Electronic relaxation spin-lattice

Schirmer, A., P. Heitjans, and V. A. Nalimova. 1998. Conduction-electron induced spin-lattice relaxation of 8Li in the high-pressure phase LiC2. Mol. Cryst. Liq. Cryst. 310 291-296. 

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... 

Within the framework of the usual partition model widely used to analyze hyperflne Interactions In transition metal systems, the proton Knight shift conduction electron to spin-lattice relaxation (Tjg) are assumed to consist of two major contributions as... 

Electron longitudinal (spin-lattice) relaxation time Proton longitudinal (spin-lattice) relaxation time Electron transverse (spin-spin) relaxation time Characteristic temperature Glass transition temperature (K)... 

Lithium-7—carbon-13 couplings, 286-87 Lithium-6—lithium-7 couplings, 286 Lithium-7—lithium-6 couplings see Lithium-6—lithium-7 couplings Lithium-6,7 NMR, 40,261-64,275,280-82,286-88 Lithium-7—proton couplings, 286 Local field static, 112-13 time dependent, 114 Lone pair electrons, 55,223-25 Longitudinal relaxation see Relaxation, spin-lattice Lysergic acid diethylamide, 181-82... 

S spin remains in tliennal equilibrium on die time scale of the /-spin relaxation. This situation occurs in paramagnetic systems, where S is an electron spin. The spin-lattice relaxation rate for the / spin is then given by ... 

Radicals escaping from a radical pair become uncorrelated as approaches zero. In the free (doublet) state they are detectable by e.s.r. spectroscopy. However, just as polarization of nuclear spins can occur in the radical pair, so polarization of electron spins can be produced. Provided that electron spin-lattice relaxation and free radical scavenging processes do not make the lifetime of the polarized radicals too short. 

OIDEP usually results from Tq-S mixing in radical pairs, although T i-S mixing has also been considered (Atkins et al., 1971, 1973). The time development of electron-spin state populations is a function of the electron Zeeman interaction, the electron-nuclear hyperfine interaction, the electron-electron exchange interaction, together with spin-rotational and orientation dependent terms (Pedersen and Freed, 1972). Electron spin lattice relaxation Ti = 10 to 10 sec) is normally slower than the polarizing process. 

In this section, the characteristics of the spectra displayed by the different types of iron—sulfur centers are presented, with special emphasis on how they depend on the geometrical and electronic structure of the centers. The electronic structure is only briefly recalled here, however, and interested readers are referred to the excellent standard texts published on this topic (3, 4). Likewise, the relaxation properties of the centers are described, but the nature of the underlying spin-lattice relaxation processes is not analyzed in detail. However, a short outline of these processes is given in the Appendix. The aim of this introductory section is therefore mainly to describe the tools used in the practical applications presented in Sections III and IV. It ends in a discussion about some of the issues that may arise when EPR spectroscopy is used to identify iron-sulfur centers. 

However, there is no indication that the presence of the observed signals correlates with the polymerization efficiency of the catalyst. In fact, systems which exhibit these signals are less effective catalysts and in some cases do not even polymerize ethylene under the chosen conditions. In contrast, systems without EPR signals correlated to Ti species are foimd to be catalytically active. It has to be emphasized at this point that the lack of an ESR signal associated to Ti + ions, in cases where no additional argon or electron bombardment has been applied, cannot be interpreted as an indication of the absence of Ti + centers at the surface. It has been discussed in the literature that small spin-lattice-relaxation times, dipole coupling, and super exchange may leave a very small fraction of Ti " that is detectable in an EPR experiment [115,116]. From a combination of XPS and EPR results it unhkely that Ti " centers play an important role in the catalytic activity of the catalysts. 

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

As discussed in Sect. 6.2, the electronic states of a paramagnetic ion are determined by the spin Hamiltonian, (6.1). At finite temperamres, the crystal field is modulated because of thermal oscillations of the ligands. This results in spin-lattice relaxation, i.e. transitions between the electronic eigenstates induced by interactions between the ionic spin and the phonons [10, 11, 31, 32]. The spin-lattice relaxation frequency increases with increasing temperature because of the temperature dependence of the population of the phonon states. For high-spin Fe ", the coupling between the spin and the lattice is weak because of the spherical symmetry of the ground state. This... 

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... 

Ammonium alums undergo phase transitions at Tc 80 K. The phase transitions result in critical lattice fluctuations which are very slow close to Tc. The contribution to the relaxation frequency, shown by the dotted line in Fig. 6.7, was calculated using a model for direct spin-lattice relaxation processes due to interaction between the low-energy critical phonon modes and electronic spins. 

When, however, phonons of appropriate energy are available, transitions between the various electronic states are induced (spin-lattice relaxation). If the relaxation rate is of the same order of magnitude as the magnetic hyperfine frequency, dephasing of the original coherently forward-scattered waves occurs and a breakdown of the quantum-beat pattern is observed in the NFS spectrum. 

The saturation behavior of a spectrum - the variation of integrated intensity with microwave power - is related to the spin-lattice relaxation time, a measure of the rate of energy transfer between the electron spin and its surroundings. Saturation often depends on the same structural and dynamic properties as line widths. 

Gayda, J.-P., Bertrand, P., Deville, A., More, C., Roger, G., Gibson, J.F., and Cammack, R. 1979. Temperature dependence of the electronic spin-lattic relaxation time in a 2-iron-2-sulfur protein. Biochimica et Biophysica Acta 581 15-26. 

The hyperfine couplings between localized electrons on paramagnetic impurities and nuclear spins often serve as the dominant source of spin-lattice relaxation for... 

Furthermore, the method of orientation selection can only be applied to systems with an electron spin-spin cross relaxation time Tx much larger than the electron spin-lattice relaxation time Tle77. In this case, energy exchange between the spin packets of the polycrystalline EPR spectrum by spin-spin interaction cannot take place. If on the other hand Tx < Tle, the spin packets are coupled by cross relaxation, and a powder-like ENDOR signal will be observed77. Since T 1 is normally the dominant relaxation rate in transition metal complexes, the orientation selection technique could widely be applied in polycrystalline and frozen solution samples of such systems (Sect. 6). 

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