EXAFS. Extended X-ray Absorption Fine Structure

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1 AOFSRR Cheiron School 2010, SPring-8 EXAFS Oct. 14th, 2010 Extended X-ray Absorption Fine Structure Iwao Watanabe Ritsumeikan University

2 EXAFS Theory Quantum Mechanics Models Approximations Experiment Light Source Monochromator Higher Harmonics Rejection Sample Preparation Detection Methods Polarization XAFS

3 Data Analysis Limited Usable Range in Experimental Data Estimation of Background Curves Fourier Transform Multi-Scattering Curve Fitting Procedure Phase Problems Debye-Waller-Like Parameter Anharmonicity in Potential

4 X-ray absorption measurement by transmission method The most reliable and basic method +1000V +1000V synchrotron double-crystal monochromator monochromatic X-ray slits sample white X-ray Bragg diffraction PC and interfaces Io Gas ionization chamber (He, N 2, Ar, Kr, etc) I calculation of absorbance I A = - log( ) Io Io current I current

5

6 XAS of Fe(III) aqueous solution I 0 μx ln I 0 I I intensity X-ray photon energy / ev

7 H 2 O 3 Fe(III) 2 Fe(III) ion in water r(fe-o)=2.01a Fe photoelectron kinetic energy / ev Focusing on K shell (1s electron) excitation E 0 X-ray photon energy / ev photoelectron wave length / A Background 0.6absorption due 0.5to other atoms and other shell electrons

8

9 XAFS: X-ray Absorption Fine Structure Fe ions in aqueous solutions XANES μ EXAFS X-ray energy / ev

10 XANES: X-ray Absorption Near Edge Structure Fe ions in aqueous solutions μ X-ray energy / ev

11

12 Wong et al. Phys.Rev.B 30 (1984) 5596

13 EXAFS: Extended X-ray Absorption Fine Structure Fe ions in aqueous solutions 2 XANES Fe(III) Fe(II) μ t 1 μ 0 EXAFS X-ray energy / ev χ( k) = μ( k) μ0( k) μ ( k) 0 2 m ( e E k = 2 h E 0 )

14 EXAFS: χ(k) spectra Fe(III) k / A -1 k : wave number, wave vector k = 2π λ 2 m ( e E k = 2 h E 0 ) ( E E0 ) kinetic energy of photoelectron

15 Simplest model to explain how the EXAFS oscillation occurs

16 H 2 O 3 Fe(III) 2 Fe(III) ion in water r(fe-o)=2.01a Fe 1 E X-ray photon energy / ev photoelectron kinetic energy / ev photoelectron wave length / A

17 X-ray photon photoelectron kinetic energy of the photoelectron Fe an electron with E k =100eV behaves as a wave with λ=1.2a h λ= : de Broglie p This wave length is just the order of normal atom-atom bond distance!!! The cause for EXAFS appearance!!! N M L energy of the photon absorbed by Fe atom E 0 4s, 4p, 4d 3s, 3p, 3d (700~800eV) 2s, 2p 7113eV (1.743A ) K 1s

18 photoelectron going out (wave) = black wave: directly emitted from the absorbing atom + red broken wave: doubly scattered at B and A X-ray absorption at atom A B neighbor atom scattering the photoelectron wave back to the absorbing atom

19 X-ray absorption at atom A photoelectron going out (wave) B = black wave: directly emitted from the absorbing atom + red broken wave: doubly scattered at B and A If they are in phase, (2r)k=2nπ (k=2π/λ) or 2r=nλ, larger photoelectron wave larger probability of finding photoelectrons (amplitude squared). If they are out of phase, (2r)k=(2n+1) π, and equal amplitudes, photoelectron waves disappear no photoelectrons found outside. The law of conservation of energy tells that when no photoelectrons are emitted, no photons should be absorbed!!! if the X-ray photons are absorbed, the photoelectrons must be emitted!!! Larger probability of finding photoelectrons STRONG X-ray absorption Smaller probability of finding photoelectrons WEAK X-ray absorption

20 H 2 O 3 Fe(III) 2 Fe(III) ion in water r(fe-o)=2.01a Fe 1 E X-ray photon energy / ev photoelectron kinetic energy / ev photoelectron wave length / A BASIC EXAFS equation N χ( k) = fi( k)exp( 2σ i k 2 ri/ λ)s 0 ( k)sin(2 kri + φi( k)) kr i i 2 i

21 BASIC EXAFS equation N χ( k) = fi( k)exp( 2σ i k 2 ri/ λ)s 0 ( k)sin(2 kri + φi( k)) kr i i 2 i amplitude part oscillation part k k k

22 χ(k) k 3 Fe(III) k / A -1 kinetic energy of the photoelectron / ev photoelectron wave number (vector) 2π k = λ

23 Fourier Transform: Simplest way to analyze the EXAFS oscillation

24 The simplest way of knowing the wave number (corresponding to the distance) is Fourier Transformation of wave on k FT Fe(III) shoter Fe O r / A Fe(II) longer Fe O

25 Fe(CN) 6 4- Fe C N Fourier Transform μx E / ev

26 Fourier Transform (Frequency Filter) will let you know the frequencies of the waves sin(kr)

27 r 1 =2.0 r 2 =2.5 or r 1 =2.0 + r 2 =2.5 mixture

28 Fourier Transform for two-shell model

29 Fourier Transform for a three-shell model This must be a BACKGROUND structure, not corresponding to a real atom-atom distance.

30

31

32 If you have a small number of cycles in k, Fourier Transform for different k ranges

33 BASIC EXAFS equation N χ( k) = fi( k)exp( 2σ i k 2 ri/ λ)s 0 ( k)sin(2 kri + φi( k)) kr i i 2 i amplitude part oscillation part By comparing the theoretical EXAFS χ(k) and experimental χ(k), you can determine; N coordination number r bond length f(k) and φ(k) are element specific atomic type of coordination

34 You may get in trouble with the data quality taken by transmission method

35 Transmission method Sample: Ge-Si powder original powder further ground to finer powder By Masaharu Nomura, Photon Factory, KEK

36 χ(k) k 3 Fe(III) ions in aqueous solution possibly, inhomogeneous sample thickness k / A -1

37 X-ray beam from monochromator X-ray flux is not homogeneous and the density pattern moves and changes along with the monochromator angle scan solid powder Inhomogeneous sample liquid or film Leads to weaker EXAFS oscillation amplitude and noisy spectrum

38 Si(311) double-crystal monochromator Output pattern before improvements on the crystal after improvements holding method

39 1mm x 1mm slit I o 0.6mm x 0.6mm hole I

40 Yield methods: Fluorescence yield and Total-conversion-electron-yield

41 X-ray absorption measurement by yield methods synchrotron double-crystal monochromator monochromatic X-ray slit sample white X-ray Bragg diffraction Io PC and interfaces calculation of absorbance I A = - log( ) Io Io current I current fluorescence X-ray, electron, luminescence, heat, etc; anything proportional to the X-ray absorption

42 Lytle detector

43 Sample: 0.01 mol dm -3 Cu(II) solution transmittance fluorescence By Masaharu Nomura, Photon Factory, KEK

44

45

46 transmittance fluorescence Cu 0.5 mm Cu foil 6 μm fluorescence fluorescence Cu foil 6 μm Cu foil 2 μm By Masaharu Nomura, Photon Factory, KEK Self-absorption effect incorrect N

47 Total-Conversion-Electron-Yield method counter electrode sample X-ray window X-ray -1000V to current amplifier He gas

48 1μ m Fe 3 O 4 1.5mm glass X-ray transmission Auger electrons μ x (He gas ionization) This method can be applied to thick samples owing to the short escape depth of Auger electron. E / ev

49 Can we distinguish oxygen from nitrogen by EXAFS?

50

51 Almost impossible!

52 Scattering amplitude Scattering phase shift Ni χ( k) = fi( k)exp( 2σ i k 2 ri/ λ)s 0 ( k)sin(2 kri + φi( k)) kr i 2 i

53 N χ( k) = fi( k)exp( 2σ i k 2 ri/ λ)s 0 ( k)sin(2 kri + φi( k)) kr i i 2 i amplitude part oscillation part f scattering amplitude φ phase shift

54 Can we distinguish oxygen atoms 15% distant from others by EXAFS?

55

56

57 James E. Penner-Hahn J. Am. Chem. Soc. 1998,120,8401 Can we distinguish sulfur from nitrogen (or oxygen) by EXAFS?

58

59

60

61 Almost impossible!

62 Can we detect the end-end atomic interaction in I-I-I molecule (I 3- ) by EXAFS?

63 I K-edge EXAFS FT for I 3 - I - I - I 3A 3A Dissolved in organic solvents (n-c 3 H 7 ) 4 N I 3 powder H. Sakane, T. Mitsui, H. Tanida, I. Watanabe. J. Synchrotron Rad. 8, 674 (2001).

64 I-I bond is very soft and vibrating: large Debye-Waller like parameter Almost impossible! Iodine K-edge EXAFS Fourier transform for the compound spectrum made up from 12 independent spectra for organic solvent solutions. H. Sakane, T. Mitsui, H. Tanida, I. Watanabe. J. Synchrotron Rad. 8, 674 (2001).

65 Large symmetrical cluster of molybdenum oxide complex

66 0.5 Mo K-edge XAFS Mo 6 O 19 2 Mo μx 0 O E / ev Almost undetectable next neighbor oxygens! Mo-Mo k / A -1 r / A

67 -1 k/å

68 EXAFS Extended X-ray Absorption Fine Structure Theory; very difficult. Experiment; looks easy. Data analysis; looks straight forward. Thanks to the advanced data analysis software.

69 EXAFS In reality, Theory; becomes even more and more complex and difficult to understand. Experiment; to obtain CORRECT spectral data is NOT an easy task. Data analysis; no one except for the GOD knows whether the conclusion from the EXAFS analysis is CORRECT.

70 EXAFS is a tricky technique. Then, what do we have to do? Use other analytical methods, knowledge of chemistry and physics, and good sense as a scientist and combine them together with the EXAFS analysis.

71 XAS Analysis Software Using IFEFFIT Current release: Release date: 1 July, 2009 ATHENA is an interactive graphical utility for processing EXAFS data. It handles most of the common data handling chores of interest, including deglitching, aligning, merging, background removal, Fourier transforms, and much more. Current release: Release date: 15 December, 2008 ARTEMIS is an interactive graphical utility for fitting EXAFS data using theoretical standards from FEFF and sophisticated data modelling along with flexible data visualization and statistical analysis. ARTEMIS includes interfaces to ATOMS and FEFF.

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