Fast amplitude-modulated pulse trains with frequency sweep (SW-FAM) in solid-state NMR of spin-7/2 nuclei

We here investigate the sensitivity enhancement of central-transition NMR spectra of quadrupolar nuclei with spin-7/2 in the solid state, generated by fast amplitude-modulated RF pulse trains with constant (FAM-I) and incremented pulse durations (SW-FAM). Considerable intensity is gained for the central-transition resonance of single-quantum spectra by means of spin population transfer from the satellite transitions, both under static and magic-angle-spinning (MAS) conditions. It is also shown that incorporation of a SW-FAM train into the excitation part of a 7QMAS sequence improves the efficiency of 7Q coherence generation, resulting in improved signal-to-noise ratio. The application of FAM-type pulse trains may thus facilitate faster spectra acquisition of spin-7/2 systems.     

Application of fast amplitude-modulated pulse trains for signal enhancement in static and magic-angle-spinning 47,49Ti-NMR spectra

It is demonstrated that the use of fast amplitude-modulated RF pulse trains with constant (FAM-I) and incremented pulse durations (SW-FAM) leads to considerable sensitivity enhancement for the central-transition signal (via spin population transfer from the satellite transitions) for solid-state NMR spectra of titanium, 47Ti (I = [Formula: see text] and 49Ti (I = [Formula: see text]. For the magic-angle spinning spectra of TiO2 and BaTiO3, the intensity of the 49Ti central-transition line was more than doubled compared to simple Hahn-echo acquisition, while for the static case, enhancement factors of 1.6 (TiO2) and 1.8 (BaTiO3) were obtained. No lineshape distortions are observed in either MAS or static spectra of both compounds. Employment of the FAM and SW-FAM sequences should be useful in the routine acquisition of 47,49Ti spectra, as the NMR signal can be detected much faster.     

Sensitivity enhancement of NMR spectra of half-integer spin quadrupolar nuclei in solids using hyperbolic secant pulses

The experimental factors influencing the enhancements achievable for the central NMR transition, m(I)=1/2-->m(I)=-1/2, of spin-3/2 and spin-5/2 nuclei in the solid state using hyperbolic secant, HS, pulses for population transfer are investigated. In the case of powder samples spinning at the magic angle, it is found that the spinning frequency, the bandwidth and the frequency offset of the HS pulse play a crucial role in determining the maximum enhancements. Specifically, the bandwidth must be set to the spinning frequency for maximum signal enhancements. The (87)Rb NMR enhancement obtained for RbClO(4) using HS pulses was relatively insensitive to the magic angle spinning frequency; however, in the case of Al(acac)(3), the (27)Al enhancement increased with MAS frequency. In order to obtain an adiabatic HS sweep, one should optimize the rf field for a given pulse duration or optimize the pulse duration for a given rf field.     

Satellite transitions in natural abundance solid-state (33)S MAS NMR of alums--sign change with zero-crossing of C(Q) in a variable temperature study

Experiences obtained from recent improvements in the performance of solid-state (14)N MAS NMR spectroscopy have been used in a natural abundance (33)S MAS NMR investigation of the satellite transitions for this interesting spin I=3/2 isotope. This study reports the first observation of manifolds of spinning sidebands for these transitions in (33)S MAS NMR as observed for the two alums XAl(SO(4))(2) x 12H(2)O with X=NH(4) and K. For the NH(4)-alum a variable temperature (33)S MAS NMR study, employing the satellite transitions, shows that the (33)S quadrupole coupling constant (C(Q)) exhibits a linear temperature dependence (in the range -35 degrees C to 70 degrees C) with a temperature gradient of 3.1 kHz/ degrees C and undergoes a sign change with zero-crossing for C(Q) at 4 degrees C (277 K). For the isostructural K-alum a quite similar increase in the magnitude of C(Q) with increasing temperature is observed, and with a temperature gradient of 2.3 kHz/ degrees C. Finally, for optimization purposes, a study on the effect of the applied pulse widths at constant rf field strength on the intensity and variation in second-order quadrupolar lineshape for the central (1/2<-->-1/2) transition of the K-alum has been performed.     

Application of amplitude-modulated radiofrequency fields to the magic-angle spinning NMR of spin-7/2 nuclei

We report pulse sequences for the sensitivity enhancement of magic-angle spinning and multiple-quantum magic-angle spinning spectra of spin-72 systems. Sensitivity enhancement is obtained with the use of fast amplitude-modulated (FAM) radiofrequency pulses. In one-dimensional magic-angle spinning experiments, signal enhancement of 3 is obtained by a FAM pulse followed by a soft 90 degrees pulse. In two-dimensional multiple-quantum magic-angle spinning experiments, FAM pulses are used for both the excitation of multiple-quantum coherences and for their conversion into observable single-quantum coherences. The observed signal enhancements are 2.2 in 3Q experiments, 3.1 in 5Q experiments, and 4.1 in 7Q experiments, compared to the conventional two-pulse scheme. The pulse schemes are demonstrated on the 45Sc NMR of Sc2(SO4)3 x 5H2O and the 139La NMR of LaAlO3. We also demonstrate the generation of FAM pulses by double-frequency irradiation.     

Enhancing sensitivity of quadrupolar nuclei in solid-state NMR with multiple rotor assisted population transfers

Rotor-assisted population transfer (RAPT) was developed as a method for enhancing MAS NMR sensitivity of quadrupolar nuclei by transferring polarization associated with satellite transitions to the central m=12-->-12 transition. After a single RAPT transfer, there still remains polarization in the satellite transitions that can be transferred to the central transition. This polarization is available without having to wait for the spin system to return to thermal equilibrium. We describe a new RAPT scheme that uses the remaining polarization of the satellites to obtain a further enhancement of the central transition by performing RAPT-enhanced experiments multiple times before waiting for re-equilibration of the spin system. For 27Al (I=5/2) in albite we obtain a multiple RAPT enhancement of 3.02, a 48% increase over single RAPT. For 93Nb (I=9/2) in NaNbO(3) we obtain a multiple RAPT enhancement of 5.76, an 89% increase over single RAPT. We also describe a data processing procedure for obtaining the maximum possible signal-to-noise ratio.     

Calculation of pulsed NMR signal in I=3/2 quadrupolar spin system

The rf pulse response of I=3/2 spin system experiencing first order quadrupolar splitting is studied using density matrix approach. A general expression is derived in terms of spin populations, quadrupole splitting and duration and amplitude of the rf pulse for calculating the NMR signal arising due to the centre line and satellite resonances for the situation where the impressed rf pulse excites the resonances selectively as well as non-selectively. The necessary 4×4 transformation matrix obtained analytically by diagonalyzing the Hamiltonian are used to get the expression for the centre line response. The satellite signals are obtained in the same way but by using the numerical values of the roots of the related quartics. The widths of the corresponding π/2-pulses are calculated for different initial spin populations. The variations of this pulse-width and the corresponding signal amplitude as a function of satellite splitting are studied.     

Efficient 5QMAS NMR of spin-5/2 nuclei: use of fast amplitude-modulated radio-frequency pulses and cogwheel phase cycling

We report here an efficient multiple-quantum magic-angle spinning (MQMAS) pulse sequence involving fast amplitude-modulated (FAM) radio-frequency pulses for excitation and conversion of five-quantum (5Q) coherences of spin-5/2 nuclei. The use of a FAM-I type pulse train for the conversion of 5Q into 1Q coherences proves to be easier to implement experimentally than the earlier suggested use of a FAM-II type sequence [J. Magn. Reson. 154 (2002) 280], while delivering at least equal signal enhancement. Results of numerical simulations and experimental 27Al 5QMAS spectra of aluminium acetylacetonate for different excitation and conversion schemes are compared to substantiate these claims. We also demonstrate the feasibility of acquiring 5QMAS spectra of spin-5/2 systems using cogwheel phase cycling [J. Magn. Reson. 155 (2002) 300] to select the desired coherence pathways. A cogwheel phase cycle of only 57 steps is shown to be as effective as the minimum conventional nested 77-step phase cycle.     

Sensitivity enhancement in natural-abundance solid-state 33S MAS NMR spectroscopy employing adiabatic inversion pulses to the satellite transitions

The WURST (wideband uniform rate smooth truncation) and hyperbolic secant (HS) pulse elements have each been employed as pairs of inversion pulses to induce population transfer (PT) between the four energy levels in natural abundance solid-state (33)S (spin I=3/2) MAS NMR, thereby leading to a significant gain in intensity for the central transition (CT). The pair of inversion pulses are applied to the satellite transitions for a series of inorganic sulfates, the sulfate ions in the two cementitious materials ettringite and thaumasite, and the two tetrathiometallates (NH(4))(2)WS(4) and (NH(4))(2)MoS(4). These materials all exhibit (33)S quadrupole coupling constants (C(Q)) in the range 0.1-1.0 MHz, with precise C(Q) values being determined from analysis of the PT enhanced (33)S MAS NMR spectra. The enhancement factors for the WURST and HS elements are quite similar and are all in the range 1.74-2.25 for the studied samples, in excellent agreement with earlier reports on HS enhancement factors (1.6-2.4) observed for other spin I=3/2 nuclei with similar C(Q) values (0.3-1.2 MHz). Thus, a time saving in instrument time by a factor up to five has been achieved in natural abundance (33)S MAS NMR, a time saving which is extremely welcome for this important low-gamma nucleus.     

Fast amplitude-modulated pulse trains with frequency sweep (SW-FAM) in static NMR of half-integer spin quadrupolar nuclei

In solid-state NMR of quadrupolar nuclei with half-integer spin I, fast amplitude-modulated (FAM) pulse trains have been utilised to enhance the intensity of the central-transition signal, by transferring spin population from the satellite transitions. In this paper, the signal-enhancement performance of the recently introduced SW-FAM pulse train with swept modulation frequency [T. Br?uniger, K. Ramaswamy, P.K. Madhu, Enhancement of the central-transition signal in static and magic-angle-spinning NMR of quadrupolar nuclei by frequency-swept fast amplitude-modulated pulses, Chem. Phys. Lett. 383 (2004) 403-410] is explored in more detail for static spectra. It is shown that by sweeping the modulation frequencies linearly over the pulse pairs (SW1/tau-FAM), the shape of the frequency distribution is improved in comparison to the original pulse scheme (SWtau-FAM). For static spectra of 27Al (I=5/2), better signal-enhancement performance is found for the SW1/tau-FAM sequence, as demonstrated both by experiments and numerical simulations.     

Optimizing STMAS

The 2D satellite transition magic angle spinning (STMAS) experiment generates efficiently high-resolution isotropic NMR spectra of half-integer quadrupolar nuclei. The experiment involves excitation and coherence transfer of satellite transitions into the central transition. It requires efficient refocusing of satellite transitions and sample spinning at a very accurate magic angle to cancel the first-order quadrupolar interaction effect. A review of all parameters relevant to optimizing the STMAS experiment is presented, including pulse sequence calibration, regulating spinning speed, magic angle adjustment, optimization of satellite transition excitation, and coherence transfer for both I = 3/2 and I > or =5/2 nuclei.     

Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems

We have recently shown that the sensitivity of single- and multiple-quantum NMR experiments of half-integer (N/2) quadrupolar nuclei can be increased significantly by introducing so-called double frequency sweeps (DFS) in various pulse schemes. These sweeps consist of two sidebands generated by an amplitude modulation of the RF carrier. Using a time-dependent amplitude modulation the sidebands can be swept through a certain frequency range. Inspired by the work of Vega and Naor (J. Chem. Phys. 75, 75 (1981)), this is used to manipulate +/-(m - 1) <--> +/-m (3/2 < or = m < or = N/2) satellite transitions in half-integer spin systems simultaneously. For (23)Na (I = 3/2) and (27)Al (I = 5/2) spins in single crystals it proved possible to transfer the populations of the outer +/-m spin levels to the inner +/-1/2 spin levels. A detailed analysis shows that the efficiency of this process is a function of the adiabaticity with which the various spin transitions are passed during the sweep. In powders these sweep parameters have to be optimized to satisfy the appropriate conditions for a maximum of spins in the powder distribution. The effects of sweep rate, sweep range, and RF field strength are investigated both numerically and experimentally. Using a DFS as a preparation period leads to significantly enhanced central transition powder spectra under both static and MAS conditions, compared to single pulse excitation. DFSs prove to be very efficient tools not only for population transfer, but also for coherence transfer. This can be exploited for the multiple- to single-quantum transfer in MQMAS experiments. It is demonstrated, theoretically and experimentally, that DFSs are capable of transferring both quintuple-quantum and triple-quantum coherence into single-quantum coherence in I = 5/2 spin systems. This leads to a significant enhancement in signal-to-noise ratio and strongly reduces the RF power requirement compared to pulsed MQMAS experiments, thus extending their applicability. This is demonstrated by (27)Al 3QMAS experiments on 9Al(2)O(3). 2B(2)O(3) and the mineral andalusite. In the latter compound, Al experiences a quadrupolar-coupling constant of 15.3 MHz in one of the sites. Finally a 5QMAS spectrum on 9Al(2)O(3). 2B(2)O(3) demonstrates the sensitivity enhancement of this experiment using a double frequency sweep.     

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.     

59Co chemical shift anisotropy and quadrupole coupling for K3Co(CN)6 from MQMAS and MAS NMR spectroscopy

59Co triple-quantum (3Q) MAS and single-pulse MAS NMR spectra of K3Co(CN)6 have been obtained at 14.1 T and used in a comparison of these methods for determination of small chemical shift anisotropies for spin I = 7/2 nuclei. From the 3QMAS NMR spectrum a spinning sideband manifold in the isotropic dimension with high resolution is reconstructed from the intensities of all spinning sidebands in the 3QMAS spectrum. The chemical shift anisotropy (CSA) parameters determined from this spectrum are compared with those obtained from MAS NMR spectra of (i) the complete manifold of spinning sidebands for the central and satellite transitions and of (ii) the second-order quadrupolar lineshapes for the centerband and spinning sidebands from the central transition. A good agreement between the three data sets, all of high precision, is obtained for the shift anisotropy (delta(sigma) = delta(iso) - delta(zz)) whereas minor deviations are observed for the CSA asymmetry parameter (eta(sigma)). The temperature dependence of the isotropic 59Co chemical shift has been studied over a temperature range from -28 to +76 degrees C. A linear and positive temperature dependence of 0.97 ppm/degree C is observed.     

Satellite-transition MAS NMR of spin I = 3/2, 5/2, 7/2, and 9/2 nuclei: sensitivity,resolution, and practical implementation

The satellite-transition MAS (STMAS) experiment offers an alternative approach to established methods such as dynamic angle spinning (DAS), double rotation (DOR), and multiple-quantum MAS (MQMAS) for obtaining high-resolution NMR spectra of half-integer quadrupolar nuclei. Unlike the multiple-quantum experiment, STMAS involves two-dimensional correlation of purely single-quantum coherences; satellite transitions in t(1) (or F(1)) and the central transition in t(2) (or F(2)). To date, STMAS has primarily been demonstrated for nuclei with spin quantum numbers I = 3/2 and, to a lesser extent, I > 5/2. However, many chemically relevant nuclei possess I > 3/2, such as (17)O and (27)Al (both I = 5/2), (59)Co (I = 7/2), and (93)Nb (I = 9/2). Here, we discuss the application of STMAS to nuclei with spin quantum numbers from I = 3/2 to 9/2. First, we consider the practical implementation of the STMAS experiment using (87)Rb (I = 3/2) NMR as an example. We then extend the discussion to include nuclei with higher spin quantum numbers, demonstrating (27)Al, (45)Sc (I = 7/2), (59)Co, and (93)Nb STMAS experiments on both crystalline and amorphous samples. We also consider the possibility of experiments involving satellite transitions other than m(I) = +/- 1/2 <--> +/- 3/2 and, using (93)Nb NMR, demonstrate the correlation of all single-quantum satellite transitions up to and including m(I) = +/- 7/2 <--> +/- 9/2. The absolute chemical shift scaling factors in these experiments are discussed, as are the implications for isotropic resolution.     

Influencing the satellite transitions of half-integer quadrupolar nuclei for the enhancement of magic angle spinning spectra

Double frequency sweeps can induce spin transitions in a set of satellites of a half-integer quadrupolar nucleus by simultaneously passing through resonance for a satellite pair. It is shown that by transferring population from the outer spin levels to the inner |1/2 and |−1/2 levels an increased intensity for central transition spectra is obtained. Although Magic Angle Spinning in principle interferes with this process, and the adiabaticity of the passages is different for every crystallite in a powder, enhanced spectra with undistorted line shapes are obtained for I=3/2 (²³Na) and 5/2 (²⁷Al) spins experiencing quadrupolar interactions with ω_Q in the range 0.1–3 MHz. Even at spinning speeds up to 30 kHz significant enhancements are obtained. An analysis of the combined effects of double frequency sweeps (DFS) and MAS indeed shows strongly different effects for different crystallites in powder ranging from no gain at all to the theoretical maximum gain of 2I. As the effects are randomly distributed over all orientations on a sphere this is averaged over the whole line shape. Therefore, undistorted powder patterns are obtained enhanced by the average gain over the individual crystallites. Saturation of the satellite transitions, which can only be achieved if spin–spin relaxation is sufficiently strong, leads to identical results. Optimization of the sweeps should be toward an optimal effect on the population transfer to the central levels and chosen short with respect to spin–lattice relaxation times.     

<Superscript>33</Superscript>S MAS NMR of a disordered sulfur-doped silicate: Signal enhancement via RAPT,QCPMG and adiabatic pulses

Three different signal enhancement techniques have been applied to ³³S magic-angle spinning nuclear magnetic resonance (MAS NMR) of a disordered silicate containing 1.15 wt% ³³S. Partial saturation of the satellite transitions was achieved using a rotor-assisted population transfer (RAPT) pulse sequence, resulting in a signal enhancement of 1.63, albeit with a slight distortion of the line shape due to selective excitation. Adiabatic inversion of the satellite transitions by various amplitude-and frequency-modulated pulse shapes (such as hyperbolic secant and wideband uniform-rate smooth truncation) was also attempted, resulting in a signal enhancement of up to 1.85, with no apparent line shape distortion. Quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) and RAPT-QCPMG sequences were also used, both of which yielded spikelet spectra that accurately reflected the MAS line shape with a greatly improved signal-to-noise ratio. It is hoped that this study demonstrates that ³³S solid-state MAS NMR is now feasible even on disordered, low-sulfur-content systems.     

Homogeneous broadenings in 2D solid-state NMR of half-integer quadrupolar nuclei

The question of the homogeneous broadening that occurs in 2D solid-state NMR experiments is examined. This homogeneous broadening is mathematically introduced in a simple way, versus the irreversible decay rates related to the coherences that are involved during t1 and t2. We give the pulse sequences and coherence transfer pathways that are used to measure these decay rates. On AlPO4 berlinite, we have measured the 27Al echo-type relaxation times of the central and satellite transitions on 1Q levels, so that of coherences that are situated on 2Q, 3Q, and 5Q levels. We compare the broadenings that can be deduced from these relaxation times to those directly observed on the isotropic projection of berlinite with multiple-quantum magic-angle spinning (MAS), or satellite-transition MAS. We show that the choice of the high-resolution method, should be done according to the spin value and the corresponding homogeneous broadening.     

Theoretical and experimental assessment of single- and multiple-quantum cross-polarization in solid state NMR

Continuous wave cross-polarization (CP) NMR experiments with magic angle spinning (MAS) are reviewed for the case of isolated spin pairs I-S, with spin quantum numbers I = ½ and S ½ (1/2, 3/2, …). For two spin-1/2 nuclei, the Hartmann-Hahn matching conditions are examined at various sample rotation rates ν_R, especially with regard to off-resonance behaviour. In addition to signal enhancement, the CPMAS experiment can be used for the selective determination of inter-nuclear distances between spin-1/2 nuclei. Theoretical examination of the CP transfers to single-quantum (1Q-CPMAS) and multiple-quantum (MQ-CPMAS) levels of quadrupolar nuclei is presented. Simple analytical formulae describing the Hartmann-Hahn matching under various experimental conditions are verified using computer simulations of the spin density matrix under MAS, and the experimental data. The strategies for the most efficient acquisition of 1Q-CPMAS and MQ-CPMAS spectra are extensively discussed.     

Investigations of low-amplitude radio frequency pulses at and away from rotary resonance conditions for I = 5/2 nuclei

Additional experimental evidence of rotary resonance effects for multiple-quantum coherence conversion in a spin-5/2 system is presented. Two-dimensional plots of the relative efficiency of MQ excitation and conversion are given as a function of radio frequency (rf) amplitude and pulse width. Data are presented for the excitation of five-quantum coherence (5QC), as well as for 5QC to three-quantum coherence (3QC) conversion, 5QC to IQC (the central transition coherence) conversion, and 3QC to IQC conversion. A two-fold increase in the signal-to-noise ratio is achieved by substituting low amplitude rf pulses in place of hard rf pulses for 5QC excitation and 5QC to 3QC conversion in a mixed multiple-quantum magic angle spinning (MAS) (MMQMAS) experiment. The anisotropic line shape for the low-amplitude rf pulse version of the MMQMAS experiment was observed to be distorted from the MAS line shape. The cause and implications of the distortion are discussed.