Evidence of nanosegregation and Jahn-Teller effect in Na$_2$C$_{60}$

Na$_2$C$_{60}$ is the only known solid fulleride salt containing the divalent fulleride ion C$_{60}^{2-}$. Calculations predict a Jahn-Teller distortion of this ion, similar to the A$_4$C$_{60}$ compounds, to which they are related by electron-hole symmetry. However, by combining various experimental methods, we found that divalent ions exist only above 450 K in solids with composition Na$_2$C$_{60}$; at room temperature and below, methods sensitive to molecular symmetry and charge (infrared absorption, ESR, NMR) detect at least two phases, most probably C$_{60}$ and Na$_3$C$_{60}$. We explain our data by a model where nanosegregated regions of the size 3-30 nm with different Na concentration coexist. The concentration gradient disappears at higher temperature by diffusion of sodium, observed by neutron scattering. High temperature infrared spectra show evidence of a uniaxial (D$_{3d}$/D$_{5d}$) distortion of the fullerene balls.