On the Distinction between Debye Bosons and Phonons

Abstract

A method is described that allows one to construct the dispersion of the Debye bosons (sound waves) from the known temperature dependence of the sound velocities. The method simply assumes that the sound velocity measured at temperature T gives the slope of the dispersion relation at excitation energy E=kB·T. The associated reduced wave vector is set equal to q/q0=a0kBT/hvL/T. In this way the dispersion of the Debye bosons can be constructed for all thermal energies for which sound velocities vL/T(T) are known. This can be up to melting temperature. Surprisingly, the dispersion of the Debye bosons continues beyond zone boundary. At melting temperature the wavelength of the Debye bosons is of the order of the atomic diameters. The sources of the Debye bosons therefore must have atomic dimensions. Spontaneous generation of Debye bosons by individual atoms is, however, a completely unexplored process. Interactions with the atomistic background of phonons or lattice defects provide damping to the Debye bosons and make vL/T(T) sample and temperature dependent. Quite generally vL/T(T) decreases as a function of increasing temperature. For high energies the dispersion relation of the Debye bosons therefore becomes visibly lower than linear. Interactions between Debye bosons and phonons can modify the dispersion of the acoustic phonons appreciably. Because of their different symmetries the dispersion relations of Debye bosons and acoustic phonons attract each other. It is observed that for low wave vector values the dispersion of the acoustic phonons can assume the linear wave vector dependence of the Debye bosons. At the end of the linear section a functional crossover to a sine-like function of wave vector occurs.