1. 5. ATOMIC DYNAMICS IN AMORPHOUS SOLIDS Crystalline solids  phonons in the reciprocal lattice

2. C p (T) = C Debye T 3 2 Crystalline solids  Debye Theory g(  ) =  2 / 2  2 v D 3

3. ATOMIC DYNAMICS Hamiltonian for lattice vibrations:  Eq. of motion: n = 1, …, N  = 1, …, r i = x, y, z If: Dynamical matrix D has 3Nr real eigenvalues  j 2 and corresponding eigenvectors u n  i (j) In periodic crystals: q  only 3r curves  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

11. 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)

12. RAMAN SPECTROSCOPY BOSON PEAK Competition between increasing g(  ) and decreasing Bose-Einstein factor ???

13. RAMAN SPECTROSCOPY BOSON PEAK Martin & Brenig theory: a peak in the coupling coefficient C(  ) due to elastoacoustic disorder ??

14. RAMAN SPECTROSCOPY BOSON PEAK [Sokolov et al. 1994] The Boson Peak is a peak in C(  ) g(  ) /  2 !!!

15. Brillouin scattering: Experimental set-up

17. BRILLOUIN SCATTERING: ethanol

18. INELASTIC NEUTRON SCATTERING

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

24. Damped Harmonic Oscillator INELASTIC X-RAY SCATTERING