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

Abstract

For a number of materials with cubic lattice structure the dispersion relations of the Debye bosons (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=c₀-B‧T^-ε. The constants c₀ 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 c₀ 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, α(T). Since the universality in α(T) holds for the same thermal energies (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 α(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

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