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# Phonon

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## Concept of Phonon

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The concept of phonon was introduced by soviet physicist Igor Tamm in 1932. The word phonon was derived from the Greek word phone, which refers to the meaning of sound or voice because long-wavelength phonons result in the production of sound. The name and the word are analogous to the photon. In analogy with the quantum energy, photon, in the electromagnetic field, the name phonon was suggested for the quantum lattice vibrational energy by Frenkel in 1935. Thus, phonons are the quanta of sound just like a photon is a quanta or the packet of energy for electromagnetic waves.

In this article, we are going to learn about the concept of phonons, what phonons are and a deep insight into the meaning of phonons for better understanding.

## What is Phonon?

• Solid crystal consists of atoms bound into a specific repeating three-dimensional spatial pattern called a lattice.

• The solids execute elastic behaviour at the atomic level, the bond between the atoms and the intermolecular bonds are elastic.

• The atoms act like they are connected with a spring, just like coupled harmonic oscillators and the thermal energy generated or any external forces will cause the atoms and molecules to oscillate. This will generate mechanical waves that carry heat and sound through the material.

• A packet of these waves can travel throughout the crystal with definite momentum and energy known as phonons.

• Now, what is phonon? The quantum of energy is a phonon. In other words, we can say, a phonon is the quantum energy of the lattice vibration, just like photons are the quantum energy of electromagnetic radiations. The energy of each phonon is given by:

Â Â Â  â‡’ E = hv

Â  â‡’E = Ä§(2Ï€)v

Â  â‡’ E = Ä§Ï‰â€¦â€¦. (1)

Â Â Â  Where,

Â  Ï‰ -The angular frequency

Â  Â  Ä§ - The reduced Planckâ€™s constant

### Phonon Meaning

• According to the phonon definition, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules condensed specifically in solids and some liquids. In other words, a phonon can be defined as a discrete unit of vibrational mechanical energy, the phonons exist with a discrete amount of energy given by E=Ä§.

• Phonons play an important role in many of the physical properties of solid states, such as they play a key role in thermal conductivity and electrical conductivity. The study of phonons is an essential concept in condensed matter physics or solid-state physics.

• Phonon Vector: When a phonon with a wave vector is created by elastic scattering of a photon or neutron from wave vector K to K', the wave vector selection rule that governs the process is given by:

Â  Â  â‡’ K = K' + G

Â Â Â Â  Where,

Â  Â  G -The reciprocal lattice vector

• Types of Phonon: When the unit cell consists of more than one atom, the crystal will contain two types of phonons. Thus, there are two types of phonons that we study in condensed matter physics:

1. Acoustic Phonon: In acoustic phonons, both positive and negative ions swing together.

1. Optical Phonon: In optical phonons, both positive and negative ions swing against each other. The optical phonons are excited easily by light.

• Phonon Energy: Since, the atoms in the unit cell are behaving like a coupled oscillator, according to the quantum theory, the energy of the harmonic oscillator is given by

â‡’ E= (1+$\frac{1}{2}$) Ä§Ï‰

Where,

Ï‰ -The angular frequency

Ä§ - The reduced Planckâ€™s constant

• Phonon Momentum: The phonon momentum is given by Ä§K,it is not the momentum of the phonon, it is often referred to as crystal momentum in general.

### Properties of Phonons

• phonons are often used as a quasiparticle, some popular research has shown that phonons and protons may indeed have some kind of mass and be affected by gravity.

• phonons are said to have a kind of negative mass and negative gravity.

• phonons are known to travel faster (with maximum velocity) in denser materials.

• It is projected that phonons would deflect away as it detects the difference in densities, exhibiting the qualities of a negative gravitational field.

• Phonons have also been predicted to play a key role.

### Phonons in Semiconductors

The lattice thermal conductivity of a number of semiconductors along with InSb, GaAs, GaSb, CdTe, and CdS has been measured between temperatures 1.7 and 300Â°K. This, together with previous works and experiments on Si and Ge, is used to investigate the validity of the relaxation time expressions for the scattering of phonons by boundaries, atomic impurities and electrons, and to discuss phonon-phonon interactions and resonance scattering effects.Â

The obtained results indicate that the boundary scattering and isotope scattering relaxation times lead to accurately calculated values of thermal conductivity only when the materials are exceptionally pure. And the structure, which has been identified as due to resonance scattering, has been observed in the data for most of the materials. Electron-phonon scattering has been noted in GaSb but the complexity of the problems make the analysis only qualitative. The phonon-phonon scattering further studied into two more processes known as the U-process and N-process.

### Did You Know?

Phonons are analogous to photons, in fact, both possess almost identical properties. The following points will elaborate on why phonons are analogous to photons:

• Both phonons and photons are bosons. That means, both particles with integral spins.

• Both photons and phonons are the quanta of energy. Photon is the quanta of energy described for electromagnetic waves, whereas phonons are the quanta of energy for the lattice vibrations.

• Photon and phonon are not conserved entities.