On the Thermal Conductivity of Metals and of Insulators

Abstract

The experimental indications are discussed that in insulators thermal conductivity is exclusively due to Debye bosons (sound waves). Phonons do not obviously contribute to thermal conductivity. In metals, thermal conductivity is exclusively due to electronic degrees of freedom. Phonons and Debye bosons do virtually not contribute to thermal conductivity of the metals. It appears that the electronic system of the metals has also continuum properties with bosons as excitations. We will call the bosons of the spatially continuous conduction band, CB-bosons. In contrast to the bosons of the elastic continuum (Debye bosons), CB bosons and their dispersion relation are not yet explored. Since bosons propagate ballistic, independent of lattice structure, they are the predominant carriers of thermal conductivity. Their large mean free path enables a very efficient heat transport over large distances. Identification of boson fields is limited to their heat capacities. The heat capacity of the Debye boson field is ~T³. The heat capacity of the CB-boson field is ~T. In the approximation of an infinite mean free path of the bosons and negligible lattice contributions, thermal conductivity is proportional to the heat capacity of the boson field. Thermal conductivity therefore allows for a separate visualization of the heat capacity of the boson fields. The two power functions of temperature (~T³ and ~T) hold up to a temperature of about 10…30 K only. At this temperature thermal energy gets transferred to the atomistic degrees of freedom (phonons, band structure states). This is a typical crossover event. For larger temperatures the boson system accumulates no longer thermal energy and its heat capacity tends to zero. In this way, a sharp maximum of thermal conductivity result at about 10…30 K. At ambient temperature the two power functions of temperature (~T³, ~T) have completely disappeared. When phonons are the relevant excitations, thermal conductivity of insulators tends to zero. In metals, crossover to the conventional (atomistic) conduction band states results in a finite and nearly temperature independent thermal conductivity.

Keywords

• Thermal conductivity,sound waves,boson fields

References

1. Prof. Harald Euler: University of Bonn [e-mail]
2. Dr. Norbert Stüsser: Helmholtz- Zentrum-Berlin [e-mail]
3. Prof. Dr.rer.nat. Hans-Werner Diehl: University of Duisburg [e-mail]
4. Prof. Dr. Stefan Blügel: FZ-Jülich, Institut PGI [e-mail]
5. Prof. Dr. Tomasz Tolinski: Polish Academy of Science, Poznan [e-mail]
6. Dr. habil, Leslaw Smardz: Polish Academy of Science, Poznan [e-mail] l