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Phonons in solids

k 1. k 2. w. p/ a. p/ a. 0. k. Phonons in solids. First Brillouin zone. Heat capacity. ~3 Nk B. T/ Q. ~ T 3. Thermal conductivity. L. S. T 1. T 2. Heat transfer is performed by the gas of phonons Umclapp process creates resistance to heat transfer

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Phonons in solids

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  1. k1 k2 w p/a p/a 0 k Phonons in solids First Brillouin zone

  2. Heat capacity ~3NkB T/Q ~T3

  3. Thermal conductivity L S T1 T2 • Heat transfer is performed by the gas of phonons • Umclapp process creates resistance to heat transfer • ( gradient of temperature inside solid is due to • this resistance) x L V S=1 E+ E- T(x) x

  4. Thermal conductivity • Thermal conductivity of NaF crystal: • at T>Qthermal conductivity K~L~T-1 • at T<Q thermal conductivity K~C~T3 NaF

  5. U(R) R 0 -U0 Thermal expansion Solids increase in volume as their temperature is raised: uniform displacement of all atoms R0

  6. Thermal expansion

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