Parlinski, Li, and Kawazoe Reply: In a recent Letter [1], we have calculated the soft mode in the cubic ZrO 2 using the standard CASTEP ab initio program [2], with the local-density approximation and pseudopotential approach, and confining the studied crystallite to a 2 3 2 3 2 fcc supercell with periodic boundary conditions and 96 atoms. The force constants were directly derived from Hellmann-Feynman (HF) forces induced by separate Zr and O atomic displacements. Detraux, Ghosez, and Gonze [3] commented that for ZrO 2 the Born effective
Using the ab initio method within the local-density approximation with ultrasoft pseudopotentials and plane-wave basis, calculating the Hellmann-Feynman forces and applying the direct method, the phonondispersion relations for ferroelectric and paraelectric rhombohedral phases of LiNbO 3 crystal have been derived. The calculated phonon frequencies for the ferroelectric phase at the ⌫ point are compared with Raman, infrared, and neutron-scattering 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 smaller than the force constants between niobium and oxygen ions. As a consequence, 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 ⌫ point. This soft mode leads to the observed paraelectric-ferroelectric phase transition. The LO/TO splitting is considered by assuming formal values of ionic charges, and by fitting the longitudinal infrared active modes to the experimental data.
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