Advanced Certificate in Powder Diffraction on the Web Course Material Master Index School of Crystallography, Birkbeck College, University of London

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Contents

• Internet Skills

The Internet Part-time Study via the Web Web Authoring

• Creating and Editing HTML (Hypertext Mark-up Language)
• HTML Topics

Starting a Document
Tag Order
Spacing
Layout
Headings and Fonts
Symbols
Special Characters
Subscripts and Superscripts
Lists
Tables
Images and Icons
Colours
Document Links
Miscellaneous

• External Links

• Introduction to Powder Diffraction

• In the Beginning
• What is Diffraction?
• What is a Powder?
• What is Powder Diffraction?
• Bragg's Law

  A little more on Crystal Planes

• Laue versus Monochromatic Methods

  A little more on Wavelength and Mononochromatic Radiation

• Single Crystal versus Powder Specimens
• Landmarks
• External Links

• Instrumentation

Laboratory Methods

• Introduction
• Generation of X-rays
• Choice of X-ray Target
• Laboratory X-ray Sources
• Filters
• Monochromators
• Mirrors
• X-ray Detectors
• Instrument X-ray Optics

Reflection Geometry
Transmission Geometry

• Samples

Preparation
Holders

• Data Acquisition

Preferred Orientation
Texture
Sample Spinning
Transparency

• External Links

Synchrotron Sources and Methods

• Background to the Synchrotron
• How do Synchrotrons Work?
• Properties of Synchrotron Radiation
• Insertion Devices
• Beam Conditioners
• Introduction to Synchrotron Powder Diffraction
• Instrument X-ray Optics

Mode (1): Flat Plate with/without Analyser Crystal
Mode (2): Multiple Foil (Hart-Parrish)
Mode (3): Debye-Scherrer
Mode (4): Use of Line/Area Detectors
Mode (5): Energy-dispersive

• Data Acquisition on a Synchrotron Powder Diffractometer

Ultra-High-Resolution Angle-Dispersive Data
Energy-Dispersive Detector Energy Calibration
Energy-Dispersive Detector Angle
Comparison of Laboratory and Energy-Dispersive Diffraction Data

• External Links

Neutron Sources and Methods

• Introduction
• Properties of the Neutron
• Neutron Detectors
• Samples & Sample Holders
• Steady-State Sources

Nuclear Reactors
Guide Halls & Guide Tubes
Monochromators
High-Resolution Diffractometers
High-Flux Diffractometers
Data Acquisition

• Pulsed Sources

Time-of-Flight Concepts
Spallation Neutrons
TOF Diffractometers
TOF Data Collection

• Future
• External Links

• Diffraction Theory

From Electron Scattering to Structure Factors

• Scattering of X-rays by a Single Electron
• Scattering of X-rays by Two Electrons
• Scattering of X-rays by a Collection of Electrons as in an Atom

Anomalous Scattering

• Scattering of X-rays by a 1-Dimensional Chain of Atoms or Molecules
• A Geometrical Representation
• Scattering of X-rays by 2- and 3-Dimensional Units

The Reciprocal Lattice

• Further Interpretations of Diffraction
• Intensity of Diffraction: the Structure Factor Equation
• A Dimensional Summary

From Structure Factors to Diffraction Intensities

• Kinematic versus Dynamic Diffraction
• Powder Diffraction
• Calculating the Intensity of Diffraction Using the Structure Factor Equation
• From the Structure Factor to Measured Intensities
• Multiplicity
• Polarisation Factor
• Lorentz Factor
• Absorption Factor
• Agreement?
• Temperature Effects

• Symmetry

3-D Symmetry Elements

• Introduction
• Rotation Symmetry

Rotation Axes
Symmetry Operators

• Rotary-Inversion Symmetry

Inversion Symmetry
Mirror Planes
Higher Order Axes

• Translational Symmetry

Lattices and Unit Cells
Crystal Systems
Bravais Lattices

• Screw Symmetry

Concepts
Two-one Screw Axis
Helical Screw Axes

• Glide Symmetry
• Symmetry Symbols

Point Groups

• Symmetry Diagrams

Flat Projection
Sterographic Projection

• Symmetry Groups

Concepts
Molecular Point Symmetry
Crystallographic Point Groups
Point-Group Diagrams
Diffraction Symmetry
Reflection Multiplicity
Polar Point Groups
Enantiomorphic Point Groups
Point-Group Determination

Space Groups

• Introduction to Space Groups
• The 230  3-Dimensional Space Groups
• Space-Group Frequencies
• Space-Group Diagrams
• Special Positions
• Asymmetric Unit
• Crystal Class
• Triclinic Space Groups

Clickable Space Group P-1

• Monoclinic Space Groups

Clickable Space Group P2₁/c

• Orthorhombic Space Groups

Clickable Space Group P2₁2₁2₁

• Centred Space Groups

Clickable Space Group C2/c

Space-Group Determination

• Introduction
• Reflection Conditions & Systematic Absences

Centred Lattices
Screw Axes
Glide Planes

• Single-Crystal versus Powder Diffraction
• Space-Group Determination in Practice
• Case Study
• Links

• Qualitative Analysis

• A Taster
• Back to the Beginning
• A Powder Diffraction File
• The Search Begins
• A Simple Question
• A Simple Answer
• And Something More
• So What About Multiple Phases?
• Present and Future Developments
• External Links

• Quantitative Analysis

  • Introduction
  • Single Peak type Methods

  Diffracting Power
  Multi-Component Systems

  • Absorption

  The Absorption Problem
  Dealing with the Absorption Problem

  • Whole-Pattern Quantitative Analysis

  Principles

  A Worked Example

  External Links

Unit-Cell Refinement

• Introduction
• Generation of hkl, d, and 2θ Values
• Standards
• Unit-Cell Refinement
• Wavelength Refinement
• Accuracy
• Interactive Programs

Program to Generate hkl, d, and 2θ Values
Program to Refine Unit-Cell Parameters

• External Links

Indexing Methods & Programs

• Principles
• Simple Methods
• Trial Methods
• Dichotomy Methods
• Zone Indexing Methods
• Monte Carlo Methods
• Pitfalls
• Interactive Program

Zone-Indexing Program

• External Links

• The Concept of Peak Shape
• Peak Shape Functions

Gaussian
Lorentzian (or Cauchy)
Pearson VII
Others

• Variations Across a Pattern
• Sources of Peak Broadening
• Crystallite Size and Strain
• Determination of Size and Strain

Rietveld Method

• Introduction
• From Intensities to Structural Parameters
• Profile Fitting

Theory
Practice

• Least-Squares Fitting
• R-Factors
• Estimated Standard Deviations
• Case Study

Tools

• Molecular Geometry

Interatomic Distances & Bond Lengths
Bond Angles
Torsion Angles

• Fourier Maps
• Constraints & Restraints

Coordinate
Geometry
Atomic Displacement
Composition

• Multiphase Refinements
• Phase Transitions
• Combined Data Sets

Rietveld in Practice

• Using Rietica

  Viewing the Data
  Preferences
  Getting Started
  Backgrounds
  Crystallographic Model
  Refinement

• Practical Problems

  Damping Parameters
  Atomic Displacement Parameters

• Historical Overview
• Strategy
• Whole Pattern Fitting

Pawley Method
LeBail Method

• Structure Solution

Direct Methods
Global Optimisation Methods

• External Links

Producing and Interpreting Crystallographic Journal Articles

• Introduction to Producing and Interpreting Crystallographic Journal Articles
• Experimental: Sample and Experimental Details
• Experimental: Structural Model Determination Details
• Experimental: Rietveld Refinement Details
• Results: Rietveld Refinement Results
• Results: Tables of Geometric Parameters
• Discussion: Description of the Structure
• Discussion: Comparison
• Supplementary Material

Use of CIF (Crystallographic Information Format)

• Introduction to Powder Crystallographic Information File (CIF)
• General CIF Terminology
• Example Sections of a CIF

Use of Structural Databases

• Introduction to Structural Databases
• General Strategies for Searching Structural Databases
• The Databases
• Case Study from the Cambridge Structural Database

External Links

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