Simple modeling of dipolar coupled Li spins and stimulated-echo spectroscopy of single-crystalline β-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.     

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

The generation of pure quadrupolar stimulated-echo spectra is successfully demonstrated for the spin-3/2 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-3/2 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.     

CP/MAS of quadrupolar S = 3/2 nuclei.

The spin dynamics of Hartmann-Hahn cross-polarization from I = 1/2 to quadrupolar S = 3/2 nuclei is investigated. A density-matrix model applicable to cases where the quadrupole frequency vQ is much larger than the rf amplitude v1S of the S spins, predicts the time development of the spin state of an isolated I, S spin pair in static situations and in three distinct cases of magic-angle-spinning speed vR. These cases are characterized as slow, intermediate, and fast, depending on the magnitude of the parameter alpha = v1S2/vQvR relative to the intermediate value of 0.4. The model predictions are supported by numerical simulations. The polarization transfer from I to S is efficient in the limits of slow and fast sample spinning. When alpha < 1, the Hartmann-Hahn condition is shifted over once or twice vR. When the spinning rate is intermediate, poor spin-locking of the quadrupolar spins prevents the accumulation of a cross-polarization signal and, in addition, depletes the spin-locked I magnetization. Experimental CP/MAS data obtained in NaOH show that the concepts developed for isolated spin pairs are also applicable to cross-polarization in a strongly coupled multi-spin system.     

Multiple quantum spin counting techniques with quadrupolar nuclei

Phase incremented and continuous irradiation multiple spin correlation methods are applied to spin [Formula: see text] nuclei with small quadrupole couplings such as (7)Li in LiCl and are shown to successfully produce a coherently coupled dipolar spin network. Application to the analogous Na salt shows successful spin correlation evolving at a slower rate due to the weaker homonuclear dipolar coupling strength between Na nuclei. The results are analysed using a statistical approach. Spin counting is non-trivial as not only multiple quantum coherences between spins are generated but also within the quadrupolar spin levels. Na(2)C(2)O(4) is investigated as a material with non-negligible quadrupole coupling and it is in this limit that the spin correlation techniques are found to break down.     

Geometry of kinked protein helices from NMR data

Residual dipolar couplings between spin-1/2 and quadrupolar nuclei are often observed and exploited in the magic-angle spinning (MAS) NMR spectra of spin-1/2 nuclei. These orientation-dependent splittings contain information on the dipolar interaction, which can be translated into structural information. The same type of splittings may also be observed for pairs of quadrupolar nuclei, although information is often difficult to extract from the quadrupolar-broadened lineshapes. Here, the complete theory for describing the dipolar coupling between two quadrupolar nuclei in the frequency domain by Hamiltonian diagonalization is given. The theory is developed under MAS and double-rotation (DOR) conditions, and is valid for any spin quantum numbers, quadrupolar coupling constants, asymmetry parameters, and tensor orientations at both nuclei. All terms in the dipolar Hamiltonian become partially secular and contribute to the NMR spectrum. The theory is validated using experimental 11B and 35/37Cl NMR experiments carried out on powdered B-chlorocatecholborane, where both MAS and DOR are used to help separate effects of the quadrupolar interaction from those of the dipolar interaction. It is shown that the lineshapes are sensitive to the quadrupolar coupling constant of both nuclei and to the J coupling (including its sign). From these experiments, the dipolar coupling constant for a heteronuclear spin pair of quadrupolar nuclei may be obtained as well as the sign of the quadrupolar coupling constant of the perturbing nucleus; these are two parameters that are difficult to obtain experimentally otherwise.     

6Li and 7li solid-state NMR spectroscopy of nitrogen ceramic phases

Two nitrogen ceramic phases, the oxynitride LiSiON and the nitride LiSi2N3, have been studied by 6Li and 7Li NMR. Magic angle spinning (MAS) NMR experiments have been carried out at two magnetic field strengths (7.05 and 14.1 T). The spectra give evidence of the relative effects of the quadrupolar and chemical shift interactions. The electric field gradient tensor of both phases has been determined accurately by iterative fitting of the 6Li and 7Li MAS NMR line shapes at the two magnetic field strengths. Due to the fact that for 7Li the quadrupolar interaction is much larger than the chemical shift interaction, it is shown that neither the small chemical shift anisotropy nor the relative orientation of the two interaction tensors can be determined accurately by 7Li MAS NMR. For 6Li, the two interactions are comparable and the value of these parameters obtained from the fits of the 6Li experimental MAS line shapes are therefore much more reliable.     

Measurement of J-couplings between spin-(1/2) and quadrupolar nuclei by frequency selective solid-state NMR

We report a REDOR-based scheme for the measurement of heteronuclear J-couplings in solid samples with well defined structure, containing spin-12 and quadrupolar nuclei, which can be used with selective RF irradiation to target a specific spin pair, and which provides direct information about the number of coupled spins.     

固体中半整数四极核的自旋扩散

首先介绍固态中自旋扩散的一般理论，包括半经典描述和建立在投影算子理论上的密度矩阵描述. 接着以丰核环境中相互偶合的自旋-1/2系统以及自旋-3/2系统为典型列举了自旋扩散速率的计算. 最近藉助多量子魔角旋转(MQMAS)方法实现半整数四极核的多量子谱自旋扩散实验，可以测量固体粉末中半整数四极核体系四极张量相对方向. 结合作者最近的计算机模拟和实验测量结果对这一新兴方向作了重点介绍，尤其指出了射频
脉冲强度、宽度及样品旋转速度对交叉峰线型的影响.     

Li 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.     

Two-photon absorption in two-dimensional conjugated quadrupolar chromophores

We present ultrafast z-scan measurements of the two-photon absorption (TPA) spectra of a pair of two-dimensionally conjugated quadrupolar donor/acceptor (D/A) chromophores. The all-donor substituted species displays a peak TPA cross section [sigma(2)=520+/-30 GM] that is more than twice that of the D-A species [sigma(2)=240+/-20 GM]. Unlike previous structure-property studies that have evaluated TPA behavior for D/A molecules through the comparison of dipolar and quadrupolar compounds, both molecules investigated herein are quadrupolar, ultimately providing a more consistent evaluation of the effects of donor and/or acceptor substitution on the TPA of conjugated chromophores.     

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.     

A Comparison between REDOR and θ-REDOR for Measuring C–D Dipolar Interactions in Solids

¹³C-observe REDOR and θ-REDOR experiments for recovering the ¹³C–²D dipolar interaction during MAS NMR are compared. It is found that limited ²D RF power may severely compromise the performance of the REDOR experiment whereas the θ-REDOR experiment can be designed to work well. Results are presented for an isolated ¹³C–²D spin pair with a large deuterium quadrupolar coupling constant and for a ¹³C coupled to three methyl deuterons undergoing fast methyl group rotation.     

Low-temperature spin-lattice relaxation of8Li in the glass Li2O·2SiO2

Nuclear spin-lattice relaxation in Li₂0·2Si0₂ glass below 200 K has been studied using the asymmetric Β-decay radiation of polarized⁸Li (T_1/2=0.Bs) nuclei produced by capture of polarized neutrons. Transients of the⁸Li polarization follow an exp(?√E/T₁) law. The dependence of the spin-lattice relaxation rate ⊥_¯1 ¹ on temperature T and magnetic field B can roughly be described by T_¯1 ¹～T/B. The interpretation is based on the assumption that for⁸Li, contrary to⁷Li in the same glass, spin-diffusion is absent and that each probe nucleus is coupled by quadrupolar interaction to an individual distribution of nearby centres typical of glasses. The fluctuation of these centres causing relaxation may be induced by either a multi-phonon or a thermally activated motional process.     

Rotor-encoded heteronuclear MQ MAS NMR spectroscopy of half-integer quadrupolar and spin I=1/2 nuclei

A new two-dimensional heteronuclear multiple-quantum magic-angle spinning (MQ MAS) experiment is presented which combines high resolution for the half-integer quadrupolar nucleus with information about the dipolar coupling between the quadrupolar nucleus and a spin I=1/2 nucleus. Homonuclear MQ coherence is initially created for the half-integer quadrupolar nucleus by a single pulse as in a standard MQ MAS experiment. REDOR recoupling of the heteronuclear dipolar coupling then allows the creation of a heteronuclear multiple-quantum coherence comprising multiple- and single-quantum coherence of the quadrupolar and spin I=1/2 nucleus, respectively, which evolves during t1. Provided that the t1 increment is not rotor synchronized, rotor-encoded spinning-sideband patterns are observed in the indirect dimension. Simulated spectra for an isolated IS spin pair show that these patterns depend on the recoupling time, the magnitude of the dipolar coupling, the quadrupolar parameters, as well as the relative orientation of the quadrupolar and dipolar principal axes systems. Spectra are presented for Na2HPO4, with the heteronuclear 23Na-1HMQ MAS experiments beginning with the excitation of 23Na (spin I=3/2) three-quantum coherence. Coherence counting experiments demonstrate that four- and two-quantum coherences evolve during t1. The heteronuclear spinning-sideband patterns observed for the three-spin H-Na-H system associated with the Na(2) site are analyzed. For an IS2 system, simulated spectra show that, considering the free parameters, the spinning-sideband patterns are particularly sensitive to only, first, the angle between the two IS internuclear vectors and, second, the two heteronuclear dipolar couplings. It is demonstrated that the proton localization around the Na(2) site according to the literature crystal structure of Na2HPO4 is erroneous. Instead, the experimental data is consistent with two alternative different structural arrangements, whereby either there is a deviation of 10 degrees from linearity for the case of two identical Na-H distances, or there is a linear arrangement, but the two Na-H distances are different. Furthermore, the question of the origin of spinning-sidebands in the (homonuclear) MQ MAS experiment is revisited. It is shown that the asymmetric experimental MQ sideband pattern observed for the low-C(Q) Na(2) site in Na(2)HPO4 can only be explained by considering the 23Na chemical shift anisotropy.     

Maximum entropy approach to the coupled quadrupole system

The spectral functions of the spin pair correlation functions in a coupled quadrupole system are evaluated using the maximum entropy formalism starting from the exact derivation of the frequency moments to fourth order at the high temperature limit. The numerical computations are carried out for different wave vectors and ratios of the anisotropic field to the quadrupolar interaction. The effects of these parameters on the spectral function are discussed.     

A simple theoretical treatment of quadrupolar effects on magic-angle-spinning solid-state NMR spectra of spin-1/2 nuclei in the limit of large quadrupole coupling constants

A simple approach is discussed for studying the effect of quadrupolar nuclei on the magic-angle-spinning solid-state NMR lines of spin-1/2 nuclei in the limit of large quadrupole coupling constants. Equations are derived both for the isotropic shifts and the Pake-like powder patterns for any quadrupolar spin and for arbitrary orientations of the internuclear vector with respect to the unique axis of an axially symmetric quadrupole tensor. First-order effects due to a small Zeeman perturbation on these lines are explored, as well as deviations from axial symmetry in the electric field gradient when S = 3/2 quadrupolar nuclei are involved. Spectral parameters likely to be observed in the case of coupling between ³¹P and ²⁰¹Hg are also discussed.     

Quadrupolar interaction study of various cations confined in porous charged polymer film of sPI ionomers

The structure of a sulfonated polyimide (sPI) ionomer membranes was investigated via the transport properties of various confined cations (7Li+, 23Na+, 87Rb+, 133Cs+). Their NMR spectra show large residual quadrupolar splitting depending on the orientation of the film in the static magnetic field B0. This behavior is the fingerprint of a macroscopic nematic ordering of charged interfaces. This is also confirmed by the anisotropy of the self-diffusion tensor measured by 1H and 7Li PGSE experiments on N(CH3)4+ and Li+ cations, respectively.     

Magnetic and electronic properties of hexairon(III) nanocluster with cyclic structure: a Mössbauer study

A molecular cluster containing a coplanar ring of iron(III) ions with spin 5/2 was investigated by Mössbauer spectroscopy. The iron spins are antiferromagnetically coupled so that the ground state has total spin S=0. Spectra in the absence of an applied magnetic field consisted of a quadrupolar doublet, the linewidth of which monotonically increased with the temperature. A quadrupolar splitting of about 0.35 mm/s was found. Calculations of the ironorbital electronic populations were carried out and the quadrupolar splitting was estimated. Its value was in agreement with the experimental one. In addition, the trend of the linewidth was explained in terms of isotropic spin fluctuations. Spectra in the presence of a 4.5 T longitudinal magnetic field were also collected. The hyperfine field was obtained from their fitting. Differences with respect to the hyperfine field obtained from susceptibility data were also interpreted in terms of spin fluctuations.     

Electric quadrupole interactions and the γ–α phase transition in Ce: the role of conduction electrons

We present a theoretical model of the “isostructural" - phase transition in Ce which is based on quadrupolar interactions due to coupled charge density fluctuations of 4f electrons and of conduction electrons. The latter are treated in tight-binding approximation. The - transition is described as an orientational ordering of quadrupolar electronic densities in a structure. The quadrupolar order of the conduction electron densities is complementary to the quadrupolar order of 4f electron densities. The inclusion of conduction electrons leads to an increase of the lattice contraction at the - transition in comparison to the sole effect of 4f electrons. We calculate the Bragg scattering law and suggest synchrotron radiation experiments in order to check the structure. Received 21 September 1999 and Received in final form 2 May 2000     

Spin-Echo Behavior of Nonintegral-Spin Quadrupolar Nuclei in Inorganic Solids

The response to spin-echo radiofrequency pulse excitation of a variety of nonintegral-spin quadrupolar nuclei (²³Na, ²⁷Al, and ⁹³Nb) in inorganic solids (single-crystal ruby and sapphire, α-Al₂O₃, γ-Al₂O₃, AlN, NaNO_3, KNbO₃, NaNbO₃, LiNbO₃, albite, and the zeolite Linde A), subject to strong quadrupolar interactions and dipolar interactions of varying strength, is reported. It is demonstrated that "soft" RF pulse excitation with a pair of selective π/2 and π pulses yields predictable spin-echo decay behavior as a function of dipolar interaction, the experimental results being in good agreement with the theoretical predictions.