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Thermal Conductivity - Coggle Diagram
Thermal Conductivity
Thermal conductivity
- The ability of material to resist flow of heat
Thermal resistivity:
- the reciprocal of thermal conductivity
- heat can be transmitted through a crystal by phonons, photons, free electrons or holes and electron holes pair
- single phonon cannot be used describe a deviation from equilibrium in one region
- phonons be localized in space within distance
Anharmonic effects
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- phonon collide with each other and these collisions limit thermal conductivity due to the flow of phonons
- consider the potential energy of 1D monoatomic
- forces between only nearest neighbors
- the two terms come from the two springs that are attached to the nth atom
- 3D crystal, Hooke's law may appear
- non-negligible springs between any one atom and its nearest, non-nearest neighbors
- forces are linear in the displacements
- normal mode decomposition of the atomic motion is exact
phonons can't interact with another
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Phonon mean free path
Thermal conductivity:
- the constant of proportionality between a temperature gradient and the rate of energy flow per unit area Q
- any distribution of phonons, it may define as nominal mean free path
- in equilibrium, situation Λ decreases rapidly with increasing phonon energy
Process
Normal Process
- consider three phonon process with wave vectors k1 and k2 collide and create wave vector k3
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The conservation energy:
- these phonons can interact and annihilate one another resulting a phonon with wave vector k3
- This process does not alter the direction of energy flow, it can't contribute to thermal resistance of crystal
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- Let say TA an arbitrary point is picked then corresponds to k1
- Using this point as origin, the ω vs k curves
- The intersection of solid and dashed curves is required solution
- This particular value have phonon of wave vector k3 and energy ℏω3 that satisfies
- The conservation laws are fulfilled with K=0 is an N-process
Umklapp Process
- K≠0
- provide thermal resistance to phonon flow
- energy flow for k1 and k2 was the right, the energy flow for k3 to the left
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The conservation law:
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- consider an arbitrary but larger, value for k1 and proceed in same manner as before
- Value k2 is obtained with circle that satisfies the conservation law
- The intersection is outside of the first Brillouin zone
- The addition of a reciprocal lattice vector, -2π/a
- The point marked with an x and k3
- This phonon with wave vector k3, the conservation laws using K≠0 are satisfied
- The flow energy reversed in direction
- So, this is a U-process