Phonon Energy Calculator
Calculate phonon energy and Bose-Einstein statistics
About Phonons
Phonons are quantized lattice vibrations in solids. They carry thermal energy and interact with electrons, affecting thermal and electrical properties of materials.
Key Formulas:
- E = ℏω (phonon energy quantum)
- n = 1/(e^(ℏω/kBT) - 1) (Bose-Einstein distribution)
- ⟨E⟩ = ℏω(n + ½) (average energy)
- ωD = kBθD/ℏ (Debye cutoff)
Phonon Branches:
- Acoustic: atoms move in phase
- Optical: atoms move out of phase
- Longitudinal (LA, LO): along propagation
- Transverse (TA, TO): perpendicular