Molecular dynamics evidence for alkali-metal rattling in the β-pyrochlores, AOs2O6 (A = K, Rb, Cs)

We have used ab initio molecular dynamics simulations validated against inelastic neutron scattering data to study alkali-metal dynamics in the β-pyrochlore osmates AOs2O6 (A=K, Rb, Cs) at 300 K to gain insight into the microscopic nature of rattling dynamics in these materials. Our results provide new evidence at the microscopic level for rattling dynamics: (1) the elemental magnitude spectra calculated from the MD show a striking dominance by the alkali metals at low energies indicating weak coupling to the cage, (2) the atomic root-mean-square displacements for the alkali metals are significantly larger than for the other atoms, e.g., 25% and 150% larger than O and Os, respectively, in KOs2O6, and (3) motions of the alkali metals are weakly correlated to the dynamics in their immediate environment, e.g. K in KOs2O6 is 6 times less sensitive to its local environment than Os, indicating weak bonding of the K. There is broadening of the elemental spectra of the alkali metals from Cs to K corresponding to a similar broadening of the local potential around these atoms as determined from potential of mean-force calculations. This feature of the spectra is partly explained by the well-known increase in the relative cage volume with decreasing atomic size of the alkali metal. We find that for the smallest rattler in this series (K) the larger relative cage volume allows this atom freedom to explore a large space inside the cage leading to vibration at a broader range of frequencies, hence a broader spectrum. Thus, since K is considered the best rattler in this series, these findings suggest that a significant feature of a good rattler is the ability to vibrate at several different but closely spaced frequencies.