Inelastic scattering processes arise due to the anharmonic nature of inter-atomic potential energy. For a harmonic oscillator, the spring constant is independent of spring deformation. However, this is not the case for the bonds between atoms, where the bond spring constant can change if the bond is strained. So as one lattice wave propagates across a plane of atoms, the atoms will be displaced slightly from their equilibrium positions and the spring constant between those atoms will be modified. When another lattice wave is incident on this strain field, it encounters a change in medium properties, such as the speed of sound and is, hence, scattered. Such scattering processes are called intrinsic processes since they can occur even in a perfect crystal.

There are two types of three-phonon inelastic scattering processes: the “normal” process and the “umklapp” process, which are also referred to as simply the N and U processes, respectively. Both these processes conserve phonon energy before and after scattering.

For the N processes phonon momentum is conserved, and thus N processes do not produce any direct resistance to heat flow. If only N processes were to exist, a solid would have infinite conductivity. Therefore, one would be tempted to neglect them in finding an effective relaxation time. However, the N-processes do distribute phonon energy to different frequencies (inelastic scattering), which may influence other frequency dependent scattering, and thus, indirectly affect resistance to heat flow.

In contrast, U processes do not conserve momentum and therefore directly resist phonon transport. At very low temperatures boundary scattering dominates. At high temperatures U processes dominates. N processes play a role in the intermediate range between the boundary scattering and U process.

[A. Majumdar, J. Heat Transfer, 1993]