Experiment 3
Phonons and Lattice Heat Capacity
Visualize acoustic and optical phonons and compare quantum models of heat capacity.
Controls
Key Equations
Monatomic Chain Dispersion:
ω = 2√(C/M) |sin(ka/2)|
Debye Low-T Limit:
Cv ∝ (T/ΘD)³
Lattice Vibration Animation
Monatomic atoms
Heat Capacity Models Comparison
Task: Monatomic vs Diatomic
Observe the atomic motion at small k (long wavelength) and large k (zone boundary). In the diatomic case, look for the optical branch behavior where atoms move in opposite directions.
Teaching Connection
The heat capacity of solids is a beautiful story of classical failure and quantum salvation. Use this to explain why diamond (high ΘD) doesn't obey Dulong-Petit at room temperature.
Reflection Questions
- At the zone boundary (k = π/a), do adjacent atoms move in the same or opposite directions?
- Why is the upper branch in a diatomic chain called the "optical" branch?
- At what temperature (relative to ΘD) do most materials reach the classical limit (Cv ≈ 3R)?