Origins:

The thermal conductivity of a system is determined by how atoms comprising the system interact. There are no simple, correct expressions for thermal conductivity. There are two different approaches for calculating the thermal conductivity of a system.

The first approach employs the Green-Kubo relations. Although this employs analytic expressions which in principle can be solved, in order to calculate the thermal conductivity of a dense fluid or solid using this relation requires the use of molecular dynamics computer simulation.

The second approach is based upon the relaxation time approach. Due to the anharmonicity within the crystal potential, the phonons in the system are known to scatter. There are three main mechanisms for scattering:

• Boundary scattering, a phonon hitting the boundary of a system;
• Mass defect scattering, a phonon hitting an impurity within the system and scattering;
• Phonon-phonon scattering, a phonon breaking into two lower energy phonons or a phonon colliding with another phonon and merging into one higher energy phonon.

Further information can be found in the publication "The Physics of Phonons" by G P Srivastava.