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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.
Reading
Kittel chapter 2: Crystal diffraction or R. Gross und A. Marx: Strukturanalyse mit
Beugungsmethoden
Diffraction from point scatterers
 
Left: Plane waves strike a single point scatterer. The blue waves are the scattered waves. Right: When there are multiple scatterers as when waves pass through a crystal, the interference of the scattered waves causes a diffraction pattern. You can see that in certain directions all of the peaks arrive at the left side of the image at the same time. This is the direction of the diffraction peak.
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 Resources
The Brillouin zone applet
W.L. Bragg, "The Diffraction of Short Electromagnetic Waves by a Crystal", Proceedings of the Cambridge Philosophical Society, 17 (1913), 43–57.
Some periodic functions in real and in reciprocal space
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
The International Centre for Diffraction Data
Symmetry points of Brillouin zones
Guide for the exercise:
X-ray diffraction within the course 511.121 Praktikum für Fortgeschrittene
International Tables for Crystallography: Structure Factor
Ashscroft and Mermin
- Chapter 5: The Reciprocal Lattice
- Chapter 6: Determination of Crystal Structures by X-ray Diffraction
- Chapter 7: Classification of Bravais Lattices and Crystal Structures
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
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