Second-order Quadrupolar Interaction Research Articles

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.

Niobium-93 MQMAS NMR Spectroscopic Study of Alkali and Lead Niobates

93Nb (I=9/2) multiple-quantum magic-angle spinning (MQMAS) NMR spectra of a series of inorganic niobates have been measured. 93Nb MQMAS spectroscopy yields spectra with typically an order of magnitude higher resolution than that obtainable with 93Nb MAS spectroscopy and 93Nb dynamic-angle spinning (DAS) spectroscopy. For example, the full-width at half-maximums of the 93Nb resonances of LiNbO3 were 9 (MAS), 5.8 (DAS), and 0.7 kHz (MQMAS). Broadening of the 93Nb MAS and DAS spectra is due to the second-order quadrupolar and homonuclear dipolar interactions, respectively. The quadrupolar products (PQ) and isotropic chemical shifts (δiso) of the 93Nb resonances of LiNbO3, NaNbO3, PbNb2O6, Pb2Nb2O7, Pb3Nb2O8, Pb5Nb4O15, Pb3Nb4O13, and Pb1.83Nb1.71Mg0.29O6.39 were determined from MQMAS spectra and range from 13.6 to 26.8 MHz and from −951 to −1113 ppm, respectively. Resonances with relatively large quadrupolar coupling constants (>30 MHz) were not observed using MQMAS spectroscopy, but were detected using nutation spectroscopy. The applicability and limitations of MQMAS spectroscopy in studying inorganic niobates containing multiple 93Nb resonances are addressed and compared with those of MAS, nutation, and DAS spectroscopies.

Solid-state 7Li NMR studies of inverse spinel LiNi xCo 1− xVO 4 cathode materials

Solid-state 7Li NMR spectroscopy revealed different Ni/Co distributions in an inverse spinel structure of LiNi x Co 1− x VO 4 cathode materials prepared by either a high-temperature solid-state reaction method (abbreviated as the HT method) or a low-temperature solution co-precipitation method (abbreviated as the LT method). Solid-state 7Li NMR measurements confirmed that the lithium nuclear spin was dominated by a chemical shift anisotropy (CSA) interaction compounded with a small second-order quadrupolar interaction. Ni/Co distribution and inhomogeneity of chemical shift tensors ( δ CSA and η CSA constants) associated with crystalline defects are accountable for the variation in spread of the MAS spinning side-band manifolds between nickel uptake and preparation methods. The NMR study also revealed that the HT method yielded broader Ni/Co distributions with greater lithium defects, while the LT method gave much more homogeneous Ni/Co distributions with smaller defects. The NMR results were consistent with XRD data that showed a gradual expansion in the unit-cell lattice with increasing Co content. All cells suffered a large irreversible loss in overall capacity in the first cycle and became stable in terms of cycle efficiency during later cycling. We have found that LiNi x Co 1− x VO 4 cathode materials prepared by the LT method with more homogeneous Ni/Co distribution and smaller crystalline defects offer a small advantage in capacity over the HT method.

Powder MAS NMR lineshapes of quadrupolar nuclei in the presence of second-order quadrupole interaction

We derive a complete analytical solution for the powder magic angle spinning (MAS) nuclear magnetic resonance (NMR) lineshape in the presence of second-order quadrupole interaction, considering a radiofrequency (rf) pulse of finite width, a finite MAS frequency, and a non-zero asymmetry parameter. 〈 I x 〉 is calculated using two approaches. The first applies time-dependent perturbation theory in the presence of the rf pulse and stationary perturbation theory (SPT) in its absence. The second is based on the Magnus expansion of the density matrix in the interaction representation during the pulse and SPT in its absence. We solve the problem in the laboratory frame using the properties of the Fourier transform and spin operators. Diagonalisation is not required. Both approaches agree well with each other under all conditions and also with the transition probability approach for the central transition. The Magnus expansion exists at all times and the effect of the non-secular terms is negligible. We describe an analytical method of averaging 〈 I x 〉 over the Euler angles and simulate the 11B MAS NMR lineshapes for crystalline and vitreous B 2O 3. A critical analysis is given of all earlier calculations of the MAS NMR lineshape.

Structural Analysis of Boron Carbide Using 2D 11B-MQMAS NMR

Abstract 2D 11B-multiple quantum magic angle spinning NMR spectra of boron carbide were measured in order to eliminate the second-order quadrupole interaction of 11B in B4C. Judging from the line width of MQMAS spectrum, not only the second-order quadrupole interaction but also the B-B dipole-dipole interaction was found to cause the line broadening of B4C in 11B-MAS NMR. They affect the line width in the ratio about 1.3 : 1 at spinning rate of 17 kHz.

Spin-locking mechanism of spin I=3/2 quadrupolar nuclei undergo magic angle spinning

The spin-locking mechanism of the spin I=3/2 quadrupolar nuclei under magic angle spinning (MAS) has been theoretically and experimentally investigated, and the criterion of adiabatic passage around zero-crossings of the quadrupole splitting was inferred from the time-dependent Shrödinger equation in this article. The theory, numerical simulations, and experiments conducted in this work all indicated that second-order quadrupole interaction and off-resonance play important roles in the spin-locking of the quadrupolar nuclei, and they were responsible for the great loss of the spin-locking signals. The spin-locking for a spin I=3/2 nucleus might be achieved by minimizing the effect of the second-order quadrupole interaction by using a radio frequency (RF) offset. This offset was realized by setting the RF to the opposite position of the isotropic second-order quadrupolar shift of single quantum coherences.

Mixed alkali effect in a three dimensional structure NASICON

The conductivity has a minimum against ionic ratio in Na2−yAgyZr1.5Mg0.5(PO4)3 with a three dimensional network which is called as a mixed alkali effect (MAE). In this paper, we discussed23Na and31P MAS NMR spectra in MAE. The central line profiles exhibit characteristic changes due to values of asymmetry parameter η. The observed profiles are produced by the second-order quadrupole interaction with the electric field gradient. The peak intensity of side band against ionic ratio in MAS NMR spectra showed a small maximum due to the Na-Ag dipolar interaction which corresponds to the conductivity minimum. The chemical shifts of31P MAS NMR showed the strong dependence of polarizability of mobile ions that share oxygens in the PO4 tetrahedra and the ZrO6 octahedra. Their results indicate that there are some ordered structures of Na-Ag dependent on the ionic ratio in MAE.

Sodium-23 MAS NMR study on nuclear quadrupole interaction in Na 1− xAg xNO 2

Ag-impurity effects on the first- and second-order quadrupole interaction (QI) at 23 Na site in an isomorphic mixed system, Na 1− x Ag x NO 2 ( x=0, 0.0084, 0.026, 0.079, 0.094, 0.16), have been investigated by employing 23 Na ( I=3/2) magic angle spinning nuclear magnetic resonance (MAS NMR) technique. The central transition (CT) and satellite transition (ST) are simultaneously observed with this system. From the spectral analysis, the quadrupole parameter and its distribution width are obtained as a function of Ag concentration. From the intensity loss of CT MAS centerband and of the envelope function of ST MAS sidebands due to impurities, the range of their influence on the second- and first-order QI is estimated. The estimated ranges contain the second and first neighbouring Na sites from the resonating 23 Na nucleus for the first- and second-order QI, respectively.

Nuclear magnetic resonance studies on Cu3Au, CuAu and CuAu3alloys

Abstract Nuclear magnetic resonance (NMR) measurements of 63 Cu nuclei have been carried out on Cu3Au, CuAu and CuAu3 alloys with different degrees of order. The spin-echo spectra obtained from the disordered and the ordered CuAu3 phases exhibit an intense sharp resonance line. On the other hand, the characteristic resonance line broadened owing to second-order quadrupole interaction appears in the spin-echo spectra from the fully ordered Cu3Au and CuAu I phases. The spectra from the partially ordered Cu3Au and CuAu I phases and the high-temperature CuAu II phase can be fitted by the superposition of the broad line for the ordered state and the sharp line for the disordered state. It is demonstrated that the order-disorder transition for these alloys occurs heterogeneously, in contrast with the result of X-ray diffraction analysis. The NMR parameters such as the Knight shift K and the quadrupole coupling constant e 2 qQ/h are evaluated for the ordered and disordered phases for three kinds of alloy of diff...

Scaling and labeling the high-resolution isotropic axis of two-dimensional multiple-quantum magic-angle-spinning spectra of half-integer quadrupole spins

(obs) ! of the center of gravity of an MQ-filtered central-transition peak in the two dimensions allows us to determine the true isotropic chemical shift of an absorption line, which is related to the mean bond angle in a compound. Only the isotropic chemical shift and the second-order quadrupole interaction for a sample rotating at the magic angle at a high spinning rate are considered during the free precession of the spin system. On the other hand, only the first-order quadrupole interaction for a static sample is considered during the pulses. The hypercomplex detection method is used to obtain a pure 2D absorption spectrum. The pulse program and the successive stages of data processing are described. For simplicity, only the density matrix for a spin I5 3 at the end of the first pulse of phase w is calculated in detail, which allows us to deduce the phase cycling of the pulse sequence that selectively detects the 63-quantum coherences generated by the first pulse. The positions of the echo and antiecho relative to the second pulse, and that of the MQ-filtered central-transition peak relative to the carrier frequency (v 0) along the F1 dimension are derived for the four half-integer quadrupole spins. The frequency offset of v 0 relative to an external aqueous solution in the F1 dimension is linearly related to that in the F2 dimension. The shearing transformation, whose main interest is to shift the beginning of the acquisition period from the end of the second pulse to the echo position and to yield a high-resolution spectrum along the F1 dimension, is presented in great detail. In the literature, two conventions are used to define the evolution period. Convention Cz takes the experimental evolution period as the evolution period, whereas convention Ck considers the echo position relative to the first pulse as the evolution period. The true isotropic chemical shift, the second-order quadrupole shift of the center of gravity of a peak, and the parameter CQh relating the quadrupole coupling constant with the asymmetry parameter are functions of d G1 (obs) and d G2 (obs) ; their relationships depend on the conventions. In fact, convention Ck introduces a scaling factor ~depending on the spin and the coherence order! that modifies not only the spectral width and the linewidth, but also the positions of the spinning sidebands in the F1 dimension. Convention Cz is recommended for linewidth comparison. The analytical expressions are checked using 87 Rb (I5 3 2 ) in the extensively studied RbNO3 powder with two carrier frequencies: 98.2 and 163.6 MHz. Our data are in agreement with those of the literature.

23Na NMR and 14N NQR in Mixed Crystals Na1-xAgxNO2

The 23Na (I = 3/2) NMR powder pattern for the m = 1/2 ↔ m = -1/2 transition, broadened by the second-order quadrupole interaction, was investigated in mixed crystals Na1-xAgxNO2 (x<̱0.16). From the intensity loss of the 23Na NMR line caused by the Ag+ -impurity, the range of the quadrupole interaction in the 23Na NMR central line was estimated. The range comprises ionic charges approximately up to the first nearest neighbour Na+ site from the 23Na nucleus, showing a large difference compared with that obtained from the 14N NQR investigation in the same system.

Double-quantum cross-polarization between half-integer quadrupolar spin systems: [formula omitted] and [formula omitted

Cross-polarization/magic angle spinning (CPMAS) experiments are reported in which both the source and recipient spin systems are based on half-integer nuclei with strong second-order quadrupolar interactions. Double-quantum (DQ) CP is particularly well suited for this purpose, as demonstrated with 11 B{ 23 Na} CPMAS spectra of sodium diborate. Furthermore, a two-dimensional 11 B{ 27 Al} heteronuclear correlation spectrum is obtained on a magnesium aluminoborate glass, demonstrating preferential connectivities among various distinct boron and aluminum sites. Novel spectral editing opportunities arise from semi-selective coherence transfer rates measured by exploiting off-resonance effects on spin-locking efficiencies.

Second-order quadrupole effects on Hahn echoes in fast-rotating solids at the magic angle

In solid-state NMR, knowledge of the quadrupole coupling constant and the asymmetry parameter from a powder spectrum allows the determination of the true chemical shift of a line, which can be correlated with the mean bond angle. However, broad powder patterns are distorted by the dead time of the receiver. The common way to recover the lost signals is to apply a Hahn echo sequence. As the quadrupole interaction is a single-spin multiple-energy level interaction, the effects of multiple-quantum ~MQ! transitions during the Hahn echo sequence are still not well understood. We apply the density-operator approach, combined with the order of coherence description, to predicting the echo locations of half-integer quadrupole spins ~I5 3 2, 5 2, 7 2, and 9 2! in a single crystal, the amplitudes of the echoes, and the excitation conditions for obtaining quantitative results on the spin population ratio. For these purposes, the expression of the MQ transition frequency or line shift is derived. Between the two pulses and during the detection period, the rotation of the crystal at the magic angle dramatically reduces the homonuclear magnetic-dipole interaction and completely removes anisotropic spectral broadening due to the heteronuclear magnetic-dipole and the first-order quadrupole interactions; the spin system is submitted to the true isotropic chemical shift and the second-order quadrupole interactions only during these two periods. We treat in a unified way the Hahn echoes @including those involved in MQ-magicangle spinning methodology# of the central transition representing the refocusing of single-quantum and MQ on-resonance coherences generated by the first pulse. During the pulses the crystal is assumed to be static and only the first-order quadrupole inteaction is considered; the echo amplitudes representing the refocusing of MQ coherences do not provide us with quantitative results on the spin population ratio. Only that associated with the refocusing of 1Q coherence gives quantitative results when the two pulse durations are short. Application to powders requires high-speed computer averaging of the echo amplitude versus one of the two pulse durations to extract the quadrupole parameters. @S0163-1829~97!00714-5#

Numerical analysis of Solomon echo amplitudes in static solids

For the first time a numerical procedure for computing the Solomon echo amplitudes of half-integer quadrupole spins (I=3/2, 5/2, 7/2, and 9/2) has been derived from a detailed analysis of the evolution of the spin system using the density operator formalism. As the first-order quadrupole interaction is taken into account throughout the experiment, consisting in exciting the spin system with two pulses either in phase or in quadrature phase and separated by a delay τ2, the results are valid for any ratio of the quadrupole coupling, ωQ, to the amplitude of the pulses, ωrf. These results are applicable to light nuclei at high magnetic field, for which the second-order quadrupole interaction and the chemical shift anisotropy are negligible. We predict (4I2−1)(2I−1)/16 echoes and their positions in the detection period τ4, (I−1/2)2 of which are allowed echoes, the others being forbidden echoes. All of these echoes are satellite-transition signals, which are superimposed on the free induction decay (FID) of the central transition following the second pulse. This means that τ2 must be short when compared to the duration of the central-transition FID. In other words, during τ2 the magnetic dipole interactions have no time to affect the evolution of the spin system. The behavior of the τ4=τ2 echoes versus the second-pulse flip angle ωrft3 is analyzed: in the hard-pulse excitation condition (ωQ/ωrf≪1), the (±1/2↔±3/2) echoes generated by two pulses in quadrature phase are twice as large as those generated by two in-phase pulses; the echoes of the other transitions have comparable amplitudes. The echo amplitudes in the soft-pulse excitation condition (ωQ/ωrf=1) are also presented.

Analytical solutions for spin [formula omitted] off-resonance line intensities in solid state NMR

The density matrix of a spin 3 2 subject to a first-order quadrupole interaction in solids and excited by an off-resonance rf pulse, is calculated analytically using the algebraic computer program MAPLE. The results are valid for arbitrary values of the rf amplitude, ω 1, quadrupolar coupling, ω Q, and offset, Δω, and applied to the analysis of cases where the offset term is not negligible. The treatment can be readily modified to include a second-order quadrupolar interaction during the pulse.

Double rotation27Al NMR in molecular sieves

Although high-resolution NMR spectra can be obtained in solids, the use of27Al NMR to investigate the structure of aluminosilicate and aluminophosphate molecular sieves has been severely limited because anisotropic second-order quadrupolar interactions, responsible for spectral broadening, cannot be eliminated by conventional magic angle spinning (MAS) or multiple pulse techniques. Here we give the principles of the double rotation (DOR) NMR technique which can remove not only the first-order broadenings but also the second-order broadenings in the NMR spectra of quadrupolar nuclei in solids. High-resolution27Al NMR using DOR is capable of resolving discrete framework aluminum sites in aluminophosphate molecular sieves, permitting quantitative investigation of site-specific adsorbate-host interactions, and of discriminating different aluminum species in zeolites.

NMR Studies on Orientational Ordering Phase Transition in Na2CsC60

Sodium-containing alkali metal fulleride, Na 2 CsC 60 , was studied by 13 C and 23 Na NMR below and above the face-centered cubic ( f c c ) to simple cubic ( s c ) phase transition temperature, T m . It is shown that the C 60 molecules rotate faster than the rotational correlation time of 1.6×10 -5 sec above ∼140 K and 2.4×10 -9 sec around 300 K. Using 23 Na NMR spectra broadened by the second-order quadrupole interaction, the electric field gradient at Na sites, e 2 q Q / h , was estimated to be 940±20 kHz and less than 0.1 kHz below and above T m , respectively. The detailed analysis suggests that Na atoms in s c phase have a covalent character with C 60 molecules. It is also suggested that Na 2 CsC 60 is the first metallic plastic crystal.

Rotation-Induced Resonance and Second-Order Quadrupolar Effects on Spin Locking of Half-Integer Quadrupolar Nuclei

The dynamics of spin locking for half-integer quadrupolar nuclei under sample rotation is investigated. It is shown both theoretically and experimentally that the spin-locking efficiency decreases significantly when the MAS rotation frequency is equal to the amplitude of the spin-locking RF field. This can be explained as a rotation-induced resonance effect. It is demonstrated that the second-order quadrupole interaction plays an important role in reducing the spin-locking efficiency and causes a significant lineshape distortion. The behavior of spin locking under DOR is shown to be similar to that under MAS. Based on this understanding of the spin-locking dynamics, an27Al CPDOR spectrum for the molecular sieve AlPO4-11 was obtained with a good signal-to-noise ratio.

Electronic Shieldings and Electric Field Gradients in Rubidium Sulfate Studied by 87Rb MAS NMR

Determination of the magnitudes and relative orientation of quadrupolar and chemical-shift tensors can be carried out from a precise analysis of the powder MAS spectra even when the second-order quadrupolar interaction is dominant. This has been illustrated by the study of the 87Rb MAS spectra of rubidium sulfate at 196.3 MHz.

Analytical expression for the magic-angle spinning nuclear magnetic resonance line shape in the presence of the second-order quadrupole interaction for the non-zero asymmetry parameter and large sample rotation frequency

An analytical expression for the magic-angle spinning nuclear magnetic resonance (MAS NMR) line shape function for the non-zero asymmetry parameter and large sample rotation frequency has been derived using the time-independent part of the quadrupole transition energy based on the stationary perturbation theory. The averaging over Euler angles in the case of a powdered sample is also done analytically, which is so far implemented in the literature by a numerical simulation procedure. While the peak positions obtained from analytical and numerical averaging procedures agree well, the peak heights are significantly different, showing the need for an analytical solution for the averaging over Euler angles, as this would otherwise lead to erroneous values for the quadrupole parameters. The MAS NMR line shape function derived in this paper can be compared directly with the experimental MAS NMR spectrum for the large sample rotation frequency, and the values of the quadrupole parameters can be obtained. We have also described a method of evaluating the quadrupole parameters for the small sample rotation frequency, using the peak heights and peak separation of the central band of the experimental MAS NMR spectrum and the MAS NMR line shape function derived in the present paper. As an example, the quadrupole parameters for vitreous B 2O 3 are computed.