Long-waves principle and dispersion relations for cubic crystal lattices in the model of dipole-dipole interactions

The paper considers monoatomic crystal lattice vibrations, caused by Van der Waals forces. A dynamical model is constructed and equations are derived, which describe monoatomic crystal lattice vibrations in the adiabatic approximation. It is shown that according to long-waves principle in the limit the received equations turn into well-known equations of elasticity theory. This makes it possible to express the force constants of the dynamical model in terms of elastic constants of the substance. The solution of the received equations allowed to derive dispersion relations for bcc and fcc lattices without any free parameters. The calculated dispersion curves for Na and Al are in good agreement with experimental data.