Irving J. Lowe

Nuclear Magnetic Dipole—Dipole Relaxation Along the Static and Rotating Magnetic Fields: Application to Gypsum

General formulas are derived for the spin—lattice relaxation times along the static magnetic field (T1) and the rotating field (T1r) due to magnetic dipole—dipole interactions. First‐order perturbation theory is used in the calculation, and it is assumed that the spin system can be described by a temperature. The correlation functions that appear in these formulas are evaluated for the case of a spin system in which each spin has just two possible equilibrium positions. The results are used to improve Holcomb and Pedersens calculation of dipole—dipole spin—lattice relaxation due to the motion of spin pairs that execute 180° rotational flips about their perpendicular bisecting axes. Applying the results to gypsum (CaSO4·2H2O) yields T1=43.4 msec at the minimum of the T1‐vs‐temperature curve for a static‐field strength B0=2348 G. The experimental value is 47±4 msec. Similarly, the calculated minimum of the T1r‐vs‐temperature curve is T1r=1.86 msec for a rotating‐magnetic‐field strength B1=20.2 G. The exper...

A modified pulsed gradient technique for measuring diffusion in the presence of large background gradients

An NMR technique for measuring the diffusion constant D in the presence of a large nonuniform background magnetic field gradient G0 is presented. The technique uses a Carr-Purcell-Meiboom-Gill of pulse train that attenuates the effects of diffusion due to the background gradient, interspersed with an alternating pulsed field gradient sequence (APFG) that attenuates the observed echo in the presence of the known applied gradient. Calculations for the observed echo amplitude are presented that show the APFG technique eliminates contributions from the cross term between the background and applied gradients. Results of tests of the technique are presented for the measurement of D in H2O in the presence of G0 ∼ 160 G/cm. Also described are the results of preliminary measurements of D in LaNi5H6; D = (6.2 ± 0.5) × 10−8 cm2/see at 331.2 K and G0 ∼ 2.9 kG/cm.

Effect of Hindered Molecular Rotation Between Unequal Potential Wells Upon Nuclear Magnetic Resonance Spin—Lattice Relaxation Times and Second Moments

The nuclear magnetic resonance spin—lattice relaxation times along the static and rotating magnetic fields, and the second moment of the nuclear magnetic resonance line shape are calculated for a system of two identical spins that undergo a hindered rotation about the perpendicular bisector of the line joining the spins. The hindered rotation treated in this model is the jumping of the spins among four equally spaced equilibrium positions, two of the positions differing in energy from the other two. For finite temperatures, this difference in energy is shown to lengthen the spin—lattice relaxation times and inhibit the narrowing of the resonance line shape.

Nuclear Magnetic Resonance Study of Molecular Motions in Solid Hydrogen Sulfide

Pulsed nuclear magnetic resonance experiments on protons in solid hydrogen sulfide have been carried out at 10 Mc/sec over the temperature range of 4.2° to 175°K. Proton spin—lattice relaxation times T1 and T1r along the static and rotating magnetic fields, respectively, and free‐induction‐decay shapes were measured. The T1r‐vs‐reciprocal‐temperature curves exhibit several minima which, together with the slopes, allow the determination of the correlation times of the molecular motions as a function of temperature. From the free‐induction‐decay shapes were derived the intermolecular and intramolecular contributions to the second moment of the proton‐resonance line shape. The temperature dependence of the second moment gives information about the molecular motions and the structure of solid hydrogen sulfide. Models of the structure and motion are proposed and examined.

A fast recovery pulsed nuclear magnetic resonance sample probe using a delay line

A sample probe for pulsed nuclear magnetic resonance that replaces the normal resonant circuit by a lumped parameter delay line is described. Theoretical analysis shows that the delay line probe has a signal‐to‐noise ratio and conversion efficiency of power into rotating magnetic field equivalent to a resonant circuit of Q =(2π) (delay time) (Larmor frequency). However, the delay line probe has a much wider bandwidth, much shorter transient decay time, and faster recovery from the rf excitation pulse. Experimental results are included that demonstrate submicrosecond recovery times for the observation of the signal.

Multipole NMR. VII: Bromine NMR quadrupolar echoes in crystalline KBr

Abstract Multipole NMR is used to calculate the responses during various pulse sequences for a solid system of spin - 1 2 nuclei subject to a strong do magnetic field and an inhomogeneous distribution of quadrupole and dipole-dipole interactions. The following sequences were treated: 90° X −τ 1 , 90° X −τ 1 −90° X −τ 2 90° X −τ 1 −90° Y −τ 2 , 90° X −τ 1 −90° X −τ 2 −90° X −τ 3 , 90° X −τ 1 −90° Y −τ 2 −90° Y −τ 3 , and 90° X −τ 1 −45° Y −τ 2 −45° Y −τ 3 . The calculations show that all of the 15 multipole polarizations (3 alignments, 6 single-, 4 double-, and 2 triple-quantum coherences) can be created in significant amounts by appropriate sequences. The calculations for each sequence have been verified by a detailed experimental study of the sequence responses for Br in a deformed single-crystal of KBr. Seven independent relaxation times were determined. The experiments provide the first evidence for octupole alignment in spin systems.

Experimental Free‐Induction‐Decay Shapes and Theoretical Second Moments for Hydrogen in Hexagonal Ice

The results of NMR free‐induction‐decay shape measurements for protons in single crystals and polycrystals of hexagonal ice are reported. The second moments of the corresponding absorption line are derived from empirical fits of the free‐induction‐decay shapes. Theoretical values for these second moments are computed for several models of the hydrogen lattice, taking into account the effect of vibrations and librations. There is good agreement between the measured and computed second moments, implying that high‐frequency proton tunneling is not present.

Measurement by NMR of the Diffusion Rate of HF in Ice

An experiment is described by which the diffusion of fluorine in monocrystalline ice cylinders is followed quasicontinuously, using the proton magnetic resonance spin—lattice relaxation time T1 to measure the HF concentration along the sample. The diffusion coefficient DF was evaluated for various temperatures between −30° and −4°C. The results show more scatter than the experimental error can account for. A least‐squares fit of our data yields DF (−10°C)=0.8×10−6 cm2/sec for the diffusivity and E=0.58 eV=13.4 kcal/mole for the activation energy, with root‐mean‐square deviations of 0.5×10−6 cm2/sec and 0.08 eV, respectively. We find that the highest concentration of diffused HF which can be absorbed by monocrystalline ice is about 4×10−5 HF/H2O. A possible explanation is offered for the large value and dispersion of the diffusivity.

A pulsed, broadband NMR spectrometer

Abstract A pulsed nuclear magnetic resonance spectrometer suitable for measurements in solids is described. The spectrometer is phase coherent, and the pulse timing is synchronous with the operating frequency of the spectrometer. The apparatus uses a versatile pulse programmer and a gated broadband rf power amplifier which delivers 1.6 kW at 60 MHz with a 3-db bandwidth of 5 to 90 MHz. With the exception of the probe, the spectrometer does not contain any tuned elements. This permits short (0.5 μsec) recovery times between the end of the rf pulse and the start of the signal. The spectrometer relies heavily upon the use of commercially available modules. A detailed description of the spectrometer construction and a discussion of typical operating characteristics are presented.

Homogeneous rf field delay line probe for pulsed nuclear magnetic resonance

The analysis of delay line coils for use in pulsed nuclear magnetic resonance, as carried out by Lowe and Engelsberg, is extended to include magnetic coupling between coil sections. The predicted cutoff frequency for the delay line is found to be considerably extended, and this is experimentally verified. The rf magnetic field distribution is theoretically analyzed for the case of a wide flat coil. The conclusion is that the field should be relatively homogeneous as long as the coil thickness is much smaller than the wavelength of the electromagnetic wave traveling down the coil axis. Several different flat coil designs using distributed capacitance are then described, along with operating characteristics of constructed models. The most successful model had a time delay of 20 nsec and a measured inhomogeneity of 4% at 60 MHz.