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THERMAL PROPERTIES, image, image, image, image, image, image, image, image…
THERMAL PROPERTIES
Debye model
Atoms are considered as harmonic oscillators that produce elastic
waves with varying frequencies from ω = 0 to ωmax.
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This changes the expression for CV because each mode of oscillation contributes a frequency-dependent heat capacity and we now have to integrate over all ω.
The relations between the energy of a phonon E, the angular
frequency ω and the wave vector q are:
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Since there is a cut-off wave vector qD=ωD/vs, all the modes are confined within a
sphere with radius qD. Thus number of modes (not number of phonons) should be
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At high temperature limit, T>>TD
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At low temperature limit, T<<TD
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Einstein model
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At low T, Einstein’s formula is essentially an
exponential falloff.
Thermal conductivity
Heat transfer
When heated, electrons, holes and phonon obtain
energy larger than the average energy.
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.
According to Debye, if the vibration of the fixed lattice in the normal mode (in perfect harmonic crystals): Phonon distribution does not change with
-Phonon distribution does not change with time.
-Thermal waves also remain constant and travels in solids at the speed of sound.
-Thermal conductivity of lattices becomes infinite.
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In reality:
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Scattering due to phonon and defects: Lattice defects such as point defects, isotope inhomogeneity and other types of defects.
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