We would measure vibrational spectra as well as quasielastic neutron scattering (QENS) spectra for beta- alumina (11Al2O3-Na2O) and Na2Ti3O7. The measurement of phonon spectra in the entire Brillouin zone over the temperature range of 300-1000 K is required for characterizing the specific phonon modes relevant to the ionic conductivity and thermal expansion behavior. The measurements would help to identify the phonons which show significant changes as a function of temperature. In addition, we propose to understand the diffusion pathways and timescales by QENS. By combining the vibrational and QENS measurements (300-1000 K) with first-principles phonon calculations and temperature-dependent molecular dynamics simulations, we expect to gain deeper insights of the origin and mechanism of ionic conductivity in amorphous phase and their relationship to phonons in these compounds.