Collective Dynamics in Disordered Systems

Collective Dynamics in Disordered Systems

Inelastic Ultraviolet Scattering with eV eV 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) Sound absorption in vitreous SiO2 Experimental highlights (2) Structural relaxation in water under pressure Outlook Collective dynamics in disordered systems Characteristic lengths ~ Lattice space in crystals 0.1 nm j 10 nm Topological Disorder ,jj,tD Characteristic times ~ Inverse Debye frequency tD 0.1 ps Relaxation times j 0.1 ps Collective dynamics in disordered systems Density Fluctuations Spectrum: S(Q,E) Space: 3 10 1 ILS 0 Raman scattering -1 10 2 10 j 0 Characteristic times

-1 10 10 IXS j 0 50 1 0m 0 50 m tD 0.1 ps -12 j 0.1 ps 10 /s tD -13 10 /s -11 10 j INS -2 10 -10 10 -9 10 -3 10 Brillouin scattering 10 -2

Characteristic lengths 0.1 nm j 10 nm -8 10 -4 10 -3 10 Time: (s) 10 2 10 IUVS E = h / (meV) 10 10 (nm) -1 10 Q = 2 / 10 0 1 10 (nm-1) 2 10 Q 0.1 1 nm-1 IUVS beamline: BL10.2 @ ELETTRA 1015 ph/s/0.1%BW Main features of IUVS beamline: Heat Load + Focusing Sync. Ei< 15 eV Figure-8 undulator Ei= 4 12 eV

Band pass filters d = 32 m = 70 m 200 Ei 3 eV 8m Sample Focusing mirror 3m = 172 Collection mirror b) E 720 eV VERTICAL Diffraction grating + slit a) Beam @ sample: Ei = 4 12 eV 1010 1013 ph/s 1x0.5 mm2 spot H 50 m c) Eo-Ei 1000 eV d) S(Q,E) in one shot e) Easy Q-change Q = 2Ein(Ei)sin()/hc CCD camera (512x2048 pixels; 13.5x13.5 m2) Q 0.05 0.15 nm-1 (Eo) Ei/Ei 10-6 -6 Eo-Ei Eo1000 /Eo 10 eV 3m L (Eo-Ei)/Ei Experimental highlights (1) Sound absorption in vitreous SiO2 1400 K 1100 K 300 K 10 e-xx L = hcs/2 L (meV) 1 0.1

0.01 1E-3 ILS 5K S (Q,E) ? T-independent sound absorption: structural origin PRL 83, 5583 (1999) 300 K 1E-4 0.01 IXS Anharmonicity: acoustic phonons coupled with thermal vibrations PRL 82, 1478 (1999) 0.1 1 -1 Q (nm ) E Experimental highlights (1) Sound absorption in vitreous SiO2 Elastic constants disorder1 Structural contribution Q2 IXS 1 ~ disorder of the elastic constants ? 0.1 Anharmonic contribution IUVS 0.01 1E-3 ILS Q2 Q** EL(Q*) Q Q 4 0.1 Q = 0.13 nm

-1 Characteristic frequency: L EL(Q*) ~ 0.5 meV L Q = 0.1 nm -1 EL ~ 0.5 meV ~ EBP? 1 -1 Q (nm ) PRL 92 (2004); PRL 97 (2006) or Intensity (A rb. U nits) L (meV) 10 300 K Characteristic length: ~ 2/Q* ~ 50 nm 250 350 450 E (eV) 1) PRL 98 (2007) 550 Experimental highlights (1) Sound absorption in vitreous SiO2 IXS + 0.1 meV L (m eV ) 1 ? 0.1 0.01 ET (2Q*) ~ EBP 2Q*? 1E-3 T Q*~ 2/? 0.1

1 -1 Q (nm ) Yes T (Q*) same trend as L (Q*) ? ~ elastic constants disorder ET (Q*) ~ 0.5 EL (Q*) < EBP No Anomaly probably related to EBP Experimental highlights (2) Water anomalies T16M Tg spectra Theory: ModeIUVS Coupling 4 HDA 10 ~ (T-T0) 12 LDA Pressure (bar) 3 Viscoelastic 10 220 framework +/- 10 K 2.3 +/- 0.2 IUVS 2+ IXS results: 10 (i.e. density) pressure Experimentalof independence determination of 1 10 relaxation structural time () Quantitative 0 agreement with 10 Mode100 Coupling Theory 1) PRE 53 (1996); PRL 49 (1982) (ps) + IXS - PRE (1999)

IXS - PRE (2007) IUVS - PRL (2004) MCT trend Critical-like behavior? 8 400 bar 4 0 250 200 2000 bar 1500 bar 1 bar S 300 Temperature (K) 300 T cs 350 400 T (K) Water400 anomalies described by a singuratity free scenario1 - Mode Coupling Thory (MCT) - Experimental highlights (2) Water anomalies T = 298 K; Q = 0.07 nm-1 Liquid-liquid phase transition hypothesis1 TH TTHMTM Pressure (bar) 44 10 CP2 10 HDA CP HDL 2 3 33 10 10 LDA

LDL 160 2 22 10 10 IXS 11 10 10 10 10 180 100 230200 280 300330 330 Temperature (K) 1) Nature 360 (1992); Nature 396 (1998) 380 380 400 bar Systematic determination of as a function of P and T 100 8 50 4 0 90 IUVS S T cs 00 IXS - PRE (1999) IXS - PRE (2007) IUVS - PRL (2004) MCT trend 1500 0 12 150 0 3000 bar DHO 80

16 Critical-likeCritical-like behavior? behavior? Counts / 300 s (ps) Tg (E) 240 250 300 60 350 500 bar 400 T (K) 30 0 -200 -100 0 E (eV) 100 200 Experimental highlights (2) Structural relaxation in water under pressure E() = E(0) + (-0) Free volume reduction trend (-dependent) atArhenius high density 323 K 288 K 273 K 3.6 ~ exp{( )-1} = (cp- ) exp{E( )/kBT} 28 ted tr c e p x E

Ea (ps) (kJ/mol) 5.4 34 1.8 end 10 1000 1010 1040 1050 1080 1090 1120 1130 3 (kg/m (kg/m )) 3 1 bar = E/> (ps) 22 0.0 1 4 kbar 0 Stiffer local structure @ high density 3 1015 +/- 5 kg/m 3 1065 +/- 5 kg/m 3 1105 +/- 5 kg/m 0.1 3.2 3.4 3.6 3.8 -1 1000 / T (K ) 4.0 Experimental highlights (2) Structural relaxation in water under pressure

Further -dependence = () exp{E()/kBT} B / exp(E()/k T) 1E-4 1E-5 ~ exp{-}exp{E()/kBT} 323 K 288 K 273 K 1E-6 1E-7 1000 1040 1080 (kg/m ) 3 1120 = 0exp{[E(0)+ (-kBT)(-0/kBT} S/ Experimental highlights (2) Structural relaxation in water under pressure k = S/ > 0 (S/)(HDAB -LDA) = 51 3 J/mol k More entropic local A/ =structure 0 [email protected] = high 209 density 12 K Further -dependence = () exp{E()/kBT} ~ exp{-}exp{E()/kBT} Quantitative Qualitative agreement agreement with liquid-liquid phase transition hypothesis = 0exp{[E(0)+ (-kBT)(-0/kBT} E/ S/ A/ Experimental highlights (2)

Structural relaxation in water under pressure (S/)(HDA-LDA) = 51 3 J/mol k A/ = 0 T = 209 12 K A/T ? Larger T-range Further -dependence = () exp{E()/kBT} ~ exp{-}exp{E()/kBT} IXS + 0.1 meV 3 cL = L/Q (10 m /s) 1.6 -1 Q nm ~ 0.1 1.5 cs Q ~ 0.07 nm-1 1.4 = 0exp{[E(0)+ (-kBT)(-0/kBT} Q ~ 0.025 nm-1 P = 1 bar 1.3 250 280 310 T (K) 340 A/ Outlook Density Fluctuations Spectrum: S(Q,E) Space: 3 2 2 10 ILS 0

Raman scattering 10 -1 10 10 j 50 0 50 10 0 IXS ? 0m 0m Characteristic times -1 10 /s -11 10 INS 10 -10 10 -9 10 -3 10 Brillouin scattering -2 10 Characteristic lengths 0.1 nm 10 nm

-8 10 -4 10 -3 10 0.1 ps -12 10 /s -2 tD 0.1 ps -13 10 Time: (s) 1 10 1 10 IUVS E = h / (meV) 10 (nm) -1 10 Q = 2 / 10 0 10 (nm-1) 1 2 10 Q 0.1 1 nm-1 Outlook N2 10000 1000

Sound speed ~ 500 m/s T ~ TC Q = 2nm-1 100 10 -24 -12 0 12 F(Q,t) 0.8 F(Q,t) (a.u.) S(Q,E) (a.u.) S(Q,E) 0.4 0.0 -0.4 24 0 100 E (meV) 1600 H2O = 5 3 ps -10 C / 1 bar -1 Q = 2nm-1 800 0 -10 -5 0 E (meV) 300 t (ps) 5 10 1.6 F(Q,t) (a.u.)

S(Q,E) (a.u.) 2400 200 0.8 0.0 -0.8 1 10 t (ps) 100 Transient grating spectroscopy Excitation pulses (pump) 0 Standing e.m. wave (Transient Grating) Sample Transmitted pulse z s 1 F(Q,t) Delayed pulse (probe) d d d t (t) 0 Diffracted pulse (signal) E2 z t0 = 0 Detector Density wave periodicity: =0/2sin s 0 Q= 4sins/0 d = asin (s0/1) time

Transient grating spectroscopy & FEL source Excitation pulses (pump) FEL source: 0 Sample Delayed pulse (probe) Tra s tted nsmi Diffra ct 1 0 pulse ed pu lse (s ignal ) Q = 4sins/0 [email protected] 0 ~ 120 10 nm N ~ 1014 ph/pulse t ~ 50 200 fs Gaussian profiles 2S ~ 9 Q-range: 2S ~ 140 Q = 0.01 1.2 nm-1 t-range: ~t 3-meters long delay line t = 0.2 104 ps Inelastic scattering in the time domain Space: 3 10 2 ILS 0 Raman scattering

10 10 10 10 10 10 -1 (nm) 1 10 0 10 -1 IXS j 50 10 0 0m /s /s TIMER m 00 TG 5 INS -2 10 -13 10 -12 10 -11 10 -10 10 -9 10 -8 -3

Brillouin scattering -4 10 -3 10 -2 10 -1 Q = 2 / 0 1 10 10 -1 (nm ) 10 2 Transient Grating Spectroscopy Time: (s) 1 2 IUVS E = h / (meV) 10 10 t > 100 fs Q < 1.2 nm-1 + F.E.L. source = TIMER Ready by the end of 2010 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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