Molecular Dynamics Simulation on Hollandite Nax(Ti8-xCrx) O16: Dependence of DC Conductivity upon Temperature and Concentration

Molecular dynamics (MD) simulations have been carried out on the hollandite Na
_x
(Ti
_8-x
Cr
_x
)O
₁₆
to determine the motions of the tunnel ions (sodium ions) in the temperature range from 291 K to 1000 K for sodium ion concentrations (x) in the range from 0.1 to 0.8. This hollandite material is a non-stoichiometric material with charge compensating sodium ions located in interstitial sites along the tunnel according to the relative proportions of titanium and chromium ions. These ions are free to move under the forces of both the ions making up the cage structure and the many body interactions of the other sodium ions. Our results agree quite well with those reported for fast ion conductors where a peak is observed in the ac-conductivity around terahertz frequencies. There is also a trend towards constant conductivity frequencies below the peak. The ion trajectories show that the peak is associated with resonance absorption due to local group vibrations whose lifetime is limited by ion-hopping between vibrating groups. The constant conductivity contribution behaves as an ionic fluid, with its value increasing as the sodium ion concentration index, x, increases, and reducing as the temperature increases.