Holographic Imaging of Atomic Structure:
Where Is It and Where Can It Go?
C.S. Fadley
UC 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 Biosciences
V.K. Yachandra,T.N. Earnest, LBNL Physical Biosciences
M. Tegze, G. Faigel--Budapest
M. Belakhovsky--Grenoble, ESRF
J. Garcia de Abajo--San Sebastian (theory)
Direct or Inside-Source Holography
Hologram Detector (scanned)
Reference
wave
Emitted
source wave
Scattered
Exciting beam
object/subject
waves
Emitter =
“inside source”
Scattering
centers:
atoms, nuclei
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.)
Inverse or Inside-Detector Holography
Neutron
scattered
Exciting beamIncoherently
Emitted
detected
neutrons
(from
protons)
= source wave
wave
(Sur et al.)
X-ray
Fluorescent
x-ray
Detector
(fixed)
Emitted
detected wave
Gamma ray/X-ray
Conversion e(nuclear resonance) or gamma ray
Neutron
(nuclear excitation)
Emitter =
“inside detector”
Scattered
object/subject
waves
Gamma ray
The basic imaging ideas:
(Gabor; Helmholtz-Kirchoff; Wolf; Szöke; Barton-Tong)
I( k )
k
3D sampled
region
O
I( k )  Φref ( k )  Φobj ( k )
2
2
The hologram
Weak,
isotropic
scattering
 Φref ( k )  Φref ( k )Φobj ( k )  Φref ( k )Φobj ( k )  Φobj ( k )
*
*
I( k )  I0 I( k )  Φref ( k )
Ho log ram : χ( k ) 

2
I0
Φref ( k )
Ho log raphic image :
U( r ) 
 χ( k )exp[ ik
3
r  ikr ]d k
2
2
2
(No phase problem!)
Inside-Source Holography
with Thermal Neutrons
Inside-Source
Neutron Hologram
Al4Ta3O13(OH)
+ Bragg peaks
Sur et al. Nature
414, 525 (2002)
ΔI
 0.5%
I
O-atom holographic Image-Centered on H
Direct or Inside-Source Holography
Hologram Detector (scanned)
Reference
wave
Emitted
source wave
Scattered
Exciting beam
object/subject
waves
Emitter =
“inside source”
Scattering
centers:
atoms, nuclei
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
Inverse or Inside-Detector Holography
Incoherently scattered
neutrons (from protons)
Exciting beam
= source wave
Detector
(fixed)
X-ray
Emitted
detected wave
Emitter =
“inside detector”
Emitted detected
wave
Fluorescent x-ray
(Gog et al.)
Gamma ray/X-ray
Conversion e(nuclear resonance) or gamma ray
(Korecki et al.)
Scattered
object/subject
waves
Neutron
(nuclear excitation)
Gamma ray
(Cser et al.)
Inside-Detector Holography
with Gamma Rays & Resonant Scattering
Resonantly
scattering
nucleus
Far-field
gamma
source
e-
Horizontal
Emitting
nucleus
Hologram--Fe epitaxial film
ΔI
 2%
I
Vertical
Korecki et al. PRL
79, 3518 (1997)
Images
Photoelectron and x-ray fluorescence holography:
(a) Inside-source holography
(direct, XFH):
Scattering
atom
Detector
(small solid
angle)
ALS und.
hnexcit
beamlines Exciting
4.0.2, 7.0.2 x-rays
Emitting
atom
(b) Inside-detector holography
(inverse, MEXH):
Scattering
atom
Object
Detector
(large solid
angle)
hnfluor
Emitting
atom
ALS b.m.
Exciting beamlines
x-rays
9.3.1
11.3.1
superbend?
Scattering of x-rays and electrons :
X-ray scattering from Ni (+Thomson + resonant effects)
|f0()|
|0()|
Electron scattering from Ni
|f()|
|()|
Inside-source - PH:
W 4f7/2 photoelectron spectra
Two site-specific holograms
Inside-source - PH:
Len et al. PRB
59, 5857 (1999)
Images centered on surface W atom
Len et al. PRB
59, 5857 (1999)
Inside-detector XFH: can be multi-energy
“MEXH”
Fe K
ΔI
 0.5 %
I
3 energies
Images
of Fe2O3
Gog et al. PRL
76, 3132 (1996)
Expt.
Theory
Inside-source XFH:
Fe K hologram
bcc Fe
Symmetrized image
2 energies-K & K
Kossel lines
ΔI
 0.3  0.5 %
I
Hiort et al. PRB
61, R830 (2000)
e
Inside-detector XFH:
Zn (0.02%) in GaAs
Zn K
2-energy
image
centered
on Zn dopant
Hayashi et al., PRB 63, 041201 (2001)
Zn K hologram, 9.7 keV
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 from
As/Si(111):
U( r ) 
 χ( k )exp[ ik
with χˆ 
3
r  ikr ]d k
2
I( k )  I0
I0
and I( k ) from int egration of log arithmic
derivative
I( hν  δ , kˆ )  I( hν  δ , kˆ )
ˆ
L( hν , k ) 
,
 I( hν  δ , kˆ )  I( hν  δ , kˆ )  δ


I( k )  I( k , kˆ )  A L( hv , kˆ )d 3 k

Luh, Miller, Chiang, PRL
81, 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)).
Forward
scatt.
Near-node photoelectron
holography:
Al 2s emission from
Al(111)
Image around
average Al emitter
Differential
cross section
Wider et al. PRL
86, 2337 (2001)
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)).
Normal hologram
 k    F j exp[ ikrj  ik  r j ]  c.c. (Fj = strength of jth scatterer)
j
Differential hologram
 k    k     k  


k  k  k 2
  F jeff k exp ikrj  ik  r j  c.c.
j

 k
F k   F j exp i r j  ikˆ  r j
 2
eff
j
Differential PH (k  0.1 Å-1)
0




 k

ˆ
  2iF j k  sin  2 r j  ik  r j 



0
(a) k=4.6Å-1 (81eV),  k = 0.2Å -1 ( E = 7 eV)
f
180o
back
=0o
fwd.
f eff
(b) k=8.8Å-1 (295eV), k = 1.0Å -1 ( E = 67eV)
f
180o
back
=0o
fwd.
f eff
Differential photoelectron holography:
normal and effective scattering factors for Cu
Cu 3p-Cu(001)-differential
holography
6
6
emitter
4
4’
3
[001] z (Å)
2
e
4’
4
3
2
[100 ]
x ( Å)
1
2’
A
1
2’
Å)
[010 ] y (
Differential photoelectron holography:
imaging of back, side, (and fwd.) scattering atoms
(Omori et al., PRL 88, 055504 (’02) and
animations 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 spinsensitive  instead of  : should permit imaging short-range magnetic
order (Kaduwela et al. PRB 50, 9656 (1994))
Simulation: MnO-AF cluster
Spin-polarized
photoelectron holography:
direct imaging of magnetic
moments in 3D:
Normal image-
  
U r  
χ k exp  ik  r  ikr  d 3 k
2
Spin-selective imagesΔ  r   U  r   U  r 
Δ'  r  
 exp  ik  r  
k
 exp  ikr   χ  k   χ  k d


3
k
k̂
Kaduwela et al. , Phys. Rev. B 50, 9656
(1994); Fadley et al., J. Phys. B
Cond. Matt. 13, 10517 (2001)
Photoelectron holographyAdvantages:
Element-, chemical state-, and spin- specific local structure
Long-range order not required
Large % effects, easy to measure
Surface sensitive, if that’s what you want
Avoids 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 status
Detectors not fast enough/linear enough to handle “snapshot”
spectra (cf. ALS project)
ALS GHz-RATE 1D DETECTOR
768 channels, 48  spacing, >2 GHz overall
Protective shell
Microchannel
plates
768 collector
strips
Ampl./Discr.
(CAFE-M)
Counter/
digital readout
(BMC)
Ceramic
substrate
Spring clamps for
circuit board
and MCP cover
Photoelectron holographyAdvantages:
Element-, chemical state-, and spin- specific local structure
Long-range order not required
Large % effects, easy to measure
Surface sensitive, if that’s what you want
Avoids false minima in structure optimization
Disadvantages:
Strong scattering leads to multiple scattering (but can be
suppressed by multi-energy datasets)
Not bulk sensitive, if that’s what you want
Requires at least short-range repeated order
Future prospects and instrumentation issues:
--Present status
Detectors not fast enough/linear enough to handle “snapshot”
spectra (cf. ALS project)
Scanning of sample angles not fast enough
--Future possibilities
Much faster multichannel detectors up to GHz range
Faster scanning of angles via snapshot mode
“Tiling” of hemisphere with analyzers to reduce angle scanning
XFH at ESRF:
Focal spot
Sample
Graphite
analyser
j
K
Detector

Graphite
analyzer
Graphit e analyser
K
2f
SR
Beam
Marchesini, Tegze, Faigel et al.,
Nucl. Inst. & Meth. 457, 601 (2001)
X-RAY FLUORESCENCE HOLOGRAPHY AT ESRF--SOME HIGHLIGHTS
(Marchesini, Tegze, Faigel et al.)
Imaging light atoms:
Nature 407, 38 (2000)
Imaging a quasicrystal:
Phys. Rev. Lett. 85, 4723 (2000)
 O around Ni in NiO
 ~150 O and Ni atoms imaged
 method works without true periodicity
 neighbours around Mn in MnAlPd
 image of average atomic distribution
Ni K Hologram
Mn K Hologram
Image
Image
Al.704 Pd.210Mn.086 Quasicrystal
ESRF--S. Marchesini et al.
Phys. Rev. Lett. 85, 4723 (2000)
First ALS Holograms
Pd L
Mn K Hologram
First application of hard
x-ray holography to
complex system
Structural information in
direct space without any
assumed model
Bragg
spots
Future data
Reconstruction
Environments around
both Mn and Pd imaged
Data at many
energiesextended range
of imaging
More precise atomic
environments in the first
5–6 coordination shells,
evidence for inflation
Rigorous test of
theoretical models
Sample
edge
Mn K
Samples:
P. Thiel
P. Canfield
X-RAY FLUORESCENCE HOLOGRAPHY AT THE ALS
Future plans
(a) Experimental setup: (Marchesini et al.)
Motion
PC
Motion
Drivers

Clock
j
•Sample heating/coolingphase-transition studies
High speed
motionacquisitiond/dt =
3600o/sec
•Applications to: strongly
correlated materials
(CMR high-T phases),
magnetic quasicrystals
(RE-Mg-Zn--I. Fisher),
bio-relevant crystals
d/dt =
Acquisition
Acquisition
2o/sec
Ge solid state det.- up to 4MHz
Monochromatic
x-rays
(b-e) First data
(c) Calc.
ALS
(d) Mn-atom image
(scales in Å)
MnO (100)
(b) Expt.
•Development of:
-Resonant and
dichroic XFH
-More efficient pixel
detectors
6
CMR: (La,Sr)3Mn2O7
(e) Expt.
1
(a.u.)
F.T.
(La, Sr) Mn
-6
0
-6 Å
6Å
O
Jahn-Teller distortions probed with x-ray fluorescence
holography: new insights on the CMR effect?
La1-xAxMnO3 , A = Ca, Sr
, Ca
Cubic
Orthorhombic
LaMnO3 shows long range
Jahn-Teller distortions (JT)
2.15
1.92
When x > 0, one theory predicts
the coupling of the itinerant
electrons with
local, short-range JT dist.
in the T > Tc insulating phase
Key to CMR effect?
Schematic view of the tetragonal Jahn-Teller
distortions in the ab plane
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.
RESONANT
X-RAY
FLUORESCENCE
HOLOGRAPHY:
A theoretical
study
(cf. Van Hove
talk)
Optical constants for Fe and Ni through the Ni K(1s) edge
Normal hologram
 k    F j exp[ ikrj  ik  r j ]  c.c.
j
Differential hologram
 k    k     k  


k   k  k 2
  F jeff k exp ikrj  ik  r j  c.c.
j

 k
F jeff k   F j exp i
r j  ikˆ  r j
 2
  2iF k

Differential PH (k  0.1 Å-1)
0
j
 k
ˆ  r 


sin
r

i
k

j
j 

2
0
Resonant inverse XFH (k  0.01 Å-1)
Resonant atom
f1+if2
0
Non-resonant atom
0
0

Resonant x-ray fluorescence holography
(a)
(b) MEXH--Fe & Ni
Fe1
Ni1
Fe2
Fe1
(c) RXFH--Fe suppressed
Ni1
Ni1
Fe2
(d) MEXH--Fe & Ni
Fe1
Ni1
Fe2
(e) RXFH--Fe suppressed
Ni1
Omori et
al., PRB 65,
014106
(2002)
FeNi3: Structure and simulated holographic images
in normal inverse (MEXH) and resonant (RXFH) modes
Resonant X-Ray Fluorescence Holography
Measuring Cd x-ray
holograms above and
below the Te L3 edge
from CdTe
Te L3 Absorption
Coefficient (in e-)
Photon energy (keV)
1 14
4
12
Identification of nearneighbour
scatterers,
‘true color’ holography.
4
3
10
8
6
4
1-2=a
a
1
2
4-2=b
2
4.0 4.2
2
4.4
3
4.6
4.8
b
CdTe structure
Some potential applications of x-ray holography:
source or
detector site
source or
detector site
average
source/
detector site
average
source/
detector site
source or
detector site
Identify via
resonant
XFH?
average
source/
detector site
source or
detector site
Identify via
resonant
XFH?
average
source/
detector site
…and ultimately more dilute species:
source or
detector site
Active sites in biorelevant
molecules
average
source/
detector site
source or
detector site
source or
detector site
average
source/
detector site
average
source/
detector site
X-ray fluorescence holographyAdvantages:
Element-specific local structure
Weak scattering, better holographic imaging
Long-range order not required
Mosaicity up to few degrees OK
Avoids false minima in structure optimization
With resonance, near-neighbor identification?
With CP radiation, short-range magnetic order imaging?
Disadvantages:
Small % effects, need approx. 109-1010 counts in hologram
Requires at least short-range repeated order
X-ray fluorescence holography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 overallhologram in
0.1-10 sec, or in one LCLS pulse
E.g., the LBNL Gammasphere:
Why not!
110 large volume, highpurity germanium detectors
The End