Phys560Notes-13 - Anharmonic Effects Assume one atom per...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Anharmonic Effects Assume one atom per unit cell. Potential energy          UU  rR R uR 234 0 harmonic potential u O u  Terms   34 , Ou Ou anharmonic effects or phonon-phonon interactions 1 + ( ) 2( ) i ss s s s aa e M N kR k- k k uR e k k 3 ... Ou aaa  3 as a perturbation 3-phonon processes; likewise, 4 4-phonon processes Phonon splitting, phonon combination, phonon scattering, etc. Scattering matrix element      ... n aaa n kk ; Fermi's golden rule cross section Energy conservation (from golden rule) Crystal momentum conservation (from matrix element), for example, 123 0  kkkK (3-phonon processes) depends on whether it is a phonon creation or annihilation process. 0 K normal process ( N-process ). 0 K umklapp process ( U-process ). Required when the momentum combinations exceed 1 st zone.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

Phys560Notes-13 - Anharmonic Effects Assume one atom per...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online