Atomic vibrations in alpha-quartz with silicon vacancies

A study of atomic structures and localized symmetrized vibrations in α-quartz with silicon vacancies in different charge states is presented. This study is performed by computer modeling on the basis of the first-principle type potentials. The equilibrium structures are optimized by minimizing the lattice energy. The phonon symmetrized local densities of states are calculated by means of a recursion method. Moreover, frequencies of localized vibrations of A- and B-symmetries induced by silicon vacancies are determined. The results are discussed in comparative manner for the silicon vacancy in three charge states. (paper)