Na23 nuclear relaxation in Na β -alumina: Barrier-height distributions and the diffusion process

作者：Russel E. Walstedt, R. Dupree, J. P. Remeika, Arantxa Fraile Rodríguez · 发表于：Physical review. B, Solid state · 年份：1977 · DOI：10.1103/physrevb.15.3442 · 被引用次数：125 · 研究领域：Solid-state spectroscopy and crystallography、Advanced NMR Techniques and Applications、Thermal Expansion and Ionic Conductivity

Measurements of the $^{23}\mathrm{Na}$ nuclear-relaxation time ${T}_{1}$ are reported for two types of Na $\ensuremath{\beta}$-alumina specimen, i.e., flux-grown crystals from our laboratory and melt-grown crystals from Union Carbide Corp. A phenomenological calculation of ${T}_{1}$ due to activated hopping motion, taking account of local variations in energy-barrier heights, is presented. This theory is used to interpret our own ${T}_{1}$ data, plus data on ${T}_{1}$ in the literature for specimens prepared by a third method, in terms of barrier-height distributions. It gives a good account of both the temperature and frequency variation of these three contrasting sets of ${T}_{1}$ data, where the differences are attributed to variations in the structure and/or arrangement of charge defects. The characteristics of the barrier-height distributions obtained are discussed in terms of preparation methods and other available data. The rather larger conductivity for melt-grown (as opposed to flux-grown) material reported by Barker et al. is found to be associated with a displacement of activation energies to lower values. Values of the quadrupolar coupling constants from the ${T}_{1}$ data fits as well as from second-order quadrupolar broadening are found to be essentially independent of sample source, suggesting that this coupling is determined primarily by the host structure. Finally, the ${T}_{1}$ fits yield values of the local vibration or "attempt" frequency ${\ensuremath{\nu...