Phonon Brillouin-Zone Folding

Fold a lattice wave into the first Brillouin zone and distinguish group velocity from acoustic approximation.

Experiment

You can interactively explore zone folding and the resulting dispersion properties in the Phonon Brillouin-Zone Folding module.

1. Try selecting a "Raw ka over pi" of 3. Notice that the Reduced ka/π wraps back to -1. Consequently, the actual discrete site displacement pattern remains completely identical, which confirms that unwrapped, shorter wavelengths are not uniquely observable on the lattice.
2. Adjust the "Spring constant" to 4 to see the direct scaling effect on the acoustic speed and dispersion curve steepness, resulting in a higher angular frequency.