Symmetric Electric Field Gradient Tensor Research Articles

On spin-lattice relaxation of nuclear quadrupole resonance in polycrystalline solids

The analysis of spin–lattice relaxation in nuclear quadrupole resonance (NQR) of spin-52 reported by Okubo and Igarashi (Z. Naturforsch. A. 56 (2001) 777) is extended to take account of the distribution of the initial non-equilibrium populations created by a resonant radio-frequency pulse in powder. The proposed theory is applicable to axially symmetric electric field gradient tensor and is examined for spin–lattice relaxation of 127I NQR in polycrystalline pyridine iodine monochloride measured at 469 MHz at 77 K.

14N Quadrupole Resonance line broadening due to the earth magnetic field, occuring only in the case of an axially symmetric electric field gradient tensor

As demonstrated before, the application of a weak static B0 magnetic field (less than 10G) may produce definite effects on the 14N Quadrupole Resonance line when the electric field gradient tensor at the nitrogen nucleus level is of axial symmetry. Here, we address more precisely the problem of the relative orientation of the two magnetic fields (the static field and the radio-frequency field of the pure NQR experiment). For a field of 6G, the evolution of the signal intensity, as a function of this relative orientation, is in very good agreement with the theoretical predictions. There is in particular an intensity loss by a factor of three when going from the parallel configuration to the perpendicular configuration. By contrast, when dealing with a very weak magnetic field (as the earth field, around 0.5G), this effect drops to ca. 1.5 in the case Hexamethylenetetramine (HMT).This is explained by the fact that the Zeeman shift (due to the very weak magnetic field) becomes comparable to the natural line-width. The latter can therefore be determined by accounting for this competition. Still in the case of HMT, the estimated natural line-width is half the observed line-width. The extra broadening is thus attributed to earth magnetic field. The latter constitutes therefore the main cause of the difference between the natural transverse relaxation time (T2) and the transverse relaxation time derived from the observed line-width (T2⁎).

Magnetism of BaFe2Se3 studied by Mössbauer spectroscopy

The compound BaFe2Se3 (Pnma) has been synthesized in the form of single crystals with the average composition Ba0.992Fe1.998Se3. The Mössbauer spectroscopy used for investigation of the valence states of Fe in this compound at temperature ranging from 4.2K till room temperature revealed the occurrence of mixed-valence state for iron. The spectrum is characterized by sharply defined electric quadrupole doublet above magnetic ordering at about 250K. For the magnetically ordered state one sees four iron sites at least and each of them is described by separate axially symmetric electric field gradient tensor with the principal component making some angle with the hyperfine magnetic field. They form two groups occurring in equal abundances. It is likely that each group belongs to separate spin ladder with various tilts of the FeSe4 tetrahedral units along the ladder. Two impurity phases are found, i.e., superconducting FeSe and some other unidentified iron-bearing phase being magnetically disordered above 80K. Powder form of BaFe2Se3 is unstable in contact with the air and decomposes slowly to this unidentified phase exhibiting almost the same quadrupole doublet as BaFe2Se3 above magnetic transition temperature.

Effect of a weak static magnetic field on nitrogen-14 quadrupole resonance in the case of an axially symmetric electric field gradient tensor

The application of a weak static B0 magnetic field (less than 1mT) may produce a well-defined splitting of the 14N Quadrupole Resonance line when the electric field gradient tensor at the nitrogen nucleus level is of axial symmetry. It is theoretically shown and experimentally confirmed that the actual splitting (when it exists) as well as the line-shape and the signal intensity depends on three factors: (i) the amplitude of B0, (ii) the amplitude and pulse duration of the radio-frequency field, B1, used for detecting the NQR signal, and (iii) the relative orientation of B0 and B1. For instance, when B0 is parallel to B1 and regardless of the B0 value, the signal intensity is three times larger than when B0 is perpendicular to B1. This point is of some importance in practice since NQR measurements are almost always performed in the earth field. Moreover, in the course of this study, it has been recognized that important pieces of information regarding line-shape are contained in data points at the beginning of the free induction decay (fid) which, in practice, are eliminated for avoiding spurious signals due to probe ringing. It has been found that these data points can generally be retrieved by linear prediction (LP) procedures. As a further LP benefit, the signal intensity loss (by about a factor of three) is regained.

14N pulsed nuclear quadrupole resonance. 1. Nutation experiments in the case of an axially symmetric electric field gradient tensor

An exact theory based on density matrix calculations is provided for assessing the nuclear quadrupole resonance (NQR) behaviour of a spin 1 (14N) subjected to a single radio-frequency pulse. It concerns a powder sample in zero magnetic field with the assumption of an axially symmetric electric field gradient tensor. Theoretical results, in terms of signal evolution as a function of the pulse length (nutation experiments), are checked against values of the radio-frequency field amplitude provided by NMR measurements performed with the same equipment. Good agreement between theory and experiment is obtained.

Spin-echoes in nitrogen-14 quadrupolar spin-system with axially symmetric electric field gradient tensor

The behaviour of the magnetisation in the spin-1 system with the axial symmetry of the electric field gradient (EFG) tensor was analysed theoretically. The behaviour of the NQR signals in hexamethylenetetramine (C 6H 12N 4) was also studied experimentally using the pulse NQR technique and sensitive equipment. It was shown that the axial symmetry of the EFG in a sample could not be the reason why spin-echo signals were not observed in conventional pulse experiments for the same type of sample. A very short spin–spin relaxation time T 2 seems to be the reason of that. The signal-to-noise ratio was sufficient for measuring T 2 in C 6H 12N 4, which had not been reported earlier. Experimental results of applying certain pulse sequences to the 14N NQR in a sample are also presented.

Transient effects in nitrogen-14 quadrupolar spin-system with axially symmetric electric field gradient tensor

The behaviour of the nuclear quadrupole resonance (NQR) signals in the effective field of a multi-pulse train has been studied for a nitrogen-14 spin-system with axially symmetric electric field gradient tensor using a modified multi-pulse technique. As a result transient echo signals in the effective field in such a spin-system were detected which demonstrates that this effect does not depend on the value of the asymmetry parameter η. The experiments permitted to reveal some peculiarities in the behaviour of the signals which are obviously characteristic of a spin-system with axially symmetric electric field gradient tensor.

Spin locking spin echo in nitrogen-14 quadrupolar spin-system with axially symmetric electric field gradient tensor

The behaviour of the nuclear quadrupole resonance (NQR) signals in hexamethylenetetramine (C 6H 12N 4) has been studied using the modified spin-locking multi-pulse (SLMP) technique. As a result a train of spin-echo (SE) signals in `observation windows' between RF pulses of a multi-pulse sequence has been detected. Spin-locking effect has also been observed in such spin-system. The dependence of the effective relaxation time T 2e and the SE signal amplitude on parameters of SLMP sequences have also been investigated which resulted in revealing certain peculiarities in the behaviour of the signals obviously characteristic of a spin-system with axially symmetric electric field gradient tensor.

Steady-state free-precession in nitrogen-14 quadrupolar spin-system with axially symmetric electric field gradient tensor

The behaviour of nuclear quadrupolar resonance (NQR) signals in hexamethylenetetramine (C 6H 12N 4) was studied using the steady-state free-precession (SSFP) pulse technique. Strong intensity variations of the steady-state signal as a function of the frequency offset and pulse spacing were observed, and these are associated with the interference of free induction decay and spin–echo signals in the steady state. Thus it was shown that the detected NQR signal may contain a spin–echo component, and the axial symmetry of the electric field gradient in the sample is not the reason why spin–echo signals were not observed in conventional pulse experiments for the same type of sample. Experimental results of applying some SSFP pulse sequences for nitrogen-14 NQR in (C 6H 12N 4) are reported.

Deuterium quadrupole coupling tensors in methyl halides: Ab initio effective core potential and liquid crystal nuclear magnetic resonance study

The deuterium quadrupole coupling tensors were calculated for the methyl halides CD3X (X=F, Cl, Br, and I) using ab initio effective core potential (ECP) methods up to the QCISD level. The effects of basis set quality and electron correlation were investigated, and a comparison with all-electron calculations was made. We also determined a new experimental value for methyl chloride by the liquid crystal nuclear magnetic resonance (LC NMR) method. Locally dense basis sets were used for the deuterium atoms and ECPs for the halogens. The Br and I ECPs were scalar relativistic. Computations at the equilibrium (re) geometry result in slightly too negative tensor elements along the molecular C3 symmetry axis for all X, as compared to the experimental LC NMR and microwave spectroscopic results. Values corresponding to the rα(300 K) geometry are in a very good agreement with experiment. As the tensors are sensitive to the length of the associated CD bond, we applied approximate vibrational corrections to the theoretical results. The current corrected values for the deuterium quadrupole coupling constants and asymmetry parameters are likely to be the most reliable available for the present set of molecules, despite that residual computational errors still remain. The common approximation of a cylindrically symmetric electric field gradient tensor at the deuterium site is shown to lead to an underestimation of the corresponding quadrupole coupling constant in methyl halides.

“Variable-angle” sample-spinning nuclear magnetic resonance spectroscopic studies of non-integral spin quadrupolar nuclei in solids: Analysis of spinning-sidebands for the case η=0

We present an average Hamiltonian analysis of the “variable-angle” sample-spinning nuclear magnetic resonance spectra of the central ( 1 2 , − 1 2 ) transition of the I= 3 2 nuclei 23Na (in Na 2MoO 4) and 11B (in a borosilicate glass) in the slow-spinning regime (ω r < W ( 1 2 , − 1 2 ), for a purely second-order quadrupolar interaction and an axially symmetric electric field gradient tensor. We obtain good agreement between theory and experiment. The technique is applicable to the analysis of systems with large quadrupole coupling constants, as well as to those with multiple sites and different coupling constants and chemical shifts.

Measurement of the deuteron quadrupole coupling constant in LiAlD 4

Assuming an axially symmetric electric field gradient tensor at the deuteron site, the quadrupole coupling constant in polycrystalline LiAlD 4 is found experimentally to be 72 kHz.

MAGNETIC PARAMETRIC NUCLEAR SPIN SATURATION

Parametric magnetic Δm = ±2 nuclear spin transitions are observed when an rf magnetic field at the frequency (Em−2 − Em)/h is applied parallel to a large, externally applied, magnetic field in a ruby crystal where the symmetry axis of the cylindrically symmetric electric field gradient tensor (the c axis in ruby) is perpendicular to the external magnetic field.

Mössbauer Study of 57Co(57Fe) in CoO at High Pressure

The room-temperature internal magnetic field Hi, electric quadrupole coupling ε, and isomer shift IS of divalent 57Fe in CoO have been measured as a function of pressure up to about 250 kbar. Radioactive samples were prepared by heating 57Co-enriched Co3O4 in vacuum above 1000°C. The main features of the velocity spectra are qualitatively similar to those of the temperature study of this system as reported by Wertheim,1 except that the fraction of trivalent 57Fe observed is substantially reduced.2,3 As the pressure is raised the velocity spectrum unfolds into a magnetic hyperfine pattern in which Hi increases from zero to about 210 kOe at 250 kbar. This value is somewhat higher than the low-temperature saturation value of approximately 180 kOe. The rate of increase of Hi with pressure, coupled with low-temperature and x-ray pressure-volume measurements,4 shows that the Néel temperature TN (291°K at atmospheric pressure) increases with decreasing volume in a manner consistent with the results of Bloch et al.5 [d(lnTN)/d(lnV)≅ −3 at atmospheric pressure]. The velocity spectra also indicate small changes in both IS and ε with pressure, the former varying from −1.16 mm/sec at atmospheric pressure to −1.08 mm/sec at 250 kbar, relative to a stainless steel absorber. Both the change in IS and saturation value of Hi are consistent with an expansion of the 3d charge density and an accompanying increase in the 3s charge and spin density at the nucleus, because of less screening. The parameter, ε=¼e2qQ, in the antiferromagnetic phase is observed to approximately double from −0.03 mm/sec at 100 kbar to −0.06 mm/sec at 250 kbar. (These values are based on the unproven assumption that Hi is parallel to the axis of an axially symmetric electric field gradient tensor.)