This is as I currently understand it: Phonon thermal conductivity is dependent on the phonon mean free path. To define phonon thermal conductivity a mechanism whereby phonons can be brought into thermal equalibruim is required. This is what I have a problem with: Phonon interactions with the crystal boundaries, imperfections, and if an anharmonic crystal, phonon-phonon scattering limit the mean free path but are not sufficient to bring phonons into thermal equalibrium. this is because these interactions are elastic and do not bring about an energy change in individual phonons, and so cannot bring about equalibrium. ie K1 + K2=K3 so Umklapp process are proposed which do cause thermal resistivity: K1 + K2 = K3 + G is this because K3-K2-K1=G=delta K ? This means that all collisions outside 1st brillouin zone can be translated back into it.?? so what? and here im lost..