Introduction to X-ray Absorption Spectroscopy, Extended X-ray Absorption Fine Structure

Transcription

1 Mini-school X-ray Absorption Spectroscopy Introduction to X-ray Absorption Spectroscopy, Extended X-ray Absorption Fine Structure Martin C. Feiters, IMM, HG , Radboud University Heijendaalsweg 153, 6525 AJ Nijmegen, NL ,

2 Programme 9.00 Martin Feiters (RU) - Introduction to X-ray Absorption Spectroscopy, Extended X-ray Absorption Fine Structure 9.45 Frank de Groot (UU) - X-ray absorption spectroscopy near the edge. (aka XANES) Coffee Break Dipanjan Banerjee (DUBBLE-ESRF) X-ray sources, optics, and detectors for absorption spectroscopy beamlines Alessandro Longo (DUBBLE-ESRF) - Introduction to EXAFS data analysis Lunch Break Martin Feiters (RU) - Coordination Chemistry and Trace Element Biology Florian Meirer (UU) - X-ray micro-spectroscopy, tomography, and operando conditions Coffee Break Mario Delgado (UU) - Holistic data analysis with Blueprint XAS Institute for Molecules Frank and de Materials Groot (UU) - The future of X-ray absorption spectroscopy Drinks 2

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4 X-ray spectrometer: schematic representation Monochromation by diffraction of a set of parallel Si crystals, following Bragg s law n λ = 2 d sin θ Wavelength λ selected by varying angle θ of Si crystal with respect to beam Higher order reflections (n > 1) are rejected by making the crystals slightly non-parallel Transmitted intensity I t depends on incident intensity I 0, sample thickness x, and absorption coefficient µ(e) by Lambert-Beer law I t = I 0 exp(-µx) The X-ray absorption spectrum is represented in the dimension of the energy dependent X-ray absorption coefficient µ(e) ln(i 0 /I t ) = µx 4

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

6 X-ray fluorescence for dilute samples The hole created by inner electron excitation can be filled by electrons from higher orbitals, which give rise to fluorescence The total fluorescence yield is more intense for K than for L-excitation The X-ray absorption spectrum can be measured as µ f = I f / I 0 M. C. Feiters and W. Meyer-Klaucke, in Practical Approaches to Biological Mini-school Inorganic X-ray Absorption Chemistry Spectroscopy, (R. R. Crichton SyNeW and Utrecht, R. Louro, June Editors; 2, ) 6

7 X-ray excitation energies Tuning into any edge in the Periodic Table K edges, 1s; L3, 2p3/2 Excitation Energy (ev) Atomic Number 7

8 Fine Structure in X-ray Absorption Spectra Type of experiment: Measurement of the X-ray absorption (or fluorescence) at wavelengths around the edge of an element of interest (= spectroscopy) Type of phenomena: Edge and fine structure: interference effects due to wave character of electron (= diffraction) XANES, XES also transitions (= spectroscopy) Type of data treatment: Energy calibration, normalization, background subtraction, simulation 8

9 Normalized X-ray fluorescence 1s Fe X-ray Absorption K edge (XANES) of Haems Mb 3d OxyMb 4s 4p Energy (ev) continuum Position and structure of Fe K absorption edge of O 2 -binding protein myoglobin depend on oxygenation state Both oxidation state (valence, Fe(II) vs. Fe(III)-O 2 - ) and average ligand distance ( Natoli rule ) affect edge position (= energy where the absorption is ½ of the maximum) Pre-edge absorptions are due to excitation of 1s electron to empty orbitals like 3d, 4s, 4p as indicated Intensity pre-edge features depends on symmetry of coordination geometry around absorber atom (Fe) 9

10 X-ray induced electron diffraction: Pebble in a pond

11 Extended X-ray Absorption Fine Structure (EXAFS) of a porphyrin first shell X-ray energy > edge: photoelectronic effect at the absorber atom Photoelectronic wave backscattered by surrounding atoms Interference of incoming and outcoming waves at absorber atom: variations in electron density as energy is scanned, kinetic energy/electron wavelength varied Energy-dependent variations in electron density give variations in X-ray absorption coefficient S. P. Cramer & K. O. Hodgson, Prog. Inorg. Chem. 25 (1979)

12 Type of information - Relation with other techniques Type of information: EXAFS: number, type, and distance of ligand atoms XANES: valence, coordination geometry Relation with other techniques: EXAFS: refinement of distance information from crystallography XANES: combine with other spectroscopic techniques EXAFS/XANES can be used, together with other spectroscopic techniques, to construct a spectroscopically effective model of a metal site XAS is applicable to any element, in any valence or spin state, in samples in any physical state (solution, frozen solution, powder, single crystal, crystalline slurry, gas) 12

13 Wherefrom. Whereto with XAS Starting from simplified physics, mathematics Going to understanding of chemical parameters (important in a biological context) like: number, type, and distance of surrounding atoms; valence state, ligand geometry

14 Physical/Mathematical Foundations Wilhelm Conrad Röntgen ( ) X-rays Christiaan Huygens ( ) wave theory of light Louis de Broglie ( ) wave character of electrons Joseph Fourier ( ) transformation, analysis of sum of oscillations Ralph de L. Kronig ( ) early theories of X-ray absorption fine structure 14

15 Normalized fluorescence counts χ(e) // Fine structure above the edge: EXAFS χ µ pre-edge XA- NES µ 0 µ E X A F S The X-ray absorption spectrum µ has a fine structure (EXAFS, Extended X-ray Absorption Fine Structure) extending a few ev above the edge, starting ev above the edge From the experimental X-ray absorption (fluorescence) spectrum µ the EXAFS or χ(k) can be extracted by χ(k) = (µ A µ o )/µ o with µ A = µ µ, where µ = hypothetical spectrum with no Fe; µ 0 = hypothetical spectrum with no surrounding atoms It is convenient to convert the energy axis to the wave vector k: k 2 = 2m e (E E o )/ħ 2 Mini-school Energy X-ray (ev) Absorption Spectroscopy, SyNeW Utrecht, June 2,

16 Comparison of mono- and diatomic molecule Kr Br-Br Quantitative rationalization of the absence and presence, respectively, of EXAFS in a monatomic gas such as Kr (a and c) and a diatomic gas such as Br 2 (b and d) D. C. Koningsberger and R. Prins, X-ray Absorption Spectroscopy Wiley-Interscience, New York (1988) 16

17 Background subtraction, extraction of fine structure χ(e) Fluorescence µ µ 0 µ µ, experiment; µ, no Fe; µ 0, no surrounding atoms; µ A = µ µ EXAFS or χ(k) = (µ A µ o )/µ o µ A = µ µ k 2 = 2m e (E E o )/ħ Institute for 7220 Molecules 7520 and Materials 7820 Energy (ev) 17

18 Background subtraction, extraction of fine structure χ(e) Fluorescence µ µ 0 µ 0.5 χ(k) * k 3 χ(k) µ, experiment; µ, no Fe; µ 0, no surrounding atoms; µ A = µ µ EXAFS or χ(k) = (µ A µ o )/µ o µ A = µ µ k 2 = 2m e (E E o )/ħ Institute for 7220 Molecules 7520 and Materials Energy (ev) k (Å -1 ) 18

19 Founders of Modern EXAFS Theory Joseph Fourier ( ) 1830) transformation, analysis of sum of oscillations Edward Stern, Dale Sayers, and Farrel Lytle accept the American Crystallographic Association s Bertram Warren Award in 1979, for their development of EXAFS D. L. Sayers, E. A. Stern, F. W. Lytle, Phys.Rev.Lett. 27 (1971)

20 EXAFS interpretation by Fourier transformation χ(k) * k 3 χ(k) /FT/ of k 3 -weighted EXAFS k (Å -1 ) R (Å) 20

21 Golden Rule and Plane Wave approximation Separate atomic and scattering contributions: µ(e) = Σ lm µ 0 lm (E) x (1 + χ lm (E)) Summed over all allowed final states lm Atomic contribution given in dipole approximation by Golden Rule : µ 0 (E) = (1/h) < ψ f e.r ψ i > 2 D(E) With e the electric vector of the photon, r the position with respect to the nucleus, and D(E) the energy density of final states Plane wave approximation for χ, with k, electron wave vector (Å -1 ) defined as: χ(k) = j Σ N j. S i (k). F j (k). e. e. sin(2kr j + φ j (k))/kr 2 j -2k 2 σ 2 j -2r j /λ

22 Plane wave/single scattering approximation of EXAFS c is a sum of j (resolved) shells of backscatters of type i k, electron wave vector (Å-1) defined as k = 2me (E-E0) h2 Fj backscattering amplitude of each of the Nj backscattering atoms of type i with sj Debye-Waller-type factor rj distance fj total phaseshift Si amplitude reduction factor l electron mean free path (D)E0 threshold energy The (bio)chemist is interested in the type of atom (choose Fj) and its number Nj and distance rj (refine in simulation). Unfortunately, refinement of (and correlation with!) the Debye Waller-type factor and DE0 cannot be avoided. Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2,

23 Calculation of Backscattering Amplitude and Phase Shift Phase shift calculations in EXCURVE based on a Muffin-Tin Potential Backscattering amplitude F i and phase shift φ j can be accurately calculated for absorber-backscatterer In modern phase shift calculations, we do not adjust the amplitude reduction factor S j nor the electron mean free path λ j 23

24 Calculation of Backscattering Amplitude and Phase Shift Phase shift calculations in EXCURVE based on a Muffin-Tin Potential Backscattering amplitude F i and phase shift φ j can be accurately calculated for absorber-backscatterer In modern phase shift calculations, we do not adjust the amplitude reduction factor S j nor the electron mean free path λ j 24

25 Fourier Transformation: Radial Distribution Function Fourier transformation of EXAFS results in radial distribution function: Peak position: distance after correction for phase shift (extract from reference compound, or calculate) Amplitude: coordination number, occupancy of shell The (bio)chemist is interested in the type of atom i (choose a calculated F j ) and its number N j and distance r j (refine simulation with calculated φ j ) Unfortunately, correlation of N j with the Debye-Waller-type factor σ j, and of r j with the threshold energy E 0 (or EF), cannot be avoided. 25

26 Effect of Atom Types Phase relation EXAFS/Fourier transform dependent on nature of atom EXAFS of S ligand is π out of phase with those of C, N, and O EXAFS of C, N, and O virtually indistinguishable ( low-z ligands); It is possible that waves of different phases interfere destructively; it may be difficult to unravel contributions of opposite phase at similar distances 26

27 Backscattering amplitude and phase characteristic for element Backscattering amplitude envelope W I Mo Br Zn F Cr O Cl N C S H k (Å -1 ) EXAFS * k 3 /FT/ k (Å -1 ) 100 I Br Cl F R (Å) 27

28 Resolution of FT techniques Compared to NMR, FT-MS, or FT-IR, the resolution of EXAFS is poor because the Fourier transform is typically taken over only a few oscillations 10 EXAFS * k k (Å -1 ) Pulsed NMR Ion Cyclotron MS /FT/ Total simulation: 2 S, 2 N (imidazole) 2 S 2.25, 2 N 2.00 Å Resolution: R = π / 2 k (Å) k = 14 Å -1 : R = π / 2 * 14 = 0.11 Å R (Å)

29 Debye-Waller(-type) factor (1) Debye-Waller factor describes effects of thermal and static disorder. Distance r j accurately (± 0.02 Å) determined. Typical data range (10 Å -1 ): distances within 0.15 Å not resolved ( R = π / 2 k (Å)); average distance determined. Increased disorder in shell composed of non-resolved contributions (static disorder) noted as more rapid decline of EXAFS amplitude at high k, and peak broadening in the Fourier transform, described by larger value for Debye-Waller factor. High value for Debye-Waller factor can be caused by variance in ligand distances (static disorder). It can also be caused by disorder due to thermal effects: probe by temperature variation.

30 A model for elemental Fe (body-centered cubic, a-fe): Are all Fe-Fe distances the same (static disorder)? Are all Fe-Fe bonds rigid (thermal disorder)?

31 Debye-Waller factor and resolution 4 4 /FT/ EXAFS * k N at 2.0 Å from Zn, R 0, increasing DW-factor k (Å -1 ) 2σ N at 2.0 Å (average) from Zn, R increasing, DW-factor 0.02 Å k (Å -1 ) R R (Å) R (Å) 31

32 Multiple Scattering Important in the EXAFS of rigid ligand systems where the angle A-B-R-A approaches 180 o (> 140 o ): Coordinating carbon monoxide Coordinating rigid heteroatomic ligand: e. g. pyridine, imidazole, Metal at center of unit: octahedral, square planar 32

33 EXAFS summary (1) XAS can be applied to samples irrespective of physical (solution, powder, frozen solution) or chemical (oxidation, spin) state Crystals and other oriented systems can be studied, but be aware of the polarization of the synchrotron beam Even whole organisms can be studied but preferentially the element under study is homogeneous with respect to its chemical environment Because long acquisition times may be needed, radiation damage should be monitored, in particular photoreduction

34 EXAFS summary (2) XANES gives information on oxidation state and coordination geometry; simulated on the basis of 3- dimensional information EXAFS (1-, 2-dimensional) gives accurate metal-ligand distances, and an indication of ligand type and coordination number; combine with XANES and Bond Valence Sum Analysis for more accurate coordination number Validation of ligand geometries from other structural (crystallographic, NMR) and computational studies Combine with other spectroscopic techniques to construct a spectroscopically effective model of a metal site

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