Theory of Spin–Lattice Relaxation

Measurement of sample temperatures under magic-angle spinning from the chemical shift and spin-lattice relaxation rate of 79Br in KBr powder

Solid-State Li NMR with Applications to the Translational Dynamics in Ion Conductors

The applicability of nuclear magnetic resonance (NMR) spectroscopy continues to expand in physics, chemistry, material science, geology, biology, and medicine. An increasing range of NMR techniques is employed for either spectroscopic studies or imaging purposes, most becoming possible because of the high magnetic fields of superconducting magnets (almost an order of magnitude higher than ordinary iron magnets), and the availability of fast computers for controlling purposes and final data processing. These improvements together with the realization of fast mechanical sample spinning and new pulse techniques have led to high-resolution solid-state nuclear magnetic resonance. Because the perturbing effect of the electric quadrupole interaction becomes less important at higher magnetic fields, the investigation of powder samples with NMR techniques has become more feasible. As a result, the number of publications concerning NMR studies of quadrupole nuclei in powder samples rapidly increased in the eighties. However, since 1987 this number of publications is rather stable and amounts to about 100 per year.

Quadrupole Effects in Solid-State Nuclear Magnetic Resonance

Relaxation times (T1) and lineshapes were examined as a function of temperature through the α-β transition for 29Si in a single crystal of amethyst, and for 29Si and 17O in cristobalite powders. For single crystal quartz, the three 29Si peaks observed at room temperature, representing each of the three differently oriented SiO4 tetrahedra in the unit cell, coalesce with increasing temperature such that at the α-β transition only one peak is observed. 29Si T1's decrease with increasing temperature up to the transition, above which they remain constant. Although these results are not uniquely interpretable, hopping between the Dauphine twin related configurations, α1 and α2, may be the fluctuations responsible for both effects. This exchange becomes observable up to 150° C below the transition, and persists above the transition, resulting in β-quartz being a time and space average of α1 and α2. 29Si T1's for isotopically enriched powdered cristobalite show much the same behavior as observed for quartz. In addition, 17O T1's decrease slowly up to the α-β transition at which point there is an abrupt 1.5 order of magnitude drop. Fitting of static powder 17O spectra for cristobalite gives an asymmetry parameter (η) of 0.125 at room T, which decreases to <0.040 at the transition temperature. The electric field gradient (EFG) and chemical shift anisotropy (CSA), however, remain the same, suggesting that the decrease in η is caused by a dynamical rotation of the tetrahedra below the transition. Thus, the mechanisms of the α-β phase transitions in quartz and cristobalite are similar: there appears to be some fluctuation of the tetrahedra between twin-related orientations below the transition temperature, and the β-phase is characterized by a dynamical average of the twin domains on a unit cell scale.

Dynamics of the α-β phase transitions in quartz and cristobalite as observed by in-situ high temperature 29Si and 17O NMR

The theory of nuclear quadrupole spin–lattice relaxation in anharmonic crystals is developed, both in terms of ordinary perturbation theory and in terms of phonon Green functions. The important relaxation processes are shown to be the direct, first-order Raman, and anharmonic Raman (aR) processes. The aR process is a second-order process due to a combination of the linear spin–lattice coupling and the cubic anharmonic lattice forces, and can be interpreted as arising from the second-order self-energy term in the single-phonon Green function. The effect on the relaxation of the higher-order phonon self-energy and lifetime effects is investigated and shown to be of minor importance. A new method of treating polarization mixing in the Dyson equation for the phonon Green functions is presented. The theory is applied to nuclear quadrupole relaxation in alkali halide crystals and the aR process is shown to be dominant. Nuclear electric dipole and electron paramagnetic relaxation are also discussed.

M. B. Walker

Papers

Theory of spin–lattice relaxation in anharmonic crystals

Theory of Quadrupolar Nuclear Spin-Lattice Relaxation Due to Anharmonic Raman Phonon Processes