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Nuclear Resonant Scattering of Nuclear Resonant Scattering of Synchrotron Synchrotron RadiationRadiation
Dénes Lajos Nagy
Thin Films as Seen by Local ProbesThin Films as Seen by Local ProbesERASMUS Intensive ProgrammeERASMUS Intensive Programme
Frostavallen (Höör), SwedenFrostavallen (Höör), Sweden, , 2-2-1122 MayMay, 2002, 2002
KFKI Research Institute for Particle and Nuclear Physicsand
Eötvös Loránd University , Budapest, Hungary
Outline Outline
Synchrotron Radiation (SR)
- History
- The machine
- SR sources
- Properties of SR
OutlineOutline
Nuclear Resonant Scattering of SR: Theory
- Conventional Mössbauer spectroscopy
- Nuclear resonant forward scattering
Nuclear Resonant Scattering of SR: Experiment
- The experimental setup
- The transverse coherence length
- Nuclear resonant inelastic scattering
Problems
Synchrotron radiation: HistorySynchrotron radiation: History
SR: polarised electromagnetic radiation produced in particle accelerators or storage rings when relativistic electrons or positrons are deflected in magnetic fields
Elder et al. (1947): first observation of SR at a 70-MeV synchrotron
Tomboulian, Hartman (1956): first spectroscopic studies at a 300-MeV machine
First-generation SR sources (1965-1980): machines built for particle physics, SR produced at bending magnets is used in parasitic regime
Synchrotron radiation: HistorySynchrotron radiation: History
Second-generation SR sources (1970-1990): machines dedicated to the applications of SR, radiation produced at bending magnets
Third-generation SR sources (1990-):machines dedicated to the applications of SR, radiation produced both at bending magnets and at insertion devices
- ESRF (Grenoble, France): 6 GeV
- APS (Argone, USA): 7 GeV
- SPring8 (Harima, Japan): 8GeV
The future: x-ray free-electron lasers (XFEL)
X-ray beams: past, present and futureX-ray beams: past, present and future
radi
o w
aves
fm - r
adio
mic
row
aves
infr
ared
visi
ble
light
ultr
avio
let
x-ra
ys
- ra
ys
cosm
ic r
ays
cell
viru
s
prot
ein
mol
ecul
eat
om
nucl
eus
prot
on
1 m
eter
SSR in the eletromagnetic spectrumR in the eletromagnetic spectrum
ESRF, GrenobleESRF, Grenoble
ESRF, GrenobleESRF, Grenoble
ELETTRA, TriesteELETTRA, Trieste
DORIS (HASYLAB), HamburgDORIS (HASYLAB), Hamburg
APS, ArgonneAPS, Argonne
SSPring8, HarimaPring8, Harima
acceleration
electron orbit
acceleration
electron orbit
non-relativistic electrons relativistic electrons
v/c << 1 v/c 1
E/m0c2
RRadiationadiation field of radially accelerated electrons field of radially accelerated electrons
Technical aspects (example: ESRF)Technical aspects (example: ESRF)
Pre-accelerators:
- LINAC: 100 keV electron gun 200 MeV
- booster synchrotron: 200 MeV 6 GeV
The storage ring:
- circumference: 845 m;
- number of electron buckets: up to 992;
- electron bunch length: 6 mm pulse duration: 20 ps and 100 ps at bending magnets and insertion devices, respectively;
- re-acceleration power at I = 100 mA: 650 kW.
Technical aspects (example: ESRF)Technical aspects (example: ESRF)
Critical wavelength of SR:
c = (4/3)(R/3), i.e., c[Å] = 5.59 (R[m]/E[GeV]3)
where R is the radius of the electron orbit in the bending magnet or in the insertion device.
Spectral brilliance of a SR source (bending magnet or insertion device):
photons/s/mm2/mrad2/0.1 % energy bandwidth
Technical aspects (example: ESRF)Technical aspects (example: ESRF)
Insertion devices: wigglers and undulators. These are two arrays of N permanent magnets above and below the electron (positron) beam. The SR is generated through the sinusoidal motion of the particles in the alternating magnetic field.
Wigglers: strong magnetic field, broad-band radiation from the individual poles is incoherently added. Intensity: . Horizontal beam divergence >> 1/.
Technical aspects (example: ESRF)Technical aspects (example: ESRF)
Undulators: weak magnetic field, narrow-band radiation from the individual poles is coherently added at the undulator maxima. Intensity: 2. Horizontal beam divergence 1/.
Bending magnetBending magnet
Wiggler / undulatorWiggler / undulator
Undulator (ESRF)Undulator (ESRF)
12,0 12,5 13,0 13,5 14,0 14,5 15,0
1015
1016
1017
1018
brill
ianc
e /
pho
tons
/s m
m2 m
rad2 0
.1%
energy / keV
Brilliance of an undulator (U23 of ID18 at ESRF)Brilliance of an undulator (U23 of ID18 at ESRF)
Properties of SRProperties of SR
Tunable energy
High degree of polarisation
High brilliance
Small beamsize
Small beam divergence
Pulsed time structure
Conventional (energy-domain) MSConventional (energy-domain) MS
Conventional (energy-domain) MSConventional (energy-domain) MS
Only one transition is excited at the same time, therefore the resultant spectrum is the incoherent sum of the indivitual transitions (the intensities are added).
Ie=3/2
Ig=1/2
3/2, +3/2
3/2, -3/2
3/2, +1/2
3/2, -1/2
1/2, -1/2
1/2, +1/2
isomer shift
electricquadrupole
splitting
electric quadrupolesplitting and magnetic
dipole perturbation
Hyperfine splitting of the Hyperfine splitting of the 5757Fe nuclear levelsFe nuclear levels
Hyperfine splitting of nuclear levelsHyperfine splitting of nuclear levels
neV
EhfneV
EhfneV
EkeV
57Fe
Nuclear resonant scattering of SR:Nuclear resonant scattering of SR:Mössbauer effect with SRMössbauer effect with SR
E. Gerdau et al. (1984): first observation of delayed photons from nuclear resonant scattering of SR (at beamline F4 of HASYLAB).
Basic problem: huge background from prompt non-resonant photons. The solution:
- monochromatisation of the primary SR,
- suppression of electronic scattering by using electronically forbidden Bragg reflections (out of date),
- fast detectors and electronics.
Nuclear resonant scattering of SR:Nuclear resonant scattering of SR:Mössbauer effect with SRMössbauer effect with SR
Bergmann et al. (1994): first observation of delayed photons from nuclear resonant forward scattering of SR.
The bandwidth of SR is much larger than the hyperfine splitting. All transitions are excited at the same time. Therefore the resultant time response is the coherent sum of the indivitual transitions (the amplitudes are added).
Nuclear resonant scattering of SR:Nuclear resonant scattering of SR:Mössbauer effect with SRMössbauer effect with SR
Not only the different transitions of the same nucleus but also transitions of different nuclei within the coherence length are excited simultaneously and the scattering takes place coherently.
The longitudinal coherence length of the resonant radiation is cn 42 m for 57Fe.
Nuclear resonant scattering of SR:Nuclear resonant scattering of SR:Mössbauer effect with SRMössbauer effect with SR
The temporal interference of the amplitudes scattered from different hyperfine-split transitions leads to quantum beats. The strength of the hyperfine interaction (e.g. magnetic field) is reflected in the frequency/frequencies of the quantum beats.
The orientation of the magnetic field and of the electric field gradient is reflected in the intensities of the different frequency components and in the depth of the beating.
Nuclear resonant scattering of SR:Nuclear resonant scattering of SR:Mössbauer effect with SRMössbauer effect with SR
Due to the full linear polarisation of SR, the nuclear resonant scattering of SR is extremely sensitive to the orientation of the hyperfine magnetic field.
0 100 200 300 400 500100
102
104
106
108 E
q=0.8 mm/s
Eq=0.5 mm/s
calc. inten
sity / a.u.
time after excitation / ns
40
60
80
100
teff/line = 1
-15 -10 -5 0 5 10 15
40
60
80
100
teff/line = 1
tran
smission
/ %
relative energy / 0
100
102
104
106
108 E
q=0 mm/s
Eq=0.8 mm/s
a
b
c
d
Quantum-beat patterns for pure electric Quantum-beat patterns for pure electric quadrupole interactionquadrupole interaction
H. GrH. Grünsteudelünsteudel
0 100 200 300 400
100
101
102
103
100
101
102
103
100
101
102
103
0 100 200 300 400
100
101
102
103
0 100 200 300 400
0 100 200 300 400
100
101
102
103
T = 107 K
T = 103 K
T = 102 KT = 102 K
T = 83 K
T = 133 K
T = 107 K
T = 103 K
forw
ard
scat
tere
d in
tens
ity / a
.u.
time / ns H. GrH. Grünsteudelünsteudel
Spin-crossover Spin-crossover transition in Fe(tpa)transition in Fe(tpa)(NCS)(NCS)22
The transition invokes a change in the quadrupole interaction.
H. GrH. Grünsteudelünsteudel
Orientation of the EFG axisOrientation of the EFG axis
a) time-domain patterns, b) energy-domain spectra with linear polarised radiation, c) energy-domain spectra with unpolarised radiation
100
101
102 experiment fit
coun
ts /
a.u.
100 200 300 400
100
101
102
coun
ts /
a.u.
time after excitation / ns
a || beam
c || beam
H. GrH. Grünsteudelünsteudel
Orientation of the EFG axisOrientation of the EFG axis
(CN3H6)2[(Fe(CN)5NO] single crystal
xyz
k
E
B
0 50 100 150 200
Inte
nsi
ty (
arb
. u
nits
, lo
g.
sca
le)
Time after excitation (ns)
1 2 3 4 5 6
xyz
B
E
k
xyz BE
k
Orientation of the hyperfine fieldOrientation of the hyperfine field(the ”Smirnov figures”)(the ”Smirnov figures”)
O. LeupoldO. Leupold
Measurement of the isomer shiftMeasurement of the isomer shift
The NRS time response depends only on the differences of the resonance line energies. Therefore the isomer shift has no influence to the quantum-beat pattern.
The isomer shift can be measured by inserting a single-line absorber to the photon beam within the longitudinal coherence length.
0 50 100 150
100
101
102
103
0 50 100 150
100
101
102
103
with referencewith reference
dc
a b
T=110 K
T=110 K
T=4.2 K
T=4.2 K
time after excitation / ns
coun
ts
time after excitation / ns
100
101
102
103
100
101
102
103
H. GrH. Grünsteudelünsteudel
Measurement of the isomer shiftMeasurement of the isomer shift
Fe2+O2(SC6HF4)(TPpivP)
single-line reference:K4Fe(CN)6
0
20
40
60
80
100
0 500 1000 1500100
102
104
106
108 Eq=2 mm/s
Eq=0 mm/s
calc. inten
sity / a.u.
time after excitation / ns-30 -20-10 0 10 20 30
0
20
40
60
80
100
teff / line=25
tran
smission
/ %
relative energy / 0
100
102
104
106
108 teff=1
teff=25
ab
cd
H. GrH. Grünsteudelünsteudel
Effect of the finite absorber thickness:Effect of the finite absorber thickness:the dynamic beatsthe dynamic beats
H. GrH. Grünsteudelünsteudel
Channel-cut monochromatorChannel-cut monochromator
cut
2 = B - cut
h22
h11
1 = B + cut
H. GrH. Grünsteudelünsteudel
Asymmetric reflectionAsymmetric reflection
The acceptance for incoming and outgoing beam is different.
Si(4 2 2)b=-0.1
Si(4 2 2)b=-10
Si(4 2 2)b=-10
Si(4 2 2)b=-0.1
Si(9 7 5)b=-1
Si(9 7 5)b=-1
Si(9 7 5)b=-0.21
Si(9 7 5)b=-4.7
Si(9 7 5)b=-20
Si(9 7 5)b=-0.05
Si(12 2 2)b=-1
Si(12 2 2)b=-1
E=6.4 meV E=4.4 meV
E=0.8 meVE=1.7 meV
ba
c d
Ge(3 3 1)b=-1
H. GrH. Grünsteudelünsteudel
High-resolution monochromatorsHigh-resolution monochromators
high heat loadmonochromator
high resolutionmonochromatorSi (1 1 1)
Si (1 1 1)
Si (4 2 2)
Si (4 2 2)
Si (12 2 2)Si (12 2 2)
E: 300 eV 3 eV 6 meV
H. GrH. Grünsteudelünsteudel
High-heat-load premonochromator and high-High-heat-load premonochromator and high-resolution nested monochromatorresolution nested monochromator
x-ray
hole
electron
depletion region
avalanche region
a b c H. GrH. Grünsteudelünsteudel
Principle of the avalanche photo diode (APD)Principle of the avalanche photo diode (APD)
undulatorx-ray beam
electron storage ringwith one electron bunch
detectorssample
measured data
fast electronicsbunch clock
ICM HRM
H. GrH. Grünsteudelünsteudel
Principle of a nuclear resonant scattering Principle of a nuclear resonant scattering experimentexperiment
detector(APD)
amplifierCFD
(all events)
TAC MCA
counter(prompt)
counter(delayed)
ADC
gate
star
t
stop
CFD(only delayed
events)bunchclock
H. GrH. Grünsteudelünsteudel
Setup of the fast timing electronics for Setup of the fast timing electronics for nuclear resonant scattering experimentsnuclear resonant scattering experiments
sample detectort
t t
beamtime
H. GrH. Grünsteudelünsteudel
The pulsed SR (left side, pulses separated by t) penetrates the sample and reaches the detector. The decay of the nuclear excited states, which takes place in the time window t (right side), reflects the hyperfine interactions of the resonant nuclei.
Setup for a nuclear resonant forward Setup for a nuclear resonant forward scattering experimentscattering experiment
The Doppler shift depends on zs only.
For point-like source and detector:
The transverse coherence lengthThe transverse coherence length
For finite source and detector there exists an effective transverse
coherence length Lc /2 with
Typical values at ESRF ID18: 0 = 120 m, S = 41 m, d =
500 m, D = 2.5 m Lc 300 Å.
With appropriate slits (e.g. of 15 m height, one 10 cm behind the
sample, another 4 cm in front of the detector) Lc 3 m.
The transverse coherence lengthThe transverse coherence length
Measured time responses with slits(a, 95 Hz: without slits)
A.Q.R. Baron et al.A.Q.R. Baron et al.
The transverse The transverse coherence lengthcoherence length
Measured time responses divided by the fit to the response at rest.
A.Q.R. Baron et al.A.Q.R. Baron et al.
The transverse The transverse coherence lengthcoherence length
H.F. GrH.F. Grünsteudel et al.ünsteudel et al.
Domain structure in iron at the Domain structure in iron at the transitiontransition
3 m 57Fe foil at 15 GPa.
–Fe: ferromagnetic, –Fe: paramagnetic. Solid line: incoherent sum using the coherent time responses of –Fe (21%), –Fe (38%) and the coherent sum of both. The effective transverse coherence length was Lc 10 Å.
–Fe response
–Fe response
coherent sum of 50% –Fe and 50% –Fe
incoherent sum of 50% –Fe and 50% –Fe
H.F. GrH.F. Grünsteudel et al.ünsteudel et al.
Domain structure in iron at the Domain structure in iron at the transitiontransition
NRS vs. conventional MSNRS vs. conventional MS
NRS is not just a repetition of conventional energy-domain Mössbauer spectroscopy; the two methods are complementary. It should be applied when unique properties of SR are used:
- small solid angle is available (e.g., at grazing-incidence experiments in thin films),
- small samples are available (small single crystals, high-pressure experiments, biological samples),
- linear polarised radiation is advantageous (determination of the hyperfine field direction),
- etc.
sample
t
t t
NFSE=0
E>0E<0
t t
E=0:
NIS
NFS
NIS
E=0
E>0E<0
beamIC
HRM
time
time
relative energy
relative energy
H. GrH. Grünsteudelünsteudel
Setup for a nuclear inelastic scattering Setup for a nuclear inelastic scattering experimentexperiment
Nuclear inelastic scattering experimentNuclear inelastic scattering experiment The pulsed SR beam is monochromatized to a
meV energy band with the high-resolution monochromator before it penetrates the ionization chamber (IC) and the sample.
The radiative decay of the resonant nuclei in the sample is measured with two APD detectors: one in forward direction (NFS), which collects data only from a small solid angle (top) and one at 90 (NIS) which collects data in a large solid angle (bottom).
Nuclear inelastic scattering experimentNuclear inelastic scattering experiment
At exact resonance energy (E) the NFS detector collects the time-depending NFS.
During scanning the energy of the incident beam by detuning the HRM the time-integrated signal of the NFS detector shows a sharp peak at E which represents the energy resolution of the monochromator system.
Nuclear inelastic scattering experimentNuclear inelastic scattering experiment
The time-integrated signal of the NIS detector shows for the same energy scan a high central peak at Eand peaks apart from the resonance energy, depending on the sample. This energy spectrum represents the probability of resonance absorption with recoil overlapped by the signal at E produced by subsequent processes of the internal conversion. The time dependence of the NIS signal shows an exponential decay after excitation, since the data are collected angle-integrated.
-60 -40 -20 0 20 40 600
200
400
600
Counts
Relative energy [meV]
Lattice dynamics in an icosahedral Lattice dynamics in an icosahedral AlAl6262CuCu25.525.5FeFe12.512.5 quasicrystal quasicrystal (A. Chumakov)(A. Chumakov)
Inelastic x-ray scattering with nuclear Inelastic x-ray scattering with nuclear resonant anayserresonant anayser
Chumakov et al., Phys. Rev. Lett. 76, 4258 (1996)
Inelastic x-ray scattering with nuclear Inelastic x-ray scattering with nuclear resonant anayserresonant anayser
E. Gerdau, H. de Waard (eds.), Nuclear Resonant Scattering of Synchrotron Radiation, special volumes 123/124 and 125 of Hyp. Int.
ReferenceReference
ProblemsProblems
1. Bunch modes at ESRF: uniform filling: 992 bunches uniformly distributed in
the storage ring, 1/3 filling: 331 bunches filling 1/3 of the ring, single-bunch filling: 1 bunch in the ring, 16-bunch filling: 16 bunches uniformly distributed in
the storage ring, hybrid filling: 331 bunches filling 1/3 of the ring + 1
bunch in front of the 331 bunches.
Which modes are suitable for nuclear resonant forward scattering experiments on 57Fe (nuclear lifetime of the resonant level: 141 ns)? And for inelastic scattering experiments on the same nucleus?
ProblemsProblems
2. Explain qualitatively, why no quantum beats but an exponential decay is observed when the axially symmetric EFG axis is perpendicular both to k and E. (1/2 3/2 transition).
3. A 57Fe foil is randomly vibrating along the photon beam with an average frequency = 10 Hz and an amplitudea = 5 mm. Describe qualitatively the conventional energy-domain Mössbauer spectrum as compared with the case of the static foil! Do the same for the nuclear resonant forward scattering of SR!
ProblemsProblems
4. A resonant photon beam is passing two subsequent 57Fe foils. Both foils are magnetised to saturation in high magnetic fields perpendicular to the sample plane, i.e., along the photon beam. Both energy- and time-domain Mössbauer experiments are performed for a) parallel b) antiparallel magnetisations of the two foils. Describe qualitatively the results of both pairs of experiments!
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