Phonons can scatter through several mechanisms as they travel through the material. These scattering mechanisms are: Umklapp phonon-phonon scattering, phonon-impurity scattering, phonon-electron scattering, and phonon-boundary scattering. Each scattering mechanism can be characterised by a relaxation rate 1/${\displaystyle \tau }$ which is the inverse of the corresponding relaxation time.

All scattering processes can be taken into account using Matthiessen's rule. Then the combined relaxation time ${\displaystyle \tau _{C}}$ can be written as:

The parameters ${\displaystyle \tau _{U}}$, ${\displaystyle \tau _{M}}$, ${\displaystyle \tau _{B}}$, ${\displaystyle \tau _{\text{ph-e}}}$ are due to Umklapp scattering, mass-difference impurity scattering, boundary scattering and phonon-electron scattering, respectively.

For phonon-phonon scattering, effects by normal processes (processes which conserve the phonon wave vector - N processes) are ignored in favor of Umklapp processes (U processes). Since normal processes vary linearly with ${\displaystyle \omega }$ and umklapp processes vary with ${\displaystyle \omega ^{2}}$, Umklapp scattering dominates at high frequency. ${\displaystyle \tau _{U}}$ is given by:

where ${\displaystyle \gamma }$ is the Gruneisen anharmonicity parameter, μ is the shear modulus, V₀ is the volume per atom and ${\displaystyle \omega _{D}}$ is the Debye frequency.

Thermal transport in non-metal solids was usually considered to be governed by the three-phonon scattering process, 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 and for certain materials at room temperature. The predicted significance of four-phonon scattering in boron arsenide was confirmed by experiments.

Mass-difference impurity scattering is given by:

where ${\displaystyle \Gamma }$ is a measure of the impurity scattering strength. Note that ${\displaystyle {v_{g}}}$ is dependent of the dispersion curves.