We propose to measure the quasielastic neutron scattering (QENS) spectra to study the diffusion dynamics in beta- alumina (11Al2O3-Na2O) and Na2Ti3O7. The measurement of QENS spectra over 300-1000 K is required to understand diffusion pathways and timescales of Na atom dynamics in these compounds. By combining the phonon and QENS measurements 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 and their relationship to phonons in these compounds. The phonon measurements are scheduled (RB1868015) at MARI during February-March 2019. The present proposal is to perform the QENS measurements as a function of temperature.