Density-functional investigation of Na₁₆A₈Ge ₁₃₆ (A = Rb,Cs) clathrates

We have studied the electronic and vibrational properties of the filled Ge-based clathrates, Na₁₆Rb₈Ge₁₃₆ and Na ₁₆Cs₈Ge₁₃₆. We have performed calculations using the generalized gradient approximation (GGA) to density-functional theory. Both materials are found to have metallic character, in agreement with experimental data. The predicted phonon dispersion curves show the low frequency, localized 'rattling' modes of the guest atoms. The calculated frequencies of these guests are in good agreement with experimentally estimated values. We have used the GGA calculated frequencies to estimate the temperature dependent isotropic atomic displacement parameter (U_iso) of the different guest atoms. The temperature dependences of the estimated U _iso are also consistent with experiment. We predict that the Rb guests in Na₁₆Rb₈Ge₁₃₆ have larger U _iso than Cs in Na₁₆Cs₈Ge₁₃₆, in agreement with experiment. This work shows that harmonic approximation based density-functional calculations may be used both to predict relatively accurate vibrational frequencies of the various guest atoms and to estimate the localized dynamic disorder created by such atoms at finite temperatures.