## Introduction

This site is dedicated to the teaching of crystallography and was developed at the EPFL in Lausanne (Switzerland). It was first developed by Wes Hardaker and further extended by Nicolas Schoeni under the responsibility of Prof. G. Chapuis. Recently, all the applets have been updated in 2016 by Nicolas Casademont et Maria Sisto.

## What types of applets can you find on this site ?

You will find applets dedicated to the three basic topics of crystallography, namely symmetry, diffraction and structure solution algorithms.

The symmetry applets range form learning the concept of point group symmetry, get familiar with the symmetry of periodic objects in two dimensions, and also learn about the space group concept for the description of crystalline structures in 3D. An additional applet will help you in finding the new atomic coordinates of a new unit cell provided the matrix transformation from the original unit cell to the new one.

For diffraction, a simple animation of Bragg’s law will help to find the constructive interferences depending on the diffraction angle. Another applet will teach how to obtain the reciprocal lattice based on the original unit cell. Two applets illustrate the concept of Ewald sphere in order to understand the diffraction principles and simulate various diffraction methods. The user will be able to play with the concept of Fourier transform to generate the crystalline structures on the basis of diffraction patterns. From any CIF file (a crystallographic standard to describe atomic structures), the user will be able to simulate either the powder of single crystals difraction pattern.

Finally, the concepts of the Patterson function and the charge filliping algorithms are illustrated for a better understanding of the phase problem in crystallography.

## How to use the applets ?

Most of the applets are written in Java and need to be downloaded.

- For these applets to work you must have the java runtime environement 7 (java 8 seems to work too) installed on your computer. If you don't have it you can download it here: jre 7 download
- To download the applets click on the download links below corresponding to your system. We provide support for most usual systems : Windows 32/64 bits, Mac OS X, Linux 32/64. If you are having any trouble making the applet work contact us

## Applets

### Symmetry

### Diffraction

### Bragg scattering

A Flash animation to illustrate constructive or destructive interferences as expressed by Bragg's law

### Reciprocal lattice generator

From a periodic diagram generated by Escher Web Sketch, 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.

### Diffraction and Fourier Transform

An applet to calculate the Fourrier Transform of a density function ρ(x) yielding the complex magnitude G(S). The density function can be either periodic or non-periodic. The applet is also able to calculate the inverse Fourier transform of G(S). Numerous tools can be applied in order to understand the role of amplitudes and phases, which are of particular importance in diffraction phenomena.

### Structure resolution

## Contact us

These applet are now maintained by Nicolas Casademont and Maria Sisto. They work for Dr. Gervais Chapuis who created them with the help of Nicolas Schoeni.