Abstract
A conventional shell model (SM) fitted to static lattice properties and just one phonon frequency, namely that of the transverse Raman frequency at the R point, has been used to calculate the phonon dispersion in cubic strontium titanate at 298 K along principal high-symmetry directions in the Brillouin zone. The agreement between these calculated data and experimental results from neutron scattering is fully comparable with that of SMs actually fitted to experimental neutron data. The usual SM cannot account for the strong temperature dependence of the soft-mode frequency and the static permittivity, but it is shown that this temperature dependence can be accounted for by small continuous variations in just two of the SM parameters. While purely phenomenological at present, these variations point to the strong dependence of metal-oxygen bonding on lattice constant.
Similar calculations for potassium niobate result in an excellent fit to the temperature dependence of the frequency of the soft TO mode. This SM has been used to calculate atomic displacements around O, Nb and K vacancies in KNbO3, with results in good agreement with INDO calculations by Kotomin and Eglitis. Ab initio HartreeFock calculations for KNbO3 predict O and K displacements in agreement with the SM and INDO results, but rather smaller Nb displacements. Charge-density plots confirm substantial electron density between O and Nb atoms due to overlap of O 2p with Nb eg orbitals.
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Jacobs, P.W.M. (2000). Use and Limitations of the Shell Model in Calculations on Perovskites. In: Borstel, G., Krumins, A., Millers, D. (eds) Defects and Surface-Induced Effects in Advanced Perovskites. NATO Science Series, vol 77. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4030-0_4
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DOI: https://doi.org/10.1007/978-94-011-4030-0_4
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