Normal Modes in a Periodic Square Lattice
Normal modes in a monatomic periodic square chain are simulated. You can adjust the number of atoms, the ratio between the two "spring constants", the two components of the wave vector (red arrow) in the first Brillouin zone (red square), and the two components of the polarization . Sound waves (small ) and stationary waves (within the boundary of the Brillouin zone) can be easily identified. Longitudinal ( parallel to ) and transverse ( perpendicular to ) waves are also clearly reproduced.
Snapshot 1: static atomic configuration for a long wavelength longitudinal normal mode
Snapshot 2: static atomic configuration for a long wavelength transverse normal mode
Snapshot 3: static atomic configuration for a normal mode with a wave vector at the boundary of the first Brillouin zone