Phonon Spectral Energy Density in Metalswith the Cubic Lattice Structure

Abstract

This study derives an expression of spectral energy density of acoustic phonons, as well as introducing the basic properties of anharmonic phonons and deriving an expression of their spectral energy density. The description of the vibrations of the atoms of the crystal lattice to this day cannot be considered completely finished, despite the existence of the theory of heat capacity at a constant volume (Debye theory). Debye's theory perfectly explains the law of cubic increase in heat capacity with temperature at low values of the latter. However, at high temperatures, the Debye model seems insufficiently substantiated. In particular, it is not clear for what physical reasons the value of the critical frequency was introduced - the phonon frequency, above which their appearance is impossible. In addition, the spectral energy density of anharmonism phonons is not considered, although this information is extremely important. It is the spectral composition of the anharmonic phonons that is necessary for an objective description of the phonon-phonon interaction in a crystal. In this paper, the principles are stated on the basis of which the spectral energy density of phonons can be calculated. The consideration is carried out for a simple cubic crystal lattice.