spectroscopy from an atomic scale point of view. In the present case, (7)Li NMR spin-lattice relaxation (SLR) rates R1ρ probed in the rotating frame of reference proved very informative in characterizing the Li self-diffusion process in the van der Waals gap between the NbS2 layers. While temperature-variable SLRρ measurements were used to determine dynamic parameters such as jump rates (τ(-1)) and the activation energy (Ea), frequency-dependent measurements were used to specify the dimensionality of the diffusion process. In particular, the effect of annealing, i.e., the distribution of Li ions between the layers, on overall Li dynamics has been studied. When plotted in an Arrhenius diagram, the R1ρ rates of an annealed sample, which were recorded at a locking frequency of 20 kHz, pass through a diffusion-induced relaxation peak whose maximum shows up at 320 K. Employing an appropriate diffusion model and appropriately accounting for a non-diffusive background relaxation, a Li jump rate τ(-1)(300 K) ≈ 1.3 × 10(5) s(-1) and an activation energy Ea of 0.43(2) eV can be deduced. Most importantly, in the high-T limit of the diffusion-induced rate peak, i.e., when ω1τ << 1 holds, the rates follow a logarithmic frequency dependence. This points to a diffusion process of low dimensionality and is in good agreement with predictions of relaxation models developed for 2D diffusion.

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.

NMR relaxometry as a versatile tool to study Li ion dynamics in potential battery materials

NMR spin relaxometry is known to be a powerful tool for the investigation of Li(+) dynamics in (non-paramagnetic) crystalline and amorphous solids. As long as significant structural changes are absent in a relatively wide temperature range, with NMR spin-lattice (as well as spin-spin) relaxation measurements information on Li self-diffusion parameters such as jump rates and activation energies are accessible. Diffusion-induced NMR relaxation rates are governed by a motional correlation function describing the ion dynamics present. Besides the mean correlation rate of the dynamic process, the motional correlation function (i) reflects deviations from random motion (so-called correlation effects) and (ii) gives insights into the dimensionality of the hopping process. In favorable cases, i.e., when temperature- and frequency-dependent NMR relaxation rates are available over a large dynamic range, NMR spin relaxometry is able to provide a comprehensive picture of the relevant Li dynamic processes. In the present contribution, we exemplarily present two recent variable-temperature (7)Li NMR spin-lattice relaxation studies focussing on Li(+) dynamics in crystalline ion conductors which are of relevance for battery applications, viz. Li(7) La(3)Zr(2)O(12) and Li(12)Si(7).

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.

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).

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.

Ion and polymer dynamics in polymer electrolytes PPO–LiClO4.II. H2 and Li7 NMR stimulated-echo experiments

We use 2H NMR stimulated-echo spectroscopy to measure two-time correlation functions characterizing the polymer segmental motion in polymer electrolytes PPO-LiClO4 near the glass transition temperature Tg. To investigate effects of the salt on the polymer dynamics, we compare results for different ether oxygen to lithium ratios, namely, 6:1, 15:1, 30:1, and infinity. For all compositions, we find nonexponential correlation functions, which can be described by a Kohlrausch function. The mean correlation times show quantitatively that an increase of the salt concentration results in a strong slowing down of the segmental motion. Consistently, for the high 6:1 salt concentration, a high apparent activation energy Ea=4.1 eV characterizes the temperature dependence of the mean correlation times at Tg<T<or approximately 1.1Tg, while smaller values Ea approximately 2.5 eV are observed for moderate salt contents. The correlation functions are most nonexponential for 15:1 PPO-LiClO4 whereas the stretching is reduced for higher and lower salt concentrations. This finding implies that the local environments of the polymer segments are most diverse for intermediate salt contents, and, hence, the spatial distribution of the salt is most heterogeneous. To study the mechanisms of the segmental reorientation, we exploit that the angular resolution of 2H NMR stimulated-echo experiments depends on the length of the evolution time tp. A similar dependence of the correlation functions on the value of tp in the presence and in the absence of ions indicates that addition of salt hardly affects the reorientational mechanism. For all compositions, mean jump angles of about 15 degrees characterize the segmental reorientation. In addition, comparison of results from 2H and 7Li NMR stimulated-echo experiments suggests a coupling of ion and polymer dynamics in 15:1 PPO-LiClO4.

From ultraslow to fast lithium diffusion in the 2D ion conductor Li0.7TiS2 probed directly by stimulated-echo NMR and nuclear magnetic relaxation

7Li stimulated-echo NMR and classical relaxation NMR techniques are jointly used for the first time for a comprehensive investigation of Li diffusion in layer-structured Li0.7TiS2. One single 2D Li diffusion process was probed over a dynamic range of almost 10 orders of magnitude. So far, this is the largest dynamic range being measured by 7Li NMR spectroscopy directly, i.e., without the help of a specific theoretical model. The jump rates obey a strict Arrhenius law, determined by an activation energy of 0.41(1) eV and a preexponential factor of 6.3(1)x10(12) s-1, and range between 1x10(-1) s-1 and 7.8x10(8) s-1 (148-510 K). Ultraslow Li jumps in the kHz to sub-Hz range were measured directly by recording 7Li spin-alignment correlation functions. The temperature and, in particular, the frequency dependence of the relaxation rates fully agree with results expected for 2D diffusion.

Analysis of one-dimensional pure-exchange NMR experiments for studying dynamics with broad distributions of correlation times

One-dimensional (1D) exchange NMR experiments can elucidate the geometry, time scale, memory, and heterogeneity of slow molecular motions (1 ms-1 s) in solids. The one-dimensional version of pure-exchange (PUREX) solid-state exchange NMR, which is applied to static samples and uses the chemical shift anisotropy as a probe for molecular motion, is particularly promising and convenient in applications where site resolution is not a problem, i.e., in systems with few chemical sites. In this work, some important aspects of the 1D PUREX experiment applied to systems with complex molecular motions are analyzed. The influence of intermediate-regime (10 micros-1 ms) motions and of the distribution of reorientation angles on the pure-exchange intensity are discussed, together with a simple method for estimating the activation energy of motions occurring with a single correlation time. In addition, it is demonstrated that detailed information on the motional geometry can be obtained from 1D PUREX spectral line shapes. Experiments on a molecular crystal, dimethyl sulfone, confirm the analysis quantitatively. In two amorphous polymers, atactic polypropylene (aPP) and polyisobutylene (PIB), which differ only by one methyl group in the repeat unit, the height of the normalized exchange intensity clearly reveals a striking difference in the width of the distribution of correlation times slightly above the glass transition. The aPP shows the broad distribution and Williams-Landel-Ferry temperature dependence of correlation times typical of polymers and other "fragile" glass formers. In contrast, the dynamics in PIB occur essentially with a single correlation time and exhibits Arrhenius behavior, which is more typical of "strong" glass formers; this is somewhat surprising given the weak intermolecular forces in PIB.

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

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

Stimulated-echo spectroscopy has recently been applied to study the ultra-slow dynamics of nuclear spin-3/2 probes such as 7Li and 9Be in solids. Apart from the dominant first-order quadrupolar interaction in the present article also the impact of the homonuclear dipolar interactions is considered in a simple way: the time evolution of a dipole coupled pair of spins with I = 3/2 is calculated in an approximation, which takes into account that the satellite transitions usually do not overlap. Explicit analytical expressions describing various aspects of a coupled quadrupolar pair subjected to a Jeener-Broekaert pulse sequence are derived. Extensions to larger spin systems are also briefly discussed. These results are compared with experimental data on a single-crystalline Li ion conductor.