X-ray and neutron diffraction studies of fcc Li2SO4 (575 to 860 °C for pure Li2SO4) show a high degree of spherical delocation of the sulphate ions. This strongly coupled rotation causes the dimensions of the cation positions to be varying all the time. This explains why all mono- and divalent cations studied so far have a high mobility in a number of sulphate phases, in contrast to the situation in other types of solid electrolytes. The sulphate phases in question are plastic with properties that resemble those of other types of plastic materials. Brillouin scattering studies show marked differences between the plastic fcc phase and molten Li2SO4, while the refractive index hardly changes at the melting point.