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

tD 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

,jj,tD

Brillouinscattering

ILS

Collective dynamics in disordered systems

Density Fluctuations Spectrum: S(Q,E)

Ramanscattering

INS

tD 0.1 ps

Characteristic times

j 0.1 ÷ ∞ ps

j

Characteristic lengths

j 10 nm

0.1 nm

tD

j

500 m/s

5000 m

/s

IXS

IUV

S

Q 0.1 ÷ 1 nm-1

j

103 102 101 100 10-1

10-8

10-9

10-10

10-11

10-12

10-13

10-3 10-2 10-1 100 101 10210-4

10-3

10-2

10-1

100

101

102

Tim

e: (s

)

Space: (nm)

E =

h /

(me

V)

Q = 2 / (nm-1)

8 m

Eo-Ei ≈ ± 1000 eV3 m

CCD camera (512x2048 pixels; 13.5x13.5 m2)

Sample

IUVS beamline: BL10.2 @ ELETTRA

Sync.

Figure-8 undulator

Ei= 4 ÷ 12 eV

Ei< 15 eV

Heat Load + Focusing

Band pass filters

Ei ≈ 3 eV

VE

RT

ICA

L

Ei/Ei ≈ 10-6

Focusingmirror

Collectionmirror

3 m

(Eo)

Diffractiongrating + slit

d = 32 m = 70°m ≈ 200

H ≈ 50 m

1015 ph/s/0.1%BW

L (Eo-Ei)/Ei

Main features of IUVS beamline:

a) Beam @ sample: Ei = 4 ÷ 12 eV1010 ÷ 1013 ph/s 1x0.5 mm2 spot

b) E ≈ 7÷20 eV

c) Eo-Ei ≈ ± 1000 eV

d) S(Q,E) in one shot

e) “Easy” Q-change

= 172°

Q = 2Ein(Ei)sin()/hc

Q ≈ 0.05 ÷ 0.15 nm-1

Eo/Eo ≈ 10-6

T-independent sound absorption: structural origin PRL 83, 5583 (1999)

IXS

1400 K

1100 K300 K

ILS

5 K

300 K

Anharmonicity: acoustic phonons coupled with thermal vibrations PRL 82, 1478 (1999)

Experimental highlights (1)Sound absorption in vitreous SiO2

e-·x

?L = hcs/2

E

S (

Q,E

)

0.01 0.1 1

1E-4

1E-3

0.01

0.1

1

10

L (m

eV

)

Q (nm-1)

250 350 450 550

Q = 0.13 nm -1

Q = 0.1 nm -1

Inte

nsity (

Arb

. U

nits)

E (eV)

Experimental highlights (1)Sound absorption in vitreous SiO2

Characteristic length: ~ 2/Q* ~ 50 nm

EL ~ 0.5 meV ~ EBP?

Characteristic frequency: EL(Q*) ~ 0.5 meV

0.1 1

1E-3

0.01

0.1

1

10

L (m

eV

)

Q (nm-1)

Anharmonic contribution

Q4

Q2Structural contribution

Q*

or

~ disorder of the elastic constants ?

ILS

IXS

IUVS

Q2

300 K

Q* EL(Q*)

L

L

PRL 92 (2004); PRL 97 (2006) 1) PRL 98 (2007)

Elastic constants disorder1

0.1 1

1E-3

0.01

0.1

1

L (m

eV

)

Q (nm-1)

Experimental highlights (1)Sound absorption in vitreous SiO2

T (Q*) same trend as L (Q*) ?

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

~ elastic constant’s disorder

Yes No

Anomaly probably related to EBP

2Q*?ET (2Q*) ~ EBP

?IXS + 0.1 meV

T Q*~ 2/?

100 200 300 400100

101

102

103

104

TMTg

Critical-likebehavior?

LDA

HDA

Temperature (K)

Pre

ssu

re (

ba

r)

250 300 350 4000

4

8

12

16

(ps

)

IXS - PRE (1999)

IXS - PRE (2007)

IUVS - PRL (2004)

MCT trend

T (K)

2000 bar1500 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 scenario1

- Mode Coupling Thory (MCT) -

Experimental determination of

structural relaxation time ()

IUVS spectra

+Viscoelastic framework

Mode Coupling Theory: ~ (T-T0)

220 +/- 10 K 2.3 +/- 0.2

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

csTS

180 230 280 330 380100

101

102

103

104

180 230 280 330 380100

101

102

103

104

100 200 300 400100

101

102

103

104

100 200 300 400100

101

102

103

104

TH

1) Nature 360 (1992); Nature 396 (1998)

-200 -100 0 100 2000

30

60

900

50

100

1500

80

160

240

Co

un

ts /

30

0 s

E (eV)

500 bar

1500 bar

3000 bar

Temperature (K)

Pre

ssu

re (

ba

r)

csTS

TMTg TH

Experimental highlights (2)Water anomalies

Critical-likebehavior?

LDA

HDA HDL

LDL

CP2

TM

IXS

IUVS

CP2 Critical-likebehavior?

Systematicdetermination of as a function of

P and T

Liquid-liquid phase transition hypothesis1

DHO

(E)

250 300 350 4000

4

8

12

16

(ps

)

IXS - PRE (1999)

IXS - PRE (2007)

IUVS - PRL (2004)

MCT trend

T (K)

T = 298 K; Q = 0.07 nm-1

1010 1050 1090 1130

0.0

1.8

3.6

5.4 323 K 288 K 273 K

(ps

)

(kg/m3)

1000 1040 1080 1120

22

28

34

(kg/m3)

Ea (

kJ/m

ol)

3.2 3.4 3.6 3.8 4.0

0.1

1

10

1000 / T (K-1)

(ps

)

1015 +/- 5 kg/m3

1065 +/- 5 kg/m3

1105 +/- 5 kg/m3

Expected trend

Structural relaxation in water under pressure

1 bar 4 kbar

~ 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)

1000 1040 1080 11201E-7

1E-6

1E-5

1E-4

323 K 288 K 273 K

/ e

xp(E

()/

k BT

)

(kg/m3)

Further -dependence

= () exp{E()/kBT}

~ exp{-}exp{E()/kBT}

= 0exp{[E(0)+

(-kBT)(-0/kBT}

∂S/∂

Structural relaxation in water under pressure

Experimental highlights (2)

Further -dependence

= () exp{E()/kBT}

~ exp{-}exp{E()/kBT}

= 0exp{[E(0)+

(-kBT)(-0/kBT}

Qualitative agreement with liquid-liquid phase transition hypothesis

Quantitative agreement with liquid-liquid phase transition hypothesis

∂S/∂

kB = ∂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)

∂A/∂T ?

Further -dependence

= () exp{E()/kBT}

~ exp{-}exp{E()/kBT}

= 0exp{[E(0)+

(-kBT)(-0/kBT}

∂A/∂

Larger T-range

250 280 310 340

1.3

1.4

1.5

1.6

c L =

L/Q

(103 m

/s)

T (K)

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)

cs

(∂S/∂)(HDA-LDA) = 51 ± 3 J/mol k

∂A/∂ = 0 T = 209 ± 12 K

Outlook

Density Fluctuations Spectrum: S(Q,E)

Brillouinscattering

ILSRaman

scattering

tD 0.1 ps

Characteristic times

0.1 ÷ ∞ ps

Characteristic lengths

10 nm

0.1 nm

IUV

S

INS

IXS

500 m/s

5000 m

/s?j

Q 0.1 ÷ 1 nm-1

103 102 101 100 10-1

10-8

10-9

10-10

10-11

10-12

10-13

10-3 10-2 10-1 100 101 10210-4

10-3

10-2

10-1

100

101

102

Tim

e: (s

)

Space: (nm)

E =

h /

(me

V)

Q = 2 / (nm-1)

1 10 100-0.8

0.0

0.8

1.6

F(Q

,t)

(a.u

.)

t (ps)

0 100 200 300-0.4

0.0

0.4

0.8

F(Q

,t)

(a.u

.)

t (ps)

F(Q,t)S(Q,E)

-10 -5 0 5 100

800

1600

2400

S(Q

,E)

(a.u

.)

E (meV)

-1

= 5 ± 3 psH2O-10 °C / 1 bar

Q = 2nm-1

-24 -12 0 12 2410

100

1000

10000

S(Q

,E)

(a.u

.)

E (meV)

Sound speed ~ 500 m/s

N2

T ~ TC

Q = 2nm-1

Outlook

Transient grating spectroscopy

s

SampleTransmitted pulse

Diffracted pulse (signal)

z

0

E2

Standing e.m. wave (Transient Grating)

t0 = 0

Q =

4sins/0

Detector

F(Q

,t)

t

time

(t)

Excitation pulses (pump)

0

0

Delayed pulse (probe)

1 d

Density wave periodicity: =0/2sin s

d = asin (s0/1)

d

d

z

t = 0.2 ÷ 104 ps

Transient grating spectroscopy & FEL source

FERMI@ELETTRA

Q-range:

t ~ 50 ÷ 200 fs

N ~ 1014 ph/pulse

0 ~ 120 ÷ 10 nm

Gaussian profiles

Q = 0.01 ÷ 1.2 nm-1

t-range:

FEL source:

~t 3-meters long delay line

Delayed pulse (probe)

Excitation pulses (pump)

s

Sample

Transmitted pulse

Diffracted pulse (signal)

0

0

1

Q = 4sins/0

2S ~ 140° 2S ~ 9°

103 102 101 100 10-1

10-8

10-9

10-10

10-11

10-12

10-13

10-3 10-2 10-1 100 101 10210-4

10-3

10-2

10-1

100

101

102

Tim

e: (s

)

Space: (nm)

E =

h /

(me

V)

Q = 2 / (nm-1)

TG

“Inelastic scattering” in the time domain

INS

Brillouinscattering

IXSILS

500 m/s

5000 m

/sRamanscattering

Transient Grating Spectroscopy

F.E.L. source

t > 100 fs Q < 1.2 nm-1

+IUV

STIMERTIMER

j

=

TIMERTIMERReady 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)