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Filippo Bencivenga

Inelastic Ultraviolet Scattering with μeV energy resolution: applications for the study of disordered systems. Filippo Bencivenga. OUTLINE Collective dynamics in disordered systems Inelastic Ultraviolet Scattering (IUVS) at ELETTRA Experimental highlights (1)

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Filippo Bencivenga

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  1. Inelastic Ultraviolet Scattering with μeV energy resolution: applications for the study of disordered systems Filippo Bencivenga

  2. OUTLINE Collective dynamics in disordered systems Inelastic Ultraviolet Scattering (IUVS) at ELETTRA Experimental highlights (1) • Sound absorption in vitreous SiO2 Experimental highlights (2) • Structural relaxation in water under pressure Outlook

  3. Collectivedynamics in disorderedsystems Characteristic lengths x  0.1 nm ~ Lattice space in crystals dj 10 nm Topological Disorder x,djtj,tD Characteristic times tD0.1 ps ~ Inverse Debye frequency tj0.1 ÷ ∞ ps Relaxation times

  4. Collectivedynamics in disorderedsystems Density Fluctuations Spectrum: S(Q,E) x Characteristic times tD tD0.1 ps dj ILS IXS tj0.1 ÷ ∞ ps Raman scattering 5000 m/s Characteristic lengths tj 500 m/s IUVS tj x  0.1 nm INS dj 10 nm Brillouin scattering Q  0.1 ÷ 1 nm-1

  5. IUVS beamline: BL10.2 @ ELETTRA 1015 ph/s/0.1%BW • Main features of IUVS beamline: • a) Beam @ sample: •  Ei = 4 ÷ 12 eV • 1010 ÷ 1013 ph/s • 1x0.5 mm2 spot • b) DE ≈ 7÷20 meV • c) Eo-Ei ≈ ± 1000 meV • d) S(Q,E) in oneshot • e) “Easy” Q-change Heat Load +Focusing Sync. Ei< 15 eV Figure-8 undulator Band pass filters Ei= 4 ÷ 12 eV DEi ≈ 3 eV 8 m Focusing mirror Diffraction grating + slit Sample 3 m VERTICAL d = 32 mm b = 70° m ≈ 200 H ≈ 50 mm Collection mirror 2q=172° Q = 2Ein(Ei)sin(q)/hc Q ≈ 0.05 ÷ 0.15 nm-1 CCD camera (512x2048 pixels; 13.5x13.5 mm2) f(Eo) DEi/Ei ≈ 10-6 Eo-Ei ≈ ± 1000 meV DEo/Eo ≈ 10-6 3 m L  (Eo-Ei)/Ei

  6. Experimentalhighlights (1) Sound absorption in vitreous SiO2 1400 K 1100 K 300 K IXS ? T-independent sound absorption: structural origin PRL 83, 5583 (1999) e-a·x ILS 300 K GL = hcs/2pa Anharmonicity: acoustic phonons coupled with thermal vibrations PRL 82, 1478 (1999) 5 K

  7. Anharmonic contribution PRL92 (2004); PRL97 (2006) Experimentalhighlights (1) Sound absorption in vitreous SiO2 Elastic constants disorder1 Characteristic length: d~ 2p/Q* ~ 50 nm 300 K Q2 Structural contribution IXS d ~ disorder of the elastic constants ? IUVS or GL Characteristic frequency: EL(Q*) ~ 0.5 meV ILS Q*EL(Q*) Q* GL Q4 Q2 EL ~ 0.5 meV ~ EBP? 1) PRL 98 (2007)

  8. Experimentalhighlights (1) Sound absorption in vitreous SiO2 IXS + 0.1 meV ? ET(2Q*) ~ EBP 2Q*? Q*~ 2p/d ? GT ET(Q*) ~ 0.5 EL (Q*) < EBP GT(Q*) same trend as GL (Q*) ? Yes No d ~ elastic constant’s disorder Anomaly probably related to EBP

  9. 1 bar r hS cT cs 1500 bar 400 bar Quantitative agreement with Mode Coupling Theory Experimental determination of structural relaxation time (t) Experimental highlights (2) Water anomalies Water anomalies described by a singuratity free scenario1 - Mode Coupling Thory (MCT) - TM Tg IUVS spectra HDA Critical-like behavior? + LDA 2000 bar Viscoelastic framework Pressure (bar) IUVS + IXS results: pressure (i.e. density) independence of t Mode Coupling Theory: t~ (T-T0)g 2.3 +/- 0.2 Temperature (K) 220 +/- 10 K 1) PRE 53 (1996); PRL 49 (1982)

  10. r hS cT cs Systematic determination of t as a function of P and T Experimental highlights (2) Water anomalies T = 298 K; Q = 0.07 nm-1 Liquid-liquid phase transition hypothesis1 d(E) Tg TH TH TM TM DHO CP2 CP2 HDA HDL Critical-like behavior? Critical-like behavior? LDL LDA Pressure (bar) IXS IUVS Temperature (K) 1) Nature 360 (1992); Nature 396 (1998)

  11. Experimental highlights (2) Structural relaxation in water under pressure E(r) = E(r0) + a(r-r0) Free volume reduction at high density Arhenius trend (r-dependent) t ~ exp{(rcp-r)-1} t= t(r) exp{E(r)/kBT} Expected trend 1 bar 4 kbar • a = ∂E/∂r> 0 Stiffer local structure @ high density

  12. Experimental highlights (2) Structural relaxation in water under pressure Further r-dependence t= t(r) exp{E(r)/kBT} t~ exp{-br}exp{E(r)/kBT} t= t0exp{[E(r0)+ (a-kBbT)(r-r0)]/kBT} ∂S/∂r

  13. Experimental highlights (2) Structural relaxation in water under pressure (∂S/∂r)(rHDA-rLDA) = 51 ± 3 J/mol k • kBb = ∂S/∂r > 0 Further r-dependence t= t(r) exp{E(r)/kBT} More entropic local structure @ high density ∂A/∂r = 0  T = 209 ± 12 K t~ exp{-br}exp{E(r)/kBT} Qualitative agreement with liquid-liquid phase transition hypothesis Quantitative agreement with liquid-liquid phase transition hypothesis t= t0exp{[E(r0)+ (a-kBbT)(r-r0)]/kBT} ∂E/∂r ∂S/∂r ∂A/∂r

  14. Experimental highlights (2) Structural relaxation in water under pressure (∂S/∂r)(rHDA-rLDA) = 51 ± 3 J/mol k Further r-dependence t= t(r) exp{E(r)/kBT} ∂A/∂r = 0  T = 209 ± 12 K ∂A/∂T ? Larger T-range t~ exp{-br}exp{E(r)/kBT} IXS + 0.1 meV Q ~ 0.1 nm-1 t= t0exp{[E(r0)+ (a-kBbT)(r-r0)]/kBT} cs Q ~ 0.07 nm-1 Q ~ 0.025 nm-1 P = 1 bar ∂A/∂r

  15. Outlook Density Fluctuations Spectrum: S(Q,E) Characteristic times tD0.1 ps dj IXS ILS ? t0.1 ÷ ∞ ps Raman scattering 5000 m/s IUVS Characteristic lengths 500 m/s INS x  0.1 nm d  10 nm Brillouin scattering Q  0.1 ÷ 1 nm-1

  16. S(Q,E) (a.u.) F(Q,t) (a.u.) F(Q,t) (a.u.) E (meV) t (ps) t (ps) t-1 S(Q,E) (a.u.) E (meV) Outlook F(Q,t) S(Q,E) N2 T ~ TC Q = 2nm-1 Sound speed ~ 500 m/s H2O -10 °C / 1 bar Q = 2nm-1 t= 5 ± 3 ps

  17. Transient grating spectroscopy Excitation pulses (pump) Standing e.m. wave (Transient Grating) l0 Sample z Transmitted pulse Delayed pulse (probe) 2qs qd l1 qd qd (Dt) l0 Diffracted pulse (signal) r E2 t0 = 0 Detector z F(Q,t) L=l0/2sin qs Density wave periodicity: time Q = 4p sin qs/l0 qd = asin (qsl0/l1) t <r> 0

  18. Transient grating spectroscopy & FEL source Excitation pulses (pump) FEL source: l0 Sample FERMI@ELETTRA Delayed pulse (probe) Transmitted pulse l0~ 120 ÷ 10 nm 2qs l1 N ~ 1014 ph/pulse Diffracted pulse (signal) t = 0.2 ÷ 104 ps Dt ~ 50 ÷ 200 fs l0 Q = 4p sin qs/l0 Gaussian profiles Q = 0.01 ÷ 1.2 nm-1 Q-range: 2qS~ 9° 2qS~ 140° ~Dt 3-meters long delay line t-range:

  19. t > 100 fs Q< 1.2 nm-1 “Inelastic scattering” in the time domain Transient Grating Spectroscopy dj IXS ILS + Raman scattering 5000 m/s TIMER F.E.L. source IUVS 500 m/s TG INS = Brillouin scattering TIMER Ready by the end of 2010

  20. Acknoweledgements • C. Masciovecchio, A. Gessini, S. di Fonzo, • S.C. Santucci, D. Cocco, M. Zangrando and R. Menk (ELETTRA) • M.G. Izzo, A. Cimatoribus and D. Ficco (University of Trieste)

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