Slide: 1 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014.

Slide: 1HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

Introduction to Nuclear Inelastic Scattering

Aleksandr Chumakov

European Synchrotron Radiation Facility


Methods to study dynamics:Methods to study dynamics:Dispersion relations:

S(q,E)Density of states:

g(E)

Thermal diffuse scattering:p(q)




g(E)


~meV ~meV

~eVAveraging over

momentum transfer Dqusing many detectors

(many scattering angles)




g(E)


~meV

~eVAveraging over

momentum transfer Dqusing

LONG TIME of interaction


Another view of inelastic scattering:Another view of inelastic scattering:

Inelastic scattering = diffraction on moving super-lattice

qkk

01

0k

q

1k

Periodic variation of density

caused by moving atoms

01 EE

Bragg law (diffraction condition):

Doppler effect (incidence on a moving surface):



During LONG TIME of interaction super-lattice disappeared

0k

q

Periodic variation of density

caused by moving atoms

no diffraction, incoherent scattering

01 EEDoppler effect

(incidence on a moving surface):



)(,.. ESdqEqS absscattinc

Nuclear Inelastic Scattering

physically:

nuclear inelastic absorption

Kohn and ac, J.Phys.:Condens.Matter 14 (2002) 11875


Content:Content:

What is Nuclear Inelastic Scattering:

physics, method, properties, data treatment

What is interesting in Nuclear Inelastic Scattering:

partial density of states, element selectivity, isotope selectivity, site selectivity

(selected examples of applications)

An extension of Nuclear Inelastic Scattering:

Inelastic X-ray Scattering with Nuclear Resonance Analysis

(application to glass dynamics)


What is nuclear inelastic scattering:What is nuclear inelastic scattering:

7 112 eV

845720

707

G 2 eV

t0 0.33 fs

E = 7.112 keV

se=26 × 10-20 cm2

G = 4.7 10-9 eV

t0 = 141 ns

E = 14.412 keV

sn= 256 × 10-20 cm2

2

iE

gfiff nee

14.412 keV

136.5

366.8

706.4Fe

57

26

Electronic and nuclear levels:



Very narrow level:

G = 4.7 neV Very long time:

t0 = 141 ns

Interaction occurs ONLY for the selected isotope:

element selectivity

isotope selectivity

site selectivity


Narrow resonance:Narrow resonance:Narrow resonance

is a built-in energy analyzerNo need to analyze the energy

of scattered radiation

inelastic scattering(neutron of x-ray)

М

А

DSmonochromator sample detector

analyzer

Ein + Eph = Eout

Inelastic Nuclear Absorption:

М Smonochromator

sample (alias analyzer)

Ein + Eph = EN Ddetectorр

products ofnuclear

absorption

N

eK

eL

conversionelectrons

atomicfluorescence

Monitoring the products of nuclear absorption:

0

flu

ore

scen

ce

energy

Seto et al, PRL 74 (1995) 3828



Energy

Ab

sorp

tio

n

detector

monochromatorDE ~ 1 meV

0.1 ns 176 ns

time

co

un

ts

pulsed structure of synchrotron radiation:

time gate

energy scan

ac and Sturhahn, Hyperfine Interact. 123/124 (1999) 781



57Fe nuclei

v+v-

-80 -60 -40 -20 0 20 40 60 80

-1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6

Velocity of atoms (km/sec)

Del

ayed

rad

iatio

n

Phonon energy = Ex-ray

- Eresonance

(meV)

E = Eres (1+v/c)

Classical interpretation of Nuclear Inelastic Scattering:monitoring velocity distribution of vibration atoms

pair correlation does not matter:no sensitivity wave vector !!!


NIS: simple and accurateNIS: simple and accurateAbsorption

- ideal averaging over wave vectors - no corrections for multiple scattering events- no corrections for contribution of coherent scattering

Isotope selectivity:- no corrections for empty can

High energy of incidence radiation (~10-30 keV):- no kinematic limitations (full range of wave vectors and energy)- work in “loss-energy” region- fixed instrumental function over an entire energy range

-80 -60 -40 -20 0 20 40 60 80

-10 -5 0 5 10

neutrons X-rays

Exact density of phonon states in an entire energy range at “any” temperature


NIS: simple and accurateNIS: simple and accurate

Determination of the density of states

from the energy dependence

of Nuclear Inelastic Scattering

Fourier logarithm Fourier

0

abso

rpti

on

energy

absorption probability

0 10 20 30 400.00

0.02

0.04

0.06

0.08

D

OS

(m

eV

-1)

Energy (meV)

density of states:

1

1BR nE

E lnLMf

normalization

REdEEES Kohn and ac, Hyperfine Interact. 125 (2000) 205


Intermediate summary:Intermediate summary:

Nuclear Inelastic Scattering - inelastic absorption of x rays by nuclei with low-energy nuclear resonances accompanied by creation and annihilation of phonons

Nuclear inelastic scattering is isotope-selective: it proceeds only for a particular nuclear isotope with a selected energy of nuclear resonance. Presently, it can be performed with Fe, Sn, Sm, Eu, Dy, K, Kr, Sb, Te, and Xe (in nearest future, possibly also with Ge, Ba и Os).

Nuclear inelastic scattering allows for measurements of the partial density of phonon states of the selected isotope in the studied sample.

Nuclear inelastic scattering allows for determination of the density of states with high accuracy , in absolute numbers of phonon states.


But:But:

Only partial density of states (not a complete one)

Only for selected elements (not for all of them)

Is it good or bad ?


Why “less” is “better”Why “less” is “better”Only partial density of phonon states:

How do atoms move relative to each other?

0 10 20 30 40 50 60 700.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0

3

2

1

Energy (meV)

De

nsi

ty o

f st

ate

s (m

eV

-1 )

ferroceneFeC10H10

10.03

1

m

mA Fe

rigid body:

23.013

1

m

mA Fe

stretching:

0.300.14

0.230.28

0 10 20 30 40 50 60 700.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Energy (meV)

Den

sity

of s

tate

s (m

eV -

1 )

Total DOS: area = 1/3N

0 10 20 30 40 50 60 700.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Energy (meV)

Den

sity

of s

tate

s (m

eV -

1 )

Partial DOS: area = ???

E

EA Fe

ac et al, Structural Chemistry 14 (2003) 109


Why “less” is “better”Why “less” is “better”Only selected elements:

How does the functional centre of a protein move?

С o u r t e s y o f P ro f . S c h u e n e m a n n . J . A m . C h e m . S o c . 1 3 4 , 4 2 1 6 ( 2 0 1 2 ) .

100 200 300 400 500 6000

50

100

50

100

150

594

581

68cou

nts

energy (cm-1)

(b)

NP2-NO

NP2

(a)

581 cm-1

594 cm-1

Fe



How does the protein move?

С o u r t e s y o f P ro f . S c h u e n e m a n n . J . A m . C h e m . S o c . 1 3 4 , 4 2 1 6 ( 2 0 1 2 ) .

69 cm-1

25 50 75 100

200

400

600

800

32 cm-1

68 cm-1

energy (cm-1)



What is the structure of the molecule?

guanidium nitroprusside:

(CN3H6)2 [Fe(CN)5NO]

Fe

CNO

groundstate

excitedI-state

excitedII-state

ground ground + excited

ground excited

Paulsen et al, JACS 124 (2002) 3007


Why “less” is “better”Why “less” is “better”Only selected isotopes:

How do atom move in the first (second, third) atomic layer?

57Fe

56Fe

W

Ślęzak et al, PRL 99 (2007) 066103


Only selected isotopes in selected sites:What determines the anomalous elasticity of nano-composite?

Why “less” is “better”Why “less” is “better”

-8 -6 -4 -2 0 2 4 6 81.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

ele

ctro

n y

eild

velocity (mm/s)

composite model

магнитное поле

0 10 20 30 40 50

Pro

ba

bili

ty

magnetic field (T)

nano-graingrain surface

interface

Mössbauerspectroscopy:

Magnetic field


Why “less” is “better”Why “less” is “better”Only selected isotopes in selected sites:

What determines the anomalous elasticity of nano-composite?

0.00

0.02

0.04

0.00

0.01

0.02

0.03

0 10 20 30 40 500.000

0.003

0.006

0.009as-quenched

Energy (meV)

d = 2 nm

Bd = 13 nm

DO

S

(meV

-1

)

D

d = 15 nm

grains interface

0.00

0.01

0.02

0.03

0.040.000

0.004

0.008

0.012

0.016

0 10 20 30 40 500.000

0.002

0.004

0.006

B

Energy (meV)

=1.5(5) nm

as-quenched =1.0(5) nm

DO

S (

meV

-1)

D

=0.6(5) nm

Stankov et al, PRL 100 (2008) 235503

Atomic dynamics of nano-grains and bulk is the sameAll anomalies comes from atomic dynamics of interface


But: only Mössbauer isotopes...But: only Mössbauer isotopes...

Nuclear inelastic scattering is isotope-selective: it proceeds only for selected nuclear isotopes

Now: Fe, Sn, Sm, Eu, Dy, K, Kr, Sb, Te и Xe

in nearest future:

Ge, Ba и Os

Can we study, for instance,

SiO2 ?


Not only Mössbauer isotopes!Not only Mössbauer isotopes!Inelastic X-ray Scattering with Nuclear Resonance Analysis

Inelastic X-ray Scattering:

Nuclear Inelastic Scattering:

Crystal analyzers:

DE = 1.4 meV or 3 meVdQ = 0.03 nm-1, DQ = [1-7] nm-1

nuclear analyzer:

DE = 0.5 meVDQ = [3-14] nm-1

Move resonancefrom sampleto detector !!!

ac et al, PRL 76 (1996) 4258.


The puzzle of glasses: The puzzle of glasses:

C.A.Angel et al., J.Phys.:Cond.Matt. 15,S1051,2003

A.Wischnewski et al.,PRB 57,2663,1998

Debye: ~E2

g(E)

g(E) / E2

R.C.Zeller et al., PRB 4,2029,1971

DOS g(E):additionalvibrationalstates !

Reduced DOS g(E)/E2:the boson peak !

Debye: ~T3

additional vibrational states? ×5

At low temperatures, heat capacity for glassesis larger than for crystals



SiO2

a-cristobalite

tetragonal

a-quartz

trigonal

coesite

monoclinic

ambient glass

amorphous

densified glass

amorphous



0

20

40

g(E

) (

10 -

3 m

eV -

1)

NRA-IXS

0

20

40

g(E

) (

10 -

3 m

eV -

1)

NRA-IXS

0 20 40 60 80 100 120 140 160 180

40

20

0

Energy (meV)

IXS

0 20 40 60 80 100 120 140 160 180

40

20

0

Energy (meV)

IXS

0

20

40 NRA-IXS

0

20

40

60

g(E

) (

10 -

3 m

eV -

1) NRA-IXS

0

20

40 NRA-IXS

0 20 40 60 80 100 120 140 160 180

40

20

0

g(E

) (

10 -

3 m

eV -

1)

IXS

0 20 40 60 80 100 120 140 160 180

60

40

20

0

IXS

0 20 40 60 80 100 120 140 160 180

40

20

0g(

E)

(10

-3 m

eV -

1)

IXS

Energy (meV)

ambient glass

densified glass

nuclear resonance analysis

crystal analyzers

a-cristobalite

a-quartz

coesite

ac et al, PRL 112 (2014) 025502



0 10 200

5

10

15

g(E

) (

10

-3 m

eV

-1 )

Energy (meV)

0 10 200

2

4

g(E

)/E

2 (10

-4 m

eV

-3 )

Energy (meV)

excess states

all statesin this energy region

Debye level:

how many states

one can expect

for acoustic sound waves

a-quartz



0 10 200

5

10

15

Energy (meV)

g(E

) (

10 -

3 meV

-1 )

0 10 200

2

4

Energy (meV)

g(E

)/E

2 (10

-4 m

eV

-3 )

0 10 20

0

5

10

15

Energy (meV)

g(E

) (

10

-3 m

eV

-1 )

0 10 200

2

4

Energy (meV)

g(E

)/E

2 (10

-4 m

eV

-3 )

0 10 20

0

5

10

15

g(E

) (

10

-3 m

eV

-1 )

Energy (meV)

0 10 200

2

4

g(E

)/E

2 (10

-4 m

eV

-3 )

Energy (meV)

0 10 20

0

5

10

15

g(E

) (

10

-3 m

eV

-1 )

Energy (meV)

0 10 200

2

4

g(E

)/E

2 (10

-4 m

eV

-3 )

Energy (meV)

a-cristobaliteambient glass a-quartzdensified glass

excess states:

all states:

5.6(3)%

8.4(5)%

excess states:

all states:

5.3(3)%

8.4(5)%

excess states:

all states:

5.9(4)%

12.8(8)%

excess states:

all states:

6.6(4)%

11.5(7)%

12 atomsin unit cell

9 atomsin unit cell



The low-densityglass and crystal

The high-densityglass and crystal

0 5 10 15 200

2

4

Energy (meV)

g(E

)/E

2 (10

-4 m

eV

-3 )

0 5 10 15 200

2

4

Energy (meV)

g(E

)/E

2 (10

-4 m

eV

-3 )

0 5 10 15 20

0

2

4

g(E

)/E

2

(10

-4 m

eV -

3)

Energy (meV)

g(E

)/E

2

(10

-4 m

eV -

3)

0 5 10 15 200

2

4

Energy (meV)

a-cristobaliter = 2.29 g/cc

a-quartzr = 2.65 g/cc

ambient glassr = 2.20 g/cc

densified glassr = 2.67 g/cc

R.C.Zeller et al., PRB 4,2029,1971

typical glassvs

typical crystal (quartz)

low-density glassvs

high-density crystal



How disorder increases

the heat capacity?

It does not do it:the higher heat capacity of glasses

is caused by their lower density


Summary:Summary:

Nuclear Inelastic Scattering (NIS): inelastic absorption of x rays

Nuclear levels are narrow: ~neVthis gives an ideal built-in energy analyzer

Nuclear interaction is slow: ~nsthis gives an ideal averaging of wave vectors (q)

NIS gives the partial density of states this shows how atoms move

NIS is isotope-selective: thus gives site-selectivity


Thank you for

your attention

Time to stop now... Time to stop now...

Slide: 1 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014.

Documents

Transcript of Slide: 1 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014.