Peculiarities of Phonon Spectra of Crystals with Cuprite Lattice Due to Sublattice Structure

Abstract

The different translational symmetry of the cuprite crystal sublattices is taken into account by unfolding the phonon spectrum from the Brillouin zone of the crystal into the Brillouin zones of the anion and metal. Such a representation of the spectrum is reasonable because 6 optical branches are essentially caused by the vibrations of anions and 12 acoustic branches are due to the vibrations of metal owing to the great value difference between their masses. The volumes of the Brillouin zones of the anion and metal sublattices are two and four times, respectively, as large as those of the crystal resulting in the qualitative differences in the corresponding unfolded spectra because of the metal tetrahedron vibrations of the distortion type in the acoustic part of the spectrum. These vibrations located on the Х′(1,0,0)–W′(1,0,1/2) and Х′(0,1,0)– W′(0,1,1/2) lines of the metal Brillouin zone are responsible for the negative thermal expansion. The unfolded spectra have only three branches in the corresponding Brillouin zones and this simplifies the selection rules for the physical processes with the participation of the sublattice particle vibrations.