Phonons can scatter through several mechanisms as they travel through the material.
Each scattering mechanism can be characterised by a relaxation rate 1/
All scattering processes can be taken into account using Matthiessen's rule.
Since normal processes vary linearly with
, Umklapp scattering dominates at high frequency.
is the Gruneisen anharmonicity parameter, μ is the shear modulus, V0 is the volume per atom and
[2] Thermal transport in non-metal solids was usually considered to be governed by the three-phonon scattering process,[3] and the role of four-phonon and higher-order scattering processes was believed to be negligible.
Recent studies have shown that the four-phonon scattering can be important for nearly all materials at high temperature [4] and for certain materials at room temperature.
[5] The predicted significance of four-phonon scattering in boron arsenide was confirmed by experiments.
is a measure of the impurity scattering strength.
Boundary scattering is particularly important for low-dimensional nanostructures and its relaxation rate is given by: where
represents the fraction of specularly scattered phonons.
parameter is not easily calculated for an arbitrary surface.
Purely specular scattering does not introduce a boundary-associated increase in the thermal resistance.
the relaxation rate becomes This equation is also known as Casimir limit.
[8] These phenomenological equations can in many cases accurately model the thermal conductivity of isotropic nano-structures with characteristic sizes on the order of the phonon mean free path.
More detailed calculations are in general required to fully capture the phonon-boundary interaction across all relevant vibrational modes in an arbitrary structure.
Phonon-electron scattering can also contribute when the material is heavily doped.
is conduction electrons concentration, ε is deformation potential, ρ is mass density and m* is effective electron mass.
[2] It is usually assumed that contribution to thermal conductivity by phonon-electron scattering is negligible [citation needed].