Total Scattering and PDF Analysis

Table of Contents 

1. Scattering Theory
    1.1 Scattering from a General Object
    1.2 X-ray and Neutron Nomenclature
    1.3 The Basic Principle of Structure Determination
    1.4 Diffraction from a Translationally Periodic Object
    1.5 Diffuse Scattering
   
   

2. Total Scattering and Pair Distribution Functions
    2.1 Defining the Total Scattering from an Object
    2.2 Powder Assumption
    2.3 Defining the Total Scattering Functions
    2.4 The Pair Distribution Function
     2.4.1 Calculation of the Total Scattering Functions
     2.4.2 Form of the PDF
     2.4.3 The Use of Total Scattering
    2.5 The Thorny Topic of Nomenclature
     2.5.1 Limits
     2.5.2 Variants on the Total Scattering Functions

3.  PDF Examples
    3.1 Example 1 - Crystalline vs. Amorphous Materials
    3.2 Example 2 - Difference in Bond Length
    3.3 Example 3 - Difference in Occupation
    3.4 Analysing the PDF and Total Scattering Data
     3.4.1 Small Box Modelling
       3.4.2 Large box modelling -
                         Reverse Monte Carlo methods

Appendix:

A.1. Describing Structures
 A.1.1 Independent Atom Model
 A.1.2 Crystal Structures
 A.1.3 Pair Correlation Functions

A.2. Basic Wave Theory
  A.2.1 Waves and Vectors
  A.2.2 Summing Waves and Interference

A.3. Fourier Transforms

A.3.1 Representing a Function as a Series
  A.3.1.1 Taylor Series
  A.3.1.2 Periodic Functions and Fourier Series
  A.3.1.3 Determining Fourier Coefficients

A.3.2 Fourier Transform
 A.3.2.1 Sine and Cosine Transforms

A.3.3 Properties of Fourier Transforms
 A.3.3.1 Some Common Results
 A.3.3.2 Convolutions and the Convolution Theorem
 A.3.3.3 Practical Fourier Transforms – Truncation Ripples

A.3.4 Example – Sawtooth Profile