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.
Equivalent statements of the diffraction condition
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.
Video about x-ray diffraction. You should know more than Bob. Specifically you should know how to determine the Bravais lattice from an x-ray diffraction measurement and for a very good grade you should be able to explain how to determine the locations of the atoms in the basis.
