Phase transitions in ${\mathrm{Na}}_2$A${\mathrm{C}}_{60}$ (A=Cs, Rb, and K) fullerides

The ternary system fullerides ${\mathrm{Na}}_2$A${\mathrm{C}}_{60}$ (A=Cs, Rb, and K) are studied by differential scanning calorimetry in the temperature range of 100 to 450 K. All show reproducible phase transitions at the transition temperatures of 299 K (ΔH=2.5±0.5 J/g) for ${\mathrm{Na}}_2$${\mathrm{CsC}}_{60}$, 313 K (ΔH=2.7±0.5 J/g) for ${\mathrm{Na}}_2$${\mathrm{RbC}}_{60}$, and 305 K (ΔH=3.1±0.5 J/g) for ${\mathrm{Na}}_2$${\mathrm{KC}}_{60}$. Orientational ordering of the fullerene unit is responsible for the observed phase transitions (${\mathit{T}}_{\mathrm{sc}\mathrm{-}\mathrm{fcc}}$) from a high-temperature face-centered-cubic (fcc) to a low-temperature simple-cubic (sc) phase. The observed ${\mathit{T}}_{\mathrm{sc}\mathrm{-}\mathrm{fcc}}$ and enthalpy can be compared to those for pristine ${\mathrm{C}}_{60}$ which has ${\mathit{T}}_{\mathrm{sc}\mathrm{-}\mathrm{fcc}}$=256.5 K (ΔH=8±0.5 J/g). The observed behavior is discussed in terms of the balance between the ${\mathrm{C}}_{60}^{3\mathrm{-}}$-${\mathrm{C}}_{60}^{3\mathrm{-}}$ intermolecular interaction and the ${\mathrm{C}}_{60}^{3\mathrm{-}}$-${\mathit{A}}^{+}$ Coulombic interaction as a function of lattice parameter.