We propose to determine temperature dependent diffusion parameters of positively charged muonium centres in w-ZnO. Specifically, we would like to exploit the zero field tools to examine the muon spin depolarization signal in order to extract the activation energy for the diamagnetic muonium in this material. Hydrogen diffusion barrier in ZnO is controversial at present. By considering differences in mass and zero point energy between the muon and the proton, the parameters obtained from zero field spin relaxation signals in this material can be interpreted to determine the hydrogen sites and the barriers between these sites.