Analysis of Phonon Dispersion Relations From Atomic Model to Continuum Theory

The phonon dispersion relations calculated by atomic model: shell model and ab initio, and by microcontinuum theory are introduced in this paper. It is found that both atomic models and microcontinuum theory can describe the common feature of phonon dispersion relation for the crystal having more than one atom per primitive cell and can give a good fit to the experimentally measured data. The optical branches are absent from the classical continuum theory and the strain gradient theory due to the neglecting of the atomic structure of the crystal. The importance of phonon dispersion relation and the applicability of microcontinuum theory are discussed.