Knowledge Bank

BeO (wurtzite lattice) and $TiO2$ (rutile lattice) are examples for crystal lattices in which the symmetry of the whole lattice is much lower than the symmetry of the local surroundings of an ion. This local symmetry is tetrahedral in BeO, octahedral in $TiO2$. To study the possible influence of these different symmetries on the force constants, the formulas for the vibration frequencies of the first-order vibration spectra (for infinite wavelength of the lattice vibrations) are established and evaluated for the force constants, utilizing the observed Raman and infrared spectra. For BeO; the experimental data are not sufficient to decide unambiguously whether the BeO forces are equal for all directions or not. The decision depends on the interpretation of two absorption bands as due to Fermi resonance splitting or as being independent bands. For $TiO2$, the Raman-effect data lead to a force system that disregards the octahedral surrounding of the Ti ions but reveals the existence of $TiO2$ molecules. These molecules can be distinguished only dynamically, not structurally. Although all other force constants are very small compared with those of the $TiO2$ molecules, they are of sufficient influence to make the spectrum dissimilar to that of a free molecule. The spectrum can be interpreted as that of coupled modified $TiO2$ molecules, with an ``effective'' force constant different from the Ti-O force constant in the crystal.