Microscopic nuclear magnetic relaxation

Diffusion measurements fall into two broad classes. Under macroscopic equilibrium, i.e. if the overall concentration within the sample remains constant, molecular diffusion can only be studied by following the diffusion path of the individual molecules ( microscopic measurement by quasielastic neutron scattering (QENS) [48,183,184], nuclear magnetic relaxation and line-shape analysis, PFG NMR) or by introducing differently labelled (but otherwise identical) molecules into the sample and monitoring their equilibration over the sample ( macroscopic measurements by tracer techniques) [185,186]. The process of molecular movement studied under such conditions is called self-diffusion. 

By assuming an Arrhenius type temperature relation for both the diffusional jumps and r, we can use the asymptotic behavior of /(to) and T, as a function of temperature to determine the activation energy of motion (an example is given in the next section). We furthermore note that the interpretation of an NMR experiment in terms of diffusional motion requires the assumption of a defined microscopic model of atomic motion (migration) in order to obtain the correct relationships between the ensemble average of the molecular motion of the nuclear magnetic dipoles and both the spectral density and the spin-lattice relaxation time Tt. There are other relaxation times, such as the spin-spin relaxation time T2, which describes the... 

It was possible to rationalize the family of Arrhenius plots measured for Nafion 117 at different water contents [46]. Under an assumption that the surface conductivity has higher activation energy, supported by microscopic considerations in Refs. 40, 43, the Arrhenius slope should become steeper with the decreasing amount of water in the membrane [39], that is, the smaller the amount of the bulk water that we have in pores. Activation energies obtained from these plots are 0.1 eV for the largest possible water contents (Activation energies of proton transfer in water, estimated from nuclear magnetic resonance relaxation times, are 0.1 eV [47].) and 0.3-0.4eV at small water contents. How to rationalize this variation. ... 

Nuclear relaxation is the return to thermodynamic equilibrium of a spin system excited by an appropriate ft equency of an electromagnetic field. The interaction of magnetic moments of excited spins with the environment creates microscopic local magnetic fields that fluctuate. These magnetic fluctuations are related to molecular motions. The longitudinal R and transverse Ri relaxation rates are modulated by the phenomenon of molecular distribution and... 

Our main aim is to understand the influence of a nano-structure manipulation via chemical methods and pulse wave effects on the grain size. Moreover, a comprehensive study of Mn NMR spectra, nuclear relaxation, measurements of the resistance and magneto-resistance have been performed to obtain a microscopic information on the magnetic structure of LSM fine particles. The investigation of the grain size effect is of a crucial importance if magnetic properties of manganites are expected to be used for a fuel cell reaction control. 

In this chapter we do not describe the theory potentially applicable to single-crystal neutron data because it is the subject of Handbook chapters by Norman and Koelling and by Liu (Vol. 17, chs. 110 and 111, respectively). Scattering overlaps with and complements two other techniques sensitive to microscopic magnetic correlations. The techniques are nuclear resonance (NMR) and muon spin relaxation (p SR) spectroscopies whose applications to heavy-fermion materials are reviewed by Nakamura et al. (1988) (NMR) and Barth et al. (1988) and Schenck (1992) (p SR). Finally, there have by now been nearly countless general reviews of experiments and theory on heavy-fermion systems, many of which have appeared in this Handbook series (Vol. 10, chs. 63 and 70, Vol. 14, chs. 94, 96 and 97, Vol. 15, ch, 98, Vol. 16, chs. 105 and 106, Vol. 17, clis. 110 and 111 and this volume, chs. 130, 132 and 133). For a recent pedagogical introduction, the reader can consult the book by Hewson (1993). 

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