Local normal modes, lattice vibrations and phase transitions

In this thesis, we propose a simplified approach to the lattice dynamics of crystals by operating within the framework of local normal modes, i.e, the normal modes of the isolated unit cell. We do this by transforming the Cartesian coordinates into the normal modes of the unit cell by using group theoretic techniques. The dynamical matrix obtained with this method is different to the one obtained through standard methods, but has the same eigenvalues and eigenvectors. Using perturbation theory, we treat the off-diagonal elements as perturbations and proceed in calculating the phonon dispersions. In doing so, we obtain approximate analytical expressions and accurate numerical solutions to phonon dispersion without explicitly solving the eigenvalue problem. This method provides insight into the symmetry analysis of the phonon modes, and opens a pathway for studying phase transitions in molecular solids and Jahn-Teller systems. A Jahn-Teller molecule is one which is not stable and distorts to a lower-symmetry geometry due to the electronic degeneracy of the highest occupied molecular orbital. If several such Jahn-Teller molecules interact with each other, they can undergo a cooperative phase transition. We use our results of the local normal mode analysis to develop a model of cooperative Jahn-Teller phase transitions. We then apply our model to a system of interacting icosahedral Jahn-Teller clusters. Since atoms tend to form clusters of icosahedral symmetry in the amorphous and liquid phases, our results serve as a paradigm for liquid-solid and glass transitions. This is a new approach which has been taken in establishing a relationship between lattice dynamics, cooperative Jahn-Teller effect and certain types of phase transitions.Open Acces