Untersuchungen zur Dynamik der Tief-, Hoch- und inkommensurablen Phasen in Quarz und AIPO4 mit inelastischer Neutronenstreuung

The mechanism of phase-transitions of the low-quartz $\rightarrow$ incommensurate $\rightarrow$ high-quartz type is investigated in quartz and A1PO$_{4}$ by inelastic neutron scattering. The incommensurate phase in quartz and AIPO$_{4}$ exhibits an extremely long wave modulation and is in fact different from most of the known incommensurate phases investigated so far. It plays a key-role in the mechanism of the phase-transition. Its existence is already in contradiction to the mechanism of a displacive transition driven by a $\Gamma$-point softmode, since in the incommensurate phase the softmode condenses within the Brillouin zone. Special attention has been paid to two points: On the one hand the temperature dependence of phonon spectra and the mode coupling have been investigated. The results have been compared with the phenomenological Landau theory, thus providing a mechanism for the transition. On the other hand lattice dynamical models have been developed in order to reveal a microscopic picture of the phase-transitions. In particular the following results have been obtained: 1. The phonon dispersion of AIPO$_{4}$ in the $\alpha$-phase at room-temperature has been measured and reproduced by lattice dynamical models (Born-von Karman, 8 parameters ; rigid ion, 11 parameters) in the low energy region (inelastic neutron scattering up to 8 THz). Furthermore, the model calculations are in good aggreement with raman data. In spite of structural differences, like different tetrahedra occupation and formal charges, different bond angles and distances, the lattice dynamical parameters are quite similar to those of quartz. Considering the introduction of Coulomb forces and effective charges within the rigid ion model, the fit to the experimental data could not be improved. This indicates an effective screening of tetrahedra centres by its first neighbours. The effective charges of the Al and P ions (0.6e, 0.8e) exhibit only slight differences and have nothing in common with the formal charges. Thus, the lattice dynamical behaviour is mainly gouverned by the oxygen framework structure. [...