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THERMAL CONDUCTIVITY - Coggle Diagram
THERMAL CONDUCTIVITY
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Phonon mean free path
The details of thermal conduction by phonons are best approached via a macroscopically defined mean free path.
The thermal conductivity 𝜅 is defined as the constant of proportionality between a temperature gradient ∇T and the rate of energy flow per unit area Q as in
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in the latter case Q depends only on the temperature difference, ΔΤ, between the ends
for any distribution of phonons, we may define a nominal mean free path
Anharmonic effects
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There is a similar equation for each of the Ν atoms. The two terms come from the two springs that are attached to the nth atom
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the normal mode decomposition of the atomic motion is exact and phonons cannot interact (collide) with another
the quadratic term is just the first nonzero term in a Taylor expansion of the potential energy about the equilibrium position.
According to Debye, if the vibration of the fixed lattice in the normal mode
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Normal Process or N-process 
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These phonons can interact and annihilate one another resulting in a phonon with a wave vector k3, as shown in Figure shown .
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we conclude that an N-process does not alter the direction of energy flow, so it cannot contribute to the thermal resistance of a crystal
Umklapp Process or U-Process , For K≠0
while the energy flow for k1 and k2 was to the right, the energy flow for k3 is to the left.
This process can provide a thermal resistance to phonon flow (i.e., provides for a finite thermal conductivity).
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heat transfer mechanism
In metals, electrons, holes and phonons can transfer or conduct thermal energy from the hotter areas to the cooler parts.
In insulators (dielectric materials), only phonon plays a role in delivering energy
When heated, electrons, holes and phonon obtain energy larger than the average energy.
In real crystals
The deviations may be attributed to the neglect of anharmonic (higher than quadratic) terms in the interatomic displacements
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When there is a temperature gradient across a solid, thermal energy is transferred from the hotter to the cooler end
-Occurs without transferring heat or mass between a thermodynamic system and its surroundings.
-A system exchanges no heat with its surroundings (Q = 0) and ΔT ≠ 0
-A change of a system, in which the temperature remains constant: ΔT =0.
-The change in internal energy ΔU = 0 (only for an ideal gas) but Q ≠ 0