Nuclear Larmor Frequency Research Articles

Observation of the Influence of Centrifugal Distortion of the Methane Molecule on Nuclear Spin Relaxation in the Gas

The spin–lattice relaxation time T1 was measured in gaseous CH4 as a function of density at room temperature between 0.006 and 7.0 amagats. T1 was found to pass through a minimum near 0.04 amagats in agreement with previous, less precise measurements. The spin–rotation interaction is the dominant relaxation mechanism in gaseous CH4. Since the spin–rotation constants are accurately known for CH4, the relaxation experiments provide a check on the theory of spin–lattice relaxation for spherical top molecules. In the conventional theory, it is assumed that the correlation function of the spin–rotation interaction is a simple exponential function of time. These experiments show that this assumption is not true for CH4 gas. The observed fine structure in the plot of relaxation rate versus density is attributed to the influence of centrifugal distortion of the CH4 molecule, which removes the degeneracy of rotational states having the same value of the quantum number J by an amount somewhat greater than the nuclear Larmor frequency of 30 MHz.

Collapse of the Magnetic Hyperfine Field by Intense rf Perturbation

By carrying the technique of rf enhancement to its extreme limit, the entire magnetic hyperfine field at an iron nucleus was made to oscillate rapidly through large angles in response to an applied rf field. When the frequency of these rf oscillations was increased to several times the nuclear Larmor frequency, the time average field seen by the iron nuclei was reduced from ∼300 kG to zero.

Rotating-Frame Nuclear-Double-Resonance Dynamics: Dipolar Fluctuation Spectrum in CaF2

A series of rotating-frame nuclear-double-resonance experiments is reported in which the NMR of the rare isotope $^{43}\mathrm{Ca}$ (natural abundance 0.13%) in Ca${\mathrm{F}}_{2}$ is detected via the observable resonance signal of the abundant $^{19}\mathrm{F}$ nuclei. The technique consists of (1) cooling the $^{19}\mathrm{F}$ dipolar-interaction energy reservoir by means of adiabatic demagnetization in the rotating frame, (2) coupling the rare $^{43}\mathrm{Ca}$ to this cooled reservoir by means of a rotating magnetic field at or near the $^{43}\mathrm{Ca}$ nuclear Larmor frequency, and (3) examining the final state of this reservoir by measuring the "dipolar" free-induction signal following a \textonequarter{}\ensuremath{\pi} rf pulse at the $^{19}\mathrm{F}$ Larmor frequency. With this basic format, results have been obtained and are reported here for (a) the relative heat capacities of the $^{43}\mathrm{Ca}$ rotating-frame Zeeman Hamiltonian and the $^{19}\mathrm{F}$ dipolar Hamiltonian terms, (b) the cross-relaxation time for the $^{43}\mathrm{Ca}$-$^{19}\mathrm{F}$ energy-transfer process as a function of rotating-frame effective field strength and orientation, (c) transient oscillations of the $^{19}\mathrm{F}$ dipolar spin temperature upon application of an rf pulse at the $^{43}\mathrm{Ca}$ resonance frequency, (d) the transverse (${T}_{2}$) relaxation process of the $^{43}\mathrm{Ca}$ nuclei, and (e) the spin-lattice relaxation time (${T}_{1}$) of the $^{43}\mathrm{Ca}$ nuclei. Theoretical expressions for results (a) and (b) are obtained using the well-known thermodynamic model to describe the state of the $^{19}\mathrm{F}$ and $^{43}\mathrm{Ca}$ spin systems. The $^{19}\mathrm{F}$-$^{43}\mathrm{Ca}$ dipolar coupling is treated as a perturbation to obtain a simple "Fermi Golden rule" expression for the cross-relaxation rate. This model, first applied to nuclear double resonance by Hartmann and Hahn, is combined here with the experimentally determined fluctuation spectrum of the $^{19}\mathrm{F}$-$^{43}\mathrm{Ca}$ coupling operator to yield calculated cross-relaxation rates in excellent agreement with the experimental results. The above-mentioned fluctuation spectrum is found to be a very nearly exponential function of the rotating-frame $^{43}\mathrm{Ca}$ Zeeman splitting over a range of cross-relaxation rates spanning nearly three orders of magnitude for two distinct orientations of the applied field relative to the crystal axes, and to be essentially independent of the orientation of the rotating-frame effective field. This rather surprising spectral form is crucial to the successful calculation of the results we find, and also leads to satisfactory agreement between theory and experiment for results (c) and (d). The transient oscillation phenomena (c) are the rotating-frame analog of the pulsed dc-field experiments carried out by Strombotne and Hahn. A density-matrix perturbation-expansion technique similar to that used by those authors is employed here to explain our results. The form of the $^{43}\mathrm{Ca}$ transverse decay process (d) is calculated by means of the Anderson-Weiss-model theory; the exponential decay time is closely approximated by a calculated result using the exponential fluctuation spectrum noted above, and the initial region of nonexponential behavior predicted by this model theory is clearly evident in our results. $^{43}\mathrm{Ca}$ ${T}_{1}$ values (e) were obtained at 300 and 355\ifmmode^\circ\else\textdegree\fi{}K with a variety of field orientations in the (100) plane of the crystal axes. The ${T}_{1}$ process is found to be isotropic and to have a temperature dependence suggesting that it is quadrupolar in origin. The temperature dependence of ${T}_{1}$ is in reasonable accord with the Van Kranendonk theory.

Bloch-Type Equations for Acoustic Nuclear-Magnetic Resonance

Acoustic nuclear-magnetic resonance differs from the conventional NMR in that an acoustic signal of frequency ω at or near the nuclear Larmor frequency ωo = (gnβnHo)ħ−1 or its first harmonic is applied to the sample instead of the customary electromagnetic signal. In the acoustic case nuclear Zeeman transitions are induced by virtue of a modulated nuclear-electric quadrupole interaction in contrast with the conventional situation where the nuclear-magnetic dipole interaction is operative. In spite of these differences, it is possible to write phenomenological equations of the Bloch form, familiar in the theory of conventional NMR, for the case of acoustic NMR, providing an appropriate choice is made for the amplitude and direction of the effective magnetic field. This macroscopic description of acoustic NMR is applicable for negligible saturation.

Zeeman splitting in Mössbauer spectra of paramagnetic materials

A discussion is given of the conditions required for and the interpretation of nuclear Zeeman splitting of Mössbauer spectra of paramagnetic materials. Recent experimental results are analyzed in terms of the ratio of the spin flip frequency of the electron spin and the nuclear Larmor frequency.

Nuclear Zeeman splitting measured through the Mössbauer effect

From the Zeeman hyperfine splitting in 57Fe, the effective magnetic field acting on the nucleus can be derived. It is shown that the Mössbauer technique is particularly suited to study the sublattice magnetization in rather complicated magnetic systemst An important parameter for the observation of the Zeeman splitting is the product of the nuclear Larmor frequency and the electron-spin correlation time. The apparens collapse of the hyperfine splitting observed in a few cases can be interpreted in term. of very rapid relaxation.

Nuclear Spin—Lattice Relaxation in Ferroelectric Triglycine Sulfate

The temperature and frequency dependence of the 1H and 19F spin—lattice relaxation times in TGS, TGSe, and TGBe have been measured both in the ferroelectric and nonferroelectric phases, using a pulse technique. The results show that though a considerable slowing down of the proton motion occurs at the Curie points, the characteristic frequencies of internal motion are, in this range, still greater than the nuclear Larmor frequencies. The changes in the linewidth observed at certain orientations in the 1H and the additional splittings in the deuteron spectra on going to the ferroelectric phase are thus not due to a freezing in of internal motion but rather to a static rearrangement of the glycine units.

Relaxation Effects in Nuclear Magnetic Resonance Absorption

The exchange of energy between a system of nuclear spins immersed in a strong magnetic field, and the heat reservoir consisting of the other degrees of freedom (the lattice) of the substance containing the magnetic nuclei, serves to bring the spin system into equilibrium at a finite temperature. In this condition the system can absorb energy from an applied radiofrequency field. With the absorption of energy, however, the spin temperature tends to rise and the rate of absorption to decrease. Through this effect, and in some cases by a more direct method, the spin-lattice relaxation time ${T}_{1}$ can be measured. The interaction among the magnetic nuclei, with which a characteristic time $T_{2}^{}{}_{}{}^{\ensuremath{'}}$ is associated, contributes to the width of the absorption line. Both interactions have been studied in a variety of substances, but with the emphasis on liquids containing hydrogen.Magnetic resonance absorption is observed by means of a radiofrequency bridge; the magnetic field at the sample is modulated at a low frequency. A detailed analysis of the method by which ${T}_{1}$ is derived from saturation experiments is given. Relaxation times observed range from ${10}^{\ensuremath{-}4}$ to ${10}^{2}$ seconds. In liquids ${T}_{1}$ ordinarily decreases with increasing viscosity, in some cases reaching a minimum value after which it increases with further increase in viscosity. The line width meanwhile increases monotonically from an extremely small value toward a value determined by the spin-spin interaction in the rigid lattice. The effect of paramagnetic ions in solution upon the proton relaxation time and line width has been investigated. The relaxation time and line width in ice have been measured at various temperatures.The results can be explained by a theory which takes into account the effect of the thermal motion of the magnetic nuclei upon the spin-spin interaction. The local magnetic field produced at one nucleus by neighboring magnetic nuclei, or even by electronic magnetic moments of paramagnetic ions, is spread out into a spectrum extending to frequencies of the order of $\frac{1}{{\ensuremath{\tau}}_{c}}$, where ${\ensuremath{\tau}}_{c}$ is a correlation time associated with the local Brownian motion and closely related to the characteristic time which occurs in Debye's theory of polar liquids. If the nuclear Larmor frequency $\ensuremath{\omega}$ is much less than $\frac{1}{{\ensuremath{\tau}}_{c}}$, the perturbations caused by the local field nearly average out, ${T}_{1}$ is inversely proportional to ${\ensuremath{\tau}}_{c}$, and the width of the resonance line, in frequency, is about $\frac{1}{{T}_{1}}$. A similar situation is found in hydrogen gas where ${\ensuremath{\tau}}_{c}$ is the time between collisions. In very viscous liquids and in some solids where $\ensuremath{\omega}{\ensuremath{\tau}}_{c}g1$, a quite different behavior is predicted, and observed. Values of ${\ensuremath{\tau}}_{c}$ for ice, inferred from nuclear relaxation measurements, correlate well with dielectric dispersion data.Formulas useful in estimating the detectability of magnetic resonance absorption in various cases are derived in the appendix.