Ab initio study of electric field effects on phonon vibrations in tetragonal ZrO2

Abstract

The effects of external electric fields on phonon-associated phenomena, such as phase transformation and diffusion in ZrO2 ceramics, have been reported from recent experiments. This study examined the effects of external direct current (DC) electric fields on the phonon vibration properties in a tetragonal ZrO2 unit cell based on the density-functional perturbation theory. Phonon dispersions and densities of states were analyzed with optimized structures under varying external DC electric fields up to 45 mV/Å. The field sensitivities of phonon characteristics exhibited significant orientation dependence and were attributed to ionic polarization associated with symmetry breaking in dielectric properties. Optical phonons showed considerable field sensitivities particularly near the Brillouin zone boundaries, such as in the M (π/a, π/a, 0) to X (0, π/a, 0) and A (π/a, π/a, π/c) to R (0, π/a, π/c) directions, where doubly degenerate phonon frequencies exhibited splitting behaviors associated with the symmetry breaking between two unique oxygen atoms in the original unit cell. In contrast, transversal acoustic phonons demonstrated a softening trend with increasing field strengths around the Z (0, 0, π/c) point, where imaginary and splitting frequencies were obtained under electric fields of >40 mV/Å, indicating the potential phase transformation from the tetragonal to orthorhombic symmetries under strong external electric fields.