# Why do phonons cause excellent heat conduction in diamonds?

Phonons are the quantum of lattice vibrations in crystals and are not to be confused with photons, the gauge bosons of the electromagnetic force. Apparently, they contribute to heat conduction, but I don’t understand why, as this is not explained in course 2062 of Aalto University.

So why is diamond a good heat conductor and how do phonons contribute/are related to this?

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Have you read around what phonons are? e.g. en.wikipedia.org/wiki/Phonon –  John Rennie Dec 4 '12 at 16:53
Just a hint: using the imperative mode in your question title or text does not usually generate the desired results. Between the possibilities of sounding like you have copied something directly from course materials and sounding like you feel entitled to direct other users efforts you a likely to annoy a lot of people. –  dmckee Dec 4 '12 at 19:21
@JohnRennie Yes, I have (see the answer outlining the wikipedia arcticle) but I still cannot understand the statement, classical reason is probably Young's modulus, more here, while the QM explanation is more like refining: if heat conductance larger, it means more energy transmission so more energetic frequencies. This was basically what my teacher hand-waved but I think there is much more to this. –  hhh Dec 16 '12 at 19:27

"Phonons -- are some sort of vibratinal lattice quarks."

Not true, phonons are not quarks but quasiparticles, more here. Phonons are also bosons.

Wikipedia misleadingly shows that phonon is not an elementary particle or a boson but my lecturer and Wikipedia article about bosons support the bosonness.

Please, note that the term "quasiparticle" differ between contextes. According to Wikipedia, "These fictitious particles are typically called "quasiparticles" if they are fermions (like electrons and holes), and called "collective excitations" if they are bosons". This is about elementary particles so do not mix them up. I understand this so that phonon is not an elementary particle so the above definitions do not hold for it. Anyway, notice that the same word "quasiparticle" is confusingly used in similar context for totally different meaning!

Phonon is a quantitative piece of energy in vibrational lattice ("fononi=kiteen värähtelyenergian kvantti", ~p.163). This quantification is eventually a result of $E=hf$. I don't use the word "particle" because phonon is not traditional elementary particle like electron, proton or a quark. It is some sort of fictious particle that appears during interaction with other materials. For example, light travelling in photons do not contain phonons but when the high-energy light hits wall, the phonon lattice emerges.

Example: Silica and Diamond

Silica and diamond have the same structure but Silica does not conduct heat. Please, note that electricity conductance do not mean heat conductance, both Silica and Diamond do not conduct electricity because of no moving electrons. In order to explain the heat conductance of diamond, one needs to consider frequencies and hence energies. In layman terms, diamond lattice is able to sustain frequencies of higher energy while Silica not. This may be different in extreme temperatures such as close to absolute zero.

The heat conductivity is a feature due to the phonon lattice.

Theory

The lattice vibrates according to partial derivatives aka Hamiltonian equations here. The Hamiltonian consists of kinetic energy and rotational energy for each thing

where we don't have potential energy between the particles because it is very close to zero (gravitational field effect very small). For me, the Hamiltonian equations look similar to the wave equation here but the earlier Hamiltonian looks different.

ERR I am probably messing something up here, cannot yet see how the two different Hamiltonians are the same...checking, the picture source here.

Bullet points from Wikipedia

I. "The thermodynamic properties of a solid are directly related to its phonon structure."

II. "At absolute zero temperature, a crystal lattice lies in its ground state, and contains no phonons"

II.I. "If more than one ground state exists, they are said to be degenerate."

Study questions

I. Is phonon a particle?

II. What does it look like?

III. Can you see the phonon with microscope?

Definitions

• Phonon is a boson, more here and a picture here.

• 'These fictitious particles are typically called "quasiparticles" if they are fermions (like electrons and holes), and called "collective excitations" if they are bosons (like phonons and plasmons),1 although the precise distinction is not universally agreed.' Wikipedia here.

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