Phonons
Lecture 19A
Debye Theory of Solids
Oscillations in a crystal
Oscillations in a crystal – like oscillations of the EM field
Can we apply our treatment of EM radiation to the
mechanical oscillations of a crystal?
• The speed of sound is much slower than the speed of light
A remarkably accurate model for predicting the highand low-temperature heat capacities for a solid
speed cs (assume constant)
• There are three possible polarizations
(two transverse + one longitudinal)
• Sound waves cannot have arbitrarily short wavelengths
Phonon modes in a box
Shortest wavelength
As with EM radiation, only certain
allowed wavelengths
Energy almost identical to photons:
Energy and phonons in a mode
Use results from blackbody radiation
The total energy
Summing over modes – similar to blackbody
1
Heat Capacity – high T
Heat Capacity – low T
Heat Capacity
2