Using quaternions to design composite pulses for spin-1 NQR

The fictitious spin-1/2 operators are well known to describe the evolution of a pure nuclear quadrupole resonance (NQR) system; particularly, the application of a radio-frequency pulse at one of the NQR transition frequencies is equivalent to a three-dimensional rotation in a space defined by the corresponding fictitious spin-1/2 operators. We demonstrate, theoretically and experimentally, that consecutive noncommuting rotations applied at the same transition frequency are well described by a single rotation given by quaternion parameterization of the rotations in ficitious spin-1/2 operator space. This new route could greatly save computing time and efforts. We extend this approach to design composite pulses that compensate for the effects of the radio-frequency field inhomogeneity for a powder sample of spin-1 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.     

一种精密的边限振荡器型NQR谱仪及其应用

本文介绍一种精密的场效应管边限振荡器型核四极矩共振(NQR)谱仪。工作频率范围14MHz~35MHz,分段连续可调。这种谱仪的灵敏度高、波形失真小。在室温下,多晶粉未状氯酸钾样品中³⁵Cl的NQR频率测量精度大约3×10^-6。重结晶样品中³⁵Cl的NQR谱一次微分信号信噪比S/N ≥ 150。用该谱仪对KClO3、NaClO3、NaCl样品进行测试,得到氯的同位素³⁵Cl和37Cl的四极耦合常数比(eQq₃5Cl/(eQq₃7Cl的实测值分别为1.2687363、1.2687306、1.2687361。在77K到393K温度区间测量了氯酸钾多晶粉未状样品中³⁵Cl的NQR共振频率和温度的关系,在冰水混合温度附近,温度每变化0.1K,NQR频率的变化是478Hz。     

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 (C6H12N4) 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 T2 seems to be the reason of that. The signal-to-noise ratio was sufficient for measuring T2 in C6H12N4, which had not been reported earlier. Experimental results of applying certain pulse sequences to the 14N NQR in a sample are also presented.     

Dominant ferromagnetism in the spin-1/2 half-twist ladder 334 compounds, Ba3Cu3In4O12 and Ba3Cu3Sc4O12

The magnetic properties of polycrystalline samples of Ba(3)Cu(3)In(4)O(12) (In-334) and Ba(3)Cu(3)Sc(4)O(12) (Sc-334) are reported. Both 334 phases have a structure derived from perovskite, with CuO(4) squares interconnected to form half-twist ladders along the c-axis. The Cu-O-Cu angles, ~90°, and the positive Weiss temperatures indicate the presence of significant ferromagnetic (FM) interactions along the Cu ladders. At low temperatures, T < 20 K, sharp transitions in the magnetic susceptibility and heat capacity measurements indicate three-dimensional (3D) antiferromagnetic (AFM) ordering at T(N). T(N) is suppressed on application of a field and a complex magnetic phase diagram with three distinct magnetic regimes below the upper critical field can be inferred from our measurements. The magnetic interactions are discussed in relation to a modified spin-1/2 FM-AFM model and the 334 half-twist ladder is compared to other two-rung ladder spin-1/2 systems.     

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.     

Emission of nuclear quadrupole resonance from polycrystalline hexamethylenetetramine

The angular dependence of the nuclear quadrupole resonance (NQR) signal intensity emitted from polycrystalline hexamethylenetetramine has been analytically investigated for all directions for non-contact detection of chemicals by nuclear quadrupole resonance. The field pattern of the NQR signal from a column sample was measured. The emitted patterns were the same as that from a united single magnetic dipole, which fitted well to the estimation based on quadrupole principle axis system. This result is helpful to design an antenna for NQR remote detection.     

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.     

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.     

Circularly Polarized RF Magnetic Fields for Spin-1 NQR

The low sensitivity of nuclear quadrupole resonance (NQR) of powders is due, in part, to the inability to efficiently excite and detect nuclei at all crystal orientations. Here we describe the use of circularly polarized RF magnetic fields for excitation followed by detection of the resultant circular RF magnetization in I=1 NQR to increase the fraction of nuclei excited and detected. We show that the technique can greatly improve the effective RF field homogeneity and increase the largest signal amplitude by a factor of 1.72. In favorable cases, the resulting circularly polarized NQR signal can be separated from linearly polarized magnetoacoustic and piezoelectric ringing artifacts that occur in some NQR materials detection applications.     

Solid-Effect Rate for Dynamic Nuclear Polarization of Spin-l/2 and Spin-1 Nuclei

The solid-effect rate equations for the dynamic nuclear polarization of spin-1/2 (tritium or hydrogen) or spin-1 (deuterium) nuclei are derived in the limiting case of the electronspin-resonance line width being much smaller than the nuclear-magnetic-resonance frequency. The exact analytical solutions of the rate equations for spin-1/2 nuclei are given, while the rate equations for spin-1 nuclei, which are nonlinear, are solved in decoupling approximation. The nuclear polarization and the electronic polarization as well as the times to polarization are calculated in low temperature limit. It is found that there is an optimal radio frequency pumping rate for the nuclear polarizations, which is not considered until now.     

Manifestation of anisotropic collisional generation of higher polarization moments in polarization of quadrupole emission

Direct observability of polarization moments of a higher order—octupole orientation of atomic angular momenta (κ=3) and their hexadecapole alignment (κ=4)—from polarization of quadrupole radiation is discussed. The case when atoms are excited through dipole absorption of light producing orientation or alignment of angular momenta with κ=1 or 2 and higher polarization moments are induced by collisions with a beam of particles is considered. It is shown that differences in the laws of transformation of polarization moments of various ranks κ in rotations of coordinate axes allow us to select the pure contribution of the higher polarization moment under study from the signal of polarization of quadrupole emission by excluding the contribution of orientation or alignment with κ=1 or 2. Optimum systems of coordinate axes for the observation of octupole orientation from circular polarization of light and for the observation of hexadecapole alignment from linear polarization of light, in which the pure contribution of the higher polarization moment under study to polarization of quadrupole emission reaches its maximum, are calculated.     

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.     

Sensitivity enhancement of NMR spectra of half-integer spin quadrupolar nuclei in solids using hyperbolic secant pulses

The experimental factors influencing the enhancements achievable for the central NMR transition, m(I)=1/2-->m(I)=-1/2, of spin-3/2 and spin-5/2 nuclei in the solid state using hyperbolic secant, HS, pulses for population transfer are investigated. In the case of powder samples spinning at the magic angle, it is found that the spinning frequency, the bandwidth and the frequency offset of the HS pulse play a crucial role in determining the maximum enhancements. Specifically, the bandwidth must be set to the spinning frequency for maximum signal enhancements. The (87)Rb NMR enhancement obtained for RbClO(4) using HS pulses was relatively insensitive to the magic angle spinning frequency; however, in the case of Al(acac)(3), the (27)Al enhancement increased with MAS frequency. In order to obtain an adiabatic HS sweep, one should optimize the rf field for a given pulse duration or optimize the pulse duration for a given rf field.     

Nonuniqueness of a massive spin-2 theory

The nonunique nature of massive spin-2 fields is explicitly shown in this paper through the construction of all possible field equations, using Dirac formalism for spin-1/2 fields. Out of these four possible theories, we point out two that do not show up scalar representations.     

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.     

NMR Studies of the Reaction Path of the o-H2/p-H2 Spin Conversion Catalyzed by Vaska’s Complex in the Solid State

We have studied the o/p spin conversion of dihydrogen in contact with frozen solutions of Vaska’s complex Ir(CO)Cl(PPh₃)₂ (1) in C₆D₆ and with polycrystalline 1 at 77 K. The main purpose of this study was to elucidate the mechanism of this type of reactions found accidentally previously (Eisenschmid et al JACS 109:8089–8091, 1987 and Eisenberg ACS 24:110–116, 1991). The formation of p-H₂ was followed after thawing of the samples by ¹H nuclear magnetic resonance (NMR) spectroscopy at 298 K, where the oxidative addition of dihydrogen to 1 occurs leading to Vaska’s dihydride Ir(CO)ClH₂(PPh₃)₂ (2) which is known to exhibit para-hydrogen-induced polarization (PHIP). The PHIP signal was shown to be proportional to the concentration of p-H₂ as elucidated from the decrease of the signal of dissolved o-H₂. The reaction was found to be faster for the frozen solution as compared to the polycrystalline powder. Optical microscopy showed that small particles of 1 are separated from the solution during the freezing process, exhibiting a larger surface area as compared to the polycrystalline powder. When a mixture of H₂ and D₂ was exposed to the frozen solutions or to the polycrystalline powder, the formation of HD was observed by ¹H NMR. This finding indicates the presence of a chemical spin conversion involving two dihydrogen molecules. Additional ¹H NMR experiments of dihydrogen in frozen C₆D₆ at 110 K indicated the formation of larger pores containing gaseous H₂ as well as dihydrogen sites in interstitial sites between benzene molecules. Moreover, in the presence of 1, a signal at ?4.5 ppm was observed which was attributed to a dihydrogen in close contact with Ir.     

NQR and magnetic characteristics of the solid solution of NaClO3-KClO3

We measured the nuclear quadrupole resonance (NQR) of the solid solutions of NaClO₃-KClO₃ in the range of concentrations from 0 to 100% molar of KClO₃ in (NaClO₃ + + KClO₃). The thermal diagram of the measured samples showed, that the solubility of the components in each other is limited. It is shown that up to 88·6% molar of KlCO₃ it is possible to identify signals at a frequency which almost exactly corresponds to the NQR frequency of NaClO₃, from this concentration the signals belong to the NQR frequency of KClO₃. At the same time the width of the line shows anomalies in samples containing up to 10% KClO₃ or up to 10% NaClO₃. Broadening of the NQR line to the value 35 kHz in this region was interpreted as a result of prevalence of the size-effect, when the solid solution consists of a mixed crystal of one of the components with such a number of cations of the other component, which is sufficient to produce a chaotic order around the resonanting Cl³⁵ nucleus and such alterations of the electrical field gradient, that they will widen the line.We have also interpreted the deviations of the resonance frequency and linewidth corresponding to the monocrystalline, polycrystalline and melted modifications of the pure NaClO₃ and KClO₃ components.The dependence of the molar magnetic susceptibility of the solid solutions on the concentration of KClO₃ in NaClO₃ + KClO₃ is not linear, it has a peak at the concentration that belongs to the eutectic state, when the chaotic order of the ions Na¹⁺, K¹⁺, (ClO₃ ^1– around any of them is most perfect. At this concentration Van Vleck's polarization paramagnetism is minimum and because it is positive, the total negative value of susceptibility of the material is maximum.     

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.