Selective averaging for high-resolution solid-state NMR spectroscopy of aligned samples

Solid-state NMR experiments benefit from being performed at high fields, and this is essential in order to obtain spectra with the resolution and sensitivity required for applications to protein structure determination in aligned samples. Since the amount of rf power that can be applied is limited, especially for aqueous protein samples, the most important pulse sequences suffer from bandwidth limitations resulting from the same spread in chemical shift frequencies that aids resolution. SAMPI4 is a pulse sequence that addresses these limitations. It yields separated local field spectra with narrower and more uniform linewidths over the entire spectrum than the currently used PISEMA and SAMMY experiments. In addition, it is much easier to set up on commercial spectrometers and can be incorporated as a building block into other multidimensional pulse sequences. This is illustrated with a two-dimensional HETCOR experiment, where it is crucial to transfer polarization from the amide protons to their directly bonded nitrogens over a wide range of chemical shift frequencies. A quantum-mechanical treatment of the spin Hamiltonians under high-power rf pulses is presented which gives the scaling factor for SAMPI4 as well as the durations of the rf pulses to achieve optimal decoupling.     

三能级体系的Z回波核磁共振粉末谱

本文提出一个Z回波核磁共振(NMR)脉冲序列,可以获得三能级体系的纯偶极或纯四极谱。Z回波NMR谱不仅与化学位移各向异性无关,而且在强射频场条件下,与射频场非均匀性无关。该方法明显优于章动NMR技术。以上结论经过理论分析和实验结果的验证。 关键词：     

Chemical shift anisotropy and offset effects in cross polarization solid-state NMR spectroscopy

The effect of an offset term in the cross-polarization (CP) Hamiltonian of a heteronuclear spin-12 pair due to off-resonant radio frequency (rf) irradiation and/or chemical shift anisotropy on one of the rf channels is investigated. Analytical solutions, simulations, and experimental results are presented. Formulating the CP spin dynamics in terms of an explicit unitary evolution operator enables the CP period to be inserted as a module in a given pulse scheme regardless of the initial density matrix present. The outcome of post-CP manipulation via pulses can be calculated on the resulting density matrix as the phases and amplitudes of all coherence modes are available. Using these tools it is shown that the offset can be used to reduce the rf power on that channel and the performance is further improved by a post-CP pulse whose flip angle matches and compensates the tilt of the effective field on the offset channel. Experimental investigations on single crystalline and polycrystalline samples of peptides confirm the oscillatory nature of CP dynamics and prove the slowing down of the dynamics under offset and/or mismatch conditions.     

Side-lobeless far-field spectrum of a short pulse from a circular aperture with Gaussian form of transmittance

The spectrum change of a Gaussian pulse in the far field is studied with the Fresnel diffraction integral when it is incident on an aperture with Gaussian form transmittance. It is found that the side-lobes of the diffracted spectral intensity, which exist in a normal circular aperture with unit transmittance, can be eliminated completely under such a condition. Also, the red shift and blue shift of the spectral intensity maximum of the incident pulse are presented.     

Adjusting Conditions for High-resolution Pulsed NMR in Solids

Adjusting conditions of pulse sequences for high-resolution nmr in solids are demonstrated by the example of the WHH4 cycle. For this pulse sequence the well-known adjusting condition [1] occurs as limiting case at sufficiently weak dipolar interaction. The relations between the pulse rotation angle and interval time proved to be dependent on the dipolar interaction. Therefore it is impossible to suppress the dipolar interaction in ordinary solids completely. If the strength of the dipolar interaction varies in a range depending on the allowable inhomogeneity of the rf field a spectrometer for high-resolution nmr in solids can be adjusted in an almost optimal way.     

Magnetic field mapping in NMR imaging

The Hahn spin preparation sequence provides a practical means for rapid and sensitive mapping of magnetic field inhomogeneity in NMR imaging applications. Choice of the rf pulse delay times tau 1 and tau 2 as well as conditions and limitations on the proposed use of this sequence for chemical shift imaging are discussed.     

Rotary resonance echo double resonance for measuring heteronuclear dipolar coupling under MAS

A rotary resonance echo double resonance (R-REDOR) experiment is described for measuring heteronuclear dipolar coupling under magic-angle spinning. Rotary resonance reintroduces both dipolar coupling and chemical shift anisotropy with an rf field matching the spinning frequency. The resonance effect from chemical shift anisotropy can be refocused with a rotary resonance echo. The R-REDOR experiment thus measures the dephasing of the rotary resonance echo from the heteronuclear dipolar coupling to determine the dipolar coupling constant. The rotary resonance experiment is suitable for measuring dipolar coupling with quadrupolar nuclei because it applies the recoupling rf only to the observed spin-1/2. The rotary resonance scheme has the advantages of a long T2' and susceptible to spinning frequency fluctuation.     

Stark效应对双模压缩真空场与原子耦合系统腔场谱的影响

研究了Stark效应对两模双光子J-C模型腔场谱的影响,推导计算出了腔场处于压缩真空态时腔场谱的计算公式和数值结果,讨论了Stark效应和初始场强对腔场谱的影响.发现初始场较弱时,Stark效应主要影响谱线的频率,对峰的强度影响不大;初始场n1=n2≥2后,Stark效应对主峰有较强的强化作用,对边峰产生抑制作用;在初始场较强时,对谱强度的影响显著.改变Stark移动参数和初始场的强度,可得到各式各样的腔场谱结构.     

Heteronuclear decoupling by multiple rotating frame technique

The paper describes the multiple rotating frame technique for designing modulated rf fields, that perform broadband heteronuclear decoupling in solution NMR spectroscopy. The decoupling method presented here is understood by performing a sequence of coordinate transformations, each of which demodulates a component of the rf field to a static component, that progressively averages the chemical shift and the dipolar interaction. We show that by increasing the number of modulations in the decoupling field, the ratio of dispersion in the chemical shift to the strength of the static component of the rf field is successively reduced in the progressive frames. The known decoupling methods like continuous wave decoupling, TPPM, etc., can be viewed as special cases of this method and their performance improves by adding additional modulations in the decoupling field. The technique is also expected to find use in design of broadband excitation, inversion and mixing sequences and broadband experiments in solid state NMR.     

Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms

In this paper, we introduce optimal control algorithm for the design of pulse sequences in NMR spectroscopy. This methodology is used for designing pulse sequences that maximize the coherence transfer between coupled spins in a given specified time, minimize the relaxation effects in a given coherence transfer step or minimize the time required to produce a given unitary propagator, as desired. The application of these pulse engineering methods to design pulse sequences that are robust to experimentally important parameter variations, such as chemical shift dispersion or radiofrequency (rf) variations due to imperfections such as rf inhomogeneity is also explained.     

斯塔克效应对两模双光子J-C模型腔场谱的影响

研究了斯塔克(Stark)效应对两模双光子Jaynes-Cummings(J-C)模型腔场谱的影响,推导计算出了腔场处于光子数态时腔场谱的计算公式和数值结果,讨论了斯塔克效应和初始场强对腔场谱的影响。发现斯塔克效应在弱场条件下对腔场谱线的频率和强度都有明显的影响,破坏了谱结构的对称性,使两模的谱线更加丰富。初始场较强时斯塔克效应对谱线的影响较弱。模Ⅰ为真空场、模Ⅱ初始场强递增时,斯塔克效应使模Ⅱ的高频峰受到较强的抑制作用,其低频峰在初始场较弱时受到抑制,初始场较强时又有强化作用,初始场更强时,模Ⅱ的谱线退化为经典的共振荧光谱,与无斯塔克效应的情况基本相同。     

Electron cyclotron resonance in a weakly magnetized radio-frequency inductive discharge

The evolution of the electron energy distribution function (EEDF) over a weak magnetic field range is investigated in magnetized radio-frequency (rf) inductive discharges under a collisionless regime where an anomalous skin effect and electron cyclotron resonance (ECR) can occur. A significant change in the low-energy range of the EEDF is found in the ECR condition during the evolution. The observed result reveals the low-energy electrons are efficiently heated by the rf ECR in the presence of the anomalous skin effect. The calculated result of the electron distribution based on kinetic theory is in good agreement with the experiment.     

Single-sided sensor for high-resolution NMR spectroscopy

The unavoidable spatial inhomogeneity of the static magnetic field generated by open sensors has precluded their use for high-resolution NMR spectroscopy. In fact, this application was deemed impossible because these field variations are usually orders of magnitude larger than those created by the microscopic structure of the molecules to be detected. Recently, chemical shift resolved NMR spectra were observed for the first time outside a portable single-sided magnet by implementing a method that exploits inhomogeneities in the rf field designed to reproduce variations of the static magnetic field. In this communication, we describe in detail the magnet system built from permanent magnets as well as the rf coil geometry used to compensate the static field variations.     

Abnormal heating of low-energy electrons in low-pressure capacitively coupled discharges

In low-pressure capacitively coupled plasmas, high-energy electrons are collisionlessly heated by large rf fields in the sheaths while low-energy electrons are confined in the bulk plasma by the ambipolar potential. Low-energy electrons are typically inefficiently heated due to their low collisionality and the weak rf electric field present in the bulk. It is shown, however, that as a result of the nonlinear interaction between the electron motion and the weak rf field present in the bulk, low-energy electrons can be efficiently heated. Electrons in the bulk that bounce inside the electrostatic potential well with a frequency equal to the rf excitation frequency are efficiently heated by the coherent interaction with the rf field. This resonant collisionless heating can be very efficient and manifest itself as a plateau in the electron energy probability function.     

Shift of relaxation-stimulated resonances in Mössbauer absortion spectra in a static magnetic field

New features are obtained for previously predicted relaxation-stimulated resonances in Mössbauer spectra of nanomagnets exposed to an external rf field: the resonances should undergo low-frequency shift upon applying a weak static magnetic field. Analytic expressions for the resonance frequencies as functions of the static field are obtained within a simplified relaxation model. This effect extends the possibilities for experimental observation of the predicted effects, because tuning to the resonance may be accomplished not only by changing frequency of the rf field but also by varying the amplitude of the alternating field and the strength of the static field.     

Heteronuclear decoupling under fast MAS by a rotor-synchronized Hahn-echo pulse train

A new heteronuclear decoupling mechanism under fast magic-angle spinning MAS is introduced. It is based on refocusing the coherences responsible for the dephase of low-gamma nuclei ((13)C, (15)N) transverse spin-polarization in the presence of strongly dipolar-coupled protons, and has the advantage that can be implemented by pulsed techniques, with all the benefits resulting from a reduced duty cycle compared with conventional decoupling by continuous rf irradiation. The decoupling efficiency of a simple rotor-synchronized Hahn-echo pulse train is analyzed both theoretically and experimentally. It was found that a substantial improvement in sensitivity and resolution can be achieved in compounds with small (1)H chemical shielding parameters even at moderate sample spinning, and some interesting applications are shown. It is also shown that much faster spinning frequencies, or alternative refocusing sequences, are needed for applications on rigid organic solids, i.e., in systems with larger (1)H chemical shifts.     

Inhomogeneous interactions in solids under slow off-magic angle spinning.

The central band of an inhomogeneous interaction under slow off-magic angle spinning (off-MAS) is no longer a scaled static spectrum with scaling factor P2(cos upsilon), that is, the spectrum distortion occurs in comparison with that under the rapid rotation condition. The dependence of this distortion in the chemical shift spectrum, for instance, on anisotropy, the asymmetry parameter, spinning rate and the angle between the spinning axis and the applied magnetic field is studied in this paper. It is shown that the distortion can be partly eliminated by using TOSS in certain circumstances. Experimental evidence is presented in this study.     

射频激发热丝化学气相沉积制备硅薄膜过程中光发射谱的研究

采用射频(rf)激发,在热丝化学气相沉积(HWCVD)制备微晶硅薄膜的过程中产生发光基元,测量了rf激发HWCVD (rf-HWCVD)的光发射谱,比较了相同工艺条件下rf-HWCVD和等离子体增强CVD(PECVD)的光发射谱,分析了rf功率、热丝温度和沉积气压对rf-HWCVD光发射谱的影响.结果表明,在射频功率<0.1W/cm²时,rf-HWCVD发射光谱反映了HWCVD高的气体分解效率和高浓度原子氢的特点,能够解释气压变化与微晶硅薄膜微结构的关系,是研究HWCVD气相过程的有 关键词： HWCVD OES 微晶硅     

Variation in the magnetic structure of a single-domain particle ensemble and its response to an rf pulse

A set of equations in the Gilbert form that describes the motion of the magnetization vector in an ensemble of interacting magnetic nanoparticles is numerically solved for the case of high-amplitude rf pulses. Based on the numerical solution, the magnetic structure of spherical particle ensembles showing cubic anisotropy at certain parameters of the variable field is studied. This phenomenon is shown to have a threshold. The dependence of the field threshold amplitude on the acting pulse repetition rate and amount of magnetic interaction is determined. It is demonstrated that a change in the magnetic structure of the interacting particle ensembles causes a change in the spectrum of the response. This fact can be used for pulsed rf writing and readout of information based on ferromagnetic resonance.     

NMR spectra under skin-effect conditions at ultralow temperatures

An investigation based on the coupled Maxwell-Bloch equations for a system of equivalent exchange-coupled spins is performed in order to explain a number of features of NMR spectra obtained in metals by Fourier-transforming of the free-induction decay at ultralow temperatures. Small angles of tilting of the nuclear magnetization by the exciting rf field are considered. It is shown that the free precession inherits the nonuniformity in the distribution of the rf field and the magnetization produced at the excitation stage inside the sample on account of the skin effect. As a result, the NMR spectrum is found to consist of a set of peaks—signals due to standing spin waves. However, such a spectrum can be observed only when the detuning of the exciting rf field is sufficiently large relative to the Larmor frequency of the spins. Otherwise, the rf field does not penetrate into the sample because of strong absorption by the spins. If the detuning is large, the dispersion signal and part of the NMR absorption signal are proportional to the equilibrium magnetization to the power 3/2. Such behavior is expected at low temperatures so that the coupling of the magnetization with the rf field is strong. The results obtained qualitatively explain the experimentally observed characteristics of the NMR spectra: the presence of kinks and structure of the NMR lines, the dependence of the shape and intensity of the spectrum on the detuning of the exciting rf field, and the nonlinear dependence of the nuclear susceptibility on the reciprocal of the sample temperature. Zh. éksp. Teor. Fiz. 114, 1836–1847 (November 1998)