The importance of the Debye bosons (sound waves) for the lattice dynamics of solids

Authors : Ulrich KÖBLER

Pages : 59-79

Doi:10.5541/ijot.649929

View : 14 | Download : 7

Publication Date : 2020-05-28

Article Type : Research Paper

Abstract :For a number of materials with cubic lattice structure the dispersion relations of the Debye bosons insert ignore into journalissuearticles values(sound waves); and of the acoustic phonons along [ζ 0 0] direction have been analyzed quantitatively. When all phonon modes are excited, that is, for temperatures of larger than the Debye temperature the dispersion of the mass-less Debye bosons exhibits a pronounced non-linearity, which is explained by interactions with the phonon background. For the exponent x in the dispersion relation ~q x of the Debye bosons, the rational values of x=1/4, 1/3, 1/2, 2/3 and 3/4 could be established firmly. The discrete values of x show that there are distinct modes of interaction with the phonons only. It is furthermore shown that for many materials the dispersion of the acoustic phonons along [ζ 0 0] direction follows a perfect sine function of wave vector, which is known to be the dispersion of the linear atomic chain. This dispersion is unlikely to be the intrinsic behavior of three-dimensional solids. It is argued that the sine-function is induced by the Debye boson-phonon interaction. Quantitative analyses of the temperature dependence of the heat capacity show that the heat capacity can be described accurately over a large temperature range by the expression c p =c 0 -B‧T -ε . The constants c 0 and B are material specific and define the absolute value of the heat capacity. However, for the exponent ε the same rational value occurs for materials with different chemical compositions and lattice structures. The temperature dependence of the heat capacity therefore exhibits universality. This universality must be considered as a non-intrinsic dynamic property of the atomistic phonon system, arising from the Debye boson-phonon interaction. The discrete modes of boson-phonon interaction are essential for the observed universality classes of the heat capacity. Safely identified values for ε are ε=1, 5/4 and 4/3. The fit values for c 0 are generally larger than the theoretical Dulong-Petit value. Universal exponents are identified also in the temperature dependence of the coefficient of the linear thermal expansion, αinsert ignore into journalissuearticles values(T);. Since the universality in αinsert ignore into journalissuearticles values(T); holds for the same thermal energies insert ignore into journalissuearticles values(temperatures); as for the ~q x functions in the dispersion of the Debye bosons it can be concluded that the Debye bosons also determine the temperature dependence of αinsert ignore into journalissuearticles values(T);. Our results show that the dynamics of the atomic lattice is modified for all temperatures by the Debye bosons. Atomistic models restricting on inter-atomic interactions therefore are neither sufficient to explain the phonon dispersion relations nor the detailed temperature dependence of the heat capacity.
Keywords : Lattice dynamics, boson fields, universality