# Presentation: 024278

## 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 SiO2

Experimental highlights (2)

Structural relaxation in water under pressure

Outlook

- 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

**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**

## Collective dynamics in disordered systems

**Brillouin**
**scattering**

**ILS**

***Density Fluctuations Spectrum: S(Q,E)***

**Raman**
**scattering**

**t****D**  0.1 ps

- Characteristic times

- j  0.1 ÷ ∞ ps

******j**

- Characteristic lengths

- j  10 nm

-   0.1 nm

******j**

** ****500 m/s**

**  ****5000 m/s**

**IUVS**

- Q  0.1 ÷ 1 nm-1

******j**

## IUVS beamline: BL10.2 @ ELETTRA

- Eo-Ei ≈ ± 1000 eV

- Ei/Ei ≈ 10-6

_**Focusing**_
_**mirror **_

_**Main features of IUVS beamline:**_
- a) Beam @ sample:
-  Ei = 4 ÷ 12 eV
- 1010 ÷ 1013 ph/s
-  1x0.5 mm2  spot
**b) ********E ≈ 7÷20 ********eV**
**c) ****E****o****-E****i**** ≈ ± 1000 ********eV**
**d) ****S(Q,E) in one shot**
**e) ****“Easy” Q-change**

- Q = 2Ein(Ei)sin()/hc
- Q ≈ 0.05 ÷ 0.15 nm-1

- Eo/Eo ≈ 10-6

## Experimental highlights (1)

***Sound absorption in vitreous SiO******2***

- e-·x

- L = hcs/2

## Experimental highlights (1)

***Sound absorption in vitreous SiO******2***

**Characteristic length: ************~ 2********/Q********* ~ 50 nm**

- EL ~ 0.5 meV ~ EBP?

**Characteristic frequency: **
**E****L****(Q*********) ~ 0.5 meV**

**Q****4**

**Q****2**

**Structural contribution**

**or**

-  ~ disorder of the
-   elastic constants ?

**ILS**

**IXS**

_**IUVS**_

**Q****2**

**300 K**

******L**

******L**

*1) PRL ****98**** (2007)*

- Elastic constants disorder1

## Experimental highlights (1)

***Sound absorption in vitreous SiO******2***

- T (Q*) same trend as L (Q*) ?

- ET (Q*) ~ 0.5 EL (Q*) < EBP

**2Q*********?**

- ET (2Q*) ~ EBP

******T**

## Experimental highlights (2)

***Water anomalies***

- IUVS + IXS results:
- pressure (i.e. density) independence of 

- IUVS spectra

- +

- Viscoelastic framework

**1) ***PRE ****53**** (1996); PRL ****49**** (1982)*

## Experimental highlights (2)

**T****H**

**1) ***Nature 3****60**** (1992); Nature ****396**** (1998)*

**Temperature (K)**

**Pressure (bar)**

**T****M**

**T****g**

**T****H**

***Water anomalies***

_**Critical-like**_
_**behavior?**_

**LDA**

**HDA**

_**HDL**_

_**LDL**_

**T****M**

_**Critical-like**_
_**behavior?**_

**DHO**

****(E)

- T = 298 K; Q = 0.07 nm-1

## Experimental highlights (2)

***Structural relaxation in water under pressure***

-  ~ exp{(cp-)-1}

- Arhenius trend (_****__**-dependent**_)

- = () exp{**E**()/kBT}

**E**() = **E**(0) + ****(-0)

**** = ∂**E**/∂> 0

- Stiffer local structure @ high density

- Free volume reduction at high density

## Experimental highlights (2)

- Further _****__**-dependence**_

- = () exp{**E**()/kBT}

- ~ exp{-****}exp{**E**()/kBT}

- = 0exp{[**E**(0)+
- (-kB****T)(-0/kBT}

***Structural relaxation in water under pressure***

## Experimental highlights (2)

- = () exp{**E**()/kBT}

- ~ exp{-****}exp{**E**()/kBT}

- = 0exp{[**E**(0)+
- (-kB****T)(-0/kBT}

- Qualitative agreement with liquid-liquid phase transition hypothesis

- _Quantitative_ agreement with liquid-liquid phase transition hypothesis

- kB**** = ∂**S**/∂ > 0

- 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)

- Further _****__**-dependence**_

- = () exp{**E**()/kBT}

- ~ exp{-****}exp{**E**()/kBT}

- = 0exp{[**E**(0)+
- (-kB****T)(-0/kBT}

- _Larger T-range_

- P = 1 bar

***Structural relaxation in water under pressure***

**c****s**

- (∂**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

**INS**

**IXS**

** ****500 m/s**

**  ****5000 m/s**

******j**

- Q  0.1 ÷ 1 nm-1

## Outlook

**F(Q,t)**

**S(Q,E)**

_****__** **__**= 5 ± 3 ps**_

**H****2****O**
- -10 °C / 1 bar
- Q = 2nm-1

_**Sound speed **_
_**~ 500 m/s**_

**N****2**
- T ~ TC
- Q = 2nm-1

## Transient grating spectroscopy

- t0 = 0

- time** **

**(********t) **

**z**

## Transient grating spectroscopy & FEL source

- FERMI@ELETTRA

_**FEL source:**_

## TIMER

- “Inelastic scattering” in the time domain

**INS**

**Brillouin**
**scattering**

**IXS**

**ILS**

** ****500 m/s**

**  ****5000 m/s**

**Raman**
**scattering**

**Transient Grating Spectroscopy**

**IUVS**

******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)