Structures and phases of superconducting alkali-metal dopedC60

A simple model for the energetics of solid doped ${\mathit{A}}_{\mathit{x}}$ ${\mathrm{C}}_{60}$ is sufficient to understand the evolution of structures for 0≤x≤6. The contributions found to be most important are hard-sphere packing constraints, the van der Waals energy, the Madelung energy, and geometric relationships between the atomic arrangements on the surface of the icosahedron and neighboring ${\mathrm{C}}_{60}$ molecules and dopants. At x=3 the A15 structure is energetically competitive, despite its larger atomic volume, and is favored for higher values of x since it has more sites available for dopants. Analysis of the available experimental data and the well-known near instability of the A15 structure suggest that the superconductivity in ${\mathrm{K}}_{\mathit{x}}$ ${\mathrm{C}}_{60}$ for x near 3 is influenced by a connected but poorly ordered metastable matrix with the A15 structure, which may be difficult to detect using conventional crystallographic techniques. The present model explains the large jump in Meissner volume at x=3, the negative sign and large magnitude of ${\mathit{dT}}_{\mathit{c}}$/dp, and the Raman spectrum at x=3. Similarities with structures of other exotic materials also follow from the model.