The common answer to this question is that a Phonon is the vibration of the lattice. My concern is whether or not this is limited to the vibration of the lattice? Are Phonons not in general waves that transport heat in materials? If so, can we not talk of form all types of materials such as gas a liquid since all forms of material do transit heat? Phonons are not limited to the the crystal lattice in solids. Am I right on this? What is your take?
In principle you are right. In all the states of matter you have that energy (heat?) is transferred in three ways: Radiation, conduction and convection. Phonons represent the conduction term, where energy is transferred without the mass transfer. Convection is the way the energy is carried by the mass that moves. Let us neglect radiation, outside the scope of the question. In a solid conduction is much larger than the convection, practically negligible. In this case, being the vibrations weakly interacting with the electron gas and crystal structure, using the second quantization approach, it is simple to consider the phonons as gas of with interaction terms with the crystal defects and electrons, calculated in the framework of perturbation theory.
On the other hand, in a gas the convection is dominant, while in a liquid you have a that the two contributions are of the same order of magnitude. The problem in using the phonon description for liquids and gases, is that the interaction of the phonon with the particles is not weak, and the perturbation theory cannot be used. It is difficult to write a quantum equation for the phonons in liquid and gases, therefore phonons are not considered, but the classical theory of energy transport is usually applied, such as the Chapman-Enskog expansion of the Boltzmann equation for gases.
dear Golden Gadzirayi Nyambuya,
by definition a phonon is the elementary excitation (quant) of the elastic field. Hence it is not a particle or a physical body, but it is used to describe elementary or collective excitations in lattice virations of dens particle dynamics (rigid body physics).
Thank you for you answer. Yes, I am aware that it is not a particle in the sense that we have an Electron as a particle. My question is, it not a Phonon a waves by which heat is transported in matter?
In principle you are right. In all the states of matter you have that energy (heat?) is transferred in three ways: Radiation, conduction and convection. Phonons represent the conduction term, where energy is transferred without the mass transfer. Convection is the way the energy is carried by the mass that moves. Let us neglect radiation, outside the scope of the question. In a solid conduction is much larger than the convection, practically negligible. In this case, being the vibrations weakly interacting with the electron gas and crystal structure, using the second quantization approach, it is simple to consider the phonons as gas of with interaction terms with the crystal defects and electrons, calculated in the framework of perturbation theory.
On the other hand, in a gas the convection is dominant, while in a liquid you have a that the two contributions are of the same order of magnitude. The problem in using the phonon description for liquids and gases, is that the interaction of the phonon with the particles is not weak, and the perturbation theory cannot be used. It is difficult to write a quantum equation for the phonons in liquid and gases, therefore phonons are not considered, but the classical theory of energy transport is usually applied, such as the Chapman-Enskog expansion of the Boltzmann equation for gases.
@ Gianpiero Colonna, thanks for your answer, it has come very close to what I am looking for.
So, in a way, a Phonon is a wave by which heat is transported by way of conduction.
A phonon by definition requires a regular structure to exist, so is not defined for liquids, gases or amorphous materials.
In solids, conduction occurs by several mechanisms. Electronic and phononic (lattice waves) heat transport are probably most important mechanisms. In ceramic materials, phononic heat conduction dominates the transport. However, in metallic materials, electronic mechanism is also quite important.
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