The mechanisms of ionic conduction in the high-temperature phases of Li2SO4, LiNaSO4 and other related compounds have for a long time been a subject of discussion. Two different models have been suggested. One, the ’paddle wheel’ model, suggests that the transport of cations is strongly correlated to the rotation of the SO4 tetrahedra. The other, called the ’percolation’ model, suggests that there is no direct correlation between the ionic conduction and SO4, rotations, but that the rotations and vibrations indirectly produce conduction pathways. In this study the total structure factors, both Bragg and diffuse scattering, have been measured by powder neutron diffraction. The data were modelled using the reverse Monte Carlo method. From detailed analysis of the three-dimensional models produced we find that ionic conduction in Li2SO4 and LiNaSO4 is a combination of both conduction processes, paddle wheel as well as percolation.