Nutation Spectra Research Articles

Singularties of the shape of the nonresonance nutation spectra of NQR powders

The singularities of nutation NQR spectra for nuclei with spin J=1, 3/2 in the absence of resonance are considered for powders. It is shown that when determining the asymmetry parameter η from the frequency characteristics of the nutation spectrum one must take into account the frequency shift of the spectrometer relative to exact resonance. Structural studies of single crystals by nutation spectroscopy are demonstrated to be feasible.

Nutation Magic-Angle-Spinning Spectra of Half-Integer Quadrupole Spin Systems

The nutation spectra of spin-32 and spin-52 nuclei under magic-angle spinning (MAS) were investigated in detail. When the nutation time is larger than a spinning period, the lineshape of a nutation spectrum is evidently changed by MAS. The center of gravity of the nutation MAS spectrum is generally shifted to lower frequency compared with the static spectrum. The shift is approximately inversely proportional to the spinning speed. When the effective quadrupole coupling constant is much larger than the irradiation field amplitude, the nutation spectra are broadened by MAS, while if the effective quadrupole coupling constant is much smaller than the RF field amplitude, the nutation spectra are generally narrowed by MAS. For certain values of the effective quadrupole coupling constant, the nutation spectrum may exhibit a minor dispersion. For a nutation time shorter than one spinning period, the lineshape is similar to that in the static case. A natural and exact computation approach for theoretical spectral simulation is presented, and the necessity for phase correction of theoretical spectra is discussed. The experimental results are in good agreement with theoretical simulations.

Solid-state 23Na, 139La, 27Al and 29Si nuclear magnetic resonance spectroscopic investigations of cation location and migration in zeolites LaNaY

23Na Magic-angle spinning (MAS), double rotation (DOR) and two-dimensional nutation nuclear magnetic resonance (NMR) and static 139La NMR spectroscopy were applied to study the location and migration of sodium and lanthanum cations in faujasites. Generally, 23Na MAS NMR spectroscopy of as-exchanged and hydrated zeolites LaNaY was used for the quantitative determination of non-localized Na + in the large cavities at a 23Na NMR shift of −9 ppm and of sodium cations observed at −13 ppm. The latter originate from Na + ions located on position SII in the large cavities, on position SI in the hexagonal prisms and on positions SII′ and/or SI′ in the sodalite cages. The 23Na MAS NMR signal at about −13 ppm was found to be caused by two coonents. The component that is characterized by a quadrupolar interaction causing a field-dependent shift and a signal at v 1 = 2 v rf in the two-dimensional quadrupolar nutation spectra is attributed to Na + enclosed in the sodalite cages. The 23Na MAS NMR spectra of dehydrated lanthanum-exchanged faujasites are characterized by a low-field Gaussian line of Na + located on SI positions in the hexagonal prisms and a high-field quadrupole pattern of Na + located on positions SII and SI′. The migration of lanthanum cations from the large cavities to position SI′ in the sodalite cages was monitored by 139La NMR spectroscopy and verified by a theoretical estimation of the electric field gradient. The lanthanum migration was found to be coupled with a strain of SiOT and AlOT angles observed by 29Si and 27Al MAS NMR high-field shifts, respectively.

On the Reconstruction of NQR Nutation Spectra in Solids with Powder Geometry

Abstract In single crystals the NQR nutation frequency depends on the relative orientation of the coil and the quadrupole axes. In powders the nutation lineshape is a superposition of spectra from the randomly oriented single crystals, so that powder patterns appear in such experiments if the recon­struction is performed by the Fourier transform method. In this paper an alternative reconstruction method of nutation spectra is suggested making use of the Hankel Transform. In this way the nutation spectra are simplified. Singularities arising with experiments for the determination of the asymmetry parameter η can easily be resolved. In the particular case of an axially symmetric quadrupolar tensor and a homogeneous radiofrequency field one can reduce the powder pattern to a single line without heterogeneous broadening with respect to orientation. Further improvement o f the nutation spectra can be achieved by taking advantage of the maximum entropy method, which strongly reduces apodisation and noise problems. Applications of the new data manipulation techniques to N Q R imaging methods published elsewhere and 2D zero-field N Q R spectroscopy are reported.

Off-Resonance Nutation NMR Spectroscopy of Half-Integer Quadrupolar Nuclei

The possibilities of off-resonance irradiation in nutation experiments of half-integer quadrupolar nuclei are demonstrated experimentally and theoretically. Off-resonance irradiation extends the applicability of nutation NMR spectroscopy at a given radiofrequency field strength to a larger range of quadrupole coupling constants. Moreover, it is possible to obtain several spectra with different resonance offsets on one spectrometer, thus facilitating the determination of the quadrupole parameters. A loss of signal to the uninformative zero-frequency signal which accompanies off-resonance irradiation can be avoided by using a frequency-stepped adiabatic half-passage or a soft selective 90° pulse as preparation for the experiment. Simulated off-resonance nutation spectra are presented as a function of quadrupole coupling constant and resonance offsets. The technique is demonstrated experimentally for a number of sodium compounds.

Distorted powder lineshapes in 27 Al CP / MAS NMR spectroscopy of solids

27Al CP / MAS NMR spectra of aluminium acetylacetonate show distinct lineshapes depending on the experimental conditions as the different orientations within the powder cross-polarize with differing efficiencies. Selective polarization transfer to the 1 2 ↔ −1 2 transition occurs at rf power levels corresponding to 3ω Al=ω H, while non-selective polarization transfer can occur at higher 27 Al rf powers. Two-dimensional quadrupole nutation spectra show that the cross-polarization lineshapes arise principally because the different orientations have different 27 Al nutation frequencies. The results obtained highlight the caution needed in the interpretation of CP/MAS NMR spectra of quadrupolar nuclei.

Comparative high resolution NMR studies of n- and p-type doped polyacetylene films

High resolution NMR provides unique abilities to study either properties of the polymer chains or behavior of the doping agent in the conducting polymers. Magic angle spinning proton decoupled 13C NMR was applied to n-type sodium doped, (CHNa y) x (y ≤ 0.3), and p-type iodine doped, [CH(I 3) y] x (y ≤ 0.19), polyacetylene films prepared by Shirakawa's method. Also 2-dimensional nutation spectra of half-integer spin ( I = 3 2 ) quadrupolar 23Na nuclei were measured. All the spectra were studied as a function of the dopant content, y, determined by weight uptake after doping. The films were controlled by measurement of the conductivity which was about 10 and 50 Ω −1 cm −1 for heavily iodine and sodium doped material, respectively. We discuss our results on: (i) formation of the extended polycarbonium ions (charged solitons), (ii) doping induced cis/trans isomerization, (iii) partial compensation of (CHNa) x films by oxygen and moisture, (iv) intersite electron-electron correlations on the polymer chain, and (v) ordering of the sodium ions and occurrence of at least two different crystal phases of the polyacetylene-sodium system.

27Al solid-state NMR studies of molybdenum bronze intercalated with aluminium polyoxycations

27Al magic-angle-spinning (MAS) NMR spectra with and without cross-polarization and quadrupole nutation spectra with MAS of the molybdenum bronze Na 0.25(H 2O) y MoO 3 intercalated with aluminium polyoxycations have been measured. Apart from the signal from 4-coordinated Al at 64.6 ppm assigned to the intercalated polyoxycations, there are three main signals from 6-coordinated Al: at 14.0 ppm, 0 ppm, and a very wide signal at ≈ −50 to 20 ppm with a maximum close to 3ω rf/2π in F 1. We assign the signal at 0 ppm to Al(H 2O) 3+ 6 ions, and discuss the possible origin of the other two signals.

Multiple-quantum MAS nutation NMR spectroscopy of quadrupolar nuclei

Theory, experiments, and simulations of two-dimensional nutation NMR spectroscopy of half-integer quadrupolar nuclei combined with magic-angle spinning (MAS) are presented. MAS enhances the overall sensitivity and improves resolution in the ω 2 2π dimension of the 2D nutation spectra. Compared to static nutation spectroscopy it is demonstrated that MAS nutation NMR puts less stringent requirements on the magnitude of the radiofrequency field strength, which is beneficial for nuclei with large quadrupole couplings. The finite nutation pulse excites all 2I(I + 1 2 ) multiple-quantum transitions for a spin- I nucleus. Multiple-quantum versions of the 2D nutation experiment are explored. Simulated 2D MAS nutation spectra are compared with experimental 23Na and 27Al spectra of NaNO 3 and Ca 3A1 2O 6·6H 2O (concrete), respectively, and with simulations of corresponding 2D nutation experiments for the static case.

Sodium Ion Exchange in Na1+xZr2SixP3-xO12 as Studied by 23Na Nutation NMR

Abstract 23Na two-dimensional nutation NMR was applied to Na1+x* Zr2SxP3-xO12 with x = 0, 1, and 2. The nutation spectrum in each compound consists of two clearly separated peaks corresponding to the two crystallographically inequivalent sodium sites. In the compound with x = 2 the nuclear quadrupole coupling constants (e2 Qq/h) and the asymmetry parameters (η) were by spectral simulation estimated to be 1.0 MHz and 0 for one site, and 1.5 MHz and 0.8 for the other site. The spectrum varies considerably on heating; the two peaks merge into a single peak at high temperatures due to fast ion exchange between the two different sites. For x = 0 and x = 1 the nutation spectra did not show any significant temperature dependence, suggesting that the rates of the sodium ion exchange are negligibly low.

Quadrupole Nutation NMR in Solids

Abstract The nutation frequency of a quadrupolar spin I depends on the quadrupole interaction. From nutation spectra, therefore, one obtains information about the direct surrounding of the atom. The theory of the straightforward and of more complicated nutation NMR experiments is outlined. Two applications of nutation NMR, to 23Na in zeolites and 27Al in alumina, are shown. In this way in CaO • 6 Al2O3 penta-coordinated aluminum has been detected

Aluminum coordination and Lewis acidity in transition aluminas

Besides the resonance lines attributable to tetrahedrally (Al IV) and octahedrally (Al VI) coordinated aluminum, the MAS NMR 27Al spectra of transition aluminas obtained from finely divided precursors gibbsite and boehmite have a line which can be assigned to pentacoordinated AI (Al V). This line which is very intense in ex-boehmite aluminas, as compared to ex-gibbsite aluminas, is also observed in the nonframework alumina moieties in acid and dealuminated zeolites. The isotropic chemical shifts of the Al VI, Al V, and Al IV resonance lines are 11.4, 38.3 and 65.6 ppm, respectively, in a field of 11.77 T. Nutation (two-dimensional) spectra of 27Al in these aluminas show a broad distribution of quadrupole coupling constants (QCCs) between ∼2 and ∼5 MHz. A broad range of distortions of the Al coordination shells corresponds to this range of QCCs. To detect electron acceptor sites (or Lewis acid centers), an EPR molecular probe has been adsorbed and the EPR spectra have been recorded before and after introduction of molecular oxygen. With dimethylaniline (DMA) the formation of a radical cation is observed and its concentration is larger on aluminas with Al V than on aluminas without detectable Al V. Molecular O 2 which is adsorbed on DMA-treated aluminas, acts as an electron scavenger picking up the electron transferred from DMA to the surface. Moreover, the g zz is in the range expected for O 2 −, indicating its interaction with an Al nucleus. The surface density in electron acceptor sites with electron affinity ∼−7.1 eV is, at the best, on the order of 0.4 × 10 12 spins/cm 2. These findings suggest either that strongly distorted shells of pentacoordinated Al are potential Lewis acid centers or that they generate such sites upon thermal activation. Other types of coordination, if sufficiently distorted, may play a similar role.

63Cu NQR Nutation Spectroscopy and Spin Counting in Copper Oxides

AbstractNutation spectroscopy of 63Cu nuclei at zero static magnetic field is explored as a method for the determination of the quadrupole asymmetry parameters η of Cu sites in copper oxides, with special emphasis on high‐Tc superconductors. Since the nutation spectra reveal the actual radio frequency (rf) intensities experienced by the 63Cu nuclei, the method also provides a verification of a quantitative Cu spin counting procedure based on integration of nuclear quadrupole resonance (NQR) echo‐signal intensities over wide frequency ranges. The paper presents numerical simulations of spectra and signal intensities that were obtained with a density‐matrix formalism whereby the spin dynamics is described as precessions in a 3D operator space. The quantitative effects of the echo refocusing pulse, rf amplitude fluctuations, and variations in η are examined. Examples of 63Cu NQR nutation spectra are shown for randomly oriented powders of Cu2O and YBa2Cu3O7.

Application of 23Na Nutation NMR to Characterize the Cation Effect in Ion-Exchanged NaY Zeolites

The two-dimensional sodium-23 nutation NMR was used to monitor the behavior of sodium ions in the partially alkali, alkali-earth or rare-earth ion exchanged NaY zeolites. The sodium-23 nutation spectra of the hydrated and rehydrated Y zeolites consist of two peaks at 1 and 2ωrf in F1 axis with chemical shifts of 0-10 ppm. For the degree of IA, IIA or RE cation exchange <45%, only one peak at 1ωrf was found. For the degree of cation exchange >45%, the second peak at 2ωrf might be observed. The correlation between the relative intensities and lineshapes of two peaks and the nature and distribution of cations in the supercages and sodalite cages with degree of exchange and heating treatment was studied.

Local Structure of Polyethylene Glycol–Nal Solid Polyelectrolyte as Studied by 13C and 23Na NMR

Abstract 13C CP/MAS NMR, 23Na powder NMR, and 23Na two dimensional nutation NMR were applied to complexes of Nal with polyethylene glycol (PEG) and tetraethylene glycol (TEG) to study the conformation of the polyethers and local structure around the Na+. 13C chemical shift data suggest strongly that the polyether chains assume the gauche conformation in the complexes. 23Na NMR spectrum of TEG–Nal complex gave a broad asymmetric line; simulation of the line shape led to e2Qq⁄h=590 kHz and η=0.7. No significant temperature dependence of the line shape was observed between 200 K and room temperature. For PEG–Nal complex e2Qq⁄h and η were estimated to be about 320 kHz and 0.7, respectively, from the nutation spectrum. On the basis of the above results, new model structures of PEG–Nal complex were presented.

Polariton–Biexciton Nonlinear Nutation and Stationary Spectrum Renormalization

AbstractTwo macrofilled coherent modes ‐ a polariton and a biexciton one ‐ are assumed to exist simultaneously in a direct‐gap semiconductor. These modes are characterized by the sets of parameters kO ωo and qo = 2ko, Ω0 = 2ω0, where k0 is the wave vector of the polariton mode and ω0 is the external pumping frequency. In the stationary case the renormalized dispersion and the particle concentrations of the strong modes k0 and q0 are obtained. A selfconsisted equation for the quasi‐momentum k0 as a function of the frequency ω0 and the external pumping intensity is deduced. in the nonstationary limit the polariton and biexciton concentrations are found to vary periodically in time within certain ranges passing through their steady equilibrium values which are the same as the stationary ones.

29-NMR Nutation Spectroscopy in the three-level systems

Two-dimensional NMR nutation spectroscopy in three-level systems has been studied. A new pulse sequence is proposed to obtain undistorted 2H nutation powder patterns. Calculated nutation spectra of powders are presented. The acquisition of quad- rupolar coupling constants from the experimental lineshape is demonstrated for a 2H-PMMA powder sample.

Two-dimensional Nutation Echo Nuclear Quadrupole Resonance Spectroscopy

Abstract We discuss two new two-dimensional nuclear quadrupole resonance experiments, both based on the principle of nutation spectroscopy, which can be used to determine the asymmetry parameter, and thus the full quadrupolar tensor, of spin-3/2 nuclei at zero applied magnetic field. The first experiment is a simple nutation pulse sequence in which the first time period (t1) is the duration of the radiofrequency exciting pulse; and the second (t2) is the normal free-precession of a quadrupolar nucleus at zero-field. After double Fourier-transformation, the result is a 2 D spectrum in which the first frequency dimension is the nutation spectrum for the quadrupolar nucleus at zero-field. For polycrystalline samples this sequence generates powder lineshapes; the position of the singularities, in these lineshapes can be used to determine the asymmetry parameters η in a very straightforward manner, η has previously only been obtainable using Zeeman perturbed NQR methods. The second sequence is the same nutation experiment with a spin-echo pulse added. The virtue of this refocussing pulse is that it allows acquisition of nutation spectra from samples with arbitrary inhomogeneous linewidth; thus, asymmetry parameters can be determined even where the quadrupolar resonance is wider than the bandwidth of the spectrometer. Experimental examples of 35Cl, 81Br and 63Cu nutation and nutation-echo spectra are presented.

Analytical description of theI= 5/2 quadrupole nutation experiment

The theory of nutation N.M.R. for a quadrupolar nucleus with spin quantum I = 5/2 is presented in an exact, analytical way. It is shown that the nutation spectrum is described by 9 different frequencies each dependent on the orientation of the quadrupole tensor relative to the external field. The frequencies are calculated from the eigenvalues of a 6th-degree secular equation that is reduced to 2 secular equations of order 3. This reduction is obtained by a transformation of bases. An extension of the nutation experiment, xx¯-nutation, is compared with the standard technique. The theoretical spectra are compared with experimental 27Al spectra of NH4Al(SO4)2 · 12H2O and zeolite NaA.

Two-dimensional zero-field nutation nuclear quadrupole resonance spectroscopy

We introduce a new two-dimensional nuclear quadrupole resonance experiment, in which the first time period (t1) is the duration of the radiofrequency exciting pulse; and the second (t2) is the normal free precession of a quadrupolar nucleus at zero field. After double Fourier transformation, the result is a 2D spectrum in which the first frequency dimension is the nutation spectrum for the quadrupolar nucleus at zero field. For single crystals, this spectrum contains narrow lines, whose frequency, for axially symmetric tensors, is proportional to sin θ, where θ is the angle between the unique axis of the quadrupolar tensor and that of the transmitter/receiver coil. For polycrystalline samples we obtain powder line shapes which are reminiscent of high-field nuclear magnetic resonance (NMR) powder patterns, and which allow determination of the asymmetry parameter η, which has previously only been obtainable using Zeeman perturbed nuclear quadrupole resonance (NQR) methods. Both theoretical spectra and several experimental examples are presented.