Ab initio calculations of phonons in LiNbO3

Using the ab initio method within the local-density approximation with ultr asoft pseudopotentials and plane-wave basis, calculating the Hellmann-Feynm an forces and applying the direct method, the phonon-dispersion relations f or ferroelectric and paraelectric rhombohedral phases of LiNbO3 crystal hav e been derived. The calculated phonon frequencies for the ferroelectric pha se at the Gamma point are compared with Raman, infrared, and neutron-scatte ring measurements, and they agree very well. The phonon Frequencies at the Z, L, and F high-symmetry points are also calculated. It is disclosed that the force constants involving lithium ions are an order of magnitude smalle r than the force constants between niobium and oxygen ions. As a consequenc e, the lithium ions do not contribute to high-frequency optical vibrations. In the paraelectric phase the phonon-dispersion curves show a soft branch with the soft mode of symmetry A(2u) at the Gamma point. This soft mode lea ds to the observed paraelectric-ferroelectric phase transition. The LO/TO s plitting is considered by assuming formal values of ionic charges, and by f itting the longitudinal infrared active modes to the experimental data.