# Umklapp Scattering & Conservation of Energy

In summary, Umklapp scattering involves the transfer of a certain number of reciprocal lattice vectors to the crystal lattice, causing a change in crystal momentum. This thermalization process also results in a change in the distribution of single phonon energies, following the Boltzmann distribution. Conservation of real momentum is not an issue as the energy of the lattice remains nearly unchanged due to its large mass.
After looking at Umklapp scattering, I believe I have finally gotten most of it down, but a few things are still not clear.

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.

Yes, the missing energy is thermalized in the lattice. But the energy that was carried away was carried by a phonon ... so phonon energy was conserved at the point of the u-event.

1 person
1) Momentum is not conserved for certain phonon collisions, and a certain number of reciprocal lattice vectors are transferred to the crystal lattice:
It seems to me I am missing something.

In deed. You have to be carefull to distinguish real momentum from crystal momentum. Phonons don't carry real momentum at all.
On the other hand, e.g. absorption of a photon will change the momentum of a crystal by a very small amount p. If the total lattice was at rest (i.e. its energy E=0), the energy carried by the lattice afterwards will be ##E=p^2/M ##. As M is practically infinitely large, E=0 even afterwards.
So conservation of real momentum is never a problem and does not interfere with energy conservation.
In the process of thermalization, the total energy remains conserved. However the distribution of the single phonons becomes Boltzmann.

1 person

## 1. What is Umklapp scattering?

Umklapp scattering is a phenomenon in solid state physics where a lattice defect or impurity causes the momentum of a particle to change in such a way that it is no longer in phase with the lattice, resulting in a scattering event.

## 2. How does Umklapp scattering affect the conservation of energy?

In Umklapp scattering, the change in momentum of the scattered particle results in a change in its energy. However, the total energy of the system is still conserved, as the lattice defect or impurity absorbs or releases the necessary energy to compensate for the change in the particle's energy.

## 3. Can Umklapp scattering occur in all materials?

Umklapp scattering is most commonly observed in crystalline materials, as the regular lattice structure is necessary for the phase change to occur. However, it can also occur in some amorphous materials with a high degree of order.

## 4. How does the temperature of a material affect Umklapp scattering?

At higher temperatures, the atoms in a material vibrate more vigorously, making it more difficult for Umklapp scattering to occur. As a result, Umklapp scattering is more likely to occur at lower temperatures.

## 5. What are the practical implications of Umklapp scattering?

Umklapp scattering plays a crucial role in many properties of materials, such as thermal conductivity and electrical resistivity. It can also affect the behavior of electrons and other particles in a material, making it an important factor to consider in various technological applications.

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