1 / 26

5. ATOMIC DYNAMICS IN AMORPHOUS SOLIDS

5. ATOMIC DYNAMICS IN AMORPHOUS SOLIDS. Crystalline solids  phonons in the reciprocal lattice. Crystalline solids  Debye Theory. g (  ) =  2 / 2 2 v D 3. C p ( T ) = C Debye T 3. 2. ATOMIC DYNAMICS. Hamiltonian for lattice vibrations:. n = 1, …, N  = 1, …, r

lucus
Download Presentation

5. ATOMIC DYNAMICS IN AMORPHOUS SOLIDS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 5. ATOMIC DYNAMICS IN AMORPHOUS SOLIDS Crystallinesolids phonons in thereciprocallattice

  2. Crystallinesolids DebyeTheory g() =  2 / 22vD3 Cp(T) = CDebyeT 3 2

  3. ATOMIC DYNAMICS Hamiltonian for lattice vibrations: n = 1, …, N  = 1, …, r i = x, y, z  Eq. of motion: If: Dynamical matrix D has 3Nr real eigenvalues j2 and corresponding eigenvectors uni (j) • In periodic crystals: q  only3rcurves j(q) : • 3 acoustic branches j(q 0)  0 • 3(r-1) optic branches j(q 0)  const.

  4. Dispersion relations (q) in amorphous solids

  5. Does exist a quantity which can describe sensibly phonon modes in amorphous solids? YES: the vibrational density of states (VDOS): g()·d= number of states with frequencies between  and d ! For crystals:

  6. COMPUTER SIMULATIONS

  7. EXPERIMENTAL TECHNIQUES

  8. RAMAN SPECTROSCOPY • In amorphous solids, there is a breakdown of the • Raman selection rules in crystals for the wavevector • ALL vibrational modes contribute to Raman scattering (first-order scattering), in contrast to the case of crystals (second-order scattering due to selction rules)

  9. RAMAN SPECTROSCOPY BOSON PEAK Competitionbetweenincreasingg() and decreasing Bose-Einstein factor ???

  10. RAMAN SPECTROSCOPY BOSON PEAK Martin & Brenigtheory: a peak in thecoupling coefficientC() duetoelastoacousticdisorder ??

  11. RAMAN SPECTROSCOPY BOSON PEAK [Sokolov et al. 1994] TheBosonPeakis a peak in C() g() / 2!!!

  12. Brillouin scattering: Experimental set-up

  13. BRILLOUIN SCATTERING: ethanol

  14. INELASTIC NEUTRON SCATTERING

  15. INELASTIC NEUTRON SCATTERING

  16. INELASTIC NEUTRON SCATTERING

  17. INELASTIC NEUTRON SCATTERING

  18. INELASTIC NEUTRON SCATTERING

  19. RAMAN SCATTERING The Boson Peak is a peak in C() g() / 2!!!

  20. INELASTIC X-RAY SCATTERING Damped Harmonic Oscillator

  21. INELASTIC X-RAY SCATTERING

  22. INELASTIC X-RAY SCATTERING

More Related