Holographic Imaging of Atomic Structure: Where Is It and Where Can It Go?
C.S. FadleyUC Davis Physics and LBNL Materials Sciences
Collaborators:S. Marchesini, N. Mannella, A. Nambu, S. Ritchey, L. Zhao--
LBNL Material Sciences and UCD (experiment, theory)D. Shuh, G. Bucher--LBNL-Chemical Sciences (solid state detector)
L. Fabris, N. Madden--LBNL Eng. (solid state detector)W. Stolte, A.S. Schlachter--ALS (BL 9.3.1)
A. Thompson--ALS (BL 11.3.1)M.A. Van Hove, S. Omori--LBNL Materials Sciences (theory)
E. Rotenberg, J. Denlinger, M. Howells, Z. Hussain, ALS (experiment)A. Szöke--LLNL (theory)
S.P. Cramer, U. Bergmann--UCD and LBNL Physical BiosciencesV.K. Yachandra,T.N. Earnest, LBNL Physical Biosciences
M. Tegze, G. Faigel--BudapestM. Belakhovsky--Grenoble, ESRF
J. Garcia de Abajo--San Sebastian (theory)
Exciting beam
Emitter = “inside source”
Hologram
Scattered object/subject waves
Reference waveEmitted
source wave
Scattering centers: atoms, nuclei
Direct or Inside-Source Holography
Inverse or Inside-Detector Holography
Refer
ence
wave
Detector(fixed)
Scattered object/subject waves
Emitter = “inside detector”
Exciti
ng bea
m
(sca
nned)
Emitted detected wave
Exciting beam Emitted detected = source wave wave
X-ray Fluorescent x-ray
Gamma ray/X-ray Conversion e-
(nuclear resonance) or gamma ray
Neutron Gamma ray(nuclear excitation)
Detector (scanned) Exciting beam Emitted source wave
X-ray/Electron Auger electron(Tonner)
X-ray Photoelectron(Szöke, Barton)
X-ray Fluorescent x-ray(Tegze, Faigel)
Electron Incoherently scattered/ Kikuchi electrons
(Saldin, de Andres) Electron Bremsstrahlung x-ray + filter
(Sorensen et al.)
Neutron Incoherently scattered neutrons (from protons)
(Sur et al.)
The basic imaging ideas:(Gabor; Helmholtz-Kirchoff; Wolf; Szöke; Barton-Tong)
2
ref obj
2 2*ref ref obj ref obj obj
2
ref02
0ref
23
*
I( k ) Φ ( k ) Φ ( k )
Φ ( k ) Φ ( k )Φ ( k ) Φ ( k )Φ ( k ) Φ ( k )
I( k ) Φ ( k )I( k ) IHo log ram : χ( k )
I Φ ( k )Ho log raphic image :
U( r ) χ( k )exp[ ik r ikr ]d k
k I( k )
O
3D sampled region
Weak,isotropicscattering
The hologram
Energy
An
gle
(No phase problem!)
Inside-SourceNeutron Hologram
Al4Ta3O13(OH)
O-atom holographic Image--Centered on H
Sur et al. Nature414, 525 (2002)
Inside-Source Holographywith Thermal Neutrons
ΔI0.5%
I
+ Bragg peaks
Exciting beam
Emitter = “inside source”
Hologram
Scattered object/subject waves
Reference waveEmitted
source wave
Scattering centers: atoms, nuclei
Direct or Inside-Source Holography
Inverse or Inside-Detector Holography
Refer
ence
wave
Detector(fixed)
Scattered object/subject waves
Emitter = “inside detector”
Exciti
ng bea
m
(sca
nned)
Emitted detected wave
Detector (scanned) Exciting beam Emitted source wave
X-ray/Electron Auger electron
X-ray Photoelectron
X-ray Fluorescent x-ray
Electron Incoherently scattered/ Kikuchi electrons Electron Bremsstrahlung x-ray + filter
Neutron Incoherently scattered neutrons (from protons)
Exciting beam Emitted detected = source wave wave
X-ray Fluorescent x-ray (Gog et al.)
Gamma ray/X-ray Conversion e-
(nuclear resonance) or gamma ray (Korecki et al.)
Neutron Gamma ray(nuclear excitation) (Cser et al.)
Inside-Detector Holographywith Gamma Rays & Resonant Scattering
Korecki et al. PRL79, 3518 (1997)
ΔI2%
I
Hologram--Fe epitaxial film
Images
Resonantlyscatteringnucleus
Emittingnucleus
Far-fieldgammasource
Horizontal
Vertical
e-
Photoelectron and x-ray fluorescence holography:
(a) Inside-source holography (direct, XFH):
(b) Inside-detector holography (inverse, MEXH):
Emitting atom
Scatteringatom
Exciting x-rays
Object
Reference
Emitting atom
Scatteringatom
Detector(large solid
angle)
Excitingx-rays
Object
Reference
h fluoror
photo-e-
hexcit
Detector(small solid
angle)
hexcit
hfluor
ALS b.m. beamlines 9.3.1 11.3.1superbend?
ALS und.beamlines 4.0.2, 7.0.2
Scattering of x-rays and electrons :
Electron scattering from Ni
|f0()|
|f()|
|0()|
|()|
X-ray scattering from Ni (+Thomson + resonant effects)
Inside-source - PH:W 4f7/2 photoelectron spectra
bu
lk
surf
ace
Two site-specific holograms
Inside-source - PH:
Len et al. PRB59, 5857 (1999)
Images centered on surface W atom
bu
lk
surf
a ce
Len et al. PRB59, 5857 (1999)
Imagesof Fe2O3
Gog et al. PRL76, 3132 (1996)
Expt. TheoryΔI0.5 %
I
Fe K
3 energies
Inside-detector XFH: can be multi-energy“MEXH”
Inside-source XFH:
Fe K hologram
Kossel lines
bcc FeSymmetrized image2 energies-K & K
Hiort et al. PRB61, R830 (2000)
ΔI0.3 0.5 %
I e
Inside-detector XFH:Zn (0.02%) in GaAs
Zn K
Zn K hologram, 9.7 keV
2-energyimage
centered on Zn dopant
Hayashi et al., PRB 63, 041201 (2001)
Some ideas to improve holographic images:
Derivative photoelectron holography: Taking differences of intensity to yield logarithmic derivative of I(k), then reintegrate: reduces noise/uncertainty in data (Chiang et al., PRL 81, 4160, (1998))
Photoelectron holography:As and Si emission fromAs/Si(111):
23
0
0
3
U( r ) χ( k )exp[ ik r ikr ]d k
I( k ) Iˆwith χ
I
and I( k ) from int egration of log arithmic
derivative
ˆ ˆI( hν δ,k ) I( hν δ,k )ˆL( hν ,k ) ,ˆ ˆI( hν δ,k ) I( hν δ,k ) δ
ˆ ˆI( k ) I( k ,k ) A L( hv ,k )d k
Luh, Miller, Chiang, PRL81, 4160 (1998)
Some ideas to improve holographic images:
Derivative photoelectron holography: Taking differences of intensity to yield logarithmic derivative of I(k), then reintegrate: reduces noise/uncertainty in data (Chiang et al., PRL 81, 4160, (1998))
Near-node photoelectron holography: Working near the node of the differential cross section: suppresses forward scattering,improves, images (Greber et al., PRL 86, 2337 (2001)).
Forwardscatt.
Differentialcross section
Near-node photoelectronholography:Al 2s emission fromAl(111)
Wider et al. PRL86, 2337 (2001)
Image aroundaverage Al emitter
e
Some ideas to improve holographic images:
Derivative photoelectron holography: Taking differences of intensity to yield logarithmic derivative of I(k), then reintegrate: reduces noise/uncertainty in data (Chiang et al., PRL 81, 4160, (1998))
Near-node photoelectron holography: Working near the node of the differential cross section: suppresses forward scattering,improves, images (Greber et al., PRL 86, 2337 (2001)).
Differential photoelectron holography: Transforming instead of : also solves the forward scattering problem (Omori et al., PRL 88, 055504 (2002)).
Differential PH (k 0.1 Å-1) 0 0
2kkk
..]exp[ cciikrFj
jjj rkk
..expeff ccriikrF
jjjj
kk
kkk
jjjjjjj ir
kiFir
kiFF rkkrkk ˆ
2sin2ˆ
2expeff
Normal hologram
Differential hologram
(Fj = strength of jth scatterer)
Diff erential photoelectron holography: normal and eff ective scattering factors for Cu
(a) k=4.6Å-1 (81eV), k = 0.2Å-1 (E = 7 eV)
f
efff
=0o180o
fwd.back
(b) k=8.8Å-1 (295eV), k = 1.0Å-1 (E = 67eV)
f
efff
=0o180o
fwd.back
12
3
4
6
e
A
2’
4’
6
4emitter
4’
3
21
2’
Cu 3p-Cu(001)- -diff erentialholography
[100] x (Å) [010] y (Å)
[001
] z (Å
)
Diff erential photoelectron holography: imaging of back, side, (and fwd.) scattering atoms
(Omori et al., PRL 88, 055504 (’02) andanimations at http:/ /electron.lbl.gov/ marchesini/dph)
Some ideas to improve holographic images:
Derivative photoelectron holography: Taking differences of intensity to yield logarithmic derivative of I(k), then reintegrate: reduces noise/uncertainty in data (Chiang et al., PRL 81, 4160, (1998))
Near-node photoelectron holography: Working near the node of the differential cross section: suppresses forward scattering,improves, images (Greber et al., PRL 86, 2337 (2001)).
Differential photoelectron holography: Transforming instead of : also solves the forward scattering problem (Omori et al., PRL 88, 055504 (2002)).
Spin-polarized photoelectron holography: Transforming spin-sensitive instead of : should permit imaging short-range magnetic order (Kaduwela et al. PRB 50, 9656 (1994))
Spin-polarizedphotoelectron holography:direct imaging of magneticmoments in 3D:
Normal image-
Spin-selective images-
Δ r U r U r
k
3
k̂
exp ik r
Δ' rexp ikr χ k χ k d k
23U r χ k exp ik r ikr d k
Simulation: MnO-AF cluster
Kaduwela et al. , Phys. Rev. B 50, 9656 (1994); Fadley et al., J. Phys. B
Cond. Matt. 13, 10517 (2001)
Photoelectron holography-Advantages:Element-, chemical state-, and spin- specific local structureLong-range order not requiredLarge % effects, easy to measureSurface sensitive, if that’s what you wantAvoids false minima in structure searches
Disadvantages:Strong scattering leads to multiple scattering (but can be suppressed by multi-energy datasets)Not bulk sensitive, if that’s what you want
Future prospects and instrumentation issues:
--Present statusDetectors not fast enough/linear enough to handle “snapshot”
spectra (cf. ALS project)
Protective shell
Microchannel plates
768 collector stripsAmpl./Discr.(CAFE-M)
Counter/digital readout (BMC)Ceramicsubstrate
Spring clamps for circuit board and MCP cover
ALS GHz-RATE 1D DETECTOR768 channels, 48 spacing, >2 GHz overall
Energy
direct
ion
Photoelectron holography-Advantages:Element-, chemical state-, and spin- specific local structureLong-range order not requiredLarge % effects, easy to measureSurface sensitive, if that’s what you wantAvoids false minima in structure optimizationDisadvantages:Strong scattering leads to multiple scattering (but can be suppressed by multi-energy datasets)Not bulk sensitive, if that’s what you wantRequires at least short-range repeated order
Future prospects and instrumentation issues: --Present statusDetectors not fast enough/linear enough to handle “snapshot”
spectra (cf. ALS project)Scanning of sample angles not fast enough
--Future possibilitiesMuch faster multichannel detectors up to GHz rangeFaster scanning of angles via snapshot mode“Tiling” of hemisphere with analyzers to reduce angle scanning
SRBeam
Detector
Graphite analyser
2f
Sample
Focal spot
K
K
Graphite analyser
Marchesini, Tegze, Faigel et al.,Nucl. Inst. & Meth. 457, 601 (2001)
XFH at ESRF:
Graphite analyzer
X-RAY FLUORESCENCE HOLOGRAPHY AT ESRF--SOME HIGHLIGHTS(Marchesini, Tegze, Faigel et al.)
Imaging light atoms: Imaging a quasicrystal: Nature 407, 38 (2000) Phys. Rev. Lett. 85, 4723 (2000)
O around Ni in NiO method works without true periodicity ~150 O and Ni atoms imaged neighbours around Mn in MnAlPd
image of average atomic distributionNi K Hologram
Mn K Hologram
Image
Image
ESRF--S. Marchesini et al. Phys. Rev. Lett. 85, 4723 (2000)
Al.704 Pd.210Mn.086 Quasicrystal First ALS Holograms
First application of hard x-ray holography to complex system Structural information in direct space without any assumed model
Future dataEnvironments around both Mn and Pd imagedData at many energiesextended range of imagingMore precise atomic environments in the first 5–6 coordination shells, evidence for inflationRigorous test of theoretical models
Pd L
Mn K
Bragg spots
Sample edgeReconstruction
Samples: P. Thiel P. Canfield
Mn K Hologram
0
6
-6
6 Å-6 Å
1 (a.u.)
MnO (100)(b) Expt. (c) Calc.
(d) Mn-atom image (scales in Å)
(a) Experimental setup: (Marchesini et al.)
Det
PC
Motion
Acquisition
Drivers
Acquisition
Motion
Clock
ALSMonochromaticx-rays
High speed motion-acquisition-d/dt = 3600o/sec
d/dt =
2o/sec
Ge solid state det.-- up to 4MHz
(La, Sr) Mn O
X-RAY FLUORESCENCE HOLOGRAPHY AT THE ALS
(b-e) First data
Future plans
•Sample heating/cooling- phase-transition studies
•Applications to: strongly correlated materials (CMR high-T phases), magnetic quasicrystals (RE-Mg-Zn--I. Fisher), bio-relevant crystals
•Development of: -Resonant and dichroic XFH -More efficient pixel detectors
(e) Expt.
CMR: (La,Sr)3Mn2O7
F.T.
La1-xAxMnO3 , A = Ca, Sr
, Ca
LaMnO3 shows long range Jahn-Teller distortions (JT)
When x > 0, one theory predicts the coupling of the itinerant
electrons with local, short-range JT dist.
in the T > Tc insulating phase
Cubic Orthorhombic
Schematic view of the tetragonal Jahn-Teller distortions in the ab plane
Key to CMR effect?
Jahn-Teller distortions probed with x-ray fluorescence holography: new insights on the CMR effect?
2.151.92
Some ideas to improve holographic images:
Derivative photoelectron holography: Taking differences of intensity to yield logarithmic derivative of I(k), then reintegrate: reduces noise/uncertainty in data (Chiang et al., PRL 81, 4160, (1998))
Near-node photoelectron holography: Working near the node of the differential cross section: suppresses forward scattering,improves, images (Greber et al., PRL 86, 2337 (2001)).
Differential photoelectron holography: Transforming instead of : also solves the forward scattering problem (Omori et al., PRL 88, 055504 (2002)).
Spin-polarized photoelectron holography: Transforming spin-sensitive instead of : should permit imaging short-range magnetic order (Kaduwela et al. PRB 50, 9656 (1994))
Resonant x-ray fluorescence holography: Taking difference holograms above and below a core-level resonance on atom A, and imaging on again,with weighting wk= +1 below resonance and -1 above resonance, and (below) and (above) calculated at three energies below, on, and above resonance, yields images in which only atom A is prominent.
Optical constants for Fe and Ni through the Ni K(1s) edge
RESONANTX-RAY FLUORESCENCE HOLOGRAPHY:A theoreticalstudy(cf. Van Hove talk)
2kkk
Differential PH (k 0.1 Å-1) 0 0
Resonant inverse XFH (k 0.01 Å-1)
Resonant atom f1+if2 0
Non-resonant atom 0 0
..]exp[ cciikrFj
jjj rkk
..expeff ccriikrF
jjjj
kk
kkk
jjjjjjj ir
kiFir
kiFF rkkrkk ˆ
2sin2ˆ
2expeff
Normal hologram
Differential hologram
(a) (c) RXFH--Fe suppressed(b) MEXH--Fe & Ni
3.55×2 Å
Fe2
Fe1Ni1
(d) MEXH--Fe & Ni (e) RXFH--Fe suppressed
FeNi3: Structure and simulated holographic images in normal inverse (MEXH) and resonant (RXFH) modes
Fe2
Ni1
Fe1
Omori et al., PRB 65, 014106 (2002)
Ni1
Fe1
Fe2
Ni1
Ni1
Resonant x-ray fluorescence holography
4.0 4.2 4.4 4.6 4.82
4
6
8
10
12
14
Resonant X-Ray Fluorescence Holography
Te L3 Absorption Coefficient (in e-)
Photon energy (keV)
CdTe structure
Measuring Cd x-ray holograms above and below the Te L3 edge from CdTe
Identification of near-neighbour scatterers, ‘true color’ holography.
1-2=a
1 2
3 4
4-2=b
1
2 3
4
a b
averagesource/
detector site
Identify viaresonant
XFH?Identify viaresonant
XFH?
Some potential applications of x-ray holography:
source or detector site
source or detector site
source or detector site
source or detector site
averagesource/
detector site
averagesource/
detector site
averagesource/
detector site
Active sites in biorelevant molecules
source or detector site
source or detector site
source or detector site
averagesource/
detector site
averagesource/
detector site
averagesource/
detector site
…and ultimately more dilute species:
X-ray fluorescence holography-Advantages:Element-specific local structure
Weak scattering, better holographic imagingLong-range order not requiredMosaicity up to few degrees OKAvoids false minima in structure optimizationWith resonance, near-neighbor identification?With CP radiation, short-range magnetic order imaging?
Disadvantages:Small % effects, need approx. 109-1010 counts in hologramRequires at least short-range repeated order
Future prospects and instrumentation issues:
--Present status
Detector-limited--e.g., graphite crystal plus avalanche photodiode (ESRF); Ge detectors up to 1 MHz over 4 elements (LBNL)hologram in approx. 1-10 hours
--Future possibilities
"Tiling" of hemisphere with Ge detectors ala Gammasphere, Si drift diodes (HASYLAB, Materlik et al.?, commercial sources Ketek and Photon Imaging?)
--Future “dream machine”
1 angular resolution, 100 eV resolution for x-rays at 6-20 keV, hemisphere coverage, 1-100 GHz overallhologram in 0.1-10 sec, or in one LCLS pulse
X-ray fluorescence holography-
E.g., the LBNL Gammasphere:
110 large volume, high-purity germanium detectors
Why not!
The End
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