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1) Momentum is not conserved for certain phonon collisions, and a certain number of reciprocal lattice vectors are transferred to the crystal lattice:

h-bar(k1+k2)=h-bar(k3 + G)

But if momentum is transferred to the lattice, which is called the thermalization of the lattice, isn't energy transferred to the lattice as well?

2) And if energy is transferred to the lattice. Why would the energy of the phonons still be conserved? It seems to me I am missing something.

3) If the lattice is "thermalized," what exactly is the consequence of this? Does it heat up/dissipate heat, similar to what happens with electrical resistance.