Spectral densities and nuclear spin relaxation in solids |
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Affiliation: | 1. Department of Physics, Jiaozuo Teachers College, Jiaozuo 454001, China;2. Key Laboratory for Special Functional Materials of Ministry of Education, Henan University, Kaifeng 475004, China;1. Department of System Safety, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka-shi, Niigata 940-2188, Japan;2. Undergraduate School of Mechanical Engineering, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka-shi, Niigata 940-2188, Japan;3. Department of Mechanical Engineering, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka-shi, Niigata 940-2188, Japan |
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Abstract: | We investigate the properties of ten spectral densities relevant for nuclear spin relaxation studies in solids. This is preceded by a brief review of nuclear spin relaxation in solids which includes a discussion of the appropriate spin-dependent interactions and the various relaxation rates which can be measured. Also, the link between nuclear spin relaxation and dielectric relaxation is discussed. Where possible and/or appropriate each of the spectral densities is expressed as a continuous distribution of Bloembergen-Purcell-Pound (or Debye) spectral densities 2ξ /(1 + ξ2 ω2) for nuclear Larmor angular frequency ω and correlation time ξ. The spectral densities are named after their originators or the shape of the distributions of correlation times or both and are (1) Bloembergen-Purcell-Pound or δ-function, (2) Havriliak-Negami, (3) Cole-Cole, (4) Davidson-Cole, (5) Fang, (6) Fuoss-Kirkwood, (7) Bryn Mawr, (8) Wagner or log-Gaussian, (9) log-Lorentzian, and (10) Fröhlich or energy box. The Havriliak-Negami spectral density is related to the Dissado-Hill theory for dielectric relaxation. The spectral densities are expressed in a way which makes them easy to compare with each other and with experimental data. Many plots of the distributions of correlation times and of the spectral densities vs. various correlation times characterizing the distributions are given. |
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