Relaxation effects in two-dimensional zero-field nutation NQR spectroscopy

The relaxation and off-resonance effects on the NQR (nuclear quadrupole resonance) nutation frequency and on the damping constant of the nutation spectrum for spinsI = 3/2 are considered. Using the solution of dynamic equations for nuclear magnetisation in the rotating frame, we obtained a general expression for determination of the asymmetry parameter η, which includes the relaxation time and frequency offset. Specific requirements for the RF (radio frequency) field allowing the presence of nutation and the sufficient resolution of nutation spectra are determined. It is shown that at low RF field it is necessary to take into account theT ₂ relaxation effect on the location of frequency singularities in the nutation spectrum. The values ofH ₁ andT ₂ must be exactly known in nutation NQR spectroscopy. The 2D NQR spin-echo separation technique was used for determination of transverse relaxation of individual spin packets in case of inhomogeneously broadened NQR lines, so that the asymmetry parameter could then be determined by the nutation experiment with consideration of relaxation effects and frequency offset. The theoretical results are confirmed experimentally for the narrow and inhomogeneously broadened 2D-nutation NQR spectra in several molecular compounds containing the³⁵Cl and⁷⁵As nuclei.     

Determination of the asymmetry parameter of EFG tensor from moments of NQR nutation spectra in powders

A novel approach to determination of the asymmetry parameter of the EFG tensor from zero-field nutation NQR spectra of the spinI = 3/2 nuclei in powder samples is reported. The proposed theoretical treatment uses lineshape analysis of the nutation NQR spectra by the method of line moments. The analytical formulas for the lineshape of the powder nutation spectrum are given. It is shown that the asymmetry parameter can be determined from the second moment 〈ω²〉 and the frequency of only one singularity ω₂ of the nutation spectrum. It is also shown that the asymmetry parameter can be determined from the second and fourth spectrum moments alone. The method is successfully demonstrated for the simulated nutation NQR spectra of the spinI = 3/2 nuclei in powder samples.     

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 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.Kaliningrad State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 66–72, June, 1995.     

Recording 2-D Nutation NQR Spectra by Random Sampling Method

The method of random sampling was introduced for the first time in the nutation nuclear quadrupole resonance (NQR) spectroscopy where the nutation spectra show characteristic singularities in the form of shoulders. The analytic formulae for complex two-dimensional (2-D) nutation NQR spectra (I = 3/2) were obtained and the condition for resolving the spectral singularities for small values of an asymmetry parameter η was determined. Our results show that the method of random sampling of a nutation interferogram allows significant reduction of time required to perform a 2-D nutation experiment and does not worsen the spectral resolution.     

Two-dimensional nutation exchange NQR spectroscopy: direct determination of rotational angles

A new method for the direct determination of rotational angles based on 2-dimensional nutation exchange NQR spectroscopy is proposed. The method involves the detection of exchange processes through NQR nutation spectra recorded after the mixing interval. The response is analysed of a system of spins I = 3/2 in zero applied field, experiencing electric quadrupole couplings, to the three-pulse sequence with incrementing pulse widths. The systems investigated here were hexachloroethane and tetrachloroethylene, which show threefold and twofold reorientational jumps about the carbon-carbon axis, respectively. It is shown that the 2D nutation exchange NQR spectrum exhibits characteristic ridges, which reveal the motional mechanism in a model-independent fashion. The angles through which the molecule rotates can be read directly from elliptical ridges in the 2D spectrum, which are also sensitive to the value of asymmetry parameter of the electric field gradient tensor.     

Non-cyclic geometric phase of nuclear quadrupole resonance signals of powdered samples

The non-cyclic geometric phase of ¹⁴N and ³⁵Cl NQR signals induced by the character of trajectory of nuclear magnetization motion upon pulse r.f. excitation of powdered samples is studied. Analytical expressions for the geometric phases of NQR signals of the nuclei of spins I=1 and 3/2 upon nuclear magnetization rotation induced by means of r.f. pulses with frequency detuned from the resonance and for any impulse duration for a separate crystallite are obtained. It is shown that the geometric phase recorded for the signal from a powdered sample at Δω=0 can be different from zero and can oscillate upon changes in duration of the r.f. excitation pulse. An alternative variant of the nutation experiment aimed at obtaining the asymmetry parameter η from locations of frequency singularities in the nutation phase spectrum for nuclei of spin I=3/2 in powder substances is proposed.     

Application of Nutations to Studying the Exchange Processes by the Method of Nuclear Quadrupole Resonance Spectroscopy

A method of direct determining the discontinuous rotational reorientation angles from NQR exchange spectra based on recording of two-dimensional nutations of magnetization after the mixing period is suggested. The possible modification of the Jeener pulse sequence with independently varying duration of pulses for obtaining a 2D exchange nutation spectrum is described. Shapes of singularities in the 2D nutation spectrum of CCl₂- and CCl₃-group reorientations, which depend on the angle _S between C–Cl bonds and on the asymmetry parameter for nonequivalent positions of nuclei participating in the exchange are examined. The 2D exchange NQR nutation spectra of ³⁵Cl in powders prepared from C₂Cl₄ and C₂Cl₆ molecular crystals are modeled. The advantages and capabilities of the method are discussed.     

Determination of the spectral parameters of nuclear quadrupole resonance from nutation spectra of powdered samples

An analytical expression I(ω) is obtained for a normalized function of the shape of an idealized nuclear quandrupole resonance nutation line of a powdered sample for spins I=3/2 (η≠0). Calculations are made of the initial moments <ωⁿ> of the nutation spectrum of the powder in the form of functions of ω₀=γB₁ and the asymmetry parameter η of the electric field gradient tensor. A method is proposed for determining the spectral parameters η and eQq_zz from the experimentally measured values of <ω>, <ω²>, <ω⁴>, and ω_1/2 of the nuclear quadrupole resonance nutation spectrum of the powder. State University, Kaliningrad. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 3–8, July, 1997.     

Two-dimensional14N NQR spectra for two-frequency excitation programs

We have determined expressions for the complex amplitudes of signals in the two-dimensional¹⁴N NQR spectrum for different two-frequency excitation programs. We have established a correspondence between the two-dimensional NQR spectra and various methods for excitation of the spin system.Kaliningrad State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 54–57, July, 1992.     

Calculations of Multipulse Sequence in NQR of Spins

The general formalism of the interaction representation with respect to an operator which is its own inverse is developed and applied to pure NQR of spins I = . Under the assumption of no relaxation and no dipolar coupling, it is shown that the calculation of the response to pure NQR multipulse sequences can be performed with the same concepts used in high field NMR, such as coherence pathways. All the tools and mathematical expressions to predict the time evolution of the signal created by a pure NQR multipulse sequence are presented explicitly. It takes into account the off-resonance irradiation as well as the angular dependence of the excitation and detection for every value of the electric field gradient asymmetry parameter. Particular attention is devoted to the powder average, which is performed via a probability function derived analytically for the first time, leading to a drastic reduction of simulation times. The theory is illustrated by the study of the optimization and excitation bandwidths of one- to three-pulse sequences and compared to experimental results on Chloranil. We show that the three-pulse “stimulated echo” sequence gives a more uniform excitation profile than the traditional two-pulse echo sequence for powder samples. Thus, the “stimulated echo” sequence could be useful to cover a large spectrum when the experiment duration, or the signal to noise ratio, are not critical parameters. Analytical expressions for the nutation spectra obtained by one or two-pulse sequences are also derived for the first time.     

A New Method of Obtaining Structural Information from 2M Exchange NMR and NQR Spectra of Powders

A method of calculating the singularities of two-dimensional correlation spectra of powders and determining the structural parameters with the help of a computer program is described. The opportunities of the method are illustrated on examples of experimental 2M exchange ¹³ C NMR spectra of dimethylsulfone, 2M exchange ² H NMR spectrum of hexamethylbenzene, and model 2M exchange nutational NQR spectrum for spin I = 3/2. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 72–75, August, 2005.     

Determination of Reorientation Angles from Two-Dimensional Exchange Spectra of Powders in Radiospectroscopy

A method for transforming a 2D exchange spectrum into an orientation representation is proposed which is based on finding the reorientation probability as a function of angles. A procedure of evaluation and analysis of two-dimensional magnetic spectra of powders is described and a method for finding the asymmetry parameter from 2D exchange spectra is proposed. The capabilities of the method are illustrated for a model ³⁵Cl 2D nutation exchange NQR spectrum of chloral hydrate CCl₃CH(OH)₂ and an experimental ¹³C 2D exchange NMR spectrum of dimethylsulphone CH₃–SO₂–CH₃. The asymmetry parameter of the chemical shift tensor for this compound is determined.     

Determination of mutual orientation of tensor interactions from two-dimensional nutation NQR-spectra of solids

Expressions for singularities of 2D correlation nutation NQR-spectra are obtained. A method is proposed for measuring orientation of two tensor interactions in powder specimens, which relies on specimen re-orientation in an rf-coil within the pulse period between the second and third pulses of a sequence of stimulated echo signal and detection of a 2D nutation NQR spectrum. Feasibilities of the method are discussed and simulated spectra for the case of nuclei with the spin I = 3/2 are reported. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 29–32, January, 2008.     

Comparison of some resolution enhancement methods applied to35Cl-NQR nutation spectroscopy

The³⁵Cl nuclear quadrupole resonance spin echo nutation spectroscopy method was used to determine asymmetry parameters,η, of the electric field gradient tensor in cyanuric chloride, 1,3,5-trichloro-cyanuric acid and 1,3-dichloro-5,5-dimethylhydantoin. For comparison of advantages and drawbacks of some data processing methods we have tried integral transforms of nutation interferogram (pseudo-FID) data (Hankel and Hartley transforms) alternative to the Fourier transform. Another processing method, which provides a power spectrum estimated from time-domain data, is the maximum entropy method (MEM), and we applied the Burg algorithm version of it. We found that MEM gives the best enhancement of the nutation spectrum resolution and the signal-to-noise ratio, provided the number of autocorrelation coefficients is chosen for optimum performance of the Burg algorithm, otherwise estimated singularities in the nutation spectrum can be obscured by multiple spurious peaks or the spectrum resolution is low. In the Hankel transform with the first-order Bessel functions the improvement in resolution is achieved at the expense of the overall signal-to-noise ratio and for noisy experimental data this transform did not show reliable results. The Hartley transform gives a resolution better than the Fourier transform but worse than the two other methods. Unlike the Hankel transform after the Hartley transform the signal-to-noise ratio is not degraded. Theη parameter determined by MEM for cyanuric chloride was 18%, which is close to previously reported values. For 1,3,5-trichloro-cyanuric acidη = 20% and for the two chlorine sites in 1,3-dichloro-5,5-dimethylhydantoinη = 0 and 12% respectively. These values are in substantial agreement with the anticipated double bond character of N-Cl bonds in the two last compounds.     

Calculations of multipulse sequence in NQR of spins 32

The general formalism of the interaction representation with respect to an operator which is its own inverse is developed and applied to pure NQR of spins I = 32. Under the assumption of no relaxation and no dipolar coupling, it is shown that the calculation of the response to pure NQR multipulse sequences can be performed with the same concepts used in high field NMR, such as coherence pathways. All the tools and mathematical expressions to predict the time evolution of the signal created by a pure NQR multipulse sequence are presented explicitly. It takes into account the off-resonance irradiation as well as the angular dependence of the excitation and detection for every value of the electric field gradient asymmetry parameter. Particular attention is devoted to the powder average, which is performed via a probability function derived analytically for the first time, leading to a drastic reduction of simulation times. The theory is illustrated by the study of the optimization and excitation bandwidths of one- to three-pulse sequences and compared to experimental results on Chloranil. We show that the three-pulse "stimulated echo" sequence gives a more uniform excitation profile than the traditional two-pulse echo sequence for powder samples. Thus, the "stimulated echo" sequence could be useful to cover a large spectrum when the experiment duration, or the signal to noise ratio, are not critical parameters. Analytical expressions for the nutation spectra obtained by one or two-pulse sequences are also derived for the first time.     

Ba nuclear resonance in YBa2Cu2Oy

The first observations of NMR and NQR of both isotopes¹³⁵Ba and¹³⁴Ba in isotopically enriched samples of YBa₂Cu₃O_y with oxygen concentrations y=6.0, 6.2, and 7.0 are described. The pure NQR frequencies and asymmetry parameter are in good agreement with theoretical predictions. The temperature dependence of the NQR frequency of Ba for y=7 is qualitatively similar to that for Cu(2) but much stronger. The temperature dependence of the longitudinal and transverse relaxation times opens new questions.     

Two-dimensional on- and off-resonance nutation FFT/MEM NQR spectroscopy

The new two-dimensional nuclear quadrupole resonance experiments 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 are discussed. The problems of reconstructing 2D-nutation NQR spectra using conventional methods and the advantages of using implementation of the maximum entropy method (MEM) are analyzed. Use of the MEM in 2D-NQR spectroscopy can lead to sensitivity improvement, reduction of instrumental artifacts and truncation errors, shortened data acquisition times and automatic suppression of noise, while at the same time increasing the resolution. The possibilities of off-resonance irradiation in nutation experiments are demonstrated experimentally and theoretically. It is shown that the off-resonance nutation spectroscopy is a useful extension of the conventional on-resonance experiments thus facilitating the determination of asymmetry parameters in multiple spectrum. The methods have been successfully demonstrated for the³⁵Cl on-and off-resonance 2D-nutation spectra in polycrystalline 2,4,6-trichloro-1,3,5-triazine.     

Transient NQR signals in the effective field of multipulse trains

This paper is a theoretical analysis of time-dependent nutation and echo signals in the effective field of multipulse trains in NQR. The results of experimental investigations of the same aspects were reported in earlier papers. The various features of dipole-dipole interactions in three-level quadrupole spin systems are discussed. It is shown that, in contrast to NMR, the dipole Hamiltonian in the interaction representation determined by the quadrupole Hamiltonian contains only three diagonal components of the dipole-dipole interaction tensor. On the other hand, the strong inhomogeneous broadening characteristic of NQR hinders exact measurement of these components by ordinary methods. The theoretical analysis suggests that the decay of the echo-signal envelope in the effective field of multipulse trains is determined solely by the dipole relaxation time, which serves as justification of a new experimental method used in measuring the characteristics of the dipole-dipole interaction tensor in spin systems with an inhomogeneously broadened spectrum. Zh. éksp. Teor. Fiz. 115, 1580–1592 (May 1999)     

Quadrupole parameters of 11B in crystalline CaO.B2O3.

The quadrupole coupling constant (Qcc) and asymmetry parameter (eta) of 11B in crystalline CaO.B2O3 have been measured employing three different NQR and NMR methods: (1) 11B and 10B NQR; (2) 11B NQR and NMR; and (3) the 11B Zeeman NQR powder pattern. It is found that Qcc = 2594.3 +/- 0.5 kHz and eta = 0.515 +/- 0.001 at 77 K, and Qcc = 2573.5 +/- 0.5 kHz and eta = 0.511 +/- 0.002 at 300 K. These values are in agreement with, but far more accurate than, values obtained from a fourth procedure: measurement of the second-order quadrupolar effects evident in the m = + 1/2<-->m = - 1/2 transition of the 11B NMR spectrum.