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Thermal Conductivity, EXAMPLE - Coggle Diagram
Thermal Conductivity
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Heat transfer mechanism
β₯ (When heated) electrons, holes and phonon obtain energy larger than average energy.
β₯ Electron, holes and phonons can transfer (in metals).
β₯ Only phonon plays a role in delivering energy (in insulators).
According to Debye π
πPhonon distribution does not change with time.
π Remain constant - thermal waves.
π Thermal conductivity becomes infinite.
In Reality
β¨ Edge scattering - bec of specimen size.
β¨ Scattering due to phonon and defects.
β¨ Crystals becomes anharmonic at temperatures higher than absolute zero.
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π The ability of material to resist flow or heat.
π Thermal resistivity is the reciprocal of thermal conductivity.
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Phonon mean free path
The details of thermal conduction by phonons are best approached via macroscopically defined mean free path.
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The thermal conductivity ΞΊ is defined as the constant of proportionally between a temperature gradient T and at the rate of energy flow per unit area Q.
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Equilibrium position - the energy transfer is a random process, in local thermal equlibrium.
π Phonons:
π Must diffuse through the sample.
π Suffering frequent collisions from the higher temperature to the lower temperature end.
U PROCESS
:pencil2: With increasing phonon momentum and thus larger wave vectors k1 and k2, their sum might point outside the first Brillouin zone (k'3).
:pencil2: k-vectors outside the first Brillouin zone are physically equivalent to vectors inside it and can be mathematically transformed into each other by the addition of a reciprocal lattice vector G.
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:!!: dominant process for thermal resistivity at high temperatures for low defect crystals
:!!: the dominant process for electrical resistivity at low temperatures for low defect crystals
:check:The thermal conductivity for an insulating crystal where the U-processes are dominant has 1/T dependence
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Anharmonic effects
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:pushpin: In 3D crystal
:linked_paperclips: Hooke's law may appear complicated because there are non-negligible "spring" between any atoms and its nearest or non-nearest neighbors
:linked_paperclips: the forces are linearly in the displacement
:linked_paperclips: leads to the harmonic Hamiltonian and phonons
:heavy_check_mark: in normal mode, phonon cannot interact with another
:heavy_multiplication_x: no phonon scattering
:heavy_multiplication_x: no thermal resistivity
:heavy_check_mark: thermal conductivity would be infinite
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EXAMPLE
electron-lattice potential scattering or an anharmonic phonon-phonon or electron-phonon scattering process, reflecting an electronic state or creating a phonon with a momentum k-vector outside the first Brillouin zone.
A process limiting the thermal conductivity in crystalline materials, the others being phonon scattering on crystal defects and at the surface of the sample.
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