Measurement of magnetic susceptibility and calculation of shape factor of NMR samples

A method for accurate measurement of magnetic susceptibility and determination of the shape factor in an NMR tube is shown. The combination of accurate shape factor determination with susceptibility measurement leads to improved accuracy when measuring chemical shift. This is important for comparing samples in different solvents or under different conditions, such as temperature, solvent, and pH.     

A computer algorithm for the simulation of any nuclear magnetic resonance (NMR) imaging method

More than a dozen Nuclear Magnetic Resonance (NMR) imaging methods have been described using different radio-frequency pulse sequences, magnetic field gradient variations, and data processing. In order to have a theoretical understanding in the most general case, we have conceived a computer program for the simulation of NMR imaging techniques. The algorithm uses the solution of the Bloch equations at each point of a simulated object. The direction of every elementary magnetic moment is computed at each instant, and stored in an array giving the global signal to be processed, whatever the pulse and gradient sequence. To test the validity of this program, we have simulated some well-known experimental results. Some applications are presented which contribute to the understanding of image distortions and to techniques such as selective radio-frequency pulse or oscillating gradients. This program can be used to unravel physical and technological causes of image distortions, to have a "microscopic" look at any parameter of an experiment, and to study the contrast given by various NMR imaging techniques as a function of the three NMR parameters, i.e., the hydrogen nuclei density rho and the relaxation times T1 and T2.     

Numerical simulation of NQR/NMR: Applications in quantum computing

A numerical simulation program able to simulate nuclear quadrupole resonance (NQR) as well as nuclear magnetic resonance (NMR) experiments is presented, written using the Mathematica package, aiming especially applications in quantum computing. The program makes use of the interaction picture to compute the effect of the relevant nuclear spin interactions, without any assumption about the relative size of each interaction. This makes the program flexible and versatile, being useful in a wide range of experimental situations, going from NQR (at zero or under small applied magnetic field) to high-field NMR experiments. Some conditions specifically required for quantum computing applications are implemented in the program, such as the possibility of use of elliptically polarized radiofrequency and the inclusion of first- and second-order terms in the average Hamiltonian expansion. A number of examples dealing with simple NQR and quadrupole-perturbed NMR experiments are presented, along with the proposal of experiments to create quantum pseudopure states and logic gates using NQR. The program and the various application examples are freely available through the link http://www.profanderson.net/files/nmr_nqr.php.     

Angular Flow in Toroid Cavity Probes

NMR signals from samples that rotate uniformly about the central conductor of a TCD (toroid cavity detector) exhibit frequency shifts that are directly proportional to the sample's angular velocity. This newly observed effect is based on the unique radiofrequency field inside TCDs, which is variable in direction. If a liquid sample is pumped through a capillary tube wound about the central conductor, the frequency shift is proportional to the flow rate. A mathematical relationship between a volumetric flow rate and the frequency shift is established and experimentally verified to high precision. Additionally, two-dimensional flow-resolved NMR spectroscopy for discrimination between components with different flow velocities yet retaining chemical shift information for structural analysis is presented. The application of the two-dimensional method in chromatographic NMR is suggested. Furthermore, utilization of the frequency-shift effect for rheologic studies if combined with toroid-cavity rotating-frame imaging is proposed.     

A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection

We propose a new moving pseudo-boundary method of fundamental solutions (MFS) for the determination of the boundary of a three-dimensional void (rigid inclusion or cavity) within a conducting homogeneous host medium from overdetermined Cauchy data on the accessible exterior boundary. The algorithm for imaging the interior of the medium also makes use of radial spherical parametrization of the unknown star-shaped void and its centre in three dimensions. We also include the contraction and dilation factors in selecting the fictitious surfaces where the MFS sources are to be positioned in the set of unknowns in the resulting regularized nonlinear least-squares minimization. The feasibility of this new method is illustrated in several numerical examples.     

Observation of a new coherent transient in NMR -- nutational two-pulse stimulated echo in the angular distribution of \gamma-radiation from oriented nuclei

A new coherent transient in pulsed NMR, the two-pulse nutational stimulated echo, is reported for the ferromagnetic system ⁶⁰CoFe using resonant perturbations on the directional emission of anisotropic \gamma-radiation from thermally oriented nuclei. The new spin echo is a result of non-linear nuclear spin dynamics due to large Larmor inhomogeneity active during radiofrequency pulse application. It is made readily observable through the gross detuning between NMR radiofrequency excitation and gamma radiation detection, and inhomogeneity in the Rabi frequency caused by metallic skin-effect. The method of concatenation of perturbation factors in a statistical tensor formalism is quantitatively applied to successfully predict and then fit in detail the experimental time-domain data. This revised version was published online in August 2006 with corrections to the Cover Date.     

Separation of 47Ti and 49Ti solid-state NMR lineshapes by static QCPMG experiments at multiple fields

Experimental procedures are proposed and demonstrated that separate the spectroscopic contribution from both (47)Ti and (49)Ti in solid-state nuclear magnetic resonance spectra. These take advantage of the different nuclear spin quantum numbers of these isotopes that lead to different "effective" radiofrequency fields for the central transition nutation frequencies when these nuclei occur in sites with a significant electric field gradient. Numerical simulations and solid-state NMR experiments were performed on the TiO(2) polymorphs anatase and rutile. For anatase, the separation of the two isotopes at high field (21.1T) facilitated accurate determination of the electric field gradient (EFG) and chemical shift anisotropy (CSA) tensors. This was accomplished by taking advantage of the quadrupolar interaction between the EFG at the titanium site and the different magnitudes of the nuclear quadrupole moments (Q) of the two isotopes. Rutile, having a larger quadrupolar coupling constant (C(Q)), was examined by (49)Ti-selective experiments at different magnetic fields to obtain spectra with different scalings of the two anisotropic tensors. A small chemical shielding anisotropy (CSA) of -30 ppm was determined.     

Diffusion measurements with the aid of nutation spin echoes appearing after two inhomogeneous radiofrequency pulses in inhomogeneous magnetic fields

Nutation echoes are generated by radiofrequency (RF) pulses with an inhomogeneous amplitude, B(1) = B(1)(r), in inhomogeneous magnetic fields, B(0) = B(0)(r). The two gradients of strengths G(1) and G(0), respectively, must be aligned in parallel for a maximum echo signal. After two RF pulses, two echoes appear at times tau(a) = 2 tau(1) + tau(2) + (G(1)/G(0))tau(1) and tau(b) = 2 tau(1) + tau(2) + 2(G(1)/G(0))tau(1), where tau(1) is the RF pulse duration and tau(2) the interpulse interval. It is shown that these echoes can favorably be employed for the determination of self-diffusion coefficients even in the poor experimental situation one often faces in low-resolution or low-field NMR. The signal intensity is comparable to that of ordinary Hahn echoes. Diffusion coefficients and spin-lattice relaxation times can be evaluated from the same experimental data set if both nutation echoes are recorded. Test experiments are in good agreement with literature data. Applications of the technique to "inside out" NMR, well logging NMR, surface coil NMR, toroid cavity NMR, etc., are suggested.     

High-resolution NMR imaging of objects with dipolar-broadened spectra

It is shown that, in some substances with dipolar-broadened conventional NMR spectra, it is possible to use long-lived coherent response signals, excited by long and weak radiofrequency pulses, for producing NMR images with high spatial resolution. Compared to other techniques, the method does not require high field gradients or strong radiofrequency fields, and therefore, can be applied to large objects.     

Demixing of severely overlapped H NMR resonances and interpretation of anomalous intensity pattern of dipolar coupled A3 spins in a weakly aligning medium

The increasing scientific and industrial interest towards metabonomics takes advantage from the high qualitative and quantitative information level of nuclear magnetic resonance (NMR) spectroscopy. However, several chemical and physical factors can affect the absolute and the relative position of an NMR signal and it is not always possible or desirable to eliminate these effects a priori. To remove misalignment of NMR signals a posteriori, several algorithms have been proposed in the literature. The icoshift program presented here is an open source and highly efficient program designed for solving signal alignment problems in metabonomic NMR data analysis. The icoshift algorithm is based on correlation shifting of spectral intervals and employs an FFT engine that aligns all spectra simultaneously. The algorithm is demonstrated to be faster than similar methods found in the literature making full-resolution alignment of large datasets feasible and thus avoiding down-sampling steps such as binning. The algorithm uses missing values as a filling alternative in order to avoid spectral artifacts at the segment boundaries. The algorithm is made open source and the Matlab code including documentation can be downloaded from www.models.life.ku.dk.     

Spectral editing of 13C NMR spectra via two-dimensional pulse techniques

Two-dimensional pulse techniques for subspectral editing in ¹³C NMR spectroscopy are described. The experiments are compared with existing one-dimensional editing methods with respect to sensitivity, information content, and practical performance. In combination with a computer program for fully automatic extraction of one-dimensional edited subspectra and radiofrequency field strength information, the two-dimensional presented experiments are useful as setup experiments in ¹³C NMR.     

The Signs of Frequencies and Phases in NMR

The signs of radiofrequency phases and frequencies used in NMR are examined carefully. Some fundamental problems with current usage are exposed by simple examples. The entire chain of events leading to the NMR spectrum is examined closely, including generation and phase-shifting of the radiofrequency carrier wave, nuclear-spin dynamics in the presence of the radiofrequency field, quadrature detection, signal digitization, post-digitization phase shifting, Fourier transformation, and spectral presentation. Recommendations are given for software modifications which should facilitate the correspondence between pulse programming, spectral presentation, and spin dynamical theory.     

Optical fiber ring resonator characterization by optical time-domain reflectometry

A novel method for characterization of optical fiber resonators by an optical time-domain reflectometry (OTDR) technique is reported. This easy-to-use technique yields accurate results for cavity lengths ranging from a few meters to several kilometers. A simple relationship is established between the round-trip cavity loss and the position where the OTDR signal is maximum. The value obtained for the round-trip cavity loss turns out to be quite insensitive to uncertainties in the determination of the OTDR maximum position.     

Shape determination for deformed electromagnetic cavities

The measured physical parameters of a superconducting cavity differ from those of the designed ideal cavity. This is due to shape deviations caused by both loose machine tolerances during fabrication and by the tuning process for the accelerating mode. We present a shape determination algorithm to solve for the unknown deviations from the ideal cavity using experimentally measured cavity data. The objective is to match the results of the deformed cavity model to experimental data through least-squares minimization. The inversion variables are unknown shape deformation parameters that describe perturbations of the ideal cavity. The constraint is the Maxwell eigenvalue problem. We solve the nonlinear optimization problem using a line-search based reduced space Gauss–Newton method where we compute shape sensitivities with a discrete adjoint approach. We present two shape determination examples, one from synthetic and the other from experimental data. The results demonstrate that the proposed algorithm is very effective in determining the deformed cavity shape.     

Signal enhancement in the triple-quantum magic-angle spinning NMR of spins-3/2 in solids: the FAM-RIACT-FAM sequence

We achieve a significant signal enhancement for the triple-quantum magic-angle spinning NMR of a spin-3/2 system, by using an amplitude-modulated radiofrequency field, followed by a selective 90 degrees pulse and a phase-shifted strong rf field, for the triple-quantum excitation, and an amplitude-modulated radiofrequency field for the conversion of triple-quantum coherence to observable single-quantum coherence. The experiment is demonstrated on the (87)Rb NMR of polycrystalline rubidium nitrate.     

In situ fluid typing and quantification with 1D and 2D NMR logging

In situ nuclear magnetic resonance (NMR) fluid typing has recently gained momentum due to data acquisition and inversion algorithm enhancement of NMR logging tools. T(2) distributions derived from NMR logging contain information on bulk fluids and pore size distributions. However, the accuracy of fluid typing is greatly overshadowed by the overlap between T(2) peaks arising from different fluids with similar apparent T(2) relaxation times. Nevertheless, the shapes of T(2) distributions from different fluid components are often different and can be predetermined. Inversion with predetermined T(2) distributions allows us to perform fluid component decomposition to yield individual fluid volume ratios. Another effective method for in situ fluid typing is two-dimensional (2D) NMR logging, which results in proton population distribution as a function of T(2) relaxation time and fluid diffusion coefficient (or T(1) relaxation time). Since diffusion coefficients (or T(1) relaxation time) for different fluid components can be very different, it is relatively easy to separate oil (especially heavy oil) from water signal in a 2D NMR map and to perform accurate fluid typing. Combining NMR logging with resistivity and/or neutron/density logs provides a third method for in situ fluid typing. We shall describe these techniques with field examples.     

Sample restriction using magnetic field gradients in high-resolution solid-state NMR

Many solid-state NMR experiments are sensitive to inhomogeneity in the radiofrequency field. We propose a method to restrict the sample volume, in magic angle spinning experiments, using a static magnetic field gradient and a selective pulse. The position of the gradient is calculated for our experimental configuration and we have simulated the effects of selective pulses to determine the excited volume. The resulting sequences are applied to a sample of sodium acetate using frequency-switched Lee–Goldburg proton–proton homonuclear dipolar decoupling. A gain of a factor of 2 on the carbon resolution is experimentally observed.     

A structure refinement strategy for NMR crystallography: an improved crystal structure of silica-ZSM-12 zeolite from 29Si chemical shift tensors

A strategy for performing crystal structure refinements with NMR chemical shift tensors is described in detail and implemented for the zeolite silica-ZSM-12 (framework type code MTW). The 29Si chemical shift tensors were determined from a slow magic-angle spinning spectrum obtained at an ultrahigh magnetic field of 21.1T. The Si and O atomic coordinate parameters were optimized to give the best agreement between experimentally measured and ab initio calculated principal components of the 29Si chemical shift tensors, with the closest Si-O, O-O, and Si-Si distances restrained to correspond with the distributions of the distances found in a set of single-crystal X-ray diffraction (XRD) structures of high-silica zeolites. An improved structure for the silica-ZSM-12 zeolite, compared to a prior structure derived from powder XRD data, is obtained in which the agreement between the experimental and calculated 29Si chemical shift tensors is dramatically improved, the Si-O, O-O, and Si-Si distances correspond to the expected distributions, while the calculated powder XRD pattern remains in good agreement with the experimental powder XRD data. It is anticipated that this "NMR crystallography" structure refinement strategy will be an important tool for the accurate structure determination of materials that are difficult to fully characterize by traditional diffraction methods.     

Self-Diffusion Measurements by Pulsed-Gradient Multiple-Spin-Echo Imaging

A new method is described which allows the spatial distribution of the self-diffusion coefficient over a sample to be determined in a single NMR imaging experiment. This technique combines NMR imaging principles with the pulsed-field-gradient multiple-spin-echo (PGMSE) method. Two basic forms of the pulse sequence for PGMSE imaging have been devised and image intensity as a function of the diffusion-gradient strength is given. The effects of the imaging gradients on the additional diffusion attenuation of image intensities are considered. Finally, the preliminary experimental verification of the PGMSE imaging technique is illustrated by measuring the diffusion coefficient for doped water using the version of the pulse sequence in which all of the 180° radiofrequency pulses are not slice-selective.     

Field characterization of therapeutic ultrasound phased arrays through forward and backward planar projection

Spatial planar projection techniques propagate field measurements from a single plane in front of a transmitter to arbitrary new planes closer to or further away from the source. A linear wave vector frequency-domain projection algorithm is applied to the acoustic fields measured from several focused transducer arrays designed for ultrasound therapy. A polyvinylidene difluoride hydrophone is first scanned in a water tank over a plane using a three-dimensional positioning system to measure the complex pressure field as a function of position. The field is then projected to a series of new planes using the algorithm. Results of the projected fields are compared with direct measurements taken at corresponding distances. Excellent correlation is found between the projected and measured data. The method is shown to be accurate for use with phase-controlled field patterns, providing a rapid and accurate method for obtaining field information over a large spatial volume. This method can significantly simplify the characterization procedure required for phased-array application used for therapy. Most significantly, the wavefront propagated back to a phased array can be used to predict the field produced by different phase and amplitude settings of the array elements. A field back-projected to the source could be used as an improved source function in acoustic modeling.