Mechanisms of spin-lattice relaxation

Figure 10.3 Schematic representation of the different mechanisms of spin-lattice relaxation, where it is assumed that initially the spin system is in an excited state. The change(s) in the phonon system...

The magnitude of T, is highly dependent on the type of nucleus and on factors such as the physical state of the sample and the temperature. For liquids Tx is usually between 10 2 and 100, but in some cases may be in the microsecond range. In solids Tx may be much longer—sometimes days. The mechanisms of spin— lattice relaxation and some chemical applications will be taken up in Chapter 8. 

Fig. 14. Important mechanisms of spin-lattice relaxation (sir), jl), jll), and jlll) represent electronic states of a molecule, k is the corresponding rate of sir...

The process of spin-lattice relaxation involves the transfer of magnetization between the magnetic nuclei (spins) and their environment (the lattice). The rate at which this transfer of energy occurs is the spin-lattice relaxation-rate (/ , in s ). The inverse of this quantity is the spin-lattice relaxation-time (Ti, in s), which is the experimentally determinable parameter. In principle, this energy interchange can be mediated by several different mechanisms, including dipole-dipole interactions, chemical-shift anisotropy, and spin-rotation interactions. For protons, as will be seen later, the dominant relaxation-mechanism for energy transfer is usually the intramolecular dipole-dipole interaction. 

Woessner s equations thus permit prediction of spin-lattice relaxation times for the dipole-dipole mechanism, which can be of help in the assignment of 13C NMR spectra. Moreover, the calculations described can be applied to the problem of internal molecular motion. 

The above dipole-dipole mechanism for spin-lattice relaxation depends on the interaction of the target nucleus with the magnetic field B of a lattice nucleus with magnetic moment The magnitude of B is governed by the equation... 

In NMR work, spin-lattice relaxation measurements indicated a non-exponential nature of the ionic relaxation.10,11 While this conclusion is in harmony with results from electrical and mechanical relaxation studies, the latter techniques yielded larger activation energies for the ion dynamics than spin-lattice relaxation analysis. Possible origins of these deviations were discussed in detail.10,193 196 The crucial point of spin-lattice relaxation studies is the choice of an appropriate correlation function of the fluctuating local fields, which in turn reflect ion dynamics. Here, we refrain from further reviewing NMR relaxation studies, but focus on recent applications of multidimensional NMR on solid-ion conductors, where well defined correlation functions can be directly measured. 

From the comparison of the measured and calculated temperature dependences of the relaxation time (see Fig. 20), it follows that the inelastic phonon scattering is the most essential mechanism of the spin-lattice relaxation for Ge. It is evident that only at low temperatures T < 30K) some other mechanisms (the most probable one is the relaxation due to a small amount of paramagnetic impurities) become dominant. At T > 300/C some additional mechanism of relaxation may also exist. The interaction of the nuclear quadrupole moment with vibrations of the nearest four Ge atoms brings about the main contribution to the spin-lattice relaxation rate. The effective modulation of the EFG by the nearest bond charges is greatly reduced because of strong correlations between their displacements. As the main result of the present investigation of spin-lattice relaxation,... 

For the individual interested in molecular motion, the important feature of spin-lattice relaxation (or other relaxation mechanisms) is the dependency on molecular motion to provide an efficient energy pathway for relaxation. Thus, molecular motions at the Larmor frequency for individual carbon atoms in a molecular framework may be mapped by Tj measurements. Since the frequency of molecular motion is temperature dependent, additional thermodynamic and kinetic information may be obtained by measuring Tj values for different carbons over a range of temperatures. In the paper by Lyerla and coworkers in this volume, measurements made for the first time over a... 

Theoretical analyses of spin-lattice relaxation have been performed by Kubo and Tomita 420), Redfield (579), and Kivelson (390). This mechanism is applicable to solids and liquids. The line shape for this type of relaxation is Lorentzian. 

Spin—lattice relaxation is the time constant for the recovery of magnetiTation along the z-axis in a NMR experiment. Various methods are available for the measurement of spin lattice relaxation times. The interested reader is referred to the series of monographs echted by Levy on Carbon-13 NMR spectroscopy [44, 45] for more details. The energy transfer between nuclear moments and the lattice , the three-dimensional system containing the nuclei, provides the mechanism to study molecular motion, e.g. rotations and translations, with correlation times of the order of the nuclear Larmour frequencies, tens to hundreds of MHz. We will limit our chscussion here to the simple inversion-recovery Tj relaxation time measurement experiment, which, in addition to providing a convenient means for the quick estimation of Tj to establish the necessary interpulse delay in two-dimensional NMR experiments, also provides a useful entry point into the discussion of multi-dimensional NMR experiments. 

Temperature Dependence of Spin-Lattice Relaxation. The spin-lattice relaxation rate T ) is comprised of various contributions to the relaxation process, including homo- and heteronuclear dipolar interactions, quadrupolar interactions, chemical shift anisotropy, spin-rotation, and others (10). When the relaxation mechanism is dominated by inter- and intramolecular dipole-dipole interactions, the will increase with temperature, pass through a maximum, and decrease with increasing temperature. Since the relaxation rate is the inverse of the relaxation time, the Ti will decrease, pass through a minimum (Timin), and then increase with increasing temperature (77). The T lmin values are proportional to the internuclear distances. 

Hirschinger et al [95] also used the anisotropy of spin-lattice relaxation to distinguish the two mechanisms, in this case the relaxation time associated with quadrupolar order, T q. A pulse sequence similar to Figure 8.2(b) was used. Quadrupolar order for the amorphous regions was shown to decay quickly, and for longer values of DE, only crystalline quadrupole order remained. The spectra could be closely simulated by a diffusion model and correlation time of 100 ps. Calculated jump lineshapes possess a central peak that is not present in the experimental data. 

The mechanism for spin-lattice relaxation is as follows. All paramagnetic species in the sample have an associated magnetic field surrounding them with which each of the other paramagnetic species may interact. In liquids, the random molecular collisions that constitute Brownian motion permit these local magnetic fields to fluctuate a fluctuation that occurs at the resonant frequency will induce a radiationless transition. The spin-lattice relaxation is characterized by a spin-lattice relaxation time, T, which thus effectively controls the degree of saturation. 

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