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) Sound absorption in vitreous SiO 2 Experimental highlights (2) Structural relaxation in water under pressure Outlook

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

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 jj Characteristic lengths  j  10 nm   0.1 nm tDtD  jj 500 m/s 5000 m/s IXS IUVS Q  0.1 ÷ 1 nm -1 jj

8 m E o -E i ≈ ± 1000  eV 3 m CCD camera (512x2048 pixels; 13.5x13.5  m 2 ) Sample IUVS beamline: 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 ≈ Focusing mirror Collection mirror 3 m (Eo)(Eo) Diffraction grating + slit d = 32  m  = 70° m ≈ 200 H ≈ 50  m ph/s/0.1%BW L  (E o -E i )/E i Main features of IUVS beamline: a) sample:  E i = 4 ÷ 12 eV  ÷ 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

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 

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 * ) LL LL PRL 92 (2004); PRL 97 (2006) 1) PRL 98 (2007) Elastic constants disorder 1

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 meV TT Q * ~ 2  /  ?

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 +/ ) PRE 53 (1996); PRL 49 (1982) cscs TT SS 

THTH 1) Nature 360 (1992); Nature 396 (1998) Temperature (K) Pressure (bar) cscs TT SS  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

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 high density Free volume reduction at high density Experimental highlights (2)

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)

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 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)

∂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 ~ nm -1 IXS 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

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 ? jj Q  0.1 ÷ 1 nm -1

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

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 dd Density wave periodicity:  = 0 /2sin  s  d = asin (  s 0 / 1 ) dd dd z

t = 0.2 ÷ 10 4 ps Transient grating spectroscopy & FEL source Q-range:  t ~ 50 ÷ 200 fs N ~ 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) Q = 4  sin  s / 0 2  S ~ 140°2  S ~ 9°

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 jj = 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)