Alessandro Cunsolo

1. Inelastic X Ray Scattering: a valuable tool to investigate the dynamics of disordered systems Alessandro Cunsolo INFM Operative Group in Grenoble and CRS-Soft, c/o Institut Laue-Langevin, Grenoble, France

2. Summary • Layout of the used IXS spectrometers • How IXS can be employed to investigate relaxation processes? • Is a transverse dynamics coupled with IXS spectra? • A single IXS spectrometer probing the whole dynamic crossover from the hydrodynamic to the single-particle regimes. • The onset of quantum effects in the dynamics of fluids studied by IXS. • Conclusions and perspectives

3. DE/E ≈ 10-8 Monochromator Si (h,h,h) 6.5 m DE/E ≈ 10-4 ≈ Undulators Pre-Monochromator Si (1,1,1) qB Toroidal mirror 75 m IXS BEAMLINE (ID16 & ID28) 5 Analyzers Si (h,h,h) Analyzer Si (h,h,h) 2q 5 Detectors Detector T-scan ≈ mK sample DE/E ≈ 10-2

4. What is a relaxation process? What effect it has on the spectral line-shape?

5. The scattering event excites propagating density fluctuations… Q Kout 2q Ki IXS hw = Ei-Eout  THz ׀Q׀ = Q=4p/lisin(q)  nm-1

6. The propagation of a density fluctuation perturbs the local equilibrium of the fluid. • Such equilibrium is then restored through energy rearrangements affecting the density wave towards some internal degree of freedom (relaxation processes). • Therefore the propagation of the density wave depends on how its period (T) compares with the relaxation time-scale (t).

7. Instantaneous energy rearrangements: the acoustic wave propagates over successive states of local equilibrium T >>t→Viscous regime

8. T << t→ Elastic regime The internal degrees of freedom of the fluid are too slow to efficiently dissipate the energy of the acoustic wave, which therefore propagates elastically…

9. The dispersion curve c∞Q Visco-elastic regime Visco-elastic crossover elastic regime Elastic regime w=1/t Q=Q*~1/d* C∞ ws(Q) ws(Q*)=1/t C(w) cSQ Viscous regime viscous regime C0= CS q w The frequency dependence of sound velocity at constant temperature and density

10. An IXS study of relaxation phenomena in water • Cunsolo et al. Physical Review Letters82, 775 (1999) • G. Monaco et al. Physical Review E60, 5505-5521 (1999)

11. The apparent sound velocity (slope of the dispersion curve) is roughly twice the adiabatic one J. Teixeira et al, PRL, 54,2681, (1985) ? cSQ The mysterious case of fast sound in water: literature results

12. Q= 2 nm-1 Q= 4 nm-1 Q= 7 nm-1 The IXS spectra of water at low Q

13. A typical DHO best fit lineshape Ws,1~1/t1 Ws,2~1/t2 hws -hws Ws,3~1/t3 Resolution limited range q1 q2 q1 An upgraded resolution would allow to study viscoelastic effects also in the overcooled phase Dispersion curve of water: first evidence of a viscoelastic behavior 1/t increases with increasing T

14. The dynamic structure factor can be written as a functionof m(Q,w) = FT[m(Q,t)] Let m(Q, t) be the memory of the variable current In a IXS experiment the measured variable is the dynamic structure factor S(Q,w) Where the correlation function C(Q,t) = <r(Q,t)r*(Q,0)> obeys to the memory function equation Some hints on the more appropriate choose for the memory function….

15. Instantaneous loose of memory Viscous limit Visco-elastic regime Exponential interpolation between the two limits……. t t t Infinitely slow loose of memory Elastic limit t

16. The memory function employed to describe water spectra fitparameters Instantaneous term Thermal contribution Viscous contribution From EoS

17. t0(433 K) t0(393 K) t0(373 K) t0(333 K) t0(313 K) t0(277 K) The q = 0 extrapolated relaxation timescales

18. activation energy ≈ 3.8 ± 0.6 Kcal/mole The Arrhenius plot of the q = 0 extrapolated relaxation time

19. The strength of the relaxation process tends to disappear on approaching Tc The q=0 extrapolated sound velocity

20. Non convoluted (model) line-shapes Raw spectra Q=2 nm-1 Convolution for an hypothetical .1 meV (lorentzian) resolution function Elastic regime Hypothetical higher resolution spectra   S(Q,w)/S(Q) (meV-1) Visco-elastic regime Viscous regime hw (meV) hw (meV) The viscoelastic behavior of the lineshape Possible effects of an improved instrumental resolution

21. Is there any evidence of a transverse dynamics in the THz response of water? E. Pontecorvo, et al. Physical Review E71, 011501/1-12 (2005)

22. Transverse dynamics: intuitive concepts If w<<1/t (viscous limit)  NO transverse propagation When w> 1/t  a transverse propagation may occur

23. The inclusion of an additional mode improves the agreement with experimental results Thespectral contribution of transverse dynamics

24. The intensity of the additional mode increases systematically with decreasing T The intensity of the additional mode increases systematically with increasing q Q = 10 nm-1 Q = 13 nm-1

25. IXS results versus MD simulations CT(Q,E) CL(Q,E) Crossover from viscoelasticity to transverse dynamics: the experimental observation of the gradual L-T mode-splitting would require a much better resolution …… M. Sampoli et al. Phys. Rev. Lett.79, 1678 (1997)

26. The transition from the hydrodynamic to the single-particle regimesT. Scopigno et al., Europhysics Letters 50, 189-195 (2000).

27. The transition from (viscous) hydrodynamic limit to the single particle one: the case of liquid lithium Q(nm-1)

28. Quantum effects in the dynamics of simple fluidsA.Cunsolo, et al. Journal of Low Temperature Physics 129, 117 (2002). A.Cunsolo, et al. Journal of Chemical Physics 123, 114509/1-7 (2005)

29. Quantum-to-classic transition in simple fluids The lengthscale probed by the experiment must be comparable with the coherence length of quantum effects & both must be comparable with the mean free path

30. Quantum effects in dynamical and structural properties of isotopes Different position of the main diffraction peak : a clear quantum effect!! For any fluid the first spectral moments is equal to the recoil energy Q = 12.8 nm-1 Contrary to expectations the spectra are different: a much sharper excitation appears in the H2 line-shape!! Corresponding states: Thermodynamic states with same reduced temperature T/Tcand densityr/rc   The Vineyard prediction: When classical fluids are in corresponding thermodynamic states they have the same statical and dynamical responses….

31. Conclusions • - IXS technique has proven its capability in providing a rich and physically informative insight on relaxation processes in disordered systems. • The combined use of IXS and MD simulation allowed to get the first experimental evidence of a transverse dynamics in liquid water • -Owing to the absence of kinematic limitations, nowadays a single IXS spectrometer can cover the whole dynamic crossover between hydrodynamic and single particle regimes. • -IXS can be successfully used to probe the onset of quantum deviations in the dynamic behavior of simple fluids.

32. No man’s land -The construction of IXS spectrometers with .1 meV resolution would provide a step forward towards a more exhaustive understanding of the THz dynamics of liquids. Moreover it would allow to partially bridge the dynamic gap existing with low q spectroscopies……

33. I’m deeply indebted to • Inelastic Scattering team:M. Krisch,A. Mermet, G. Monaco, C. Masciovecchio, F. Sette and R. Verbeni • Universita’ di Firenze: M. Sampoli • Universita’ di Roma: G. Ruocco, T. Scopigno and E. Pontecorvo

34. Possible applications of high pressure techniques

35. Pressure connector Cell body out sample Sealing system in out X-ray beam in X-ray beam Scattered beam Scattered beam 10 mm High pressure-high temperature sample environment • Large Volume HP Cells • Low pressures ( Kbar) • “Large” samples ( cm3) • Versatility (High-T & Low-T) Cell body Nut Sample

36. Preliminary test for a novel-concept HP monochromator Analyzer Si (n,n,n) DE/E ≈ 10-8 HP- monochromator Si (n,n,n) qB ≈ sample qB

37. T V(t) The analogous of the sound wave t t << T The analogous of an almost viscous response A(t) A(t) t >> T The analogous of an almost elastic response t Analogy between viscoelasticity and the response of a RC circuit to a square wave t