New regularization method for EXAFS analysis [Elektronische Ressource] : application to uranium and plutonium sorption onto kaolinite / Tatiana Reich

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• Physik

Informations

• Publié par: johannes_gutenberg-universitat_mainz
• Publié le: 01 janvier 2008
• Nombre de lectures: 14
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

New Regularization Method
for EXAFS Analysis

Application to Uranium and
Plutonium Sorption onto Kaolinite



Dissertation
zur Erlangung des Grades


“Doktor der Naturwissenschaften”


im Promotionsfach Kernchemie

am Fachbereich Chemie, Pharmazie
und Geowissenschaften
der Johannes Gutenberg-Universität Mainz



Tatiana Reich
geb. in Tscheljabinsk/Russland


Mainz, 2008



Dekan:

1. Berichterstatter:
2. Berichterstatter:


Tag der mündlichen Prüfung: 11.11.2008











To my husband
and all who enjoy EXAFS INDEX

Acronyms, abbreviations, and symbols
Summary
Zusammenfassung
1. Introduction _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1
2. EXAFS general concepts _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 4

2.1 Fundamental physics of X-ray absorption _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 4
2.2 X-ray absorption data collection at synchrotron radiation sources _ _ _ _ _ _ 5
2.3 y absorption spectra and XAFS _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 6
2.4 Single- and multiple-scattering in XAFS theory _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 8
2.5 Structural information in XAFS _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 9
2.6 EXAFS data analysis _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 13
2.6.1 EXAFS equation _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 13
2.6.2 Fourier transform _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 14
2.6.2.1 General principles _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 14
2.6.2.2 Fourier transform techniques _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 16
2.6.2.3 Inverse Fourier transform _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 17
2.6.2.4 EXAFS data analysis methods based on Fourier transform technique _ _ _ _ 18
2.6.2.5 Types of problems in data analysis with Fourier transform technique _ _ _ _ 19
2.6.3 Partial radial distribution functions (RDFs) probed by EXAFS _ _ _ _ _ _ _ _ 20
2.6.4 Application of regularization method to ill-posed EXAFS problem _ _ _ _ _ 23

3. Methodological development of Tikhonov regularization method _ _ _ _ 27

3.1 Introduction _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 27
3.2 Tikhonov variation method _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 27
3.3 Method of separating functionals _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 29
3.4 Iteration method with filtration in real space _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 35
3.5 Calculation of structure parameters _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 36

4. Testing of the modified Tikhonov regularization method _ _ _ _ _ _ _ _ _ 38

4.1 Introduction _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 38
4.2 Soddyite _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 39
4.2.1 Model calculations _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 39
4.2.1.1 Tikhonov solutions _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 41
4.2.1.2 Method of separating functionals _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 46
4.2.1.3 Iteration method with filtration in real space _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 50
i 4.2.1.4 Main conclusions based on model calculations for soddyite _ _ _ _ _ _ _ _ _ 53
4.2.2 Experimental data of soddyite _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 55
4.2.2.1 Multiple-scattering correction _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 56
4.2.2.2 Treatment by the modified regularization method _ _ _ _ _ _ _ _ _ _ _ _ _ _ 57
4.2.3 Main conclusions based on calculations for soddyite _ _ _ _ _ _ _ _ _ _ _ _ _ 67
4.3 Sorption of U(VI) onto kaolinite _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 69
4.3.1 Speciation of U(VI) as a function of uranium concentration _ _ _ _ _ _ _ _ _ 72
4.3.2 function of pH _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 80
4.3.3 function of CO _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 88 2
4.3.4 Changes of U(VI) speciation at kaolinite surface upon drying _ _ _ _ _ _ _ _ 93
4.3.4.1 Ambient and low temperature measurements _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 93
4.3.4.2 Ambient temperature measurements _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 98
4.3.5 Conclusions based on calculations of U(VI) speciation at kaolinite surface 101
4.4 Sorption of Pu onto kaolinite _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 104
4.4.1 Experimental _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 104
4.4.1.1 Batch experiments _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 104
4.4.1.2 EXAFS experiments and data treatment _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 105
4.4.2 Results and discussion _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 106
5. Conclusions and outlook _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 110

APPENDIX I: Soddyite-data acquisition and least-squares fitting _ _ _ _ _ _ _ 116
APPENDIX II: Sorption of U(VI) onto kaolinite data acquisition _ _ _ _ _ _ _ _ 123
Figure index _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 131
References _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 134
Acknowledgements
Lebenslauf
Erklärung

iiACRONYMS, ABBREVIATIONS, and SYMBOLS

α Regularization parameter
-10Å Ångstrom (10 m)
A(k,r) Kernel of EXAFS equation
ANKA Angströmquelle Karlsruhe (Germany)
χ(E) Normalized oscillating part of the X-ray absorption in energy space
χ(k) art of the X-ray absorption in k space
χ (r) Fourier transformed pseudo radial distribution function
8 −1c Speed of light, 2.998 × 10 m ⋅s
C Concentration of an element in a material
δ (k) Phase shift on atomic potential of absorbing atom c
DCM Double-crystal monochromator
ˆ∈ ⋅r Dipole operator
E X-ray photon energy, eV
E Absorption threshold energy, eV 0
ESRF European Synchrotron Radiation Facility (France)
−19eV Electron volt, 1eV = 1.602 × 10 J
EXAFS Extended X-ray absorption fine structure
f (k) Effective backscattering amplitude eff
F Goodness of fit in least-square fitting method
Φ(k) Phase shift on atomic potential of neighboring atom
FT Fourier transformation
FWHM Full width at half-maximum, Å
g(r) Partial radial atomic distribution function
−16h Planck’s constant, h =h 2 π = 6.582 × 10 eV ⋅s
ITransmitted X-ray photon intensity
I Incident X-ray photon intensity 0
IIntensity of fluorescence radiation f
I Identity matrix of size p pp
INE Institut für Nukleare Entsorgung (Germany)
-1k Photoelectron wave number, Å
λ De Broglie wavelength
λ(k) Photoelectron mean-free path
iiiΛ Value of separating functional
2μ(E) Experimental X-ray absorption coefficient, cm /g
2μ (E) Atomic background absorption, cm /g 0
2Δ μ (E ) Jump in the atomic background absorption, cm /g 0 0
-6 -1μM Micromol (10 mol L )
−31m Electron rest mass, 9.1094 ×10 kg
M Tikhonov functional
MSMultiple scattering
−1ν X-ray photon frequency, s
N Coordination number or number of equivalent scatterers
N Number of independent parameters in least-square fitting method P
ψ Initial state wave function i
ψ Final state wave function f
ψ (k) Total phase shift, ψ (k) = 2 δ (k) + Φ(k) c
ψ ψ Transition matrix element f i
pH Negative logarithm (base 10) of hydrogen ion concentration
ppm parts per million
PRDF Pseudo radial distribution function
Density of a material ρ0
Density of available final states ρ(T)
r Interatomic distance, Å
ΔR Expected resolution in distance in PRDF, Å
RDF Partial radial distribution function
ROBL Rossendorf Beamline
RSMS Real space multiple scattering theory
2 2σ Debye-Waller factor, Å
2S Overall amplitude factor 0
SS Single scattering
τ Peak width in RDF
T Kinetic energy of photoelectron, eV
ˆU Separating functional
W(k) Window function
2x Surface density of absorbing material, g/cm
XAFS X-ray absorption fine structure
ivXANES X-ray absorption near-edge structure
XRD Single-crystal X-ray diffraction
vSUMMARY

Extended X-ray absorption fine structure (EXAFS) spectroscopy is a powerful tool for
direct speciation of heavy metals in a wide range of environmentally relevant systems.
To determine structural parameters, i.e., coordin