The nature of terahertz motions in a one-dimensional disordered structure

Molecular dynamics simulations are used to investigate the dynamics of the disordered pseudo one-dimensional sodium ion system in the Hollandite Na_xCr_xTi_8−xO₁₆ (x = 1.7). An absorption peak at a frequency of about 4.8 × 10¹² Hz is identified with phonon-like vibrations of the ions in the potential wells produced by the framework lattice. It is shown that sodium ion displacements into neighbouring cavities start to take place around 0.1 ps after the start of the simulation, and that these limit the lifetime of the intra-well vibrations. At longer times the displacements become coupled and produce a near dc contribution to the conductivity.