Lattice dynamics of YBa2Cu3O7−x in oxygen-vacancy ordered ortho-II and ortho-III superstructures

Abstract A lattice-dynamics of YBa 2 Cu 3 O 7− x in superstructures ortho-II and ortho-III of oxygen ordering ( x =0.5 and x =0.33) is calculated in the frameworks of shell model with transferable interatomic potential parameters. Frequencies and eigenvectors for 75 vibration modes of ortho-II and 114 phonons of ortho-III are analysed and their connection with the phonon dispersion in YBa 2 Cu 3 O 7 and YBa 2 Cu 3 O 6 is investigated. In spite of the great complication of phonon spectra due to a multiplication of a unit cell in superstructures ortho-II and ortho-III a lot of their long-wave phonons are still close to the short-wave eigenmodes of ortho-I and are not expected to be observable in optical experiments. All Γ -phonons of ortho-I lattice manifest themselves in the long-wave spectra of high-order phases. The intrinsic Γ -modes of apical oxygen of YBa 2 Cu 3 O 6 arise in both superstructures as well. Only a restricted set of long-wave phonons can be regarded as the inherent ortho-II and ortho-III modes and could be useful as the reference vibrations for the purpose of superstructure characterization.