\contentsline {section}{\numberline {1}Introduction}{1}{section.1}
\contentsline {subsection}{\numberline {1.1}How to use this document}{1}{subsection.1.1}
\contentsline {subsection}{\numberline {1.2}Free documentation}{2}{subsection.1.2}
\contentsline {subsection}{\numberline {1.3}Typographic and presentation conventions}{2}{subsection.1.3}
\contentsline {section}{\numberline {2}Introduction to FEFF}{4}{section.2}
\contentsline {subsection}{\numberline {2.1}Scattering Paths}{4}{subsection.2.1}
\contentsline {subsubsection}{\numberline {2.1.1}Paths and shells}{4}{subsubsection.2.1.1}
\contentsline {subsubsection}{\numberline {2.1.2}Important paths}{5}{subsubsection.2.1.2}
\contentsline {subsection}{\numberline {2.2}Using FEFF}{5}{subsection.2.2}
\contentsline {subsubsection}{\numberline {2.2.1}FEFF's modular structure}{5}{subsubsection.2.2.1}
\contentsline {subsubsection}{\numberline {2.2.2}ATOMS: Crystalline materials in FEFF}{6}{subsubsection.2.2.2}
\contentsline {subsubsection}{\numberline {2.2.3}The contents of the FEFF input file}{7}{subsubsection.2.2.3}
\contentsline {subsubsection}{\numberline {2.2.4}Copper metal data and paths}{9}{subsubsection.2.2.4}
\contentsline {subsubsection}{\numberline {2.2.5}Files from a FEFF run}{10}{subsubsection.2.2.5}
\contentsline {section}{\numberline {3}Polarization in FEFF: Hexagonal GaN}{12}{section.3}
\contentsline {subsection}{\numberline {3.1}Polarization dependent data}{12}{subsection.3.1}
\contentsline {subsection}{\numberline {3.2}Polarization dependence in FEFF}{12}{subsection.3.2}
\contentsline {section}{\numberline {4}Introduction to FEFFIT: copper metal}{15}{section.4}
\contentsline {subsection}{\numberline {4.1}Background removal with AUTOBK}{15}{subsection.4.1}
\contentsline {subsubsection}{\numberline {4.1.1}Principles of AUTOBK}{15}{subsubsection.4.1.1}
\contentsline {subsubsection}{\numberline {4.1.2}Use of AUTOBK}{16}{subsubsection.4.1.2}
\contentsline {subsubsection}{\numberline {4.1.3}Results of an AUTOBK run}{17}{subsubsection.4.1.3}
\contentsline {subsection}{\numberline {4.2}Setting up a FEFFIT input file}{18}{subsection.4.2}
\contentsline {subsubsection}{\numberline {4.2.1}The EXAFS equation for a path}{19}{subsubsection.4.2.1}
\contentsline {subsubsection}{\numberline {4.2.2}Path parameters and math expressions}{19}{subsubsection.4.2.2}
\contentsline {subsection}{\numberline {4.3}A simple fitting model for copper}{20}{subsection.4.3}
\contentsline {subsubsection}{\numberline {4.3.1}Simple math expressions}{20}{subsubsection.4.3.1}
\contentsline {subsubsection}{\numberline {4.3.2}Math expressions for \texttt {delr}}{20}{subsubsection.4.3.2}
\contentsline {subsubsection}{\numberline {4.3.3}Math expressions for \texttt {sigma2}}{21}{subsubsection.4.3.3}
\contentsline {subsubsection}{\numberline {4.3.4}Path paragraphs for the fourth shell}{21}{subsubsection.4.3.4}
\contentsline {subsubsection}{\numberline {4.3.5}Path degenaracy}{22}{subsubsection.4.3.5}
\contentsline {subsubsection}{\numberline {4.3.6}Path importance}{23}{subsubsection.4.3.6}
\contentsline {subsubsection}{\numberline {4.3.7}The middle atom in multiple scattering paths}{23}{subsubsection.4.3.7}
\contentsline {subsubsection}{\numberline {4.3.8}Multiple scattering mean square displacements}{24}{subsubsection.4.3.8}
\contentsline {subsubsection}{\numberline {4.3.9}Fit to the copper metal data}{24}{subsubsection.4.3.9}
\contentsline {subsection}{\numberline {4.4}FEFFIT output files}{26}{subsection.4.4}
\contentsline {subsubsection}{\numberline {4.4.1}Log and prm files}{26}{subsubsection.4.4.1}
\contentsline {subsubsection}{\numberline {4.4.2}Measurement uncertainty}{26}{subsubsection.4.4.2}
\contentsline {subsubsection}{\numberline {4.4.3}Output data files}{26}{subsubsection.4.4.3}
\contentsline {subsection}{\numberline {4.5}Background refinement in FEFFIT}{27}{subsection.4.5}
\contentsline {section}{\numberline {5}Statistics in FEFFIT}{29}{section.5}
\contentsline {subsection}{\numberline {5.1}Definitions of statistical parameters}{29}{subsection.5.1}
\contentsline {subsection}{\numberline {5.2}Reduced $\chi ^2$}{30}{subsection.5.2}
\contentsline {section}{\numberline {6}Understanding guess, set, and path parameters}{33}{section.6}
\contentsline {section}{\numberline {7}Multiple data set fits}{34}{section.7}
\contentsline {subsection}{\numberline {7.1}Europium Titanate}{34}{subsection.7.1}
\contentsline {subsection}{\numberline {7.2}The FEFFIT input file for europium titanate}{34}{subsection.7.2}
\contentsline {subsubsection}{\numberline {7.2.1}Using \texttt {include} files}{35}{subsubsection.7.2.1}
\contentsline {subsubsection}{\numberline {7.2.2}The \texttt {next data set} keyword}{35}{subsubsection.7.2.2}
\contentsline {subsubsection}{\numberline {7.2.3}Fitting multiple edges simultaneously}{36}{subsubsection.7.2.3}
\contentsline {subsubsection}{\numberline {7.2.4}Path lengths and mean square displacements}{36}{subsubsection.7.2.4}
\contentsline {subsubsection}{\numberline {7.2.5}$S_0^2$ for the Ti edge}{37}{subsubsection.7.2.5}
\contentsline {subsubsection}{\numberline {7.2.6}Multiple energy shifts as phase corrections}{37}{subsubsection.7.2.6}
\contentsline {subsubsection}{\numberline {7.2.7}Phase corrections for multiple scattering paths}{39}{subsubsection.7.2.7}
\contentsline {subsubsection}{\numberline {7.2.8}Fit to the two edges}{40}{subsubsection.7.2.8}
\contentsline {subsection}{\numberline {7.3}Fitting many temperatures simultaneously}{40}{subsection.7.3}
\contentsline {subsubsection}{\numberline {7.3.1}Using \texttt {local} variables}{40}{subsubsection.7.3.1}
\contentsline {subsubsection}{\numberline {7.3.2}Reusing \texttt {include} file}{41}{subsubsection.7.3.2}
\contentsline {subsection}{\numberline {7.4}Why do multiple data set fits?}{42}{subsection.7.4}
\contentsline {section}{\numberline {8}Complex structural models}{43}{section.8}
\contentsline {subsection}{\numberline {8.1}Lead Titanate}{43}{subsection.8.1}
\contentsline {subsection}{\numberline {8.2}A structural model for lead titanate}{44}{subsection.8.2}
\contentsline {subsubsection}{\numberline {8.2.1}Fit parameters}{44}{subsubsection.8.2.1}
\contentsline {subsubsection}{\numberline {8.2.2}Calculating path lengths}{45}{subsubsection.8.2.2}
\contentsline {subsubsection}{\numberline {8.2.3}Math expressions for the Pb and Ti distances}{46}{subsubsection.8.2.3}
\contentsline {subsubsection}{\numberline {8.2.4}\texttt {delr} path parameters for lead titanate}{46}{subsubsection.8.2.4}
\contentsline {subsection}{\numberline {8.3}Multiple scattering paths in lead titanate}{47}{subsection.8.3}
\contentsline {section}{\numberline {9}Measuring bond angles}{48}{section.9}
\contentsline {subsection}{\numberline {9.1}Bond angles and MS paths}{48}{subsection.9.1}
\contentsline {subsection}{\numberline {9.2}Methods of measuring bond angle}{49}{subsection.9.2}
\contentsline {subsubsection}{\numberline {9.2.1}The best possible solution}{49}{subsubsection.9.2.1}
\contentsline {subsubsection}{\numberline {9.2.2}What we can do}{50}{subsubsection.9.2.2}
\contentsline {subsection}{\numberline {9.3}Interpolation parameters in FEFFIT}{50}{subsection.9.3}
\contentsline {subsubsection}{\numberline {9.3.1}Path parameters in interpolation path paragraphs}{51}{subsubsection.9.3.1}
\contentsline {subsubsection}{\numberline {9.3.2}The structure of {\texttt {`paths.dat'}}}{52}{subsubsection.9.3.2}
\contentsline {subsubsection}{\numberline {9.3.3}Interpolation paths in \texttt {paths.dat}}{54}{subsubsection.9.3.3}
\contentsline {subsubsection}{\numberline {9.3.4}Running FEFF with hand-written {\texttt {`paths.dat'}} files}{56}{subsubsection.9.3.4}
\contentsline {subsection}{\numberline {9.4}Other things to try}{57}{subsection.9.4}
\contentsline {section}{\numberline {10}Modeling doped materials}{58}{section.10}
\contentsline {subsection}{\numberline {10.1}Silver Bromide Chloride}{58}{subsection.10.1}
\contentsline {subsection}{\numberline {10.2}The problem of mixed materials}{58}{subsection.10.2}
\contentsline {subsubsection}{\numberline {10.2.1}Handling dopants in FEFF}{59}{subsubsection.10.2.1}
\contentsline {subsubsection}{\numberline {10.2.2}A mixed first shell}{60}{subsubsection.10.2.2}
\contentsline {subsubsection}{\numberline {10.2.3}Fit to the first shell}{61}{subsubsection.10.2.3}
\contentsline {subsection}{\numberline {10.3}Building better fitting models}{62}{subsection.10.3}
\contentsline {section}{\numberline {11}Modeling highly disordered materials}{64}{section.11}
\contentsline {subsection}{\numberline {11.1}Calculating Cumulants from an Effective Pair Potential}{64}{subsection.11.1}
\contentsline {subsubsection}{\numberline {11.1.1}A Simple Effective Pair Potential}{64}{subsubsection.11.1.1}
\contentsline {subsubsection}{\numberline {11.1.2}Computing Cumulants}{65}{subsubsection.11.1.2}
\contentsline {subsubsection}{\numberline {11.1.3}Using Cumulants in FEFFIT}{66}{subsubsection.11.1.3}
\contentsline {subsubsection}{\numberline {11.1.4}The FEFFIT Input File}{66}{subsubsection.11.1.4}
\contentsline {subsection}{\numberline {11.2}Using Histograms for Arbitrary Distributions}{68}{subsection.11.2}
\contentsline {subsubsection}{\numberline {11.2.1}Approximating a Function with a Histogram}{68}{subsubsection.11.2.1}
\contentsline {subsubsection}{\numberline {11.2.2}Specifying a Histogram in FEFFIT}{70}{subsubsection.11.2.2}
\contentsline {subsubsection}{\numberline {11.2.3}A Histogram for Hydrated Eu}{71}{subsubsection.11.2.3}
\contentsline {section}{\numberline {12}Molecules in Solution}{76}{section.12}
\contentsline {section}{\numberline {A}Additional topics}{77}{section.A}
\contentsline {subsection}{\numberline {A.1}Acronyms}{77}{subsection.A.1}
\contentsline {subsection}{\numberline {A.2}Scattering diagrams}{77}{subsection.A.2}
\contentsline {subsection}{\numberline {A.3}Parsing input files}{78}{subsection.A.3}
\contentsline {subsection}{\numberline {A.4}The \texttt {eins} and \texttt {eins2} functions}{78}{subsection.A.4}
\contentsline {subsection}{\numberline {A.5}The \texttt {nodegen} keyword}{80}{subsection.A.5}
\contentsline {subsection}{\numberline {A.6}Solving the three-legged path equations}{80}{subsection.A.6}
\contentsline {subsection}{\numberline {A.7}Editing the \texttt {`files.dat'} file}{80}{subsection.A.7}
\contentsline {subsection}{\numberline {A.8}The \texttt {`geom.dat'} file and making huge numbers of paths}{80}{subsection.A.8}
\contentsline {subsection}{\numberline {A.9}Various small programs}{81}{subsection.A.9}
\contentsline {subsection}{\numberline {A.10}Perl modules}{82}{subsection.A.10}
\contentsline {subsection}{\numberline {A.11}EASE: The EXAFS Analysis System for Emacs}{82}{subsection.A.11}
\contentsline {subsection}{\numberline {A.12}UWXAFS Binary Files}{83}{subsection.A.12}
\contentsline {section}{\numberline {B}Bibliography}{84}{section.B}
\contentsline {section}{\numberline {C}Contributing to ATOMS and IFEFFIT}{87}{section.C}
\contentsline {section}{\numberline {D}Distributing this document: The GNU Free Document License}{88}{section.D}
\contentsline {section}{\numberline {E}Example analysis problems}{97}{section.E}
\contentsline {section}{\numberline {F}Future development of this document}{98}{section.F}
\contentsline {section}{\numberline {G}Index}{100}{section.G}