Long-waves principle and phonon spectra of cubic crystal lattices

In the article the authors obtain and solve a system of equations, describing vibrations of the monoatomic body-centered and face-centered cubic lattices during the force interaction possessing van der Waals nature. They demonstrate that the system allows implement of the long waves principle according to which the equations of crystal lattice vibrations are to resolve themselves into the equations of elastic deformation wave propagation in a crystal as in the continuous medium. The comparison of the received and classical equations allows to show the force constants of the dynamical model in terms of elastic constants of a given substance, and to calculate the phonon spectra of some body-centered and face-centered cubic lattices crystals.