Phonons

A phonon is a quantized vibration, or quantized energy, of a crystal lattice. Every collective harmonic vibration can be represented by phonons. The difference of harmonic vibration and quantum vibration is the scale you can see it at. Harmonic vibrations are visible by the naked eye, a quantum vibration is a vibration of atoms, which can not be seen by the eye. Phonons are then too small to see. They are on the scale of 1 billionth of a meter. There are phonons present in every crystal lattice. When they are excited, then they are able to transfer energy.

There is also a direct relationship between the temperature and the excited states of phonons. The higher the temperature, the greater the vibrations of the atoms and therefore the more excited phonons with a higher frequency. Similarly, the more internal energy in a crystal lattice, the greater number of excited phonons. Elastic waves in a crystal are represented of excited phonons and those phonons are created by raising the temperature and likewise destroyed when the temperature is lowered.

There are important key terms one must know to understand phonons. Like any harmonic oscillator, phonons consist of wave properties.

Wave - A wave is a disturbance traveling through a medium by which energy is transferred from one particle of the medium to another without causing any permanent displacement of the medium itself. The peaks of the wave are the maximum amount of energy. There are two types of wave we are interested in, longitudinal and transverse wave. Both types can co-exist.

Longitudinal Wave - a longitudinal wave is like a sound wave in air, where the pulse travels parallel to the direction of disturbance.
Transverse Wave - a transverse wave is like a leaf floating in a lake. When a wave comes, the leaf goes up and then back down. So a transverse wave is where the motion is perpendicular to the direction of disturbance.

Wavelength – A wavelength is the distance between any two repeating points, as shown in the diagram.

Frequency – The frequency of a wave is the number of times a point repeats in a certain amount of time. In a crystal, different phonons can have different frequencies.

Quasi-particle - A quasi-particle is collective motion of many particles moving together as a wave and interacting with each other like a single, free particle. Quasi-particles can contain a great deal of information of the system.

The energy is directly proportional to the number of phonons excited and their frequencies.

Here are different ways phonons are similar to photons:

Both have particle and wave like properties.
Both are considered bosons. That means that two or more can have the same states. The opposite is fermions, which, cannot be in the same state.
Both are considered a quantum of energy.
Both are quasi-particles.
Cannot see either.
Thermal vibrations in a crystal lattice are thermally excited phonons, just like thermally excited photons of black-body electromagnetic radiation in a cavity.

One of the reasons that phonons are so important to investigate is because they are so frequently ignored. When a scientist thinks of quantum sized problem, he doesn’t take phonons into effect. When that happens, large amounts of error can happen, after all phonons are quantum energy. Phonons are also an untapped resource for energy that can become useful in the future.

Phonons can be experimentally measured by Raman spectra. Basically, light, most commonly a laser is emitted at a material. Phonons are then absorbed or emitted by the laser, which would then result in the energy of the laser photons either shifting up or down. This shift can calculate the phonon modes and the low frequencies in the system. Raman spectra can also find vital information like the temperature and the crystal’s orientation and structure.

Phonons are different when compared to the scale. For instance, in bulk materials, like an object seen by the human eye, is easily defined. But when you go to the nano scale, everything is much more complicated and rigid. In comparison, when looking at a mosaic from a distance, the lines seem clear, however, taking a closer look, you see the detail of what makes each part of the picture different, and then have to study each tile. Atoms and their bonds work in the same way. Everything is made of up atoms, just how everything is controlled by quantum mechanics. Classical mechanics are made just to represent quantum mechanics clearer.