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Inelastic Ultraviolet Scattering with μeV energy resolution: applications for the study of disordered systems Filippo Bencivenga
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OUTLINE Collective dynamics in disordered systems Inelastic Ultraviolet Scattering (IUVS) at ELETTRA Experimental highlights (1) Sound absorption in vitreous SiO 2 Experimental highlights (2) Structural relaxation in water under pressure Outlook
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Collective dynamics in disordered systems t D 0.1 ps Characteristic lengths j 10 nm 0.1 nm Characteristic times j 0.1 ÷ ∞ ps ~ Lattice space in crystals ~ Inverse Debye frequency Topological Disorder Relaxation times , j j,t D
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Brillouin scattering ILS Collective dynamics in disordered systems Density Fluctuations Spectrum: S(Q,E) Raman scattering INS t D 0.1 ps Characteristic times j 0.1 ÷ ∞ ps jj Characteristic lengths j 10 nm 0.1 nm tDtD jj 500 m/s 5000 m/s IXS IUVS Q 0.1 ÷ 1 nm -1 jj
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8 m E o -E i ≈ ± 1000 eV 3 m CCD camera (512x2048 pixels; 13.5x13.5 m 2 ) Sample IUVS beamline: BL10.2 @ ELETTRA Sync. Figure-8 undulator E i = 4 ÷ 12 eV E i < 15 eV Heat Load + Focusing Band pass filters E i ≈ 3 eV VERTICAL E i /E i ≈ 10 -6 Focusing mirror Collection mirror 3 m (Eo)(Eo) Diffraction grating + slit d = 32 m = 70° m ≈ 200 H ≈ 50 m 10 15 ph/s/0.1%BW L (E o -E i )/E i Main features of IUVS beamline: a) Beam @ sample: E i = 4 ÷ 12 eV 10 10 ÷ 10 13 ph/s 1x0.5 mm 2 spot b) E ≈ 7÷20 eV c) E o -E i ≈ ± 1000 eV d) S(Q,E) in one shot e) “Easy” Q-change = 172° Q = 2E i n(E i )sin( )/hc Q ≈ 0.05 ÷ 0.15 nm -1 E o /E o ≈ 10 -6
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T-independent sound absorption: structural origin PRL 83, 5583 (1999) IXS 1400 K 1100 K 300 K ILS 5 K 300 K Anharmonicity: acoustic phonons coupled with thermal vibrations PRL 82, 1478 (1999) Experimental highlights (1) Sound absorption in vitreous SiO 2 e - ·x ? L = hc s /2
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Experimental highlights (1) Sound absorption in vitreous SiO 2 Characteristic length: ~ 2 /Q * ~ 50 nm E L ~ 0.5 meV ~ E BP ? Characteristic frequency: E L (Q * ) ~ 0.5 meV Anharmonic contribution Q4Q4 Q2Q2 Structural contribution Q*Q* or ~ disorder of the elastic constants ? ILS IXS IUVS Q2Q2 300 K Q * E L (Q * ) LL LL PRL 92 (2004); PRL 97 (2006) 1) PRL 98 (2007) Elastic constants disorder 1
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Experimental highlights (1) Sound absorption in vitreous SiO 2 T (Q * ) same trend as L (Q * ) ? E T (Q * ) ~ 0.5 E L (Q * ) < E BP ~ elastic constant’s disorder YesNo Anomaly probably related to E BP 2Q * ? E T (2Q * ) ~ E BP ? IXS + 0.1 meV TT Q * ~ 2 / ?
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TMTM TgTg Critical-like behavior? LDA HDA Temperature (K) Pressure (bar) 2000 bar 1500 bar 400 bar 1 bar Experimental highlights (2) Water anomalies Quantitative agreement with Mode Coupling Theory IUVS + IXS results: pressure (i.e. density) independence of Water anomalies described by a singuratity free scenario 1 - Mode Coupling Thory (MCT) - Experimental determination of structural relaxation time ( ) IUVS spectra + Viscoelastic framework Mode Coupling Theory: ~ (T-T 0 ) 220 +/- 10 K 2.3 +/- 0.2 1) PRE 53 (1996); PRL 49 (1982) cscs TT SS
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THTH 1) Nature 360 (1992); Nature 396 (1998) Temperature (K) Pressure (bar) cscs TT SS TMTM TgTg THTH Experimental highlights (2) Water anomalies Critical-like behavior? LDA HDA HDL LDL CP 2 TMTM IXS IUVS CP 2 Critical-like behavior? Systematic determination of as a function of P and T Liquid-liquid phase transition hypothesis 1 DHO (E)(E) T = 298 K; Q = 0.07 nm -1
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Expected trend Structural relaxation in water under pressure 1 bar4 kbar ~ exp{( cp - ) -1 } Arhenius trend ( -dependent) = ( ) exp{E( )/k B T} E( ) = E( 0 ) + ( - 0 ) = ∂E/∂ > 0 Stiffer local structure @ high density Free volume reduction at high density Experimental highlights (2)
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Further -dependence = ( ) exp{E( )/k B T} ~ exp{- }exp{E( )/k B T} = 0 exp{[E( 0 )+ ( -k B T)( - 0 /k B T} ∂S/∂ Structural relaxation in water under pressure Experimental highlights (2)
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Further -dependence = ( ) exp{E( )/k B T} ~ exp{- }exp{E( )/k B T} = 0 exp{[E( 0 )+ ( -k B T)( - 0 /k B T} Qualitative agreement with liquid-liquid phase transition hypothesis Quantitative agreement with liquid-liquid phase transition hypothesis ∂S/∂ k B = ∂S/∂ > 0 ∂E/∂ ∂A/∂ More entropic local structure @ high density (∂S/∂ )( HDA - LDA ) = 51 ± 3 J/mol k ∂A/∂ = 0 T = 209 ± 12 K Structural relaxation in water under pressure Experimental highlights (2)
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∂A/∂T ? Further -dependence = ( ) exp{E( )/k B T} ~ exp{- }exp{E( )/k B T} = 0 exp{[E( 0 )+ ( -k B T)( - 0 /k B T} ∂A/∂ Larger T-range Q ~ 0.07 nm -1 Q ~ 0.1 nm -1 Q ~ 0.025 nm -1 IXS + 0.1 meV P = 1 bar Structural relaxation in water under pressure Experimental highlights (2) cscs (∂S/∂ )( HDA - LDA ) = 51 ± 3 J/mol k ∂A/∂ = 0 T = 209 ± 12 K
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Outlook Density Fluctuations Spectrum: S(Q,E) Brillouin scattering ILS Raman scattering t D 0.1 ps Characteristic times 0.1 ÷ ∞ ps Characteristic lengths 10 nm 0.1 nm IUVS INS IXS 500 m/s 5000 m/s ? jj Q 0.1 ÷ 1 nm -1
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F(Q,t) (a.u.) t (ps) F(Q,t) (a.u.) t (ps) F(Q,t) S(Q,E) S(Q,E) (a.u.) E (meV) -1 = 5 ± 3 ps H 2 O -10 °C / 1 bar Q = 2nm -1 S(Q,E) (a.u.) E (meV) Sound speed ~ 500 m/s N 2 T ~ T C Q = 2nm -1 Outlook
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Transient grating spectroscopy s Sample Transmitted pulse Diffracted pulse (signal) z 0 E2E2 Standing e.m. wave (Transient Grating) t 0 = 0 Q = 4 sin s / 0 Detector F(Q,t) t time ( t) Excitation pulses (pump) 0 0 Delayed pulse (probe) 1 dd Density wave periodicity: = 0 /2sin s d = asin ( s 0 / 1 ) dd dd z
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t = 0.2 ÷ 10 4 ps Transient grating spectroscopy & FEL source FERMI@ELETTRA Q-range: t ~ 50 ÷ 200 fs N ~ 10 14 ph/pulse 0 ~ 120 ÷ 10 nm Gaussian profiles Q = 0.01 ÷ 1.2 nm -1 t-range: FEL source: ~t~t 3-meters long delay line Delayed pulse (probe) Excitation pulses (pump) s Sample Transmitted pulse Diffracted pulse (signal) 0 0 1 Q = 4 sin s / 0 2 S ~ 140°2 S ~ 9°
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TG “Inelastic scattering” in the time domain INS Brillouin scattering IXS ILS 500 m/s 5000 m/s Raman scattering Transient Grating Spectroscopy F.E.L. source t > 100 fsQ < 1.2 nm -1 + IUVS TIMER jj = TIMER Ready by the end of 2010
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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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