PHY452H1S Basic Statistical Mechanics. Lecture 21: Phonon modes. Taught by Prof. Arun Paramekanti
Posted by peeterjoot on April 4, 2013
Peeter’s lecture notes from class. May not be entirely coherent.
These are notes for the last class, which included a lot of discussion not captured by this short set of notes (as well as slides which were not transcribed).
If we model a solid as a set of interconnected springs, as in fig. 1.1, then the potentials are of the form
with kinetic energies
It’s possible to introduce generalized forces
Assuming a Fourier representation
This looks like a harmonic oscillator with
This is plotted in fig. 1.2. In particular note that for for we can use a linear approximation
Experimentally, looking at specific for a complex atomic structure like Gold, we find for example good fit for a model such as