Giulio Monaco Università di Trento (I) outline ...€¦ · - soft X-ray absorption spectroscopy...

High -resolution inelastic x-ray scattering

Giulio MonacoUniversità di Trento (I)

Slide: 1

Università di Trento (I)

outline :

• Introduction and theoretical foundation• Instrumentation• Selected results

University of Trento

Scattering kinematicsdΩ

2θii Ek ,r

1. Introduction and theoretical foundation

Slide: 2

• Energy transfer: Ei − Ef = E

• Momentum transfer: Qkk fi

rrr=−

Qr

E,

photon

G. Monaco – High-resolution inelastic x-ray scattering – Grado, 27/09/2013University of Trento

IXS: applications - I

Electron dynamics ε(q,ω)- plasmons- many-body phenomena- soft X-ray absorptionspectroscopy

S(Q,ω)


Slide: 3

-30 -20 -10 0 10 20 300

200

400

600

800

coun

ts in

80

secs

energy transfer [meV]

Phonons

spectroscopy

Lattice dynamics- elasticity- thermodynamics- phase stability- e--ph coupling

University of Trento G. Monaco – High-resolution inelastic x-ray scattering – Grado, 27/09/2013

Impulse distribution of electrons- chemical bonding- local structures

Compton scatteringIXS: applications - II


Slide: 4

Electronic structure- element selective- valence selective- spin selective

Resonant X-ray emission


Schematic IXS spectrum


Slide: 5

• Energy transfer: Ei − Ef = ∆E = 1 meV – 1 keV

• Momentum transfer: = 1 – 180 nm-1 Qkk fi

rrr=−


Hamiltonian for the photon -electron interaction - I

+×∇⋅−+

−= ∑ ∑∑ )(2

)()(2

1

''

2

jjj j

jjjj

jj mc

erV

c

e

mH rAσrAp

h

∑∑ ++ −×⋅− + λλω 1eeh

The use of the following Hamiltonian within a perturbation scheme to second

order in (v/c) leads to the same results of a rigorous quantum field calculation:


Slide: 6

∑∑

++

−×⋅− +

λλ λλω

KK KKrAprEσ

2

1)()()()(

2cc

c

e

mc

ejjj

jj h

h

The vector potential operator can be expressed as:

[ ]∑ +⋅−+∗−⋅ +=λ

ωω λλλλω

πK

rKrK

K

KK KKKKrA tiitii eceeceV

c)()()()(

2)(

2h

with:•

−−∇= AEc

1φ AB ×∇=


Hamiltonian for the photon -electron interaction - II

∑=j

ji mc

eH )(

22

2

2

1 rA jj

ji mc

eH prA ⋅−= ∑ )(2

Interaction between the radiation field and the electrons:

[ ])(3 jji

eH rAσ ×∇⋅−= ∑

h

×⋅−=•

∑ )()(42

2

4 jjji

eH rArAσ

h


Slide: 7

Unperturbed Hamiltonian:

∑

+= +

λλ λλω

KK KK

2

1)()( ccH R h

[ ])(23 j

jji mc

H rAσ ×∇⋅−= ∑ ×⋅−= ∑ )()(

4 424 jjj

ji cmH rArAσ

( )jjj j

jjjj

j cm

erV

mH pσp ×∇⋅++= ∑ ∑∑ φ

'22'

20 4

)(2

1 h


The Kramers-Heisenberg formulaAccording to Fermi’s golden rule the transition probability per unit time is given

to second order by:

)()(

22

23232

41 FIN NI

iiiiii EE

EE

IHHNNHHFIHHFw −

−++

++= ∑ δπh


Slide: 8

Double differential scattering cross-section for the transition |i> →|f>:

( ) )(

2

211

2

2

222

2

ωδωω

ωσ

hh

+−+⋅

=

∂Ω∂∂

∑ ∗⋅

→fi

j

i

fi

EEAiefmc

e j eerq

Out of resonance, the A-term is ħω(mc2)-1 smaller than the Thomson one.

Usual definitions:21 ωωω −=

21 KKq −=


Thomson scattering - I

with the classical electron radius:

)('

'

2

211

220

22

2

ωδωω

ωσ

hh

+−⋅

=

∂Ω∂∂

∑∑∑∑⋅⋅−∗

fij

i

j

i

jji

fi

EEieffeigr jj rqrqee

Amc

er 5

2

2

0 103 −⋅≈=


Slide: 9

)(),( '

'

ωδω h+−= ∑∑∑∑⋅⋅−

fij

i

j

i

jji

fi

EEieffeigqS jj rqrq

and the dynamic structure factor:

Following van Hove, we can use another picture. We introduce the electron

density operator:

∑ −=j

j )()( rrr δρ ∑⋅−=

j

i jerqq)(ρor


Thomson scattering - II

∫+∞

∞−

+−= ),()0,(2

1),( tedtqS

ti qq ρρπ

ω ω

h

∫ ∑+∞

∞−

⋅⋅−−=ji

tiiti ji eeedt )()0(

2

1 rqrqω

πh


Slide: 10

van Hove space-time correlation function:

∞−

∑∫ −+−='

'3 ))('())0('('),(

jjjj trdtG rrrrrr δδ

∫= ),,'(' 23 tnrd rr

[ ]∫⋅−−+= rqrq iegrdS 1)(1)( 3ρStatic correlations:


The dynamic structure factor

∑=j

jQTEFjQGEQS ),,,(),(),(rrr

[ ]))(())((11

),,,( qEEqEEjQTEFrr

r

r+−−⋅= δδ

Scattering function:

with:


Slide: 11

[ ]))(())(()(exp1

),,,( qEEqEEqE

kT

EjQTEF jj

j

r +−−⋅

−−= δδ

and:

2

2/1)( ))(ˆ()(),( ∑ −⋅+− ⋅=d

dj

drQiQW

d MqQeQfjQG dd rrrr rrr

σ


Single crystal: selection rules - I


Slide: 12

well-defined momentum transfer for given scattering geometry


Diamond

Single crystal: selection rules – II

E, Q

k in

kout


Slide: 13

Pavone et al., PRB 48, 3156 (1993)

Diamond



Slide: 14

0 500 1000 1500 2000 2500 3000

100

1000

10000

100000

Inte

nsity

[arb

. uni

ts]

wave numbers [cm-1]

Raman scatteringBrillouin light scattering


Information derived from IXS data


Slide: 15

• Sound velocities• Elasticity• Interatomic force constants (potential)

• Dynamical instabilities (phonon softening)

• Anharmonicity• Phonon-electron coupling

• Thermodynamics (CV, SV, θD, …)


X-rays and phonon studies?

Two citations from standard text books

“When a crystal is irradiated with X-rays, the processes of photoelectric absorption and fluorescence are no doubt accompanied by absorption and emission of phonons. The energy changes involved are however so large compared with phonon energies that information about the phonon spectrum of the crystal cannot be obtained in this way.”


Slide: 16

W. Cochran in Dynamics of atoms in crystals, (1973)

“…In general the resolution of such minute photon frequency is so difficult that one can only measure the total scattered radiation of all frequencies, … As a result of these considerations x-ray scattering is a far less powerful probe of the phonon spectrum than neutron scattering. ”

Ashcroft and Mermin in Solid State Physics, (1975)


Infrared absorption - 1881W. Abney and E. Festing, R. Phil. Trans. Roy. Soc. 172, 887 (1881)

Brillouin light scattering - 1922L. Brillouin, Ann. Phys. (Paris) 17, 88 (1922)

Raman scattering – 1928C. V. Raman and K. S. Krishnan, Nature 121, 501 (1928)

Vibrational spectroscopy: historical insight


Slide: 17

TDS: Phonon dispersion in Al – 1948P. Olmer, Acta Cryst. 1 (1948) 57

INS: Phonon dispersion in Al – 1955B.N. Brockhouse and A.T. Stewart, Phys. Rev. 100, 756 (1955)

IXS: Phonon dispersion in Be – 1987B. Dorner, E. Burkel, Th. Illini and J. Peisl, Z. Phys. B – Cond. Matt. 69, 179 (1987)

NIS: Phonon DOS in Fe – 1995M. Seto, Y. Yoda, S. Kikuta, X.W. Zhang and M. Ando, Phys. Rev. Lett. 74, 3828 (1995)


1987 – first IXS measurements


Slide: 18

HASYLAB


Inelastic Scattering from Phonons


Slide: 19

Thermal neutrons:

Ei = 25 meV

ki = 38.5 nm-1

∆E/E = 0.01 – 0.1

Brockhouse (1955) Burkel, Dorner and Peisl (1987)

Hard X-rays:

Ei = 18 keV

ki = 91.2 nm-1

∆E/E ≤ 1x10-7


IXS versus INS

• no correlation between momentum- and energy transfer• ∆E/E = 10-7 to 10-8

• Cross section ~ Z2 (for small Q) • Cross section is dominated by photoelectric absorption (~ λ3Z4)• no incoherent scattering

IXS ( ) ( ) ( )EQSQfk

kr

E,2

212

120

2 rrr εεσ ⋅=Ω∂∂

∂


Slide: 20

• no incoherent scattering• small beams: 10 µm or smaller

( )EQSk

kb

E,

2

122 r

=Ω∂∂

∂ σINS

• strong correlation between momentum- and energy transfer• ∆E/E = 10-1 to 10-2

• Cross section ~ b2

• Weak absorption => multiple scattering• incoherent scattering contributions• large beams: several cm


Scientific themes

Disordered systems, small crystals

10-2

10-1

100

101

102

E (m

eV

)IXS

INS

∆Ε


Slide: 21

• Phonons in crystalline materials• Interplay between structure and dynamics• Relaxations on the picosecond time scale• Nature of sound propagation and attenuation

Q = 4π/λ⋅sin(θ/2)∆E = Ei - Ef10

-110

010

110

210

-4

10-3

10

Q ( nm-1)

∆Ε


Small sample volumes: 10 -4 – 10-5 mm3

Ø 45 µµµµm t=20 µµµµm

bcc Mo single crystal


Slide: 22

Diamond anvil cell

• (New) materials in very small quantities• Very high pressures > 1Mbar• Study of surface phenomena

ruby

helium


High resolution IXS:instrumentation

Slide: 23

instrumentation


ESRF: a European collaboration

2. Instrumentation

Slide: 24

The ESRF is financed by 19 countries.


Experimental IXS set-up

sample

Monochromator:Si(n,n,n), θ = 89.98º

Ei

Ef

detector

2. Instrumentation

Slide: 25

Si(n,n,n), θB = 89.98ºn=7-13λ1 tunable

Analyser:Si(n,n,n), θB = 89.98ºn=7-13λ2 constant

Spot size: 30 x 60 µm2 (H x V)


IXS set-up: energy scanning

sample

Ei

Ef

detector

2. Instrumentation

Slide: 26

Ef


ID28 at the ESRFbeamline layout

2. Instrumentation

Slide: 27


Collimating compound refractive beryllium lenses

Be compound refractive lenses installed 28.5 m far from the source. Their role is twofold:

• vertical collimation of the beam to bettermatch the angular acceptance of the Si(111)premono;

• small footprint on the mirror

2. Instrumentation

Slide: 28

• small footprint on the mirror

Si (n n n) reflection

# holes

(R=1 mm)

Transmission Residual divergence

[µrad]

gain

8 13 0.96 2 1.02

9 16 0.92 2 1.06

11 24 0.92 2 1.20

13 34 0.90 2 1.30


Main monochromatorϑB=89.98°, α=85o

AIM:• Reduce the bandwidth from ~1·10-4

to 10-7-10-8

• Accept the whole beam (V-divergence: 20 µrad)

SOLUTION:Backscattering crystal operating at high

2. Instrumentation

Slide: 29

Si(n n n)

Reflection

E

[eV]

∆E

[meV]

∆E/E 3 x U35 flux

[photons/s]

7 13839 5.3 3.8·10-7 1.0·10-11

8 15816 4.4 2.8·10-7 7.6·10-10

9 17793 2.2 1.2·10-7 2.4·10-10

11 21747 0.83 4.7·10-8 4.6·10-9

12 23724 0.73 3.1·10-8 3.4·10-9

13 25701 0.5 1.9·10-8 1.0·10-9

Backscattering crystal operating at high reflection order


1000

2000

3000

4000

fwhm=1.4

fwhm=1.4

fwhm=1.6

fwhm=1.8

3 und-16b

1 und-2/3

2 und-2/3

3 und-2/3

Int

ens

ity

(a.u

.)Heat load on the monochromator

∆Τext=Pd t k-1

2. Instrumentation

Slide: 30

-3 -2 -1 0 1 2 30

1000

Energy (meV)

#u35 ΦΦΦΦ P ∆∆∆∆Text ∆∆∆∆EHL ∆∆∆∆ETOT

[photons/s] [ mW ] [ mK ] [ meV ] [ meV ]

1 1.3⋅1013 45 15 0.6 1.5

2 2.6⋅1013 90 31 1.2 1.8

3 3.9⋅1013 135 46 1.8 2.3

∆ΕHL = 0.7 ⋅E ⋅α ⋅∆Τext


Focusing scheme

Pt coated toroidal/cylindrical mirror with variable meridional radius

backscattering mono sample stage

vertically collimating lens

multilayer

2. Instrumentation

Slide: 31

1) H and V focusing with toroidal mirror – focal spot: 250 x 100 µm2 H x V

2) H focusing with multilayer, V focusing with cylindrical mirror– focal spot: 30 x 60 µm2 H x V

options:

with variable meridional radius


Sample goniometer

High -resolution spectrometer

2. Instrumentation

Slide: 32

Focusing optics

Spectrometer arm

Reflection ∆∆∆∆E [meV] Qmax(7) [nm-1]

(7 7 7) 7 64

(8 8 8 ) 5.5 73

(9 9 9) 3.0 82

(11 11 11) 1.7 100

(13 13 13) 0.9 119


Spectrometer: analysers and detector

2. Instrumentation

Slide: 33

- ~10.000 cubes of 0.6x0.6x2.3 mm3

- perfect crystal properties- collection of sufficient solid angle

- 5 x 1.5 mm Si diodes at 20° incidence- 1 count/20’- Canberra – Eurisys - Signal loss: 4% (15%) at n=11 (n=13)


Temperature-energy conversion

80

100

120

140

10 100

-1

0

1

2

2

theory IXS INS

Ene

rgy

[meV

]

theo-IXS Raman-IXS

∆E/E

[%]

theo-INS

LA and LO branch of diamond along [111]

2. Instrumentation

Slide: 34

Verbeni et al., Rev. Sci. Instr. 79, 083902 (2008)

0,0 0,1 0,2 0,3 0,4 0,50

20

40

60

60 80 100120140160

-2

-1

0

1

Ene

rgy

[meV

]

q [r.l.u.]

Energy [meV]

E/E

[%]

theo-INS Raman-INS

Comparison with neutron, Raman results (for the Γ point), and theory


0,00

0,01

0,02

0,03

Bergamin

∆E/E

Comparison with various αααα(T) determinations

2. Instrumentation

Slide: 35

-0,01

-2.2-0.22

Bergamin Lyon Okada

∆T [Kelvin]

( ) ( ) ( )( )

( ) 26

160

000

K10004.0016.0

K10002.0581.2

TTC5.22TT

−−

−−

⋅±=β

⋅±=α

−β+=α=α o

Bergamin et al., J. Appl. Phys. 82, 5396 (1997); Verbeni et al., Rev. Sci. Instr. 79, 083902 (2008).


The instrument resolution function

• ∆E and Q-independent• Lorentzian shape

2. Instrumentation

Slide: 36

-40 -20 0 20 401E-4

1E-3

0,01

0,1

Sig

nal [

arb.

uni

ts]

Energy Transfer [meV]

• Resolution• Contrast


High -resolution IXS:examples of applications

Slide: 37

examples of applications


Phonon dispersion of fcc d-Plutonium

Pu is one of the most fascinating and exotic element known• Multitude of unusual properties• Central role of 5f electrons• Radioactive and highly toxic

3. Selected results

Slide: 38

Wong et al. Science 301, 1078 (2003); PRB 72, 064115 (2005)

• Radioactive and highly toxic

typical grain size: 90 µµµµmfoil thickness: 10 µµµµm

strain enhanced recrystallisation of fcc Pu-Ga (0.6 wt%) alloy


Plutonium: The IXS experiment• Energy resolution: 1.8 meV at 21.747 keV• Beam size: 20 x 60 µm2 (FWHM)• On-line diffraction analysis

60

LA (0.2;0.2;0.2)

200

TA (0.2;0.2;0.2)

3. Selected results

Slide: 39

-20 -10 0 10 200

20

40

Cou

nts

in 1

80 s

ecs

Energy [meV]-10 -5 0 5 10

0

100

200

Co

unt

s in

18

0 se

cs

Energy [meV]


Plutonium: phonon dispersion

3. Selected results

Slide: 40

• Born-von Karman force constant model fit- good convergence, if fourth nearest neighbors are included

Expt

B-vK fit 4NN

Expt

B-vK fit 4NN


Plutonium: elasticityProximity of Γ-point: E = Vq

VL[100] = (C11/ρ)1/2

VT[100] = (C44/ρ)1/2

VL[110] = ([C11+C12+2C44]/ρ)1/2

VT1[110] = ([C11 - C12] /2ρ)1/2

<001>

<110>

<111>

3. Selected results

Slide: 41

T1 11 12

VT2[110] = (C44/ρ)1/2

VL[111] = [C11+2C12+4C44]/3ρ)1/2

VT[111] = ([C11-C12+C44]/3ρ)1/2

C11 = 35.3±±±±1.4 GPa

C12 = 25.5±±±±1.5 GPa

C44 = 30.5±±±±1.1 GPahighest elastic anisotropy of all known fcc metals


Plutonium: density of states

( )2

2

0 1)/exp(

)()/exp(3

max

−∫

=

TkE

dEEgTkE

Tk

ENkC

B

BE

BBv

Specific heat

1 K

-1)

6 3R →→→→

3. Selected results

Slide: 42

0.0 0.2 0.4 0.6

(arb. units)

0.0 0.2 0.4 0.6 Density of states

• Born-von Karman fit- density of states calculated

g(E)

Temperature (K)

0 50 100 150 200 250 300

Cv

(cal

mol

e-1

0

2

4

θθθθD(T→→→→0) = 115K

θθθθD(T →→→→ ∞∞∞∞) = 119.2K


Scattering from powders

100

200

Cou

nts

phonon energy

15

20

25

30

35

40

Ene

rgy

[meV

]

Phonon dispersion

3. Selected results

Slide: 43

direction of momentum transfer is not defined:

integration over shell with radius |Q|

low Q – long-wave limit

orientational average of LA phonon energy linked to the elasticity

(000) (220)

(11 )1

(111)

(002) (222)

(113)

(331)

(004)-20 -10 0 10 20

0

E [meV]0 2 4 6 8 10 12 14 16

0

5

10

Ene

rgy

[meV

]

q [nm-1]


IXS from polycrystalline samplesDetermination of orientation averaged properties

• aggregate sound velocities: VL, (VT)• phonon density of states: VD, CV, ΘD, …

3. Selected results

Slide: 44


Ruby Gasket

Sample

Diamond anvil cell (DAC) techniques

3. Selected results

Slide: 45

1200 1250 1300 1350 1400 1450 1500 1550 16000

5000

10000

15000

20000

25000

30000

R2

R1

D

Inte

nsità

(u.

a.)

∆ν (cm-1)

Pressure measurement byfrequency shift of rubyfluorescence


100

150Q=6.14 nm-1

Cou

nts

[100

s]

Q=9.46 nm-1

hcp iron: raw spectra and phonon dispersion

20

30

40

Pho

non

Ene

rgy

[meV

]

C*

P =55 GPa

3. Selected results

Slide: 46

0 25 500 25 500

50

Energy [meV]

Cou

nts

[100

s]

Energy [meV]0 2 4 6 8 10 12 14

0

10

20

Pho

non

Ene

rgy

[meV

]

Momentum Transfer [nm-1]

FeFe

VP from initial slope of dispersion curve via sine fit:

VP = 1519·E [meV]/Q[nm-1]University of Trento G. Monaco – High-resolution inelastic x-ray scattering – Grado, 27/09/2013

10000

12000 IXS PREM

V

Sou

nd V

eloc

ity [m

/s]

Density dependence of V P and VS

3. Selected results

Slide: 47

9000 10000 11000 12000 13000

4000

6000

8000

VS

VP

Sou

nd V

eloc

ity [m

/s]

Density [Kg/m3]ρ

ρ

/GV

/G3

4KV

2S

2P

=

+=

Fiquet et al., Science 291, 468 (2001); Antonangeli et al., EPSL 225, 243 (2004)


Microscopic regime not complete understanding

The puzzle of the microscopic dynamics

3. Selected results

Slide: 48

Free particle regime: kinetic theory

Macroscopic regime hydrodynamics

v=ħω/q


Short range order in liquids

bccbccbccbcc

fccfccfccfcc

cI16cI16cI16cI16

3. Selected results

Slide: 49

Raty et al., Nature 449, 448 (07)Raty et al., Nature 449, 448 (07)Raty et al., Nature 449, 448 (07)Raty et al., Nature 449, 448 (07)

Es. sodium: the short range order of the liquid evolves with P and T following similar transformations as in the solid phase

3 3 3 3 GPaGPaGPaGPa, 650 K, 650 K, 650 K, 650 K




The dynamic structure factor of sodium

The spectrum of the

Inelastic x-ray scattering data @ ID16, E=23.724 keV, ∆E=1.4 meV

3. Selected results

Slide: 50

The spectrum of the liquid is a broadened version of the one for

the (poly)crystal

Giordano & g.m., PNAS 107, 21985 (10)Giordano & g.m., PNAS 107, 21985 (10)Giordano & g.m., PNAS 107, 21985 (10)Giordano & g.m., PNAS 107, 21985 (10)


Long

The order fingerprint

Theory

First Brillouin zone:

The longitudinal and transverse dispersion

curves in the liquid reflect those for the

3. Selected results

Slide: 51

Trasv

P

L

reflect those for the polycrystal:

an orientational average over the high symmetry branches of

the single crystal

(density scaling of frequencies for the

solid)Giordano & g.m., PNAS 107, 21985 (10)Giordano & g.m., PNAS 107, 21985 (10)Giordano & g.m., PNAS 107, 21985 (10)Giordano & g.m., PNAS 107, 21985 (10)


The disorder fingerprint

3. Selected results

Slide: 52


The disorder fingerprint

3. Selected results

Slide: 53

Local order dispersion Average disorder broadening

Giordano & g.m., PNAS 107, 21985 (10)Giordano & g.m., PNAS 107, 21985 (10)Giordano & g.m., PNAS 107, 21985 (10)Giordano & g.m., PNAS 107, 21985 (10)


4

5

At low q (< 1 nm-1) macroscopic hydrodynamics is recovered

Liquids: reaching the macroscopic limit

At high q (> 1 nm-1) the dynamics is q-dependent

3. Selected results

Slide: 54

250 300 350 400 450 5000

1

2

3

4

T ( K )

τ

( ps

)g.m. et al., PRE 60, 5505 (1999)g.m. et al., PRE 60, 5505 (1999)g.m. et al., PRE 60, 5505 (1999)g.m. et al., PRE 60, 5505 (1999)Pontecorvo et al., PRE 71, 011501 (2005)Pontecorvo et al., PRE 71, 011501 (2005)Pontecorvo et al., PRE 71, 011501 (2005)Pontecorvo et al., PRE 71, 011501 (2005)


The universal anomalies of glasses

3. Selected results

Slide: 55

Pohl et al., Rev. Mod. Phys. 74, 991 (02)Pohl et al., Rev. Mod. Phys. 74, 991 (02)Pohl et al., Rev. Mod. Phys. 74, 991 (02)Pohl et al., Rev. Mod. Phys. 74, 991 (02) Zeller and Pohl, PRB 4, 2029 (71)Zeller and Pohl, PRB 4, 2029 (71)Zeller and Pohl, PRB 4, 2029 (71)Zeller and Pohl, PRB 4, 2029 (71)


The dynamic structure factor of glycerolInelastic x-ray scattering data @ ID16, E=23.724 keV, ∆E=1.4 meV

3. Selected results

Slide: 56

g.m. & Giordano, PNAS 106, 3659 (09)g.m. & Giordano, PNAS 106, 3659 (09)g.m. & Giordano, PNAS 106, 3659 (09)g.m. & Giordano, PNAS 106, 3659 (09)


3.4

3.5

3.6

(

km/s

)

9

12

( m

eV

)

Dispersion curve

3. Selected results

Slide: 57

0 1 2 3 4 5 6

3.2

3.3

3.4

v l

( km

/s )

q ( nm-1 )

LowLowLowLow----frequency data from:frequency data from:frequency data from:frequency data from: Grubbs & MacPhail, JCP 100, 2561 (94); Grubbs & MacPhail, JCP 100, 2561 (94); Grubbs & MacPhail, JCP 100, 2561 (94); Grubbs & MacPhail, JCP 100, 2561 (94);

Comez et al., JCP 119, 6032 (03); Masciovecchio et al., PRL 92, 247401 (04) Comez et al., JCP 119, 6032 (03); Masciovecchio et al., PRL 92, 247401 (04) Comez et al., JCP 119, 6032 (03); Masciovecchio et al., PRL 92, 247401 (04) Comez et al., JCP 119, 6032 (03); Masciovecchio et al., PRL 92, 247401 (04)

0 1 2 3 4 5 60

3

6

Ω (

me

V )

q ( nm-1 )


1

10 IR

q2

( m

eV )

Acoustic attenuation

3. Selected results

Slide: 58

0 1 2 3 4 5 6

0.1 q4

2Γ

( m

eV )

q ( nm-1 )

The q4 to q2 transition takes place

close to the Ioffe-Regel limit defined

as λIR=2l (Ω/π=2Γ)

23

2

22 E

v

vCT

D

thlv

ρτγ

h=Γanharmonic

contribution:

g.m. & Giordano, PNAS 106, 3659 (09)g.m. & Giordano, PNAS 106, 3659 (09)g.m. & Giordano, PNAS 106, 3659 (09)g.m. & Giordano, PNAS 106, 3659 (09)


The case of SiO 2: IXS

3. Selected results

Slide: 59

Baldi et al., PRL 110, 185503 (13)Baldi et al., PRL 110, 185503 (13)Baldi et al., PRL 110, 185503 (13)Baldi et al., PRL 110, 185503 (13)


The case of SiO 2: DOS

3. Selected results

Slide: 60

Chumakov et al. (submitted)Chumakov et al. (submitted)Chumakov et al. (submitted)Chumakov et al. (submitted)


Concluding remarks

Slide: 61

Concluding remarks


Complex sample environmentLevitation

ααααi=0.61ααααc ααααi=(0.03 - 3.4)ααααc

B.M. Murphy et al.; PRL 95 (2005)H. Reichert et al.; PRL 98 (2007)

Surface sensitivity

Slide: 62

Argon gas flow; CO2 laser: 2020 KA.H. Said et al.; PRB 74 (2006)

Ø 45 µµµµm; t=20 µµµµm

bcc Mo single crystal

ruby

helium

High pressure+ laser heating


IXS at the ESRF

ID26: X-ray absorption and emission spectroscopy

ID28: Phonons

Slide: 63

ID20: Electronic excitations

ID15B: Compton: 30%

ID8: soft X-ray IXS: 20%


Giulio Monaco Università di Trento (I) outline ...€¦ · - soft X-ray absorption spectroscopy...

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Transcript of Giulio Monaco Università di Trento (I) outline ...€¦ · - soft X-ray absorption spectroscopy...