PHZ3400 Phonons

Law of Dulong and Pettit: failure of classical physics

$C_{v}={\frac {\partial \epsilon (T)}{\partial T}}=3nk_{B}$

-Works fine at high temperature, but at low temperature the quantum mechanical nature of the material dominates. The Debye model gives the correct interpretation at low temperature.

Quantization of sound waves: phonons

Bose-Einstein distribution

$n(\mathrm {B} \hbar \omega )={\frac {1}{e^{\mathrm {B} \hbar \omega }-1}}$

Thermodynamics of phonons

Debye model

- Analogous to Planck's Blackbody Radiation Law, except this deals with phonons instead of photons.