Hollandite Nax$(Ti_{8-x}Cr_x)O_{16}$의 이온 전송과 고유전율 특성

Ion Transport and High Frequency Dielectric of the Hollandite Nax$(Ti_{8-x}Cr_x)O_{16}$

The Velocity Autocorrelation Function (VAF) of the sodium ions is calculated for a range of temperature from 250K to 1000K and converted into the linear ac-conductivity and ac-susceptibility response via Fourier transformation. A peak is found in the conductivity around $6\times10^{12}$ Hz that has some of the character of a Poley absorption. Here it is shown to be due to an harmonically 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.