First-Principle Calculations of Structure, Lattice Dynamics and Phase Transitions

We describe the application of the first-principle calculations and the direct method to study phonons. In particular, on the examples of SnO 2 and ferroelectric LiNbO 3 crystals we show how to establish the dynamical structure factor of the coherently and inelastically scattered neutrons, and how to predict the phonon peak intensities in a number of Brillouin zones. We found that there are Brillouin zones were only very few phonon branches have appreciable intensities, and this feature could allow to measure the phonon dispersion relations for complex crystals.