Thermoelectric materials are of significant technological interest and present some fundamental scientific questions.
An extremely useful concept is the dimensionless thermoelectric figure of merit. The optimum material with have a high electrical conductivity and thermoelectric power (Seebeck coefficient), but also a low thermal conductivity. This has led to the notion of a Phonon Glass Electron Crystal (PGEC): a material which has the low thermal conductivity characteristic of a glass and the high electrical conductivity characteristic of a crystal. How might one achieve this?
In simple kinetic theory [with well-define acoustic phonon quasi-particles] the thermal conductivity is proportional to the phonon velocity and the phonon mean-free path. In glasses there is so much structural disorder the concept of phonon quasi-particles and a mean-free path is ill defined. In the quasi-particle picture one could reduce the thermal conductivity either by decreasing the phonon mean-free path or by decreasing the phonon speed, or both. The former can happen via a large anharmonicity, which is what is responsible for phonon-phonon scattering. The latter can happen in a soft material or by strongly coupling the acoustic phonons to low frequency optical phonons.
An extremely useful concept is the dimensionless thermoelectric figure of merit. The optimum material with have a high electrical conductivity and thermoelectric power (Seebeck coefficient), but also a low thermal conductivity. This has led to the notion of a Phonon Glass Electron Crystal (PGEC): a material which has the low thermal conductivity characteristic of a glass and the high electrical conductivity characteristic of a crystal. How might one achieve this?
In simple kinetic theory [with well-define acoustic phonon quasi-particles] the thermal conductivity is proportional to the phonon velocity and the phonon mean-free path. In glasses there is so much structural disorder the concept of phonon quasi-particles and a mean-free path is ill defined. In the quasi-particle picture one could reduce the thermal conductivity either by decreasing the phonon mean-free path or by decreasing the phonon speed, or both. The former can happen via a large anharmonicity, which is what is responsible for phonon-phonon scattering. The latter can happen in a soft material or by strongly coupling the acoustic phonons to low frequency optical phonons.
There is a really nice News and Views article Thermoelectrics: Half-full Glasses by Cronin Vingin in Nature Materials that puts in context neutron scattering experiments, on two different classes of materials. [I thank Elvis Shoko for bringing this article to my attention and for helpful discussions]. The first class of materials are clathrates and the second skutterudites. Examples, are methane hydrate and BaFe4Sb12, respectively.
[Aside: previously I posted about superconductivity in skutterudites]. The picture below shows a clathrate structure.
Although, chemically distinct a common structural feature is that both have large cavities within which an atom can "rattle" around in. This means that associated with these motions there are low frequency "optical" phonons which are very anharmonic. These modes then couple to acoustic phonons via coupling to motions of the cage.
The figure is taken from a recent PRB, the introduction to which I found gave a particularly helpful overview.
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