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  and umklapp processes vary with , Umklapp scattering dominates at high frequency.  is given by:
where  is the Gruneisen anharmonicity parameter,  is the shear modulus,  is the volume per atom and  is the Debye frequency.