Triple-quantum MAS-NMR of quadrupolar nuclei

From two-dimensional multiquantum NMR spectra of quadrupolar nuclei, it is now possible to obtain much greater resolution than in a classical single-quantum magic-angle spinning or variable-angle spinning spectrum. We describe here a very simple pulse scheme which efficiently excites the desired multiquantum NMR coherence and a new acquisition procedure which yields to pure-absorption mode 2D spectra. Experimental spectra for ⁸⁷Rb in polycrystalline rubidium nitrate illustrate the method.     

From crystalline to glassy gallium fluoride materials: an NMR study of Ga and Ga quadrupolar nuclei

Owing to the implementation of acquisition techniques specific for nuclei with very large quadrupolar interaction (full shifted echo and variable offset cumulative spectra (VOCS)), NMR spectra of ⁶⁹Ga and ⁷¹Ga are obtained in crystallised (PbGaF₅, Pb₃Ga₂F₁₂, Pb₉Ga₂F₂₄ and CsZnGaF₆) and glassy (PbF₂–ZnF₂–GaF₃) gallium fluorides. Simulations of both static (full echo or VOCS) and 15 kHz MAS spectra allow to obtain consistent determinations of isotropic chemical shifts and very large quadrupolar parameters (ν_Q up to 14 MHz). In the crystalline compounds whose structures are unknown, the number and the local symmetry of the different gallium sites are tentatively worked out. For the glassy systems, a continuous Czjzek's distribution of the NMR quadrupolar parameters accounts for the particular shape of the NMR spectrum.     

Incomplete double frequency sweeps to select small quadrupolar coupling static powder patterns

Difference spectra based on the magnitude of the quadrupolar coupling of a site has been observed under static conditions utilizing a double frequency sweep pulse sequence to enhance the central transition of a small electric field gradient (EFG) environment. Through the use of convergent sweeps that only cover the inner satellite transitions of the smaller EFG site, an echo spectrum results that favors the smaller site, which can then be used in conjunction with normal echo spectra to create a difference spectrum that consists primarily of the smaller site. The simplification of the static lineshape data permits simulation for the extraction of chemical shift anisotropy (CSA) information for the site. The method is demonstrated using ⁹³Nb NMR for samples with multiple niobium environments due to mixtures of compounds, MgNb₂O₆/LiNbO₃, or due to crystallographic structure, KCa₂Nb₃O₁₀.     

Through-space R3-HETCOR experiments between spin-1/2 and half-integer quadrupolar nuclei in solid-state NMR

We present several new methods that allow to obtain through-space 2D HETCOR spectra between spin-1/2 and half-integer quadrupolar nuclei in the solid state. These methods use the rotary-resonance concept to create hetero-nuclear coherences through the dipolar interaction instead of scalar coupling into the HMQC and refocused INEPT experiments for spin n/2 (n>1). In opposite to those based on the cross-polarization transfer to quadrupolar nuclei, the methods are very robust and easy to set-up.     

MAS NMR spectra of quadrupolar nuclei in disordered solids: the Czjzek model

Structural disorder at the scale of two to three atomic positions around the probe nucleus results in variations of the EFG and thus in a distribution of the quadrupolar interaction. This distribution is at the origin of the lineshape tailing toward high fields which is often observed in the MAS NMR spectra of quadrupolar nuclei in disordered solids. The Czjzek model provides an analytical expression for the joint distribution of the NMR quadrupolar parameters upsilon(Q) and eta from which a lineshape can be predicted. This model is derived from the Central Limit Theorem and the statistical isotropy inherent to disorder. It is thus applicable to a wide range of materials as we have illustrated for 27Al spectra on selected examples of glasses (slag), spinels (alumina), and hydrates (cement aluminum hydrates). In particular, when relevant, the use of the Czjzek model allows a quantitative decomposition of the spectra and an accurate extraction of the second moment of the quadrupolar product. In this respect, it is important to realize that only rotational invariants such as the quadrupolar product can make sense to describe the quadrupolar interaction in disordered solids.     

固体四极体系NMR及其应用

比较详细介绍了近年来固体四极核体系核磁共振技术的发展,及其在物理,化学与材料等科研领域的应用情况,简单讨论了本实验室在这些方面的一些工作。     

Two-dimensional one pulse MAS of half-integer quadrupolar nuclei

We show that the two-dimensional one pulse (TOP) representation of magic-angle spinning nuclear magnetic resonance data of half-integer quadrupolar nuclei has significant advantages over the conventional one-dimensional spectrum. The TOP spectrum, which correlates NMR frequency to spinning sideband order, provides a rapid determination of the number of sites as well as the size of the their quadrupolar coupling. Additionally, synchronous acquisition spectra of the central and satellite transition resonances can be separated by different projections of the TOP spectrum, with higher resolution spectra often found in the satellite transitions projection. A previously perceived problem of centerband aliasing in TOP can be eliminated with an algorithm that uses larger subspectral widths and the sideband order dimension to distinguish centerbands from sidebands.     

Observation of "hidden" magnesium: first-principles calculations and 25Mg solid-state NMR of enstatite

²⁵Mg NMR parameters have been determined for two polymorphs of enstatite (MgSiO₃), an important magnesium silicate phase present as a major component of the Earth's upper mantle. The crystal structures of both polymorphs contain two crystallographically distinct magnesium sites; however, only a single resonance is observed in ²⁵Mg MAS NMR spectra recorded at 14.1 and 20.0 T. First-principles calculations performed on geometry-optimised crystal structures reveal that the quadrupolar interaction for the second site is expected to be very large, resulting in extensive broadening of the spectral resonance, explaining its apparent absence in the NMR spectrum. ²⁵Mg QCPMG NMR experiments employing variable offset cumulative spectroscopy (VOCS) are used to observe the broadened site and enable measurement of NMR parameters. The large difference in quadrupolar interaction between the two crystallographic magnesium sites is rationalised qualitatively in terms of the distortion of the local coordination environment as well as longer-range effects using a simple point charge model.     

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.     

Multi-quantum echoes in GdAl2 zero-field high-resolution NMR

In this paper we present a series of high-resolution zero-field NMR spectra of the polycrystalline intermetallic compound GdAl₂. The spectra were obtained with the sample at 4.2 K in the ordered magnetic state and in the absence of an external static magnetic field. Using a sequence composed of two RF pulses, we obtained up to five multi-quantum echoes for the ²⁷Al nuclei, which were used to construct the zero-field NMR spectra. The spectra obtained from the FID observed after the second pulse and the even echoes exhibited higher resolution than the odd ones. In order to explain such behavior, we propose a model in which there are two regions inside the sample with different inhomogeneous spectral-line broadenings. Moreover, with the enhanced resolution from the FID signal, we were able to determine quadrupolar couplings with great precision directly from the respective spectra. These results were compared with those obtained from the quadrupolar oscillations of the echo signals, and showed good agreement. Similar data were also obtained from ¹⁵⁵Gd and ¹⁵⁷Gd nuclei.     

Slow turning reveals enormous quadrupolar interactions (STREAQI)

We introduce a new solid-state NMR method, which uses very slow sample rotation to visualize NMR spectra whose width exceeds feasible spectrometer bandwidths. It is based on the idea that if we reorient a tensor by a known angle about a known axis, the shifts in the NMR frequencies observed across the spectral width allow us to reconstruct the entire tensor. Called STREAQI (Slow Turning Reveals Enormous Anisotropic Quadrupolar Interactions), this method allows us to probe NMR nuclei that are intractable to current methods. To prove the concept and demonstrate its promise we have implemented the method for several 79Br containing samples with quadrupolar coupling constants in the range of 10-50 MHz.     

High resolution heteronuclear correlation NMR spectroscopy between quadrupolar nuclei and protons in the solid state

A high resolution two-dimensional solid state NMR experiment is presented that correlates half-integer quadrupolar spins with protons. In this experiment the quadrupolar nuclei evolve during t1 under a split-t1, FAM-enhanced MQMAS pulse scheme. After each t1 period ending at the MQMAS echo position, single quantum magnetization is transferred, via a cross polarization process in the mixing time, from the quadrupolar nuclei to the protons. High-resolution proton signals are then detected in the t2 time domain during wPMLG5* homonuclear decoupling. The experiment has been demonstrated on a powder sample of sodium citrate and 23Na-1H 2D correlation spectra have been obtained. From the HETCOR spectra and the regular MQMAS spectrum, the three crystallographically inequivalent Na+ sites in the asymmetric unit were assigned. This MQMAS-wPMLG HETCOR pulse sequence can be used for spectral editing of half-integer quadrupolar nuclei coupled to protons.     

A new sequence for the MQMAS/HETCOR experiment

Two-dimensional (2D) multiple quantum MAS (magic angle spinning) spectroscopy has been combined with cross-polarisation to obtain a heteronuclear correlation spectrum between a quadrupolar spin-3/2 and a spin-1/2 nucleus. The advantage over the conventional correlation experiment is the increased resolution obtained in the multiple quantum dimension. Pure absorption 2D spectra can be obtained by implementing a zero quantum filter between the evolution of multiple quanta and the subsequent cross-polarisation step. The current experiment shows a considerable improvement in sensitivity compared to a previously introduced sequence.     

Oxygen sites in the zeolite stilbite: a comparison of static, MAS, VAS, DAS and triple quantum MAS NMR techniques

Static, magic angle spinning (MAS), variable angle spinning (VAS), dynamic angle spinning (DAS) and triple quantum magic angle spinning (3QMAS) NMR techniques were applied to separate and quantify oxygen signals from Al–O–Si and Si–O–Si sites of ¹⁷O-enriched samples of the mineral stilbite, a natural zeolite. DAS experiments showed that there was a distribution of quadrupolar coupling constants, asymmetry parameters and isotropic chemical shifts. Two methods were used to study the quantification problem of DAS and 3QMAS. Our results showed that DAS was quantitative. In 3QMAS, signal intensity from sites with larger quadrupolar coupling constants was reduced because of less efficient excitation. All techniques have shown a clear difference in rates of exchange between the two types of sites with interchannel H₂O molecules.     

Quantum logical operations for spin 3/2 quadrupolar nuclei monitored by quantum state tomography

This article presents the realization of many self-reversible quantum logic gates using two-qubit quadrupolar spin 3/2 systems. Such operations are theoretically described using propagation matrices for the RF pulses that include the effect of the quadrupolar evolution during the pulses. Experimental demonstrations are performed using a generalized form of the recently developed method for quantum state tomography in spin 3/2 systems. By doing so, the possibility of controlling relative phases of superimposed pseudo-pure states is demonstrated. In addition, many aspects of the effect of the quadrupolar evolution, occurring during the RF pulses, on the quantum operations performance are discussed. Most of the procedures presented can be easily adapted to describe selective pulses of higher spin systems (>3/2) and for spin 1/2 under J couplings.     

Homonuclear correlation experiments for quadrupolar nuclei, spinning away from the magic angle

We present a set of homonuclear correlation experiments for half-integer quadrupolar spins in solids. In all these exchange-type experiments, the dipolar interaction is retained during the mixing time by spinning the sample at angles other than the “regular magic angle” (54.7°). The second-order quadrupolar interaction is averaged by different strategies for the different experiments. The multiple-quantum off magic angle spinning (MQOMAS) exchange experiment is essentially a regular MQMAS experiment where the quadrupolar interaction is averaged by combining magic angle spinning with a multiple- to single-quantum correlation scheme. The sample is spun at the magic angle at all times except during the mixing time which is added to establish homonuclear correlation. In the multiple-quantum P₄ magic angle spinning (MQP₄MAS) exchange experiment, the sample is spun at one of the angles at which the fourth-order Legendre polynomial vanishes (P₄ magic angle), the remaining second-order quadrupolar interaction now governed by a second-rank tensor is refocussed by the multiple to single-quantum correlation scheme. In the dynamic angle spinning (DAS) exchange experiment, the second-order quadrupolar interaction is averaged by correlating the evolution from two complementary angles. These experiments are demonstrated and compared, in view of their specific advantages and disadvantages, for ²³Na in the model compound Na₂SO₃.     

Noise Reduction in Quadrupolar Echo Spectra at Short Echo Times

The phase cycling scheme Exorcycle embedded into the quadrupolar echo pulse sequence is presented as a tool for reducing ringing effects in broad quadrupolar spectra.     

Singularities in the lineshape of a second-order perturbed quadrupolar nucleus and their use in data fitting

Even for large quadrupolar interactions, the powder spectrum of the central transition for a half-integral spin is relatively narrow, because it is unperturbed to first order. However, the second-order perturbation is still orientation dependent, so it generates a characteristic lineshape. This lineshape has both finite step discontinuities and singularities where the spectrum is infinite, in theory. The relative positions of these features are well-known and they play an important role in fitting experimental data. However, there has been relatively little discussion of how high the steps are, so we present explicit formulae for these heights. This gives a full characterization of the features in this lineshape which can lead to an analysis of the spectrum without the usual laborious powder average.The transition frequency, as a function of the orientation angles, shows critical points: maxima, minima and saddle points. The maxima and minima correspond to the step discontinuities and the saddle points generate the singularities. Near a maximum, the contours are ellipses, whose dimensions are determined by the second derivatives of the frequency with respect to the polar and azimuthal angles. The density of points is smooth as the contour levels move up and down, but then drops to zero when a maximum is passed, giving a step. The height of the step is determined by the Hessian matrix—the matrix of all partial second derivatives. The points near the poles and the saddle points require a more detailed analysis, but this can still be done analytically. The resulting formulae are then compared to numerical simulations of the lineshape.We expand this calculation to include a relatively simple case where there is chemical shielding anisotropy and use this to fit experimental ¹³⁹La spectra of La₂O₃.     

半整数四极体系中心跃迁的多次激发NMR谱(英文)

本文对半整数四极体系中心跃迁的多次激发NMR进行了研究,结果表明该方法能够较大地提高接收信号的强度.另外对多次激发脉冲序列的激发带宽问题作了讨论,在实验上用40％NaCl 60％NaNO_2粉末混合物对以上结论作了验证.     

化学位移各向导性对半整数自旋四极核的2D NMR章动的影响(英文)

考察了化学位移各向异性对半整数自旋四极核2DNMR章动的影响．用数值方法对2DNMR章动实验的演化期的Hamiltonian矩阵进行对角化，然后用帐篷法进行粉末平均，获得了自旋为I＝3／2、5／2、7／2和9／2的四极核在不同化学位移各向异性下的2DNMR章动谱．实验结果与理论计算符合较好．