Download - 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
Slide: 2HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
Methods to study dynamics:Methods to study dynamics:Dispersion relations:
S(q,E)Density of states:
g(E)
Thermal diffuse scattering:p(q)
Slide: 3HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
Methods to study dynamics:Methods to study dynamics:Dispersion relations:
S(q,E)Density of states:
g(E)
Thermal diffuse scattering:p(q)
~meV ~meV
~eVAveraging over
momentum transfer Dqusing many detectors
(many scattering angles)
Slide: 4HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
Methods to study dynamics:Methods to study dynamics:Dispersion relations:
S(q,E)Density of states:
g(E)
Thermal diffuse scattering:p(q)
~meV
~eVAveraging over
momentum transfer Dqusing
LONG TIME of interaction
Slide: 5HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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):
Slide: 6HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
Another view of inelastic scattering:Another view of inelastic scattering:
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):
Slide: 7HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
Another view of inelastic scattering:Another view of inelastic scattering:
)(,.. ESdqEqS absscattinc
Nuclear Inelastic Scattering
physically:
nuclear inelastic absorption
Kohn and ac, J.Phys.:Condens.Matter 14 (2002) 11875
Slide: 8HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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)
Slide: 9HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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:
Slide: 10HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
What is nuclear inelastic scattering:What is nuclear inelastic scattering:
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
Slide: 11HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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
Slide: 12HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
What is nuclear inelastic scattering:What is nuclear inelastic scattering:
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
Slide: 13HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
What is nuclear inelastic scattering:What is nuclear inelastic scattering:
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 !!!
Slide: 14HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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
Slide: 15HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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
Slide: 16HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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.
Slide: 17HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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 ?
Slide: 18HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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
Slide: 19HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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
Slide: 20HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
Why “less” is “better”Why “less” is “better”Only selected elements:
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)
Slide: 21HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
Why “less” is “better”Why “less” is “better”Only selected elements:
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
Slide: 22HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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
Slide: 23HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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
Slide: 24HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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
Slide: 25HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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 ?
Slide: 26HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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.
Slide: 27HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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
Slide: 28HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
The puzzle of glasses: The puzzle of glasses:
Slide: 29HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
The puzzle of glasses: The puzzle of glasses:
SiO2
a-cristobalite
tetragonal
a-quartz
trigonal
coesite
monoclinic
ambient glass
amorphous
densified glass
amorphous
Slide: 30HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
The puzzle of glasses: The puzzle of glasses:
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
Slide: 31HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
The puzzle of glasses: The puzzle of glasses:
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
Slide: 32HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
The puzzle of glasses: The puzzle of glasses:
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
Slide: 33HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
The puzzle of glasses: The puzzle of glasses:
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
Slide: 34HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
The puzzle of glasses: The puzzle of glasses:
How disorder increases
the heat capacity?
It does not do it:the higher heat capacity of glasses
is caused by their lower density
Slide: 35HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
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
Slide: 36HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014
Thank you for
your attention
Time to stop now... Time to stop now...