The Optical and Acoustic Branches of an Infinite Diatomic Chain
Highlights of the activity
- For this activity, the class is placed into four sections. Each section is given a limiting case for the dispersion relation of the infinite diatomic chain. Each group will plot their calculated value on a dispersion relation graph at the front of the room.
- After each group has placed their point on the board, connecting the dots will give a rough graph that shows the separation in the optical and acoustic branches.
Reasons to spend class time on the activity
When students are presented the dispersion relation equation for the infinite diatomic chain, the expression can at first be quite daunting. Having students analyze the equation in the context where the masses of the two atoms is identical will help students familarize with the consequences of having a $\pm$ sign and with how increasing the wave number $k$ will change oscillation frequency. The resulting points plotted also leads well into a discussion on the frequency gap between $\omega_{-}\left(k=\frac{\pi}{a}\right)$ and $\omega_{+}\left(k=\frac{\pi}{a}\right)$.