Laboratory of Crystallography LCR

Interactive course of Crystallography

This course introduces the basic concepts of crystallography and is freely available on the web for everyone. The symmetry of crystalline material and the properties of diffraction are presented by means of interactive applets. The description of structures is greatly facilitated by the combination of drawing tools and easy access to databases.

More specifically, the following applets are available :

• cellConverter
  An applet to transform a unit cell ant its content to another cell. Based on the originial CIF file, the applet generates a new CIF file resulting from the transformation specified by the user.
   
• Charge flipping
  An applet to solve the phase problem in diffraction by the charge flipping algorithm. The user can create a 2D crystalline structure and follow the evolution of the algorithm in solving the structure.
   
• Crystal symmetry environment (CSE)
  An applet to represent (among others) the general and special positions of the 230 space groups.
   
• crystalOgraph
  An applet to represent any type of crystalline structure given the lattice parameters, the space group and the atomic coordinates of symmetry independent atoms. It is also possible to import directly a structure from the ICSD database or from a CIF file.
   
• Diffraction and Fourier Transform
  An applet to calculate the Fourrier Transform of a density function ρ(x) yielding the complex magnitude G(S). The applet is also able to calculate the inverse Fourier transform of G(S). The density function can be either periodic or non-periodic. Numerous tools can be applied in order to understand the role of amplitudes and phases which are of particular importance in diffraction phenomena.
   
• diffractOgram
  An applet to simulate any type of diffraction pattern based on the Ewald sphere and the reciprocal lattice. In particular, Laue patterns, Debye Scherrer diagrams, rotating crystals and even precession photographs can be generated.
   
• Escher Web Sketch 2
  An applet to simulate any symmetry decoration of the plane (17 two-dimensional planar groups).
     
• Ewald sphere animation
  Mpeg: 5.1 MB - 2.8 MB
  QuickTime: 4.7 MB - 2.3 MB
  Video sequence illustrating the diffraction phenomenon based on the Ewald sphere.

• Initiation to the discovery of symmetry
  An applet to discover the point group symmetry of platonic and other polyhedra. In particular, rotations, inversion and combinations of them can be simulated.
   
• Powder diffraction files (For license reason, this applet is only available at the EPFL campus) 
  An applet to extract the powder diffraction patterns from a database. Each pattern can be retrieved by specifying some characteristics, e.g. its element contents and number, the name of the compound, the pdf number of the compound or the d-values of the most intensive lines.
   
• Reciprocal lattice generator
  From a periodic diagram generated by EWS, the user is guided step by step by the applet in order to create the reciprocal lattice corresponding to the periodicity of the initial periodic pattern.
   
• reciprOgraph
  An applet to simulate the X-ray diffraction intensities for single crystal in reciprocal space and powder diffraction patterns. Structures can be selected from the ICSD database or from CIF files.

Additional resources:

The website of the International Union of crystallography (IUCr) maintains a list of public resources dedicated to crystallography education available at this link.