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/