X-ray Absorption SpectroscopyEric Peterson 9/2/2010

OutlineGeneration/Absorption of X-raysHistorySynchrotron Light SourcesData reduction/AnalysisExamples

Crystallite size from Coordination NumberLinear combination analysis

Lytle, F. W. (1999). "The EXAFS family tree: a personal history of the development of extended X-ray absorption fine structure." Journal of Synchrotron Radiation 6: 123-134.Vonbordwehr, R. S. (1989). "A History of X-Ray Absorption Fine-Structure." AnnalesDe Physique 14(4): 377-466.

Extended X-ray Absorption Fine Structure (EXAFS)X-ray Absorption Near-Edge Structure (XANES )X-ray Absorption Spectroscopy (XAS)EXAFS + XANES (XAFS)

EXAFS regionXANESregion

EXAFS regionCan analyze quantitatively

XANESNo quantitative theory as of yet

William Conrad RoentgenDiscovery of X-rays November 8, 1895

Mrs. Roentgen’s hand-an early X-ray absorption experiment

Generation of X-rays

Any time that you combine high voltage with a vacuum, a significant amount of X-rays can be produced!

Interaction of high energy electronswith the anode creates X-rays

Generation of X-rays

In reality there is a significant overlap of gamma and X-ray Energies (frequencies).Better to think of gamma rays being associated with transitions

in the nucleus and X-rays associated with electronic transitions.

Bremsstrahlung

Characteristic X-rays

K

K

inte

nsi

ty Characteristic X-rays

Bremsstrahlung

A typical X-ray spectrum

Absorption of X-rays

Beer-Lambert Law teII 0

t

eI

I

0

In practice

Symbol SI unit

Attenuation coefficient m-1

density g/m3

Mass attenuation coefficient(what’s usually tabulated)

m2/g

Incident x-ray intensity

Transmitted x-ray intensity

10

100

1000

10000

0 1 2 3 4

absorption

(cm2/g)

energy (KeV)

carbon

calcium

Absorption contrastleads to image contrast

1905 Albert Einstein-Photoelectric Effect (1921 Nobel Prize Physics)

Concerning an Heuristic Point of View Toward the Emission and Transformation of Light. Annalen der Physik 17 (1905): 132-148.

hchE

1900 Max Planck-Planck Postulate (1918 Nobel Prize Physics)

Change metal to change

1909 Charles Barkla-Systematic study of X-ray emission and absorption

K, L series originally B,A series

Incident X-rays

Cu K

Absorbing foil

E,

abso

rpti

on

Plotted absorption of various Metals (y) vs. absorption in aluminum (x)

William Laurence Bragg and William Henry Bragg-Diffraction of X-rays by a crystal (1915 Nobel Prize Physics)

sin2dn

1913 Maurice de Broglie- The first x-ray spectrometer (rotating crystal)

Use Bragg’s Law to select from a “white” x-ray source (ie. A range of ’s) by varying

1913 Henry Mosley-Systematic relationship between characteristic x-ray frequencies in terms of Bohr atom.

1913 Niels Bohr-Structure of the atom(1922 Nobel Prize Physics)

Experimental capability as of ~1913

Theoretical picture as of ~1913

Generate Characteristic X-rays

Bohr Atom

0.4

4

0

1000

2000

3000

4000

5000

6000

5 6 7 8 9 10

fluorescence absorption

Energy (KeV)

Cu K

Cu K

Cu K edge

Edge represents the energy needed to transport an electron from the K shell into the continuum

Characteristic X-ray energy represents the energy lost by an electron falling from an outer shell to aninner shell

0.4

4

0

1000

2000

3000

4000

5000

6000

5 6 7 8 9 10

absorption

Energy (KeV)

fluorescence

Cu K

Cu K

Ni K edgeCu K edge

An aside… Can use a Nickel foil to filter Cu K radiation (common practice in X-ray diffraction)

1918 Hugo Fricke- first description of absorption edge fine structure

chromiumphosphorus

Reversed

K-edges

1920 Louis de Broglie-electron wave-particle duality(1929 Nobel Prize Physics)

1920 J Bergengren-absorption edge shifts with chemical valance in phosphorus

1921 Erwin Schrödinger - Quantum mechanics (1933 Nobel Prize Physics)

Experimental observations regarding X-ray absorption edge fine structure circa 1930:

What we know now:(i-iii) EXAFS measures something about the local structure surrounding the absorbing atom(iv) E-space to k-space transformation(v) A result of increasing Debye-Waller factors (atomic vibration)(vi) Thermal expansion in reciprocal (k) space

1931 Ralph Kronig-Modern X-ray absorption spectroscopy (Kronigstructure)

1933 Hendrick Petersen (Kronig’s Ph.D. student)- the EXAFS equation

1971 Sayers, Stern, and Lyttle-Fourier transform of the EXAFS equationto give a radial structure function

What’s happening at the absorption edge:

0.0

0.5

1.0

1.5

2.0

0 2 4 6

(r) (Å-3)

r (Å)

Something ~real

Still need more intense X-ray source though….Increased Energy (fine structure) resolutiondecreasing beam intensity increasing data collection time

As of 1971 we could potentially do this:

EXAFS and XANES- sensitive probes of the chemical environment of the absorbing atom-XANES is especially sensitive to valence and coordination geometry-does not require a crystalline (or even solid) sample

Something measured

E(eV)

(E))

Rotating crystal spectrometers only pass a small fraction of the bremsstrahlungNeed a more intense source of bremsstrahlung X-rays

1947 Discovery of synchrotron light

Sealed source-Limited by heatgenerated by e-

striking the anode

Rotating anode

http://xuv.byu.edu/docs/previous_research/euv_imager/documentation/part4/images/16img.jpg

105

106

107

108

109

1014

Brookhaven National Synchrotron Light Source (NSLS)

NSLSII

Synchrotron light sources started becoming accessible ~1970’s

Monochromatic

X-rays to sample

White x-raysFrom ring

Double crystal monochromator(n =2dsin )

First Generation: Parasitic operation and storage ringsSecond Generation: Dedicated sourcesThird Generation: Optimized for brightnessFourth Generation: On the drawing boards

Beam conditioning

Energy Range

Mono Crystal

Resolution (ΔE/E)

FluxSpot Size

(mm)

Total Angular Acceptance

(mrad)

4.9– 30 keV

Si(311) 2 x 10-4

1010 ph/sec (@ monochromator bandpass @ 10 keV, 100mA, 2.5 GeV)

25H x 1.0V

4

Beamline X23A2 specifications:

Ring

Beam

Beam

Monochromator

ExperimentHutch

sample

I0It

Beam

0

50

100

150

200

250

300

350

0:00:00 4:48:00 9:36:00 14:24:00 19:12:00 0:00:00 4:48:00

Beam Current(mA)

time

X-RAY STORAGE RING PARAMETERS AS OF JULY 2009 Stored Electron Beam Energy 2.80 GeVMaximum Operating Current 300 mA Lifetime ~20 hours Circumference 170.08 meters

Analysis of XAS data

Analysis of XAS data

EXAFS regionCan analyze quantitatively

XANESNo quantitative theory as of yet

EXAFS regionCan analyze quantitatively

(Thanks to Sayers, Stern, and Lyttle)

XANESNo quantitative theory as of yet

XAS – X-ray Absorption SpectroscopyXANES - X-ray Absorption Near Edge SpectroscopyEXAFS - Extended X-ray Absorption Fine StructureXAFS – X-ray Absorption Fine Structure (XANES + EXAFS)

Analysis of XAS data

Want to extract the wiggles

Extracting the EXAFS signal

Pre-edge line

Post-edge line

Background function

Extracting the EXAFS signal

Extracting the EXAFS signalNormalized absorption edge

E(eV) k(Å-1)

Extracting the EXAFS signal

Fourier transform window

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 2 4 6

(r) (Å-3)

r (Å)

Fourier transform of (k)

Absorbing atom (Pd in this case)Is at zero Å

To a first approximation, the peaks correspond to nearest neighbor shells

Pd

O

Peak positions are shifted about 0.5 Åsmaller than the true shell radii. For example the true Pd-Pd 1st shell distance is 2.8 Å.

Data from Pd on alumina, heated 300 C 2 hours in H2/N2

Sample is a mix of Pd metal and Pd oxide

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 2 4 6

(r) (Å-3)

r (Å)

Fit (Pd metal only)

+++++ data

Fit (Pd metal + PdO)

Can fit the data in r-space-try different models-refine adjustable parameters ( r, C.N., Debye-Waller, etc.)

including PdOgives better fit

EXAFS can measure average atomic coordination numbers (C.N.)

C.N.=4

C.N.=6

C.N.=12

7.51612

12146612.. averageNC

dnominal=0.8 nm

0

2

4

6

8

10

12

14

0 2 4 6 8 10

C.N.

diameter (nm)

Small particles have a large fraction of atoms on the surface (under-coordinated) relative to those in the bulk (C.N. 12 for F.C.C)

For spherical particlesR=particle radiusr=nearest neighbor distance

C.N. /size correspondence is reasonableeven for non-spherical particles

C.N.=4

C.N.=6

C.N.=12

7.51612

12146612.. averageNC

dnominal=0.8 nmdcalc(5.7)=0.74 nm

0

2

4

6

8

10

12

14

16

200 400 600 800 1000reduction temperature °C

size nm

Pd particle size as a function of reduction temperature

TEMvsn

XRD

EXAFS

2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.5

x 104

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Palladium metal foil

PdO on -alumina

XANES analysis using linear combinations of reference patterns

XANES region is sensitive to valance, coordination

PdO

Pd

sample

Linear combinations of reference patterns

PdO

Pd

Pd on -alumina

Linear combinations of reference patterns

PdZn on -alumina

PdOPd

PdZn

Linear combinations of reference patterns

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

500 600 700 800 900 1000

PdO

Pd

PdZnweightingfactor

reduction temperature (K)

PdO and Pd were not seen in XRD, but areapparent in XAS

Phase analysis mirrorscatalytic behavior

Conclusions

Useful Software (free except for FEFF8 and FEFF9)Athena data reduction, linear combination analysisArtemis model refinementFEFF(6-9 ) absorption spectra simulation

EXAFS provides a view of local structure/chemical environment of the absorbing atom

EXAFS analysis can provide quantitative information regardingnearest neighbors, coordination number, atomic distances, andDebye-Waller factor/disorder

Samples can be crystalline, amorphous, solid, liquid, or even gas

Through linear combination analysis, XANES can also provide quantitative information, especially regarding absorbing atom valence and coordination environment