Molecular dynamics simulation of the hollandite Nax(Ti8-xCrx)O16: ion transport and high frequency dielectric absorption

Molecular dynamics (MD) simulations have been used to model the dynamics of the charge-compensating sodium ions in the non-stoichiometric hollandite Na_x(Ti_8-xCr_x)O₁₆. These interstitial ions reside in ´tunnels´ in the crystal structure and move under the forces of both the ions making up the cage structure and the many body interactions of the other sodium ions in the tunnel. The Velocity Autocorrelation Function (VAF) of the sodium ions is calculated for a range of temperature from 250 K to 1000 K and converted into the linear ac-conductivity and ac-susceptibility response via Fourier transformation. A peak is found in the conductivity around 6×10¹² Hz that has some of the character of a Poley absorption. Here it is shown to be due to anharmonically coupled site vibrations of the sodium atoms, which extend only over a limited range. At frequencies below the peak the conductivity tends towards a constant, i.e. dc value corresponding to a constant flow of ions through the simulation cell. At high temperatures the conductivity due to this ion transport process behaves like a metal with an insulator to metal transition occurring around a specific temperature.