6Li NMR in lithium borate glasses

In anticipation of using fluctuations in the nuclear dipolar and quadrupolar interaction as a probe of lithium ion motion in lithium borate glasses, the static values of these interactions were measured using a variety of echo techniques. The static quadrupolar echo spectrum of ⁷Li and a calculation of the dipolar interaction in crystalline Li₂B₄O₇ (same chemical composition as the glass under study) were used to estimate the strength of the two interactions. These indicate that the dipolar and quadrupolar interactions for ⁶Li will be of similar size and the dipolar interaction will be dominated by the unlike spin interaction between the ⁶Li and the ¹⁰B, ¹¹B spins. An appropriate theoretical model is proposed and explicit expressions for the echo amplitude are calculated in terms of the dipolar and quadrupolar second moments. This single spin model takes into account the quadrupolar interaction but treats the dipolar interaction as an effective magnetic field. Experimental results are presented which show the essential validity of the model and measurements lead to reasonable values for the dipolar and quadrupolar second moments. The relative merits of the various echo techniques are discussed.     

On the theory of NMR spin echoes in solids

A general expression in terms of two-time correlation functions is derived for the spin echo responses to 90°-τ-β⁰_φ pulse sequences of quadrupolar spins coupled through dipolar interactions. The second moments of the correlation function are calculated for a system of spin one nuclei and shown to be in accordance with the experimental observations. Furthermore, results are presented for the fourth moments.     

Homonuclear vanadium-51 dipolar couplings in inorganic solids obtained via hahn spin echo decay NMR spectroscopy

Dipolar dephasing of the magnetization following a Hahn spin echo pulse sequence potentially provides a quantitative means for determining the dipolar second moment in solids. In this work, the possibility of employing Hahn spin echo decay spectroscopy to obtain quantitative ⁵¹V–⁵¹V dipolar second moments is explored. Theoretical spin echo response curves are compared to experimental ones for a collection of crystalline vanadium-containing compounds. This work suggests that ⁵¹V dipolar second moments can be obtained by selectively exciting the central m = 1/2 → −1/2 by a Hahn echo sequence for vanadate compounds with line broadening no greater than approximately 220 ppm. For vanadates with greater broadening of the central transition due to chemical shift, second-order quadrupolar, and dipolar interactions, off-resonance effects lead to an oscillatory time dependence of the spin echo. Experimentally determined second moments of the normalized echo decay intensities lie within 10–33% of the calculated values if the second moments are extrapolated to zero evolution time due to the time scale dependence of spin exchange among neighboring vanadium nuclei. Alternatively, the second moments can be obtained to within 10–25% of the calculated values if the broadening of the central transition due to chemical shift and second-order quadrupolar effects can be estimated.     

Theoretical and experimental study of quadrupolar echoes for half-integer spins in static solid-state NMR

Numerical simulations of powder spectra produced by a two-pulse sequence applied to a quadrupolar nuclei system of half-integer spin number make it possible to propose simple experimental instructions to record static echo spectra with minimum lineshape distortion. Calculations take into account quadrupolar (first and second orders), shielding, scalar and inhomogeneous dipolar interactions as well as the radiofrequency pulse specifications (strength, duration, phase). The suggested instructions have been checked experimentally in different cases: for a large spin number system with Li⁹³NbO₃, when two interactions are present with a ^63/65Cu complex, and in the two-site system of ⁸⁷Rb₂SO₄.     

Proton NMR studies of the NaAlH4 structure

Advanced nuclear magnetic resonance (NMR) techniques were applied to study the local environments of hydrogen in NaAlH₄. Through a combined application of the magic echo (ME) and the magic Hahn echo (MHE) sequences the hetero- and homonuclear contributions to the dipolar second moment (M₂) were determined separately. The obtained values are compared with the second moments calculated by the van Vleck formulae, using structural data determined by neutron scattering on NaAlD₄. This comparison indicates structural differences between NaAlH₄ and NaAlD₄. A model is suggested for the orientation of the [AlH₄]⁻ tetrahedra in NaAlH₄, for which the calculated second moments are in good agreement with the experimentally observed values.     

A Study of Dipolar Interactions and Dynamic Processes of Water Molecules in Tendon byH andH Homonuclear and Heteronuclear Multiple-Quantum-Filtered NMR Spectroscopy

The effect of proton exchange on the measurement of¹H–¹H,¹H–²H, and²H–²H residual dipolar interactions in water molecules in bovine Achilles tendons was investigated using double-quantum-filtered (DQF) NMR and new pulse sequences based on heteronuclear and homonuclear multiple-quantum filtering (MQF). Derivation of theoretical expressions for these techniques allowed evaluation of the¹H–¹H and¹H–²H residual dipolar interactions and the proton exchange rate at a temperature of 24°C and above, where no dipolar splitting is evident. The values obtained for these parameters at 24°C were 300 and 50 Hz and 3000 s⁻¹, respectively. The results for the residual dipolar interactions were verified by repeating the above measurements at a temperature of 1.5°C, where the spectra of the H₂O molecules were well resolved, so that the¹H–¹H dipolar interaction could be determined directly from the observed splitting. Analysis of the MQF experiments at 1.5°C, where the proton exchange was in the intermediate regime for the¹H–²H dipolar interaction, confirmed the result obtained at 24°C for this interaction. A strong dependence of the intensities of the MQF signals on the proton exchange rate, in the intermediate and the fast exchange regimes, was observed and theoretically interpreted. This leads to the conclusion that the MQF techniques are mostly useful for tissues where the residual dipolar interaction is not significantly smaller than the proton exchange rate. Dependence of the relaxation times and signal intensities of the MQF experiments on the orientation of the tendon with respect to the magnetic field was observed and analyzed. One of the results of the theoretical analysis is that, in the fast exchange regime, the signal decay rates in the MQF experiments as well as in the spin echo or CPMG pulse sequences (T₂) depend on the orientation as the square of the second-rank Legendre polynomial.     

The glories of ESEEM: Measuring electron-nuclear dipolar couplings in orientationally disordered solids

In orientationally disordered solids, the anisotropy of spin interactions can cause a spectral line-broadening that severely complicates the acquisition and analysis of ESEEM (electron spin echo envelope modulation) spectra. The reduction or removal of powderbroadening is accomplished in ESEEM spectroscopy through the cancellation of antagonistic, static interactions. Three, distinct examples of this approach to spectral line-narrowing in nuclear spin one-half systems are described, together with their implications regarding the determination of electron-nuclear dipolar couplings. Applications involving¹⁵N and¹H nuclei in protein and model systems are discussed.     

Relaxation-induced dipolar exchange with recoupling-An MAS NMR method for determining heteronuclear distances without irradiating the second spin

A new magic-angle spinning NMR method for distance determination between unlike spins, where one of the two spins in question is not irradiated at all, is introduced. Relaxation-induced dipolar exchange with recoupling (RIDER) experiments can be performed with conventional double-resonance equipment and utilize the familiar π-pulse trains to recouple the heteronuclear dipolar interaction under magic-angle spinning conditions. Longitudinal relaxation of the passive spin during a delay between two recoupling periods results in a dephasing of the heteronuclear coherence and consequently a dephasing of the magnetization detected after the second recoupling period. The information about the dipolar coupling is obtained by recording normalized dephasing curves in a fashion similar to the REDOR experiment. At intermediate mixing times, the dephasing curves also depend on the relaxation properties of the passive spin, i.e., on single- and double-quantum longitudinal relaxation times for the case of I = 1 nuclei, and these relaxation times can be estimated with this new method. To a good approximation, the experiment does not depend on possible quadrupolar interactions of the passive spin, which makes RIDER an attractive method when distances to quadrupolar nuclei are to be determined. The new method is demonstrated experimentally with ¹⁴N and ²H as heteronuclei and observation of ¹³C in natural abundance.     

Lithium ordering and NMR linewidth in Li0.33TiS2

The low temperature ⁷Li linewidths and second moments have been analyzed for Li_0.33 TiS₂ and Li_0.97 TiS₂. Moment calculations demonstrate that the linewidth is a sensitive indicator of order on a two dimensional lattice of dipoles. The calculated dipolar second moment is not consistent with a simple √3 a_o superlattice in Li_0.33 TiS₂, but is consistent with a random arrangement of lithium ions and several more complex superlattices recently proposed by Kanamori and Kaburagi.     

Coherent tunneling of lithium defect pairs in KCl crystals

The tunneling of two lithium ion impurities on next-nearest neighbor sites in potassium chloride are investigated both experimentally and theoretically. The strong dipolar interaction leads to coherent tunneling motion of the two defect ions between degenerate off-center positions. Comparing data of rotary echo experiments for impurity pairs ⁷Li—⁷Li, ⁶Li—⁶Li, and ⁷Li—⁶Li with theory permits a thorough investigation of the isotope effect and of the effect of the interaction on the tunnel states. Our findings confirm the tunneling model with <111> off-center states to be valid even for strongly interacting impurities. Using degenerate perturbation theory in terms of two-particle states, we obtain essentially exact expressions for the tunneling spectrum and the dynamical susceptibility which agree well with the measured data.     

Revision of spin echoes in pure nuclear quadrupole resonance

Goldman's spin-1/2 formalism has been used for describing the response of an I=3/2 spin system to a two-pulse sequence in a pure nuclear quadrupole resonance experiment. A detailed analysis of the polarization evolution and quadrupolar echo generation is carried out through the use of explicit expressions for secular homo- and heteronuclear dipolar interactions. In striking contrast with previous studies, it is predicted that Van Vleck's second moments governing a classical solid-echo or Hahn sequence differ from those obtained by equivalent means in magnetic resonance. In fact, it is shown that, although measured moments still complement each other, the combined use of standard sequences does not allow the separate determination of homo- and heteronuclear dipolar contributions to the linewidth, not even in an indirect manner. In this context, the importance and potential usefulness of a crossed coil probe are also briefly discussed.     

Nuclear spin relaxation of 8Li adsorbed on surfaces

Nuclear spin relaxation experiments with ⁸Li adsorbed on various surfaces provide new information in surface science which is not obtainable othervise. Both dipolar (Korringa) and quadrupolar relaxation due to diffusion are observed. However, in addition, a fast and presently not understood spin relaxation mechanism is present while dosing during the first 0.5 s the surface with polarized ⁸Li. Most strange in this respect is the fact that those ⁸Li atoms which survive depolarization through this mechanism depolarize afterwards with modest spin lattice relaxation rates. The origin of the fast spin lattice relaxation mechanism is presently unknown. This revised version was published online in July 2006 with corrections to the Cover Date.     

PAN为基凝胶聚合物电解质自扩散系数的NMR研究

利用脉冲梯度场NMR方法直接测量了不同温度下的不同组分的PAN为基凝胶聚合物电解抽PAN-EC/PL-LiClO₄中锂离子的自扩散系数D.结果表明,锂离子的自扩散系数D依赖于锂盐质量分数x％,关且在x从5到20范围内,x=10时D有最大值.这与锂离子跳跃的传输机制及同时受到增塑剂EC与聚合物PAN网络的相互作用有关. 关键词：     

19F-decoupling of half-integer spin quadrupolar nuclei in solid-state NMR: application of frequency-swept decoupling methods

In solid-state NMR studies of minerals and ion conductors, quadrupolar nuclei like ⁷Li, ²³Na or ¹³³Cs are frequently situated in close proximity to fluorine, so that application of ¹⁹F decoupling is beneficial for spectral resolution. Here, we compare the decoupling efficiency of various multi-pulse decoupling sequences by acquiring ¹⁹F-decoupled ²³Na-NMR spectra of cryolite (Na₃AlF₆). Whereas the MAS spectrum is only marginally affected by application of ¹⁹F decoupling, the 3Q-filtered ²³Na signal is very sensitive to it, as the de-phasing caused by the dipolar interaction between sodium and fluorine is three-fold magnified. Experimentally, we find that at moderate MAS speeds, the decoupling efficiencies of the frequency-swept decoupling schemes SW_f-TPPM and SW_f-SPINAL are significantly better than the conventional TPPM and SPINAL sequences. The frequency-swept sequences are therefore the methods of choice for efficient decoupling of quadrupolar nuclei with half-integer spin from fluorine.     

The statistical mechanics of ion-dipole-tetrahedral quadrupole mixtures

We examine the solution of the Ornstein-Zernike equations for the correlation functions of a fluid mixture in which the molecular interactions consist of a hard sphere plus a multipolar potential that contains coulombic, dipolar as well as quadrupolar terms. In particular we consider the case in which the molecule has a dipole moment in the z direction of the molecular axis system and a non-linear tetrahedral quadrupole tensor of the form Θ _xx = - Θ _yy , Θ _zz = 0 = Θ_αβ, α ≠ β in the molecular frame. This model is a good representation of the dipolar and quadrupolar properties of water and our analysis will form the basis for constructing a Civilized Model electrolyte in which ions are dissolved in a solvent whose molecules possess water-like multipole moments. One of our main results is that for any theory which retains only the subset of rotational invariants that either appear in the interaction potentials or are generated by angular convolution from those appearing in the interaction potentials, e.g. the linearized hypernetted chain (LHNC) or mean spherical approximations (MSA), the equations for an ion-dipole-tetrahedral quadrupolar mixture only differ from those for an ion-dipole-linear quadrupole mixture (Θ _xx = Θ _yy = - 1/2Θ _zz , Θ_αβ = 0, α ≠ β) in minor details. We have investigated the thermodynamic properties of a fluid of hard spheres with the dipole and tetrahedral moments of water using thermodynamic perturbation theory. We find that contributions to the thermodynamic properties from dipole-quadrupole interaction are very important. For a pure hard sphere tetrahedral quadrupolar fluid there is considerable difference between the results from perturbation theory and from the MSA, for which we have obtained an analytic solution.     

Zum selektiven NMR-Spinecho-Verhalten bei Systemen mit I = 1 im Festkörper am Beispiel des Kaliumoxalatmonohydrats

Investigation of the Selective N.M.R. Spin Echo Response of I = 1 Systems in Solids Demonstrated on Potassium Oxalate Monohydrate The theory of the nonselective spin echo response in solids for dipolar-coupled spins I = 1 with quadrupole interaction by BODEN et al. [5] is modified for the case of selective irradiation to only one line of the n.m.r. spectrum. The theoretical results are compared with ¹H-n.m.r. experiments on dipolar-coupled protonpairs of a (KCOO)₂ · H₂O single crystal. This is possible because in this material the interpair dipolar interaction is substantially smaller than the intrapair dipolar interaction. An echo response results which has some similarities to the behaviour of spin systems with heteronuclear coupling.     

Stimulated-Echo NMR Spectroscopy of Be and Li in Solids: Method and Application to Ion Conductors

The generation of pure quadrupolar stimulated-echo spectra is successfully demonstrated for the spin- probe ⁹Be in a single crystal of triglycine fluoberyllate. This solid exhibits a paraelectric-to-ferroelectric phase transition. From experiments carried out for various mixing times no indications for a slow soft mode could be detected in this crystal. Then ion conducting lithium metal phosphates were studied using ⁷Li, another spin- probe which allows for a non-selective excitation of the entire NMR spectrum. In the indium and the scandium phosphates ultra-slow Li hopping processes could be detected directly via the stimulated-echo technique in a time range of up to four orders of magnitude. Due to the relatively large gyromagnetic ratio and thus strong dipolar interactions of ⁷Li no pure quadrupolar echoes could be generated. However, from a variation of the evolution times the quadrupolar effects could be separated from the dipolar ones. Finally, the differences in the ion hopping times of lithium indium phosphate and of lithium scandium phosphate are briefly discussed.     

Dynamic polarization of 7Li nuclei in solutions containing radical ions

Dynamic nuclear polarization parameters, obtained at 75 G, are reported for ⁷Li ions in collision with several radical anions and with one radical cation. All systems show large negative ⁷Li N.M.R. enhancements indicative of weak scalar relaxation. However, radical induced relaxation rates derived from ⁷Li T ₁ measurements suggest stronger complexing of lithium ions with radical anions than with the radical cation as would be expected from simple coulombic considerations. Translational modulation of the dipolar interaction best accounts for proton and radical cation dipolar relaxation rates while rotational modulation best accounts for the corresponding radical anion rates; this supports the interpretation above. A model for the lithium radical collision is proposed which implies that, for radical anions, scalar coupling is only apparently weak and that the low ⁷Li scalar relaxation rates observed result from scalar correlation times (τ_c = 10^-8-10^-9 s) longer than any yet observed by this technique. The model predicts that, for certain ranges of τ_c, increasing strength of complex formation should lead to smaller scalar relaxation rates and more negative enhancements, in contrast with the behaviour of fluorocarbons where the reverse was true. The predicted dependence of enhancement upon τ_c also suggests that ⁷Li enhancements should be extremely sensitive to variations in the chemical properties of the system.     

Electron spin-echo envelope modulation at S-band. 3: Analysis of nuclear quadrupole interaction effects

In the present paper the nuclear modulation of electron spin echo signals at S-band is investigated in the case of interacting nuclei with a quadrupole moment high enough to cause nuclear quadrupole couplings not negligible with respect to the nuclear Zeeman and dipolar hyperfine couplings. Both the two-pulse and three-pulse electron spin echo envelope modulation (ESEEM) due to²⁷Al and¹⁴N are simulated at different values of the nuclear quadrupole coupling by numerical diagonalization of the nuclear Hamiltonians. The behavior of their amplitude and periods is discussed on the basis of the ratios between the strengths of the nuclear quadrupole interaction and the nuclear Zeeman and the dipolar hyperfine interactions. The interpretation of their trends in terms of the eigenfunctions and eigenvectors of the nuclear Hamiltonians is carried out by using analytical equations obtained by perturbation approaches. First order perturbation treatments for integer and half-integer nuclear spin quantum numbers are developed when the nuclear quadrupole coupling is the main interaction. A discussion on the limits of the interpretation based on the perturbation approach is also given by comparing the magnitude Fourier transform of the patterns calculated by exact diagonalization and analytical equations.     

13C Dipolar spectroscopy of nitromethane

The ¹³C dipolar N.M.R. spectrum of ¹³CH₃ ¹⁴NO₂ has been recorded at 25 K. The principal values of the ¹³C shielding tensor, obtained by a computer fit of the experimental lineshape, are similar to those found in other ¹³CH₃ groups. ¹⁴N quadrupolar parameters and direct dipolar couplings are also reported. In fitting the spectrum we find that an effective trace must be added to the dipolar interaction to account for librational motion.