Therefore, these processes are also known as Umklapp (U) processes and can only occur when phonons with sufficiently large q -vectors are excited, because unless the sum of q 2 and q 3 points outside of the Brillouin zone the momentum is conserved and the process is normal scattering (N-process). The probability of a phonon to have energy E is given by the Boltzmann distribution P ∝ ∝ e − − E / k T . To U-process to occur the decaying phonon to have a wave vector q 1 that is roughly half of the diameter of the Brillouin zone, because otherwise quasimomentum would not be conserved.