On the Thermal Conductivity of Metals and of Insulators

Year 2017, Volume: 20 Issue: 4, 210 - 218, 29.11.2017

Ulrich Köbler

https://doi.org/10.5541/eoguijt.316073

Cited By: 16

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

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