PHY.F20 Molecular and Solid State Physics

Crystal diffraction

Everything moves like a wave and exchanges energy and momentum like a particle. When waves move through a crystal they diffract. Light, sound, neutrons, atoms, and electrons are all diffracted by crystals.

Kittel chapter 2: Crystal diffraction or R. Gross und A. Marx: Strukturanalyse mit Beugungsmethoden

Equivalent statements of the diffraction condition

Bragg's lawBragg-Gleichung
Laue condition Laue-Bedingung
Diffraction condition 1Diffraktion Bedingung 1
Diffraction condition 2Diffraktion Bedingung 2

The shape and the dimensions of the unit cell can be deduced from the position of the Bragg reflections; the content of the unit cell, on the other hand, must be determined from the intensities of the reflections.

Solid State Physics, Ibach and Lüth

Advanced Certificate in Powder Diffraction on the Web
CSIC Crystallography website
The Brillouin zone applet
e-Crystallography online course from EPFL Lausanne
Matter: an interactive website for learning about diffraction
Reciprocal Lattice and X-ray Diffraction simulation program from the solid state simulation project
x-ray scattering in one dimension in perfect and imperfect crystals simulation program from the solid state simulation project
PowderCell - a program to visualize crystal structures, calculate the corresponding powder patterns and refine experimental curves
Concerning the Detection of X-ray Interferences Max von Laue, Nobel Prize in Physics 1914
The Diffraction of X-Rays by Crystals Lawrence Bragg, Nobel Prize in Physics 1915
W.L. Bragg, "The Diffraction of Short Electromagnetic Waves by a Crystal", Proceedings of the Cambridge Philosophical Society, 17 (1913), 4357.
The International Centre for Diffraction Data
Guide for the exercise: X-ray diffraction within the course 511.121 Praktikum für Fortgeschrittene
International Tables for Crystallography: Structure Factor
Advanced Certificate in Powder Diffraction on the Web
Brillouin zones at the University of Cambridge
Jpowder: A Java based powder diffraction data visualizer
Teaching pamphlets from the International Union of Crystallography

  • 1. A non-mathematical introduction to X-ray diffraction. C. A. Taylor
  • 2. An introduction to the scope, potential and applications of X-ray analysis. M. Laing
  • 3. Introduction to the Calculation of Structure Factors. S. C. Wallwork
  • 4. The Reciprocal Lattice. A. Authier
  • 5. Close-packed structures. P. Krishna and D. Pandey
  • 6. Pourquoi les groupes de Symétrie en Cristallographie. D. Weigel
  • 7. Crystal structure analysis using the `superposition' - and `complementary' - structures. L. Höhne and L. Kutchabsky
  • 8. Anomalous Dispersion of X-rays in Crystallography. S. Caticha-Ellis
  • 9. Rotation Matrices and Translation Vectors in Crystallography. S. Hovmöller
  • 10. Metric Tensor and Symmetry Operations in Crystallography. G. Rigault
  • 11. The Stereographic Projection. E. J. W. Whittaker
  • 12. Projections of Cubic Crystals. Ian 0. Angell and Moreton Moore
  • 13. Symmetry. L. S. Dent Glasser
  • 14. Space Group Patterns. W. M. Meier
  • 15. Elementary X-Ray Diffraction for Biologists. Jenny P. Glusker
  • 16. The Study of Metals and Alloys by X-ray Powder Diffraction Methods. H. Lipson
  • 17. An Introduction to Direct Methods. The Most Important Phase Relationships and their Application in Solving the Phase Problem. H. Schenk
  • 18. An Introduction to Crystal Physics. Ervin Hartmann
  • 19. Introduction to Neutron Powder Diffractometry. E. Arzi
  • 20. Crystals - A Handbook for School Teachers. Elizabeth A. Wood. This classic text is now available as a Web resource in several different language translations.
  • 21. Crystal Packing. Angelo Gavezzotti and Howard Flack. Includes illustrations of the two-dimensional space groups
  • 22. Matrices, Mappings and Crystallographic Symmetry. Hans Wondratschek