We propose to study Li diffusion in the all solid-states battery (ASSB) candidate Li4-zSi1-zPzO4 by means of quasielastic neutron scattering.We believe that the LISICON-type (LIthium Super Ionic CONductor) solid solutions between Li4SiO4 and Li3PO4 deserve deeper investigations thanks to their chemical stability and light weight (important criteria for ASSBs). Indeed, varying the amounts of vacancies and/or interstitial sites within these solid solutions results in a remarkable increase of three orders of magnitude of the ionic conductivity. The interest is to develop ASSBs using such kind of solid electrolytes.