Stray-field imaging of quadrupolar nuclei of half integer spin in solids

A report is presented on the observation of Hahn echoes from the following quadrupolar nuclei of half integer spin (I) in polycrystalline solids in the large static magnetic field gradient (37.5 T/m) which exists in the fringe field of a superconducting solenoid: ⁷Li, ²³Na, ¹¹B, ⁶⁵Cu (I = 3/2); ²⁷Al (I = 5/2); ⁵¹V, ⁵⁹Co (I = 7/2); and ¹¹⁵In (I = 9/2). ²³Na echo-trains from NaCl (with non-selective excitation) and from Na₂SO₄ (with selective excitation) are compared quantitatively for two different RF pulse sequences: 90_x-(τ-90_y-τ-echo-)_n and 90_x-(τ-90_x-τ-echo-)_n. The signals obtained from RF pulses corresponding to non-selective 90 ° pulses were shown to be quantitative, whereas in the selective case smaller signals were obtained since only the central transition contributed. The loss of signal from this cause can be distinguished from small signals resulting from low density of nuclei by use of the second sequence. A ⁷Li image obtained from LiF in a cylindrical glass-vial is shown.     

The decay of Sc and V

The decays of ⁴⁸Sc and ⁴⁸V have been studied with Ge(Li) diodes, scintillation spectrometers and a double focussing beta-ray spectrometer. The 3507 keV level, from which originates the quadruple cascade (9.4±0.5)% in the ⁴⁸Sc decay, is also de-excited by a 1212 keV cross-over transition to the 2295 keV (4⁺) level and supports the assumption, that the 3507 keV level has a spin 6⁺. The first member of the reported triple cascade in the ⁴⁸V decay is shown to be a doublet of 928.9±0.7 (1.2±0.2)% and 944.3±0.5 keV (8.0±0.5)% gamma rays, both followed by the 1311.4–983.3 keV cascade. Evidence was found, that the 2421 keV (2⁺) level is excited by weak gamma rays from high-energy levels. The K/β⁺ ration in the ⁴⁸V decay is 0.69±0.05 The Q-values of ⁴⁸Sc and ⁴⁸V are calculated to be 3986±7 keV and if 4015±4 keV, respectively. The energy of the gamma ray of ⁴⁷Sc, which is present as an impurity, is 159.2±0.5 keV.     

F/Si distance determination in fluoride-containing octadecasil by Hartmann–Hahn cross-polarization under fast magic-angle spinning

¹⁹F/²⁹Si Hartmann–Hahn continuous wave cross-polarization (CP) has been applied under fast magic-angle spinning (MAS) to a powder sample of octadecasil. Strong oscillations occur during CP on a sideband matching condition between the isolated ²⁹Si–¹⁹F spin pairs formed by the silicons in the D4R units and the fluoride anions. The magnitude of the dipolar coupling constant was deduced directly from the line-splitting between the intense singularities of the Pake-like patterns obtained by Fourier transformation of the oscillatory polarization transfer. The corresponding Si–F internuclear distance, r=2.62±0.05 Å, is found to be in very good agreement with the X-ray crystal structure and the value of 2.69±0.04 Å recently reported from rotational echo double resonance (REDOR) and transferred echo double resonance (TEDOR) nuclear magnetic resonance (NMR) experiments. Furthermore, the CP technique is still reliable under fast MAS where both REDOR and TEDOR sequences suffer from severe artefacts due to finite pulse lengths. In octadecasil, a spinning frequency of 14 kHz is shown to be necessary for an effective suppression of ¹⁹F–¹⁹F spin diffusion. The influences of experimental missettings and radiofrequency (RF) field inhomogeneity are taken into account.     

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.     

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.     

Revision of spin echoes in pure nuclear quadrupole resonance

Goldman's spin-1/2 formalism has been used for describing the response of an I=3/2 spin system to a two-pulse sequence in a pure nuclear quadrupole resonance experiment. A detailed analysis of the polarization evolution and quadrupolar echo generation is carried out through the use of explicit expressions for secular homo- and heteronuclear dipolar interactions. In striking contrast with previous studies, it is predicted that Van Vleck's second moments governing a classical solid-echo or Hahn sequence differ from those obtained by equivalent means in magnetic resonance. In fact, it is shown that, although measured moments still complement each other, the combined use of standard sequences does not allow the separate determination of homo- and heteronuclear dipolar contributions to the linewidth, not even in an indirect manner. In this context, the importance and potential usefulness of a crossed coil probe are also briefly discussed.     

A solid-state V NMR characterization of vanadium sites in LiCoxNi1−xVO4

LiCo_xNi_1−xVO₄ compounds (x=0, 0.2, 0.5, 0.8, 1.0) have been prepared for lithium ion batteries by different preparation methods, namely, wet-chemistry (WC) and solid-state (SS) routes. ⁵¹V nuclear magnetic resonance (NMR) has been employed to accurately assess the vanadium environments in these materials and results show that vanadium atoms are distributed in octahedral and tetrahedral sites. The fractions of vanadium atoms in tetrahedral/octahedral sites depends on composition and sample preparation conditions. The tetrahedral site, which is particularly dominant in samples produced via the WC route, is more affected by paramagnetic interactions and its ⁵¹V NMR spectrum is essentially Gaussian in shape. The octahedral site, on the other hand, exhibits first-order quadrupolar broadened satellites. Even though tetrahedral sites for a given x are comparable for WC and SS materials, there are some differences amongst octahedral environments, namely in the distributions of quadrupolar broadened satellites. The larger satellite distribution observed for WC materials is indicative of a larger distribution of structural defects for these as compared to SS materials.     

Solid state (47,49)Ti, (87)Sr and (137)Ba NMR characterisation of mixed barium/strontium titanate perovskites

Solid state ^47,49Ti, ¹³⁷Ba, ⁸⁷Sr NMR spectra have been recorded on Ba_xSr_1−xTiO₃ (0 x 1) perovskite samples prepared by the powder sintering method. Multinuclear solid state NMR shows great potential for characterising such systems since the quadrupolar parameters are very sensitive to any geometric deformation around the studied nucleus. ^47,49Ti NMR powder lineshapes appear strongly influenced by the presence of even a small amount of barium (or strontium) in the coordination second sphere of the probed titanium site: substitution of strontium by barium induces the broadening of the peaks, due to quadrupolar effects, while the isotropic chemical shift increases. ¹³⁷Ba NMR spectra exhibit a distribution of the quadrupolar interaction, that could be tentatively quantified, C_Q increasing with the amount of strontium. Preliminary results were also obtained on ⁸⁷Sr NMR showing behaviour comparable to ¹³⁷Ba NMR, i.e. a broadening of the peaks due to an increasing quadrupolar interaction with the amount of barium distorting the environment of the strontium sites.     

New evidence for a subshell gap at N=32

An 879.9(2) keV γ-ray transition has been identified following the β decay of ⁵⁸V and assigned as the 2⁺₁→0⁺₁ transition in ⁵⁸Cr₃₄. A peak in the energies of the first excited 2⁺ states for the even–even chromium isotopes is now evident at ⁵⁶Cr₃₂, providing empirical evidence for a significant subshell gap at N=32. The appearance of this neutron subshell closure for neutron-rich nuclides may be attributed to the diminished π1f_7/2–ν1f_5/2 monopole proton–neutron interaction as protons are removed from the 1f_7/2 single-particle orbital.     

Double resonance experiments in a single resonance probe: detecting Na–V dipolar interactions in sodium vanadates

²³Na-{⁵¹V} double resonance TRAPDOR experiments are presented on two different sodium vanadates. This is the first time that the heteronuclear dipolar interaction between nuclei, whose Larmor frequencies lie within a range of 0 to 3 MHz is detected in order to monitor connectivity and internuclear distance information in these systems.     

On the theory of NMR spin echoes in solids

A general expression in terms of two-time correlation functions is derived for the spin echo responses to 90°-τ-β⁰_φ pulse sequences of quadrupolar spins coupled through dipolar interactions. The second moments of the correlation function are calculated for a system of spin one nuclei and shown to be in accordance with the experimental observations. Furthermore, results are presented for the fourth moments.     

Level structure of V from the Ti(p, nγ)V reaction

Measurements of level positions and decay modes in ⁴⁷V were carried out using the ⁴⁷Ti(p, nγ)⁴⁷V reaction. Spin and mixing ratio assignments are made for levels below 1.8 MeV excitation using a statistical compound nuclear calculation. The level structure of ⁴⁷V is compared with recent theoretical predictions.     

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.     

Quantitative Comparison of REAPDOR and TRAPDOR Experiments by Numerical Simulations and Determination of H–Al Distances in Zeolites

Quantitative H–Al distances in acid sites of two zeolites with MFI and IFR framework topology were obtained by numerical simulation of ¹H{²⁷Al} rotational echo adiabatic passage double resonance (REAPDOR) experiments. A ²⁷Al offset-dependent data set yields for each resolved ¹H NMR line a corresponding nuclear electric quadrupole coupling constant of the neighboring ²⁷Al site. This information is used for analyzing a second data set for on-resonance irradiation, where the dipolar evolution time (number of rotor cycles) was varied, to yield the ¹H–²⁷Al dipolar coupling constant. Numerical simulations indicate that the REAPDOR method does not depend significantly on the polar angles, defining the orientation of the electric field gradient tensor of ²⁷Al with respect to the Al–H dipolar vector. In contrast, the transfer of populations in double resonance sequence is sensitive to these angles, and it can be thus used to measure them.     

A study of the Ti(He, t) and Ni(He, t) reactions to isobaric analogue states

The (³He, t) reaction populating 0⁺ and 2⁺ states in ^{58, 60}Cu and ^{46, 48}V which are isobaric analogue states (IAS) of the 0⁺ ground states and 2⁺ first excited states in ^{58, 60}Ni and ^{46, 48}Ti have been studied at an incident ³He energy of 24.6 MeV. Triton spectra were measured for the targets ^46,48Ti, ^natNi and ⁵⁸Ni and angular distributions for the 0⁺ and 2⁺ IAS of ^{46, 48}Ti and ^{58, 60}Ni determined. The data were obtained using a magnetic spectrometer and position-sensitive detectors. The results have been analysed using DWBA theory. The 0⁺ → 0⁺ transitions to analogue states are described quite well using a microscopic form factor derived from a nucleon-nucleon interaction. However, with a Gaussian form, the m.s. radius of this interaction is only limited to the region 0–9 fm². Comparisons with data at other incident energies indicate that the strength of the effective interaction is strongly energy dependent. The Coulomb energies and (³He, t) angular distributions of the states assigned as the 2⁺ analogues in ⁴⁸V and ^58,60Cu are not described well by the models investigated. The ⁴⁶V 2⁺ IAS angular distribution is reproduced by a microscopic calculation, however. The ratios of the 0⁺ → 2⁺ IAS to the 0⁺ → 0⁺ IAS transitions are used to deduce a quadrupole deformation for the valence neutrons. The difference in the quadrupole deformations of the matter and proton distributions, as determined by other means, is found to be correlated with those of the valence neutrons. Several transitions to non-analogue states are also investigated.     

A multiple-field (23)Na NMR study of sodium species in porous carbons

The sodium environments in porous carbon materials prepared from NaOH activation of a char were investigated by means of multiple-field solid-state ²³Na NMR measurements, carried out at magnetic fields of 4.7, 8.45 and 14.1 T, with single-pulse excitation and magic angle spinning (MAS). The recorded spectra showed a relatively featureless resonance with linewidth and peak shift strongly dependent on the magnetic field strength and on the hydration level of the samples. The existence of second-order quadrupolar effects was inferred, although the structural disorder and the mobile character associated with the Na environment precluded the direct observation of typical quadrupolar features in the MAS NMR spectra. The analysis of the spectra collected at multiple magnetic fields yielded the values of −2.8 ppm for the isotropic chemical shift and 1.8 MHz for the quadrupole coupling constant, which were interpreted as due to Na⁺ ions bonded to oxygenated groups at the edges of the graphene planes within the carbon pore network.     

The g-factor of the 3/2 153 keV state in V

The g-factor of the 3/2⁻ state at 153 keV in ⁴⁹V was measured with the ⁴⁸Ti(p, γ)⁴⁹V reaction and the differential spin-precession method. The g value and the remeasured mean life are g = 1.58 ± 0.08 and τ = 28.7 ± 0.5 ns. The result is compared with some theoretical predictions.     

Vanadium-51 solid-state NMR electric field gradient tensors: a DFT-embedded ion and isolated cluster study of crystalline vanadium oxides

Density functional theory (DFT) calculations (6–311+G(2d,p)/B3LYP level of theory) of ⁵¹V electric field gradient (EFG) tensor elements are performed for embedded and isolated cluster models of orthovanadates. The structural models used to calculate the EFGs of ⁵¹V are (I) an isolated H₄VO₄⁺ cluster, (II) an isolated H_nVO₄ⁿ⁻³ cluster (n=number of next-neighbor cations) (III) an isolated orthovanadate anion, VO₄^−x, and (IV) a VO₄^−x ion embedded in a finite point-charge array whose electrostatic potential, at the embedded ion, is equivalent to that of the infinite lattice. For models III and IV, a charge x is assigned estimating the covalence of the system. Models III and IV provide results in good agreement with the experiment. Calculations, employing the embedded and isolated VO₄^−x models, are used to discuss site assignments for AlVO₄. Correlations between quadrupole coupling parameters and deviations of the orthovanadate structure from ideal tetrahedral symmetry are shown.     

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.     

Hyperfine fields at Y nuclei in Y(Fe1−xTx)3 (T = Al, Co)

The spin echo spectra of ⁸⁹Y hyperfine fields in Y(Fe_1−xT_x)₃ with low concentration x consist of two main lines and of satellite lines caused by the replacement of the Fe atoms by the T atoms. Values of the magnetic moments of the T atoms are estimated by observing the satellite lines.