EXAFS: Basic Principles and Data Analysis

1. X-Rays and Electrons.- 1.1 Introduction.- 1.2 Generation of X-Rays.- 1.3 Properties of X-Rays and Electrons.- 1.3.1 Wave-Particle Duality of Photons.- 1.3.2 Photoelectric Effect.- 1.3.3 Wave-Particle Duality of Electrons.- 1.4 Electronic Structure of Atoms.- 1.4.1 Models of the Atom.- 1.4.2 Electronic Transitions.- 1.5 Absorption Coefficients and Absorption Edges.- 1.5.1 Absorption Coefficients.- 1.5.2 Absorption Edges.- 1.5.3 True Absorption and Scattering.- 1.6 Interactions of Photons and Electrons with Matter.- 1.6.1 Excitations and Relaxations.- 1.6.2 Scattering.- 1.6.3 Electrons.- 2. Extended X-Ray Absorption Fine Structure (EXAFS) Spectroscopy.- 2.1 EXAFS Spectroscopy.- 2.2 Theory.- 2.3 Data Analysis.- 3. EXAFS Parameters.- 3.1 Variables and Functions.- 3.2 Effects of Important Parameters.- 3.3 Convention of Changing E0.- 4. Theory of EXAFS.- 4.1 Introduction.- 4.2 Derivations of EXAFS Theory.- 4.2.1 Lee and Pendry (1975).- 4.2.2 Lee (1976).- 4.2.3 Boland, Crane, and Baldeschwieler (1982).- 4.2.4 Curve-Wave Theory.- 4.3 EXAFS of L Edges.- 4.4 The Photoelectron and the Excited Atom.- 4.4.1 Lifetime of the Core Hole.- 4.4.2 Core Hole Relaxation.- 4.4.3 Potential Experienced by Photoelectron.- 4.4.4 Multi-electron Excitations.- 5. Improvement of EXAFS Theory.- 5.1 Energy Threshold - The Phase Problem.- 5.1.1 Choosing E0.- 5.1.2 Phase Transferability.- 5.1.3 VaryingE0.- 5.2 Inelastic Scatterings - The Amplitude Problem.- 5.2.1 Central Atom: Shake Up/Off Processes.- 5.2.2 Scatterer: Electron Inelastic Mean Free Path.- 5.3 Static and Thermal Disorder Effects.- 5.3.1 Small Disorders.- 5.3.1.1 Symmetric Pair Distribution.- 5.3.1.2 Discrete Bonds.- 5.3.1.3 Harmonic Vibration.- 5.3.2 Large Disorders.- 5.3.2.1 Derivation of the Generalized EXAFS Formalism.- 5.3.2.2 Moments of g(r).- 5.3.2.3 Symmetric Pair Distributions.- 5.3.2.4 Asymmetric Pair Distributions.- 5.3.2.5 Anharmonic Vibration Potentials.- 5.3.2.6 Comparison of EXAFS and Diffraction.- 5.4 Multiple Scattering EXAFS Formalism.- 6. Data Analysis in Practice.- 6.1 Data Reduction.- 6.1.1 Conversion of Experimental Variables.- 6.1.2 Background Removal.- 6.1.3 Normalization and ?0 Correction.- 6.1.4 Conversion ofE to k.- 6.1.5 Weighting Scheme.- 6.1.6 Deglitching and Truncation.- 6.2 Fourier Transform (FT).- 6.3 Fourier Filtering (FF).- 6.4 Curve Fitting (CF).- 6.4.1 Parameterization.- 6.4.2 Phenomenological EXAFS Models.- 6.4.3 Least-squares Refinements.- 6.4.4 Correlations.- 6.4.5 Errors.- 6.5 Parameter Correlation and the FABM Method.- 6.5.1 Fine Adjustment Based on Models.- 6.5.2 Criteria for the Selection of Good Models.- 6.6 The "Difference" Technique.- 6.7 The Min-Max Method.- 6.8 Decomposition into Amplitude and Phase.- 6.8.1 Phase Information.- 6.8.2 Amplitude Information (The Ratio Method).- 6.9 The Beat-node Method.- 6.9.1 Derivations of Eq. 6.33-1. X-Rays and Electrons.- 1.1 Introduction.- 1.2 Generation of X-Rays.- 1.3 Properties of X-Rays and Electrons.- 1.3.1 Wave-Particle Duality of Photons.- 1.3.2 Photoelectric Effect.- 1.3.3 Wave-Particle Duality of Electrons.- 1.4 Electronic Structure of Atoms.- 1.4.1 Models of the Atom.- 1.4.2 Electronic Transitions.- 1.5 Absorption Coefficients and Absorption Edges.- 1.5.1 Absorption Coefficients.- 1.5.2 Absorption Edges.- 1.5.3 True Absorption and Scattering.- 1.6 Interactions of Photons and Electrons with Matter.- 1.6.1 Excitations and Relaxations.- 1.6.2 Scattering.- 1.6.3 Electrons.- 2. Extended X-Ray Absorption Fine Structure (EXAFS) Spectroscopy.- 2.1 EXAFS Spectroscopy.- 2.2 Theory.- 2.3 Data Analysis.- 3. EXAFS Parameters.- 3.1 Variables and Functions.- 3.2 Effects of Important Parameters.- 3.3 Convention of Changing E0.- 4. Theory of EXAFS.- 4.1 Introduction.- 4.2 Derivations of EXAFS Theory.- 4.2.1 Lee and Pendry (1975).- 4.2.2 Lee (1976).- 4.2.3 Boland, Crane, and Baldeschwieler (1982).- 4.2.4 Curve-Wave Theory.- 4.3 EXAFS of L Edges.- 4.4 The Photoelectron and the Excited Atom.- 4.4.1 Lifetime of the Core Hole.- 4.4.2 Core Hole Relaxation.- 4.4.3 Potential Experienced by Photoelectron.- 4.4.4 Multi-electron Excitations.- 5. Improvement of EXAFS Theory.- 5.1 Energy Threshold - The Phase Problem.- 5.1.1 Choosing E0.- 5.1.2 Phase Transferability.- 5.1.3 VaryingE0.- 5.2 Inelastic Scatterings - The Amplitude Problem.- 5.2.1 Central Atom: Shake Up/Off Processes.- 5.2.2 Scatterer: Electron Inelastic Mean Free Path.- 5.3 Static and Thermal Disorder Effects.- 5.3.1 Small Disorders.- 5.3.1.1 Symmetric Pair Distribution.- 5.3.1.2 Discrete Bonds.- 5.3.1.3 Harmonic Vibration.- 5.3.2 Large Disorders.- 5.3.2.1 Derivation of the Generalized EXAFS Formalism.- 5.3.2.2 Moments of g(r).- 5.3.2.3 Symmetric Pair Distributions.- 5.3.2.4 Asymmetric Pair Distributions.- 5.3.2.5 Anharmonic Vibration Potentials.- 5.3.2.6 Comparison of EXAFS and Diffraction.- 5.4 Multiple Scattering EXAFS Formalism.- 6. Data Analysis in Practice.- 6.1 Data Reduction.- 6.1.1 Conversion of Experimental Variables.- 6.1.2 Background Removal.- 6.1.3 Normalization and ?0 Correction.- 6.1.4 Conversion ofE to k.- 6.1.5 Weighting Scheme.- 6.1.6 Deglitching and Truncation.- 6.2 Fourier Transform (FT).- 6.3 Fourier Filtering (FF).- 6.4 Curve Fitting (CF).- 6.4.1 Parameterization.- 6.4.2 Phenomenological EXAFS Models.- 6.4.3 Least-squares Refinements.- 6.4.4 Correlations.- 6.4.5 Errors.- 6.5 Parameter Correlation and the FABM Method.- 6.5.1 Fine Adjustment Based on Models.- 6.5.2 Criteria for the Selection of Good Models.- 6.6 The "Difference" Technique.- 6.7 The Min-Max Method.- 6.8 Decomposition into Amplitude and Phase.- 6.8.1 Phase Information.- 6.8.2 Amplitude Information (The Ratio Method).- 6.9 The Beat-node Method.- 6.9.1 Derivations of Eq. 6.33-40.- 6.10 The Lee and Beni Method.- 6.11 The r Space Method.- 6.12 The Phase Linearization Method.- 6.13 The Regularization Algorithm.- 6.14 Other More Specialized Methods.- 7. Theoretical Amplitude and Phase Functions.- 7.1 Introduction.- 7.2 Theoretical Methods.- 7.3 Theoretical Amplitude and Phase Functions.- 7.4 Properties of Amplitude and Phase Functions.- 7.4.1 Amplitude.- 7.4.2 Scatterer Phase.- 7.4.3 Central Atom Phase Shift.- 7.4.4 Effect of Electronic Configuration.- 7.4.5 Charge Effect.- 7.4.6 Comparison of ?al (l = 0, 1, 2) Functions.- 7.4.7 Relativistic Effect.- 7.5 Comparison of Theory and Experiment.- 8. Multiple Scattering and Bond Angle Determination.- 8.1 Scattering Amplitude and Phase.- 8.1.1 F(?,k) and ?(?,k).- 8.2 Multiple Scattering.- 8.2.1 ABC Systems.- 8.2.1.1 Approximations.- 8.2.1.2 Anisotropic ABC Systems.- 8.2.2 Multiple Scattering: AB1B2C Systems.- 8.2.3 Multiple Scattering: Linear or Nearly Linear AB1B2 ??? BnC Systems.- 8.3 Comparison of Theory and Experiment.- 8.4 Angle Determination.- 8.4.1 ABC Systems.- 8.4.1.1 Empirical Approach.- 8.4.2 AB1 ??? BnC Systems.- 8.5 Conclusion.- Appendix I. The Periodic Table.- Appendix II. X-Ray Absorption Edges and Characteristic X-Ray Emission Lines.- Appendix III. Victoreen's C and D Values for True Absorption.- Appendix IV. Fluorescence Yields.- Appendix V. Backscattering Amplitude, Backscattering Phase, and Central Atom Phase.