|
| |
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
For the exam
- You should know that every periodic function can be expressed as a Fourier series, f(r) = ΣfGexp(iG·r), where the G's are the reciprocal lattice vectors.
- You should be able to determine the reciprocal lattice vectors of any Bravais lattice.
- You should know that the reciprocal lattice of an orthorhombic lattice (a,b,c) is also an orhtorhombic lattice (2π/a,2π/b,2π/c);
the reciprocal lattice of fcc is bcc and the reciprocal lattice of bcc is fcc.
- You should be able to construct the first Brillouin zone of any reciprocal lattice.
- You should know the different forms of the diffraction condition given in the table below.
- You should be able to explain how the Bravais lattice and the size of the unit cell can be determined in a diffraction experiment.
- You should know how to calculate structure factors. These are the complex coefficients of the Fourier series.
- You should know how the square of the structure factor can be measured in a diffraction experiment and how this information can be used to determine the basis of the crystal structure. (The basis is the pattern of atoms that are repeated at every Bravais lattice site to create the crystal.)
- You should be able to define: powder diffraction, neutron diffraction, LEED, and Ewald shphere.
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
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), 43–57.
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
|
