inelastic ultraviolet scattering with μev energy resolution: applications for the study of...
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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)
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