The effects of incommensurability on the phonon modes in the one-dimensional superionic conductor K-hollandite

Polarized Raman and infrared spectra of the one dimensional (1-D) superionic conductor (K_2xMg_xTi(_8?x)O₁₆; x = 0.77) have been measured over the phonon frequency region 10–1000 cm^?1 as a function of temperature and pressure. The majority of the IR and Raman active modes predicted by group theory for the (Ti, Mg)O₆ framework were observed. The frequencies and their IR and Raman scattering cross-sections for the incommensurate lattice of K⁺ ions were calculated using a one dimensional linear chain model. This model assumes Coulomb interaction between nearest neighbors that are located in a sinusoidal potential due to the framework lattice. Several broad Raman bands were attributed to amplitudon type modes from the one dimensional incommensurate K⁺ ion sublattice. The IR active phason modes could not be identified unambiguously due to the underlying TiO framework vibrations which are known to possess large anharmonicity and oscillator strenghts.