Ionic Conductivity and Vibrations of Glasses, and Molecular Dynamics of Lithium Iodide.

In Chapter 2 a statistical mechanical theory of ionic conductivity is developed and applied to the family of superionic conductors B_2 O_3 - 0.5Li_2 O - xLi_2 SO_4 . The theory is based on the assumtion that Li _2 O and Li_2 SO_4 behave as weak electrolytes which dissociate to provide free Li^+ ions and a large increase in conductivity. The agreement with experimental data is good. We extend this theory to account for the interactions of the free Li^+ ions with themselves, using a Debye-Huckel formalism. We find that although the number of free ions is increased, compared to results without this interaction, the ionic mobility is decreased such that the overall conductivity is slightly decreased. In Chapter 3, a central force network dynamics model for glasses is used to discuss the light scattering data for this family of lithium doped borate glasses, but with x = 0 and the concentration of the modifier, Li _2 O varying. The addition of the modifier causes local structural changes, including the transformation of three-coordinated borons to four-coordinated. A very simple structural model for the glass gives good qualitative agreement with experiment. The results of a lattice dynamics calculation fall within the allowed frequency band limits predicted by the network dynamics theory. We believe the success of this model illustrates the importance of short range order on the vibrational spectra of covalently bonded glasses. In Chapter 4, a molecular dynamics simulation has been performed on the crystal lithium iodide, LiI. A rigid ion potential was used with parameters fit to thermal expansion, isothermal compressibility, lattice energy and the frequency of the transverse optical mode at the zone center. Dispersion relations calculated with this potential are compared to those obtained from dipole-dipole deformation and shell model calculations. The current-current correlation function has been calculated at T = 200 and 400K, and from this the absorption and dispersion have been obtained. Anharmonic broadening is observed at the higher temperature. In addition, the mean square displacement of the two ions, and the radial distribution function are calculated.