University of California Berkeley MSE 200A Fall 2017 Heat Conduction by Phonons

University of california berkeley mse 200a fall 2017

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University of California, Berkeley MSE 200A Fall, 2017 Heat Conduction by Phonons Scattering of phonons in perfect crystals due to phonon-phonon collisions Low energy phonons perform elastic collisions - energy conserved High-energy phonons perform inelastic collisions – energy transferred to lattice Phonon thermal conductivity Low at low T due to low C V Low at high T due to inelastic collisions Maximum at T ~ Θ D /3 k phonon only important in materials with high Θ D Diamond ( Θ D ~ 2000K) is an insulator with high thermal conductivity Much excitement in microelectronics k = 1 3 C v v l = 1 3 C v v 2 τ κ T θ Crystal Glass
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Heat Conduction by Phonons Scattering of phonons in imperfect crystals due to phonon-defect collisions <l> is the mean spacing between defects Phonon thermal conductivity is low Polygranular solids Defective solids Glasses High Θ D materials only have high k when they are nearly perfect Defective diamond films are no particular good k = 1 3 C v v l = 1 3 C v v 2 τ κ T θ Crystal Glass
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Heat Conduction by Phonons Phonon momentum and energy are limited Phonons respond weakly to T unless T is a fraction of Θ D k = 1 3 C v v l = 1 3 C v v 2 τ p = ! k h a e k E = ! ω ! ω max
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Kinetics Rate of change in response to thermodynamic forces Deviation from local equilibrium continuous change T heat flow temperature changes µ atom flow composition changes Deviation from global equilibrium discontinuous change G ( F) discontinuous change of state phase change
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Mass flux in response to a gradient in chemical potential ( μ ) Assume constant T,P Flux of solute Evolution of composition J B = nD dc dx Atom Diffusion J B = M d dx g c = M d μ dx = M μ c dc dx J B 23 J B 12 c c c 1 2 3 Fick s First Law g = g ( T , P , c ) g c T , P = μ ( T , P , c ) c t = J B x = nD 2 c x 2 Fick s Second Law
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 J B = nD dc dx Diffusion J B 23 J B 12 c c c 1 2 3 The diffusivity (D) is the material property that governs diffusion Diffusion in solids requires Atoms jump from position to position Atom jumps result in net flux Diffusion mechanism depends on atom site Interstitial Substitutional
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J.W. Morris, Jr.
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  • Fall '08
  • Staff
  • Thermodynamics, University of California, Phase transition, J.W. Morris

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