X-ray Absorption Spectroscopy Eric Peterson 9/2/2010 Outline Generation/Absorption of X-rays History Synchrotron Light Sources Data reduction/analysis Examples Crystallite size from Coordination Number Linear 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." Annales De 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) XANES XANES region No quantitative theory as of yet EXAFS region EXAFS region Can analyze quantitatively
William Conrad Roentgen Discovery of X-rays November 8, 1895 Mrs. Roentgen s hand-an early X-ray absorption experiment
Generation of X-rays Interaction of high energy electrons with the anode creates X-rays Any time that you combine high voltage with a vacuum, a significant amount of X-rays can be produced!
Generation of X-rays Bremsstrahlung Characteristic 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.
intensity A typical X-ray spectrum K Characteristic X-rays K Bremsstrahlung
Absorption of X-rays Beer-Lambert Law I I e 0 t In practice I e t I 0 Symbol SI unit Attenuation coefficient m -1 density g/m 3 Mass attenuation coefficient (what s usually tabulated) m 2 /g Incident x-ray intensity Transmitted x-ray intensity
Absorption contrast leads to image contrast 10000 absorption 1000 calcium (cm 2 /g) 100 carbon 10 0 1 2 3 4 energy (KeV)
1900 Max Planck-Planck Postulate (1918 Nobel Prize Physics) E h hc 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.
absorption Incident X-rays Absorbing foil Change metal to change Cu K K, L series originally B,A series 1909 Charles Barkla-Systematic study of X-ray emission and absorption Plotted absorption of various Metals (y) vs. absorption in aluminum (x) E,
William Laurence Bragg and William Henry Bragg -Diffraction of X-rays by a crystal (1915 Nobel Prize Physics) n 2d sin
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 Niels Bohr-Structure of the atom (1922 Nobel Prize Physics) 1913 Henry Mosley-Systematic relationship between characteristic x-ray frequencies in terms of Bohr atom.
Experimental capability as of ~1913
Bohr Atom Theoretical picture as of ~1913 Generate Characteristic X-rays
Edge represents the energy needed to transport an electron from the K shell into the continuum fluorescence 6000 5000 4000 3000 2000 1000 Characteristic X-ray energy represents the energy lost by an electron falling from an outer shell to an inner shell Cu K Cu K edge Cu K 4 absorption 0 5 6 7 8 9 10 Energy (KeV) 0.4
An aside Can use a Nickel foil to filter Cu K radiation (common practice in X-ray diffraction) 6000 5000 Cu K Ni K edge Cu K edge 4 fluorescence 4000 3000 absorption 2000 1000 0 5 6 7 8 9 10 Energy (KeV) Cu K 0.4
chromium K-edges phosphorus 1918 Hugo Fricke- first description of absorption edge fine structure Reversed
1920 J Bergengren-absorption edge shifts with chemical valance in phosphorus 1920 Louis de Broglie-electron wave-particle duality (1929 Nobel Prize Physics) 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 (Kronig structure) 1933 Hendrick Petersen (Kronig s Ph.D. student) - the EXAFS equation
1971 Sayers, Stern, and Lyttle- Fourier transform of the EXAFS equation to give a radial structure function
What s happening at the absorption edge:
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 As of 1971 we could potentially do this: 2.0 1.5 (E)) (r) (Å -3 ) 1.0 0.5 E(eV) Something measured 0.0 0 2 4 6 r (Å) Something ~real Still need more intense X-ray source though. Increased Energy (fine structure) resolution decreasing beam intensity increasing data collection time
Rotating crystal spectrometers only pass a small fraction of the bremsstrahlung Need a more intense source of bremsstrahlung X-rays Sealed source- Limited by heat generated by e - striking the anode Rotating anode 1947 Discovery of synchrotron light
Brookhaven National Synchrotron Light Source (NSLS) 10 14 NSLSII 10 9 10 8 10 7 10 6 10 5 http://xuv.byu.edu/docs/previous_research/euv_imager/documentation/part4/images/16img.jpg Synchrotron light sources started becoming accessible ~1970 s
First Generation: Parasitic operation and storage rings Second Generation: Dedicated sources Third Generation: Optimized for brightness Fourth Generation: On the drawing boards Beam conditioning Monochromatic X-rays to sample Double crystal monochromator (n =2dsin ) White x-rays From ring Beamline X23A2 specifications: Energy Range 4.9 30 kev Mono Crystal Resolution (ΔE/E) Flux Si(311) 2 x 10-4 monochromator bandpass 10 10 ph/sec (@ @ 10 kev, 100mA, 2.5 GeV) Spot Size (mm) 25H x 1.0V Total Angular Acceptance (mrad) 4
Experiment Hutch Ring Monochromator Beam Beam
sample I t I 0 Beam
X-RAY STORAGE RING PARAMETERS AS OF JULY 2009 Stored Electron Beam Energy 2.80 GeV Maximum Operating Current 300 ma Lifetime ~20 hours Circumference 170.08 meters 350 300 Beam Current (ma) 250 200 150 100 50 0 0:00:00 4:48:00 9:36:00 14:24:00 19:12:00 0:00:00 4:48:00 time
Analysis of XAS data
Analysis of XAS data
Analysis of XAS data XANES XANES No No quantitative quantitative theory theory as of yet as of yet Want to extract the wiggles EXAFS region EXAFS region Can analyze quantitatively Can analyze quantitatively (Thanks to Sayers, Stern, and Lyttle) XAS X-ray Absorption Spectroscopy XANES - X-ray Absorption Near Edge Spectroscopy EXAFS - Extended X-ray Absorption Fine Structure XAFS X-ray Absorption Fine Structure (XANES + EXAFS)
Extracting the EXAFS signal Post-edge line Pre-edge line
Extracting the EXAFS signal Background function
Extracting the EXAFS signal Normalized absorption edge
Extracting the EXAFS signal E(eV) k(å -1 )
Fourier transform window
Fourier transform of (k) (r) (Å -3 ) 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 Absorbing atom (Pd in this case) Is at zero Å O Pd To a first approximation, the peaks correspond to nearest neighbor shells Peak positions are shifted about 0.5 Å smaller than the true shell radii. For example the true Pd-Pd 1 st shell distance is 2.8 Å. 0 2 4 6 r (Å) Data from Pd on alumina, heated 300 C 2 hours in H 2 /N 2 Sample is a mix of Pd metal and Pd oxide
Can fit the data in r-space -try different models -refine adjustable parameters ( r, C.N., Debye-Waller, etc.) (r) (Å -3 ) 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 including PdO gives better fit 0 2 4 6 r (Å) +++++ data Fit (Pd metal + PdO) Fit (Pd metal only)
EXAFS can measure average atomic coordination numbers (C.N.) C.N.=4 C.N.=6 C.N.=12 d nominal =0.8 nm C. N. average 12 6 6 12 4 6 1 1 12 5.7
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) R=particle radius r=nearest neighbor distance For spherical particles C.N. 14 12 10 8 6 4 2 0 0 2 4 6 8 10 diameter (nm)
C.N. /size correspondence is reasonable even for non-spherical particles C.N.=4 C.N.=6 d nominal =0.8 nm C.N.=12 d calc (5.7)=0.74 nm C. N. average 12 6 6 12 4 6 1 1 12 5.7
Pd particle size as a function of reduction temperature size nm 16 14 12 10 8 6 4 2 0 200 400 600 800 1000 reduction temperature C v s n XRD TEM EXAFS
XANES analysis using linear combinations of reference patterns XANES region is sensitive to valance, coordination 1.2 PdO on -alumina 1 0.8 Palladium metal foil 0.6 0.4 0.2 0-0.2 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.5 x 10 4
Linear combinations of reference patterns PdO sample Pd
Linear combinations of reference patterns Pd on -alumina Pd PdO
Linear combinations of reference patterns PdZn on -alumina PdO PdZn Pd
0.55 0.5 weighting factor 0.45 0.4 0.35 0.3 PdO Pd PdZn PdO and Pd were not seen in XRD, but are apparent in XAS 0.25 0.2 0.15 500 600 700 800 900 1000 reduction temperature (K) Phase analysis mirrors catalytic behavior
Conclusions EXAFS provides a view of local structure/chemical environment of the absorbing atom EXAFS analysis can provide quantitative information regarding nearest neighbors, coordination number, atomic distances, and Debye-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 Useful Software (free except for FEFF8 and FEFF9) Athena data reduction, linear combination analysis Artemis model refinement FEFF(6-9 ) absorption spectra simulation