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

Year 2020, , 59 - 79, 28.05.2020

Ulrich Köbler

https://doi.org/10.5541/ijot.649929

Cited By: 6

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

Supporting Institution

none

Project Number

none

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