Relaxation, Debye spin-lattice

Several types of spin-lattice relaxation processes have been described in the literature [31]. Here a brief overview of some of the most important ones is given. The simplest spin-lattice process is the direct process in which a spin transition is accompanied by the creation or annihilation of a single phonon such that the electronic spin transition energy, A, is exchanged by the phonon energy, hcoq. Using the Debye model for the phonon spectrum, one finds for k T A that... 

S nuclear quadrupole coupling constants have been determined from line width values in some 3- and 4-substituted sodium benzenesulphonates33 63 and in 2-substituted sodium ethanesulphonates.35 Reasonably, in sulphonates R — SO3, (i) t] is near zero due to the tetrahedral symmetry of the electronic distribution at the 33S nucleus, and (ii) qzz is the component of the electric field gradient along the C-S axis. In the benzenesulphonate anion, the correlation time has been obtained from 13C spin-lattice relaxation time and NOE measurements. In substituted benzenesulphonates, it has been obtained by the Debye-Stokes-Einstein relationship, corrected by an empirically determined microviscosity factor. In 2-substituted ethanesulphonates, the molecular correlation time of the sphere having a volume equal to the molecular volume has been considered. 

The proposed method is based upon the quantitative measurement of the contribution of differently charged nitroxide probes to the spin-lattice relaxation rate (1/T i) of protons in a particular molecule, followed by the calculation of local electrostatic potential using the classical Debye equation (Likhtenshtein et al., 1999 Glaser et al., 2000). In parallel, the theoretical calculation of potential distribution with the use of the MacSpartan Plus 1.0 program has been performed. 

Flere (1 - f) and (1 - S) are the losses brought about by the corresponding process and gfastj/3 (t -> oo) = 0 (see Fig. 6). The factor / can be regarded as a generalized non-ergodicity parameter and, hence, it is expected to show a similar anomaly as the Debye-Waller factor /g (see Fig. 5). Such decomposition of the correlation function is useful in spin-lattice relaxation studies, as will be discussed in Section 3.2.4. 

The prefactor /, has also been associated with the Debye frequency of the lattice modes. The diffusion of H in the fee metals Pd, Ni, Cu and Al, reduced to the elementary hop rate between the neighbouring sites, shows classical behaviour (6.2) above room temperature . Note that many experimental methods, including neutron inelastic and quasielastic scattering, NMR line narrowing and spin-lattice relaxation, internal friction and ultrasonic damping, can give important information about the H motion on various timescales, that complements that obtained from ordinary diffusion measurements. 

Spin-lattice relaxation is concerned with the following problem. In a solid the thermal reservoir consists of the natural vibrations of the constituent ions about their equilibrium positions, vibrations that increase in amplitude with temperature. The quantized lattice vibrations, Debye waves or phonons, travel with the velocity of sound. The paramagnetic system consists of ions carrying magnetic moments associated with electronic orbit and spin, and, more remotely, nuclei. Some mechanism of energy transfer must exist to establish thermal equilibrium between two such disparate systems. 

Phonon mode changes, determination of Debye temperature, determination of effective mass, determination of anisotropy of lattice vibration, electron hopping in spinels, diffusion, determination of jump frequency and diffusion coefficient, paramagnetic spin relaxation, spin-spin relaxation, spin-lattice relaxation, superparamagnetism, determination of grain size... 

The corresponding reorientational relaxation times for these linear anions were also studied by the infrared pump/probe technique by Li et al. [162]. However, NMR spin-lattice relaxation times have been employed for other polyatomic ions, using the nuclei NforNOj" [162], forClO " [163], N for NH/ [164], and C for several tetraalkylammonium cations [165] according to Masuda and coworkers. The results are shown in Table 5.10. It was concluded that these times do not follow the expected (Stokes-Einstein-Debye) hydrodynamic solvent sequences according to the solvent... 

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