Determination of quadrupole parameters with a composite pulse for spurious signal suppression

Spurious signals such as the piezoelectric signal from a ferroelectric crystal or the ringing signal from the NMR probe head tuned for low gyromagnetic ratio nuclei are often observed in pulsed NMR. Both signals are cancelled using the Hahn echo sequence with appropriate phase cyclings. The present paper applies a composite-pulse sequence to cancel the ringing signal. The main advantage of this sequence over the Hahn echo sequence is in the simplicity of optimizing the line intensity: the optimization of only one pulse duration for this sequence but of two pulse durations and the interpulse delay for the Hahn echo sequence. We are interested in half-integer quadrupole spins (I = 3/2, 5/2, 7/2, and 9/2), which means that we must consider the first-order quadrupole interaction during the pulses. For simplicity, we deal mainly with spin I = 3/2 nuclei. Since the central-line intensity depends on the ratio of the quadrupole coupling constant (QCC) to the amplitude of the RF pulse, we can determine the QCC from a featureless lineshape by fitting the variation of the experimental central-line intensity for increasing pulse duration with theoretical results. Contrary to the one-pulse sequence where the central-line intensity is proportional to the pulse duration if the latter is short, there is no such condition with the composite-pulse sequence. In other words, this sequence does not allow us to quantify the relative spin populations in powders. The size of the sample must be much smaller than that of the RF coil in order for the RF magnetic field to become homogeneous for the sample. We used (87)Rb (I = 3/2) in an aqueous solution of RbCl and in RbNb2O5F powder, (131)Xe (I = 3/2) of xenon gas physisorbed in Na-Y zeolite, and (23)Na (I = 3/2) in two well-known powders (NaNO3 and NaNO2) to support our theoretical result.     

Velocity autocorrelation spectra of fluid in porous media measured by the CPMG sequence and constant magnetic field gradient

Carr-Purcell-Meiboom-Gill (CPMG) train of radiofrequency pulses applied to spins in the constant magnetic field gradient is an efficient variant of the modulated magnetic field gradient spin echo method, which provides information about molecular diffusion in the frequency domain instead of in the time domain as with the two-pulse gradient spin echo. The frequency range of this novel technique is broad enough to sample the power spectrum of displacement fluctuation in water-saturated pulverized silica (SiO2) and provides comprehensive information about the molecular restricted motion as well as about the structure of the medium.     

Multi-dimensional inverse Laplace spectroscopy in the NMR of porous media

Multi-dimensional NMR methods based on Inverse Laplace Transformations (ILT) may be used to examine the behavior of liquid state molecules in a porous matrix. The ILT is particularly useful when the signal is characterized by multi-exponential decay, for example in spin relaxation or in the dephasing of the NMR spin echo signal associated with molecular diffusion under the influence of pulsed magnetic or internal field gradients. Both correlation and exchange experiments are possible, the latter providing insight regarding the migration of molecules between regions characterized by different local dynamics.     

Phase Correction-Adaptive Line Enhancement for Noise Reduction of Low-Field NMR

The amplitude of low-field nuclear magnetic resonance (NMR) is weak, and the echo is buried in the noise. The reduction of noise is critical to accurately extract echo amplitude. Phase correction-adaptive line enhancement (PC-ALE) is proposed to noise suppression based on the principle of ALE and NMR spin-echo characteristics. The echo amplitude is calculated after two-stage processes; phase shift from time-delay and filter tap would be compensated effectively in frequency domain. Simulation and experiments show that PC-ALE has prominent performance on noise suppression, envelope recovery, as well as the correction of the phase shift. The amplitude from the method of sample average nearby the middle of the echo is more accurate than the maximum peak when the PC-ALE is applied to noise suppression of spin-echo.     

Diffusion and relaxation effects in general stray field NMR experiments

We analyze the evolution of magnetization following any series of radiofrequency pulses in strongly inhomogeneous fields, with particular attention to diffusion and relaxation effects. When the inhomogeneity of the static magnetic field approaches or exceeds the strength of the RF field, the magnetization has contributions from different coherence pathways. The diffusion or relaxation induced decay of the signal amplitude is in general nonexponential, even if the sample has single relaxation times T(1), T(2) and a single diffusion coefficient D. In addition, the shape of the echo depends on diffusion and relaxation. It is possible to separate contributions from different coherence pathways by phase cycling of the RF pulses. The general analysis is tested on stray field measurements using two different pulse sequences. We find excellent agreement between measurements and calculations. The inversion recovery sequence is used to study the relaxation effects. We demonstrate two different approaches of data analysis to extract the relaxation time T(1). Finite pulse width effects on the timing of the echo formation are also studied. Diffusion effects are analyzed using the Carr--Purcell--Meiboom--Gill sequence. In a stray field of a constant gradient g, we find that unrestricted diffusion leads to nonexponential signal decay versus echo number N, but within experimental error the diffusion attenuation is still only a function of g(2)Dt(3)(E)N, where t(E) is the echo spacing.     

Multi-quantum echoes in GdAl2 zero-field high-resolution NMR

In this paper we present a series of high-resolution zero-field NMR spectra of the polycrystalline intermetallic compound GdAl₂. The spectra were obtained with the sample at 4.2 K in the ordered magnetic state and in the absence of an external static magnetic field. Using a sequence composed of two RF pulses, we obtained up to five multi-quantum echoes for the ²⁷Al nuclei, which were used to construct the zero-field NMR spectra. The spectra obtained from the FID observed after the second pulse and the even echoes exhibited higher resolution than the odd ones. In order to explain such behavior, we propose a model in which there are two regions inside the sample with different inhomogeneous spectral-line broadenings. Moreover, with the enhanced resolution from the FID signal, we were able to determine quadrupolar couplings with great precision directly from the respective spectra. These results were compared with those obtained from the quadrupolar oscillations of the echo signals, and showed good agreement. Similar data were also obtained from ¹⁵⁵Gd and ¹⁵⁷Gd nuclei.     

Low temperature NMR in domain walls of YFeO3

The properties of the ⁵⁷Fe NMR in a single crystal of a canted antiferromagnet YFeO₃ were studied at low temperatures. The effects of a magnetic field, applied along the antiferromagnetic easy axis, on the wall NMR are described. The application of a magnetic field causes a drastic increase of NMR signal intensity at 4.2 K. Temperature decrease below 4.2 K produces similar changes in NMR signal. The increase of NMR signal intensity is connected with the increase of the enhancement factor η in the domain wall. It appears that η increases when the domain walls becoming narrower. Within the framework of crystal field theory the influence of Fe⁴⁺ ions on magnetocrystalline anisotropy of YFeO₃ is analysed.     

Numerical solution to the Bloch equations:paramagnetic solutions under wideband continuous radio frequency irradiation in a pulsed magnetic field

A novel nuclear magnetic resonance(NMR) experimental scheme,called wideband continuous wave NMR(WB-CW-NMR),is presented in this article.This experimental scheme has promising applications in pulsed magnetic fields,and can dramatically improve the utilization of the pulsed field.The feasibility of WB-CW-NMR scheme is verified by numerically solving modified Bloch equations.In the numerical simulation,the applied magnetic field is a pulsed magnetic field up to 80 T,and the wideband continuous radio frequency(RF) excitation is a band-limited(0.68-3.40 GHz) white noise.Furthermore,the influences of some experimental parameters,such as relaxation time,applied magnetic field strength and wideband continuous RF power,on the WB-CW-NMR signal are analyzed briefly.Finally,a multi-channel system framework for transmitting and receiving ultra wideband signals is proposed,and the basic requirements of this experimental system are discussed.Meanwhile,the amplitude of the NMR signal,the level of noise and RF interference in WB-CW-NMR experiments are estimated,and a preliminary adaptive cancellation plan is given for detecting WB-CW-NMR signal from large background interference.     

Radiative detection of NMR studies of domain nuclei in enriched ferromagnetic iron

Combined host (∼95 at% enriched stable ⁵⁷Fe) and very dilute impurity (∼0.01 at% radioactive ⁶⁰Co) NMR signals have been obtained on the one sample of polycrystalline Fe foil utilising perturbations to the gamma anisotropy from in situ thermally oriented ⁶⁰Co nuclei for both resonances. The NMR-TDNO signals on the ⁵⁷Fe sites have been followed down to applied magnetic fields well below the host magnetic saturation and exhibited two distinct components; a strong, narrow homogeneous signal, superimposed over a broader inhomogeneous signal. The impurity ⁶⁰Co⁵⁷Fe inhomogeneous resonance has been studied with three pulse NMRON and the irreversible decay of the nuclear spin echo measured as a function of applied magnetic field. This revised version was published online in August 2006 with corrections to the Cover Date.     

Secondary Nuclear Spin Echo Signals in Thin Yttrium Iron Ferrite Garnet Films

The results are presented of experimental and theoretical study of the phenomenon of secondary nuclear spin echo in magnetically ordered materials in which the formation of additional echo signals is due to dynamic hyperfine coupling. Numerical simulation of the effect of the amplitude (ω1) and the durations of the first (t1) and the second (t2) exciting pulses on the echo signals is performed. It is found that the maximum amplitude of the secondary echo is formed under the conditions ω1t1 = 0.5π and ω1t2 ≈ 0.6π. It is shown that secondary echo signals can be observed upon inhomogeneous excitation of the spectral line ω1 ≤ Δω, where Δω is the inhomogeneous spectral line width. At a temperature of T = 4.2 K, additional double-pulse spin 3τ-echo signals from iron nuclei are experimentally observed in an epitaxial yttrium ferrite garnet film enriched with 57Fe magnetic isotope to 96%. The experimentally observed phase relationships between the primary and secondary echo signals, as well as the dependence of the echo signal amplitude on the amplitude and duration of the exciting pulses, are in good agreement with the results of numerical simulation of the dynamics of nuclear magnetization with regard to the dynamic hyperfine coupling. It is shown that the secondary echo exhibits the effect of spectral line narrowing, and the amplitude of the secondary echo is proportional to the nuclear magnetic resonance (NMR) enhancement factor in magnets, η. In the case of 57Fe NMR in an yttrium iron garnet (YIG) film, the amplitude of the 3τ-echo is two to three orders of magnitude smaller than the amplitude of the primary 2τ-echo, which corresponds to η ≈ 440. The detection of weak secondary echo signals proves to be possible due to the use of a phase-coherent NMR spectrometer with digital quadrature detection at the carrier frequency and signal accumulation.     

The nutation spin echo and its use for localized NMR

A suitably matched combination of unidirectional gradient pulses of the radio frequency amplitude B(1) and of the main magnetic field B(0) produces an unconventional type of spin echo, the nutation echo. The echo signal becomes volume selective if the gradients to be matched are inhomogeneously distributed in space. An example is a combination of a constant B(0) gradient and the inhomogeneous B(1) gradient of a surface coil. We suggest a method for localized NMR on this basis. Nutation echoes can also be used to map the spatial distribution of B(1) gradients of an arbitrary radio frequency coil geometry with the aid of a small probe sample. Copyright 2000 Academic Press.     

NMR spin echoes for molecular rotators with C(3) symmetry

NMR spin echoes are calculated for a rotator consisting of three spin-(1/2) nuclei whose three-particle wave function obeys C(3) symmetry. On decomposing the nuclear dipole-dipole interactions in terms of irreducible operators of the representations of the group C(3) it is found that for spins belonging to the A-representation, the echo amplitude is maximized for a RF pulse sequence. The dependences of the echo formation on the orientation of the rotor and on the strengths of the dipolar interactions and the magnetic field inhomogeneities are discussed. Copyright 2000 Academic Press.     

Effect of the inner structure of domain walls on the stability of an isolated stripe domain in a pulsed field

This paper studies the effect of the inner structure of domain walls on the stability of an isolated stripe domain localized in a thin ferromagnetic film against a pulse of magnetic field applied perpendicularly to the film surface. It is found that the value of the critical amplitude of the pulsed signal strongly depends on the value of the magnetizing field in which the system was initially placed. It is also established that the difference on stability of domains with unipolar and bipolar walls in pulsed fields diminishes as the amplitude of the magnetizing field decreases. Finally, the dependence of the region of stability in a pulse field on the parameters of the system is determined for various domain types. Zh. éksp. Teor. Fiz. 116, 1694–1705 (November 1999)     

Radiofrequency magnetic field gradient echoes have reduced sensitivity to susceptibility gradients

The amplitudes of gradient-echoes produced using static field gradients are sensitive to diffusion of tissue water during the echo evolution time. Gradient-echoes have been used to produce MR images in which image intensity is proportional to the self-diffusion coefficient of water. However, such measurements are subject to error due to the presence of background magnetic field gradients caused by variations in local magnetic susceptibility. These local gradients add to the applied gradients. The use of radiofrequency (RF) gradients to produce gradient-echoes may avoid this problem. The RF magnetic field is orthogonal to the offset field produced by local magnetic susceptibility gradients. Thus, the effect of the local gradients on RF gradient-echo amplitude is small if the RF field is strong enough to minimize resonance offset effects. The effects of susceptibility gradients can be further reduced by storing magnetization longitudinally during the echo evolution period. A water phantom was used to evaluate the effects of background gradients on the amplitudes of RF gradient-echoes. A surface coil was used to produce an RF gradient of between 1.3 and 1.6 gauss/cm. Gradient-echoes were detected with and without a 0.16 gauss/cm static magnetic field gradient applied along the same direction as the RF gradient. The background static field gradient had no significant effect on the decay of RF gradient-echo amplitude as a function of echo evolution time. In contrast, the effect of the background gradient on echoes produced using a 1.6 gauss/cm static field gradient is calculated to be significant. This analysis suggests that RF gradient-echoes can produce MR images in which signal intensity is a function of the self-diffusion coefficient of water, but is not significantly affected by background gradients.     

频域稀疏采样和激光成像方法

激光的单色性和自然图像频谱稀疏且集中在低频区间的特点,使图像频谱稀疏采样成像成为可能.基于小规模激光探测器,引入参考激光,本文提出了频域稀疏采样激光成像方法.介绍了频域稀疏采样激光成像的原理和成像系统结构,推导了激光回波重构复频谱的表达式,给出了重构频谱和复图像的仿真结果并分析了信号参数对重构效果的影响,同时采用相干系数、均方误差和结构相似度来评价其重构效果.规模为256×256的激光回波复图像仿真表明, 5个拼接1/4×1/4规模频域探测器组成的近似十字型稀疏采样结构,在约31.25%(5/16)的频域稀疏采样条件下,仍可获得较好的重构频谱和重构复图像.     

针对磁共振射频脉冲的时频域分析方法比较研究

射频脉冲可实现样本自旋体系的精确操控,进而产生预期的核磁共振(NMR)信号,在NMR信号产生过程中扮演重要角色.该文分别采用短时傅里叶变换(STFT)、连续小波变换(CWT)和维格纳-威利分布(WVD)几种时频域分析方法对射频脉冲(优化形状脉冲)进行特性分析和比较.结果表明,三种方法各自具有优缺点,结合各自优势对射频脉冲进行各种方法分析,可以更好地理解复杂脉冲的幅度、相位特性在时频域的分布情况.该文的研究方法将为直观理解复杂射频脉冲对自旋体系的作用机制提供参考.     

Constant-time multidimensional electrophoretic NMR

Multidimensional electrophoretic NMR (ENMR) has been introduced to determine structures of coexisting proteins and protein conformations in solution. Signals of different proteins are separated in a new dimension of electrophoretic flow according to their characteristic electrophoretic mobilities. The electrophoretic interferograms have been generated in the flow dimension in two approaches by incrementing either the amplitude or the duration of the electric field. The ENMR method of incrementing the duration of the electric field, however, introduces severe signal decays due to molecular diffusion and spin relaxation, limiting the effectiveness of the method. In this study, an improved method of constant-time multidimensional ENMR (CT-ENMR) has been proposed and successfully tested. The time delays between the magnetic field gradients and the RF pulses are kept constant in this new method so that the molecular diffusion and spin relaxation processes contribute to only a constant factor of signal amplitude. As an alternative approach of incrementing the amplitude of the electric field, this novel method significantly enhances our capability and potential in characterizing structural changes of interacting proteins during biological signaling processes. The CT-ENMR method is particularly useful in studies where the amplitude-incrementing of the electric field is not optimal. For example, the CT-ENMR method is superior when the electric field is applied in the direction not parallel to the static magnetic field B(0) to the xy-magnetization. The new method was successfully demonstrated with a sample solution containing 100 mM 4,9-dioxa-1,12-dodecanediamine and 100 mM L-aspartic acid in D(2)O.     

Single-sided mobile NMR with a Halbach magnet

A single-sided mobile NMR apparatus with a small Halbach magnet was constructed for the first time. It is lightweight, compact and exhibits good sensitivity. The weight of the device is only 2 kg, and the NMR signal of the pencil eraser block can be detected in one shot using the device. This study describes the characteristics of this instrument, including the profile of static magnetic flux density, B0, the sensitivity in the depth direction and its effectiveness in one-dimensional profiling. Its usefulness in differentiating soft materials and evaluating the extent of damage of a material is demonstrated based on T2 relaxation data. The moisture absorbance also can be observed from the increase of the echo amplitude of the NMR spin echo signal.     

RF resonance techniques for continuous muon beams

RF excitation was first used in μSR in 1958 [1]. However, even with the advent of modern meson facilities the use of RF techniques in μSR has not flourished, in part due to the muon's short lifetime, but mainly because unlike NMR RF fields are simply not used to detect the muon's polarization. Nevertheless, a cursory survey of the relative power and sophistication of these two related fields leaves little doubt that the pursuit of RF resonance within μSR will add significantly to its analytical capability. At TRIUMF over the past few years we have worked toward developing RF capabilities suitable for use in a CW meson facility. Several spectroscopic applications utilizing time integral techniques have been tested. These include detection of final states in semiconductor and substituted radical systems, the very pretty two photon absorption (TPA) experiments, and the use of low field swept frequency excitation to measure nuclear hyperfine parameters in Mu like system. Of course, the most celebrated use of RF in magnetic resonance is its application to spin dynamics via various spin echo techniques. The adaptation of the spin echo to μSR is discussed and examples of both transverse and longitudinal field echoes are presented.     

Study of the coercive force in ferromagnetic dysprosium metal by RF field enhancement

The RF field enhancement factor η is calculated for the domains and domain walls of ferromagnetic Dy metal. In the domains η ? 30, while in the walls it depends on the coercive force which limits the wall motion. The study of η from spin echo signals of nuclei in the walls is used to determine this coercive force in powder of Dysprosium metal, before and after annealing.