Alkali-metal stoichiometry and structure of ${\mathrm{K}}_4$${\mathrm{C}}_{60}$ and ${\mathrm{Rb}}_4$${\mathrm{C}}_{60}$

Alkali-metal fulleride samples ${\mathrm{K}}_{\mathrm{x}}$ ${\mathrm{C}}_{60}$ and ${\mathrm{Rb}}_{\mathrm{x}}$ ${\mathrm{C}}_{60}$ with stoichiometries close to x=4 were examined with x-ray powder-diffraction measurements at room temperature. We have shown through Rietveld refinements that ${\mathrm{A}}_4$ ${\mathrm{C}}_{60}$ is a line phase with charge per lattice site that is closer to integer than in any other fulleride. The ${\mathrm{C}}_{60}$ molecules are disordered between two possible orientations within the body-centered-tetragonal lattice with the three orthogonal twofold rotation axes aligned with the unit-cell translation vectors in space group I4/mmm. The x-ray diffraction results exclude any quadrupole distortion of the fullerene molecule beyond about 0.04 Å. These results suggest that ${\mathrm{K}}_4$ ${\mathrm{C}}_{60}$ and ${\mathrm{Rb}}_4$ ${\mathrm{C}}_{60}$ may be Mott insulators.