EXAFS: Basic Principles and Data Analysis

The phenomenon of Extended X-Ray Absorption Fine Structure (EXAFS) has been known for some time and was first treated theoretically by Kronig in the 1930s. Recent developments, initiated by Sayers, Stern, and Lytle in the early 1970s, have led to the recognition of the structural content of this technique. At the same time, the availability of synchrotron radiation has greatly improved both the acquisition and the quality of the EXAFS data over those obtainable from conventional X-ray sources. Such developments have established EXAFS as a powerful tool for structure studies. EXAFS has been successfully applied to a wide range of significant scientific and technological systems in many diverse fields such as inorganic chemistry, biochemistry, catalysis, material sciences, etc. It is extremely useful for systems where single-crystal diffraction techniques are not readily applicable (e.g., gas, liquid, solution, amorphous and polycrystalline solids, surfaces, polymer, etc.). Despite the fact that the EXAFS technique and applications have matured tremendously over the past decade or so, no introductory textbook exists. EXAFS: Basic Principles and Data Analysis represents my modest attempt to fill such a gap. In this book, I aim to introduce the subject matter to the novice and to help alleviate the confusion in EXAFS data analysis, which, although becoming more and more routine, is still a rather tricky endeavor and may, at times, discourage the beginners.

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.