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Anomalous X-ray Diffraction (AXRD)
Joanna Bettinger & Sumohan Misra
joannab@slac.stanford.edumisra@slac.stanford.edu
5th Annual SSRL School on Synchrotron X-ray Scattering Techniques in Materials and Environmental Sciences: Theory and Application
June 1st, 2010
Outline
• Introduction
• Preliminary Simulations
• CuInS2 nanoparticles
• ZnRh2O4 powders
• Data Collection and Analysis
• ZnRh2O4 (Thickness Dependence)
• CuInS2 Nanoparticles (Attenuation Factors)
• MnCr2O4 & NiMn2O4 (Kramers-Kronig Transformation)
SSRL Beamline 2-1
Why AXRD??
• Sensitive to neighboring elements in the periodic table (e.g., can distinguish between Ga & Ge or Cu & Zn)
• Sensitive to a specific crystallographic phase(e.g., can investigate Cu2S layer growing on CuInS2)
• Sensitive to a specific crystallographic site in a phase (e.g., can investigate the tetrahedral and the octahedral site of ZnRh2O4 spinels)
Anomalous X-ray Diffraction (AXRD)
fn = f0(Q) + f ′(E) + i f ′ ′(E)f0(Q) = normal (E independent)f ’(E) = anomalous (E dependent)f ’’(E) = absorption (E dependent)
2hklhkl FI =
( )( )∑=
++=atoms
n
lzkyhxinlkh
nnneEfF1
2),,( )( π
• fn is the atomic scattering factor• xn, yn, zn are the (fractional) positions of the nth atom
• Atomic scattering strength (fn) varies near X-ray absorption edge• Varying X-ray energy near absorption edge → total intensity changes• fn depends on oxidation state of the element
Variation for Zn
Energy, E (eV)
9000 9200 9400 9600 9800 10000 10200
Scat
teri
ng S
tren
gth
10
12
14
16
18
20
22
24
Scat
teri
ng S
tren
gth
0
2
4
6
8
10
f0+ f'f''
AXRD – Combination of Structural & Chemical Technique
Structural (XRD) Chemical (XAS)
X-rays diffract from specific planes
Diffraction peak
Near resonant absorption energy
X-raysabsorbed
RESULT
Diffracted peak intensity ↓ depending on elements present on diffracting planes
0.0
0.2
0.4
0.6
0.8
1.0
2.182.23
2.28
9600 9650 9700 9750 9800
Inte
nsity
, I (a
.u.)
Q (Å-1 )
Energy, E (eV)
AXRD – Different Approaches
•Resonant X-ray Scattering (RXS) ---- Elemental site occupancies•Diffraction Anomalous Near-Edge Structure (DANES) ---- Site-specific valences and coordination (like XANES)•Diffraction Anomalous Fine Structure (DAFS) ---- Site-specific bond lengths, etc. (like EXAFS)
0.0
0.2
0.4
0.6
0.8
1.0
2.182.23
2.28
9600 9650 9700 9750 9800
Inte
nsity
, I (a
.u.)
Q (Å-1 )
Energy, E (eV)Energy, E (eV)
9300 9400 9500 9600 9700 9800 9900 10000 10100
Inte
nsity
, I (a
.u.)
1000
1200
1400
1600
1800
DANES
DAFSRXS
Zn edge↓
Preliminary Simulations
• CuInS2 (CISu) nanoparticles have been dopedwith Zn, Ga, Fe and Ag to improve theiroptoelectronic properties
We are using Anomalous XRD to understand the dopant locations e.g., substitutional, interstitial and/or segregated
http://www.advanced-energy.com
Doped-CuInS2 Nanoparticles
%Dopants in CISu0 5 10 15 20
Eg (e
V)
1.25
1.30
1.35
1.40
1.45
1.50
1.55
1.60
1.65
Ga Zn Fe
Band gap • Fe: drop in gap• Zn: increase in gap• Ga: little change
•The dopants are not incorporated homogeneously
Preliminary Simulations – CuInS2
Variation for Zn
Energy, E (eV)
9000 9200 9400 9600 9800 10000 10200
Scat
teri
ng S
tren
gth
10
12
14
16
18
20
22
24
Scat
teri
ng S
tren
gth
0
2
4
6
8
10
f0+ f'f''
• Define Crystal Structure • Define Tabulated Atomic Scatt. Factors vs. E
• Calculate Structure Factor for doped CuInS2
Cu/InS
• Define structure factor of complete hexagonal structure (as a function of dopant concentration)
Energy, E (eV)
8600 8800 9000 9200 9400 9600 9800 1000
Inte
nsity
, I (a
.u.)
0.75
0.80
0.85
0.90
0.95Cu-edge Zn-edge
( )( )nlznkynhxie
Of
Inf
ZnCuf
lkhF
++++
−=
π2*)*
2
1*
2
1(
),,(
ZnCuZnCu fxfxf *)1(* −+=−
x = % of Zn
Simulations for Zn doped-CuInS2
Peak (101)
Energy, E (eV)8860 8910 8960 9010 9060 9500 9600 9700 9800 9900
Inte
nsity
, I (a
.u.)
0.70
0.75
0.80
0.85
0.90
Inte
nsity
, I (a
.u.)
0.88
0.90
0.92
0.94
0.96
CISu-0% ZnCISu-5% ZnCISu-10% ZnCISu-20% Zn
Cu-edge Zn-edge
Zn doped-CISu
111 Reflection (Mixed)
Zn
RhInverse
Normal
ZnRh2O4 spinels
422 Reflection (Tetrahedral)Zn
Rh
Inverse
Normal
• How do you make a spinel a p-type TCO (how do you hole dope)?• Extrinsic Doping: Li+ on Zn2+ site
(Li.05Zn.95Rh2O4)• Intrinsic Doping: Zn2+ in place of Rh3+
(Zn1.05Rh1.95O4)• Vacancies: Vacancy in place of Zn or Rh
(Zn0.95Rh2O4)• p-type TCOs also found as other spinels
(NiCo2O4)• AXRD essential in probing the crystal
structure!
Optically Transparent Conductor: ZnRh2O4 Spinels
Motivation: Spinel oxides as p-type transparent conducting oxides (TCOs)• In collaboration with Thomas Mason, Nicola Perry, Arpun Nagaraja
(Northwestern University)• http://www.centerforinversedesign.org/
phy.bris.ac.uk
Tunable properties
many cation types and distributions possible
Zn Rh
Preliminary Simulations – ZnRh2O4
• Define Crystal Structure • Define Tabulated Atomic Scatt. Factors vs. E
• Calculate Structure Factor for ZnRh2O4 spinels
Zn, RhOxygen
• Define structure factor of complete structure
Zn Rh
Inverse
Normal
222 Reflection (Octahedral)
111 Reflection (Mixed)
Zn
RhInverse
Normal
422 Reflection (Tetrahedral)Zn
Rh
Inverse
Normal
Simulations for ZnRh2O4: Effect of Inversion
AXRD: Extremely useful to probe inversion in spinel oxides by probing which element sits on a particular interstitial site.
MixedSpinel
(0 <ν < 1)Normal spinel (ν = 0)
(Rh) (Zn) (Rh)B A B
Inverse spinel (ν = 1)
(Rh) (Rh) (Zn)B A B
AB2O4 degree of inversion
Data Collection&
Analysis
SSRL Beamline Capabilities
SSRL Scattering beamlines: ~ 5-22 keVHigher energy can be accessed at APS
Data Collection and Analysis
Collection:• Find reflection• Optimize beamline setup• Optimize peak scan (width and
count time)• Measure peak at energy steps
around absorption-edge• Take integrated intensity (area
under peak)– Mindful of background
subtraction• Plot as a function of energy
0.0
0.2
0.4
0.6
0.8
1.0
2.182.23
2.28
9600 9650 9700 9750 9800
Inte
nsity
, I (a
.u.)
Q (Å-1 )
Energy, E (eV)
Analysis:• Thickness effects• E-dependent attenuation factors (air, ion chambers, Be window)• Refining RXS/DANES (Kramers-Kronig)
Example 1: ZnRh2O4 Spinels
What we expect: What we measure:
Why are these so different? Why does the intensity stay low for the experimental data after
the absorption edge?
• As the energy is varied through the absorption edge, there is a stepfunction in diffracted intensity.
• For thin samples, this has a negligible effect, but for thicker samples(bulk powders, etc.) it becomes dominant and must be accounted for.
•How do we account for thickness effects? At what thickness do theseeffects become important?
Zn 422 Reflection
Inte
nsity
(a.u
.)
Energy (eV)
Infinitely thin sample
Includes thickness effects
Example 1: ZnRh2O4 Spinels (Thickness Dependence)
• Why is thickness important?• For very thin samples, the whole sample will have diffracted
intensity.• For thicker samples, the diffracted intensity will be coming
from a small finite surface layer.
• ZnRh2O4 samples < 500 nm can ignore thickness effects. These are pressed pellets ( > 1 mm) Thickness very important.
Example 1: ZnRh2O4 Spinels
• For flat plate geometry, θin = θout , very thick samples (like pressed pellets):
Diffracted intensity ID ∝ IO/2µ
• In simulations, divide ideal AXRD intensity by 2µ to get the thickness-normalized intensity.
Simulations assume normal spinel Zn only found in tetrahedral sites.
111 (Mixed Td and Oh) 222 (Octahedral) 422 (Tetrahedral)
Ideal AXRD intensity
“Actual” – includes thickness effect
Energy (eV) Energy (eV) Energy (eV)
Inte
nsity
(a.u
.)Example 1: ZnRh2O4 Spinels
111 (Mixed)
Energy (eV)
υ = 0.125
222 (Octahedral)
Energy (eV)
υ = 0.121
422 (Tetrahedral)
Energy (eV)
υ = 0.095
•AXRD performed on bulk ZnRh4O2 powders.•Thick samples step function at Zn edge due to absorption.•Expect an inversion of υ = 0 (normal spinel) but instead found an inversion of approximately 10% by comparing experimental data to simulations at 111, 222, and 422 reflections.•Preliminary fit (doesn’t include oxidation state).
Example 1: ZnRh2O4 Spinels
ZnRh2O4 Spinels: Conclusion
• Used SSRL beamline 2-1 to probe the Zn edge in bulk ZnRh2O4powder.• Samples for photovoltaic applications (transparent
conducting oxides).• AXRD essential to probe the cation distribution (which effects the
electronic properties).• Comparing experimental data with thickness-dependent
simulations reveals these samples are about 10% inverse (10% of Zn on octahedral sites).
MixedSpinel
(0 <ν < 1)Normal spinel (ν = 0)
(Rh) (Zn) (Rh)B A B
Inverse spinel (ν = 1)
(Rh) (Rh) (Zn)B A B
Atom Site x y z
Cu/In 2b 1/3 2/3 0
S 2b 1/3 2/3 0.375
Example 2: CuInS2 Nanoparticles
Wurtzite-CuInS2 (Hexagonal), (ZnO-type)
Cu/InS
• AXRD probes substitution on the crystal lattice site
Steve T. Connor (Stanford)
X-ray Diffraction Pattern for CuInS2
Q (Å-1)2.0 2.5 3.0 3.5 4.0
Inte
nsity
(a.u
.)
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18(101)
(002)
(102)
(110)
(100)
(103)
(200)
(112)
(201)
Hexagonal Wurtzite-CISu (ZnO-type)
• It is very important to identify the right Bragg peak
20% Zn doped-CISu
Energy, E (eV)9500 9550 9600 9650 9700 9750 9800 9850
Inte
nsity
, I (a
.u.)
0.0126
0.0128
0.0130
0.0132
0.0134
0.0136
0.0138
(101) Zn edge
5% Zn doped-CISu
Energy, E (eV)9450 9500 9550 9600 9650 9700 9750 9800 9850
Inte
nsity
, I (a
.u.)
0.0108
0.0110
0.0112
0.0114
0.0116
0.0118
0.0120
(101) Zn edge
10% Zn doped-CISu
Energy, E (eV)9450 9500 9550 9600 9650 9700 9750 9800 9850
Inte
nsity
, I (a
.u.)
0.0106
0.0108
0.0110
0.0112
0.0114
0.0116
0.0118
0.0120
(101) Zn edge
Zn doped—CuInS2
X-ra
y Tr
ansm
issi
on
0.762
0.764
0.766
0.768
0.770
0.772
0.774
0.776
0.778
0.780
AirPath Length: 410 mm
X-ra
y Tr
ansm
issi
on
0.94
0.95
0.96
0.97
0.98
0.99
1.00
1.01
Ion ChamberPath Length: 38 mm
Energy, E (eV)
9550 9600 9650 9700 9750 9800
X-ra
y Tr
ansm
issi
on
0.9768
0.9770
0.9772
0.9774
0.9776
0.9778
0.9780
0.9782
0.9784
Be-windowThickness: 0.2 mm
Attenuation Factors
X-ra
y Tr
ansm
issi
on
0.762
0.764
0.766
0.768
0.770
0.772
0.774
0.776
0.778
0.780
AirPath Length: 410 mm
X-ra
y Tr
ansm
issi
on
0.94
0.95
0.96
0.97
0.98
0.99
1.00
1.01
Ion ChamberPath Length: 38 mm
Energy, E (eV)
9550 9600 9650 9700 9750 9800
X-ra
y Tr
ansm
issi
on
0.9768
0.9770
0.9772
0.9774
0.9776
0.9778
0.9780
0.9782
0.9784
Be-windowThickness: 0.2 mm
20% Zn doped-CISu
Inte
nsity
, I (a
.u.)
0.0126
0.0128
0.0130
0.0132
0.0134
0.0136
(101)Zn edge
20% Zn doped-CISu
Energy, E (eV)
9550 9600 9650 9700 9750 9800
Inte
nsity
, I (a
.u.)
0.0172
0.0174
0.0176
0.0178
0.0180
0.0182
0.0184
0.0186
(101)Zn edge
Attenuation Factors
5% Ga loaded-CISu
Energy, E (eV)10150 10200 10250 10300 10350 10400 10450 10500 10550
Inte
nsity
, I (a
.u.)
0.006
0.007
0.008
0.009
0.010
0.011
0.012
0.013
(101) Ga edge
Ga loaded—CuInS2
20%Ga loaded-CISu
Energy, E (eV)10150 10200 10250 10300 10350 10400 10450 10500 10550
Inte
nsity
, I (a
.u.)
0.0015
0.0020
0.0025
0.0030
0.0035
0.0040
0.0045
0.0050
(101) Ga edge
•Zn goes into the CuInS2 lattice structure
•Ga does not.•Where does Ga go???
•EXAFS measurements
Refinement of Simulations
• Need to refine the simulations
0 2000 4000 6000 8000 10000 12000 14000
5
10
15
20
25
Mn K-edge
RXS
DANES
Data
Simulations
Brittany Nelson-Cheeseman (UC-Berkeley/APS)
• Goal: Fitting both the RXS and DANES aspects of the data to get both site occupancy and site-specific valences
• Problem: Unknown fine structure near absorption edge to input into simulation
Use known f′′ fine structure (XANES) of real samplesUse Kramers-Kronig relation to get f′ (DANES)
Mn K-edge
Energy (eV)
RXS
DANES
• Kramers-Kronig Relation: If we know f′ or f′′, can calculate the other
Refining the RXS/DANES Simulations
dEEfEfEE
E∫∞
−=
00 2
02)("2)('
π
8000 8500 9000
1
2
3
4
5
0 2000 4000 6000 8000 10000 12000 14000
5
10
15
20
25
0 2000 4000 6000 8000 10000 12000 14000
0.5
1
1.5
2
2.5
3
3.5
f ′(Real)(Reflected)
f ′′(Imaginary)(Absorbed)
XANESData
TabulatedValues
TabulatedValues
Tabulated ValuesTabulated Values
f ′ ′(Imaginary)(Absorbed)
TransformedFrom
XANES DataTabulated
ValuesTabulatedValues
Obtaining Simulation Fine Structure
f ′(Real)(Reflected)
to compare with data
KKT
Obtaining Simulation Fine Structure
0 2000 4000 6000 8000 10000 12000 14000
5
10
15
20
25
0 2000 4000 6000 8000 10000 12000 14000
0.5
1
1.5
2
2.5
3
3.5
f ′(Real)(Reflected)
f ′ ′(Imaginary)(Absorbed)
6400 6500 6600 67000.0
0.1
0.2
0.3
0.4
Mn K-edge DANES 422
Inte
grat
ed In
tens
ity (a
.u.)
Photon Energy (eV)
422 Data 422 Fit (ν =0.88) 422 Simulation
(ν =0.88; Mn2+ )Td
Tetrahedral Sites
Octahedral Sites
Comparison of Refined Simulation with Data
NiMn2O4
υ = 88% 88% of Ni on Octahedral sites
Energy Resolution of the beamline
Summary
• Zn goes in CISu hexagonal crystal structure• Ga does not go in CISu hexagonal crystal structure• Energy dependent attenuation factors are important• To include the fine structures, the simulations need
to be refined using Kramers-Kronig Transformation
AXRD Experiment Routine
• Choose suitable beamline• Preliminary simulations
• Choose suitable reflection to collect data• Data Collection
• Measure peak at energy steps around absorption-edge• Data Analysis
• Take integrated intensity (area under peak)• Plot as a function of energy• Thickness effects• E-dependent attenuation factors (air, ion cham., Be window)• Refining RXS/DANES (Kramers-Kronig)
Conclusions
AXRD is an effective tool for structural characterization of
Bulk, Thin-films & Nanomaterials
Acknowledgements
• Mike Toney’s Group, Apurva Mehta & John Bargar (SSRL)• Brittany Nelson-Cheeseman (UC-Berkeley/APS)• Steve T. Connor, Yi Cui, Rodrigo Noriega, Alberto Salleo
(Stanford University)• Thomas Mason, Nicola Perry, Arpun Nagaraja
(Northwestern University)
Resources
• Resonant Diffraction, Jean-Louis Hodeau et al. Chem. Rev. 2001, 101, 1843• Elements of X-Ray Diffraction (3rd Edition), B. D. Cullity.• Anomalous X-Ray Scattering for Materials Characterization, Y. Waseda.• Atomic scattering factors
• http://www.ccp14.ac.uk/ccp/web-mirrors/lmgp-laugier-bochu/-- f′ & f′′• http://ftp.esrf.eu/pub/scisoft/xop2.3//DabaxFiles/f0_WaasKirf.dat -- f0
• Mass Coefficients• http://physics.nist.gov/PhysRefData/XrayMassCoef/
• X-ray transmission• http://henke.lbl.gov/optical_constants/
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