Effective and Debye temperatures of alkali-metal atoms in graphite intercalation compounds

The vibrational energies of the alkali-metal atoms in graphite intercalation compounds have been analyzed to yield effective temperatures T_∥ and T_⊥ and the corresponding Debye temperatures Θ_∥ and Θ_⊥ parallel and perpendicular to the graphite planes. In the context, T_∥ and T_⊥ differ from the thermodynamic temperature as they include the kinetic energy of the zero-point vibrational motion of the alkali-metal atoms. It was found that the value of T_⊥ at 0 K is independent on the stage and that a universal linear relation of T_⊥ as a function of (MXd)^-1/2 exists (where MX, the atomic mass of the alkali-metal atom and d, the distance between two graphene layers sandwiching an alkali-metal layer). This demonstrates that the effective force constant between the alkali-metal and the binding graphene layers, calculated per alkali-metal atom, is always the same for all compounds. By applying an ``infinite-mass'' correction to T_∥, a similar linear relation between the corrected values T_∥^', Θ_∥^', and (MXd)^-1/2 has been found. These relations can be used for predicting T_⊥, Θ_⊥, T_∥^', and Θ_∥^' for cases for which no experimental data are reported.