Phonon Dispersion Calculator

Calculate phonon dispersion relations for 1D crystal models

Chain Type:

Lattice Constant (Å): *

Spring Constant (N/m): *

Atomic Mass (amu): *

Wavevector k (as fraction of π/a): (optional)

About Phonon Dispersion

Phonon dispersion relations describe how the frequency of lattice vibrations depends on the wavevector. They are fundamental to understanding thermal and acoustic properties of solids.

Key Features:

Monoatomic: ω = 2√(K/m)|sin(ka/2)|
Diatomic: Acoustic + Optical branches
Band gap appears when m1 ≠ m2
Group velocity: vg = dω/dk