situation only arises when the wavelenght becomes comparable with the
interatomic spacing… T.E. Faber, 1972. Is there an intermediate regime bridging
the ...
Do we really need 0.1 meV ? Tullio Scopigno University of Rome “La Sapienza”– I
Towards 0.1 meV energy resolution
•Position: viscoelastic transitions in liquids, dispersion curves in xals •Linewidth: dynamical heterogeneities in glasses, phonon lifetimes •Lineshape: other that LA modes, non hydrodynamic behaviours
A few open issues for the physics of disordered systems
1-Hydrodynamics Light scattering Ultasounds
10 10 5 0 10 5 0
110 nm
-1
102 nm
-1
94 nm
5 0 10 5 0
-1
86 nm-1 78 nm
-1
3.5
15 10 5 0
70 nm
-1
64 nm
-1
3.0
15 10 5 0
60 nm
-1
20
56 nm
-1
10 5 0 10 0 15 10 5 0
10
2.5
30 20 10 0
0
2-isothermal?
S(Q)
2.0
5-Free particle
1.5
IXS INS
1.0 0.5
ISTS IUVS IXS
0.0 0
20
40
60
80
-1
Q (nm ) 3-High Frequency IXS INS
Tullio Scopigno, Giancarlo Ruocco, Francesco Sette, REVIEWS OF MODERN PHYSICS, 77, 881 (2005)
4-Kinetic IXS INS
Where does positive dispersion come from?
The positive dispersion of sound
Outside hydrodynamics: the sound velocity
v
Example: Liquid-like to solid-like transition
c∞
But not only!!! Disorder-induced relaxations
adiabatic
US
No men’ men’s land
1
Often occurs around ~2 nm-1 → ω~1.3 meV @ 1000 m/s
IXS / INS
Q (nm-1)
Where does the positive dispersion come from?
Ubiquity of positive dispersion in LIQUIDS
Where does the positive dispersion come from?
Ubiquity of positive dispersion in GLASSES Hard spheres (MCT)
v-SiO2 IXS Ruzicka et al, PRE 2002
W Goetze et al, PRE 2000 v-SiO2 MD W. Kob et al, c.m. 1999
adiabatic
2
Lennard Jones NMA Ruocco et al, PRL 2000
c (km/s)
Alkali (MD) TS et al, PRE 2002
1
Glassy selenium IXS TS et al, PRL 2003 0
0
5
-1
Q (nm )
10
Other than LA modes…
Other than LA modes
Dispersion in liquids: viscoelasticity and transverse modes
C.Petrillo et al., PRE 62, 3611 (2000) F.Sacchetti et al., PRE 69, 061203 (2004)
G.Ruocco et al. J. Phys.: Condens. Matter 11, R259 (1999) G.Monaco et al. PRE 60, 5505 (1999)
Other than LA modes
Quasi-transverse modes in glasses
B. Ruzicka et al., Phys.Rev.B, 69 100201 (2004)
Going extreme: towards a new “dynamical” classification of fluids?
Is there an intermediate regime bridging the adiabatic and the high frequency domain?
Is there an intermediate regime bridging the adiabatic and the high high frequency domain? domain? •Only possible in liquid metals
Isothermal regime?
ωτ th < 1
… Of course, if DQ2 becomes comparable with Ω, the central peak overlaps with the two side ones… ones… But even in a typical liquid metal, where D is relatively high, this situation only arises when the wavelenght becomes comparable with the interatomic spacing… spacing…
ωτ th ≈
cT Q * Q < 1 ⇒ > cT DT 2 DT Q
T.E. Faber, 1972 > 200 nm-1 ordinary liquids > 0.1 nm-1 liquid metals
Is there an intermediate regime bridging the adiabatic and the high high frequency domain? domain?
Li
Thermal
Na Viscous
“..But as far as the calculation of dynamical structure factor, $S(q,\omega)$ is concerned, it is well known that only the ionic thermal conductivity enters into the calculation.”
Al
Is there an intermediate regime bridging the adiabatic and the high high frequency domain? domain?
Speculation: the sound velocity…
v c∞ adiabatic
US
No men’ men’s land
1
IXS / INS
Q (nm-1)
Is there an intermediate regime bridging the adiabatic and the high high frequency domain? domain?
cs
ct
Acoustic damping in glasses
Acoustic damping in Glasses Propagation and damping @> 1nm-1 is not the extrapolation of hydrodynamics 10
Γ (meV)
1
BLS (T=300K) [22] BLS (300K) [3] IUVS (T=300K) This work IXS (T=1050K) [21]
0.1
T-independent
0.01
T-dependent
Change in acoustic damping @ 0.01meV < E < 1meV 0.1nm-1< Q < 1nm-1 C.Masciovecchio et al. 92 247401 (2004)
SiO2
1E-3 0.1
-1
1
Q (nm )
d-SiO2 and Li2O-2B2O3: crossover to Q4 regime @ 1nm-1 B. Rufflè et al., PRL 96, 045502 (2006); Comment: G.Ruocco et al., PRL 98, 079601 (2007); Reply:B. Rufflè et al., PRL 98, 079602 (2007)
SiO2: crossover to Q4 (E4) regime @ 0.1nm-1 (0.01meV) C.Masciovecchio et al., PRL 97, 035501 (2006)
24 October 2007 @ ESRF 2008-2017 Upgrade Meeting HRRS CDR’s discussion The scientific case for 0.1 meV
The “Dynamical Matrix” GAS/FLUIDS
LIQUIDS
GLASSES
XALS
Short wavelength limit of acoustic excitations Phonon spectrum Hydrodynamic ÅÆ viscoelastic merging Coarse graining vs elasticity: microscopic relaxation Extreme conditions
Extreme conditions
CM and electron density
ESRF UP •INELX •PHIXS •NR-HE •NR-NSM
Other than LA modes (transverse, optic) Low dimentional systems: nanostuctures, surfaces and interfaces V-DOS and collective properties: the Boson Peak Vibrations vs Relaxations