On this page, we present tools and ideas which will help the interested specialist in his endeavour to explore the complexity of crystalline structures in particular in the field of aperiodic crystallography. The tools presented here are freely available for everyone on the web. For comments and questions please contact Gervais Chapuis or Ivan Orlov.


    Update 4 Award-winning symmetry teaching applet for iPhone is available at http://escher.epfl.ch/iphone/
    Update 3 Superspace Finder v.2 relates (3+1)D and 3D space groups in analytical form.
    Update 2 First symmetry teaching applet for Mobile Phones is available (2D groups only for a while)
    Update 1 Charge Flipping software (SuperFlip) - Windows, MacOSX releases and source code.

    • Superspace group finder - v.2

      Attention! The official web page of Superspace Finder has moved to http://it.iucr.org/resources/finder/
      From now on the database is hosted and supported by the IUCr.

      The database contains the set of all possible three-dimensional space groups resulting from hyper-sections of the (3+1)-dimensional superspace groups. It can thus be considered as an extension of the scanning tables given in Part 6 of International Tables for Crystallography Volume E, in which the two-dimensional sectional layer groups of the 230 space groups are listed. Superspace Group Finder is particularly useful for finding common superspace groups for series of modular or flexible structures and phase transitions, and for exploring the symmetry of all commensurate cuts for a specific (3 + 1)-dimensional group.

      For citations: Orlov, I., Palatinus, L. & Chapuis, G. (2008). J. Appl. Cryst. 41, 1182-1186.

    • Superflip

      This program allows a solution of crystal structucure in arbitrary dimension using the charge-flipping algorithm. It can thus be used to solve periodic structures as well as incommensurately modulated structures, composites and even quasicrystals.

    • Superspace Harvester

      The applet helps to find a superspace model for a set of structures by simulating the diffraction pattern for each structure on a semi-transparent layer. By superposing the layers you identify common spots which in the superspace approach would correspond to the same main reflection. All other peaks are expected to be satellites - different colors attributed to patterns help you figure out a modulation for each particular case. Show interface screenshot.
      Drag-and-drop CIF files to the program window to start exploring.

    • Crystal Symmetry Environment database (CSE)

      Recently reincarnated from the CSESM project of Janssen, Janner, Thiers and Ephraim, this database provides information concerning space groups of arbitrary dimensions. It allows manipulation and inspection of the groups, e.g. generators, Wyckoff positions, point group symmetry and systematic extinctions. Space groups of 2-,3-,4- and (3+1)- dimensions are currently available. The new Java interface enables the visualisation of structures possessing a selected space group. Please note thatas the project is under active development, bugs are still possible. Reports and suggestions would be highly appreciated.

    • NADA

      Based on the orientation matrix of the main reflections and rough estimates of the modulation wave vector(s) components, NADA re-indexes the peaks (main and satellite reflections) with integers in higher dimensions (hklm1, hklm1m2 or hklm1m2m3, respectively) and then simultaneously refines the orientation matrix and modulation wave vector(s) components. Refinement is carried out by the least squares method using the observed spatial peak positions. Standard uncertainties on all refined parameters are calculated analytically.

    • Bravais classes: 4D to 3D correspondence

      This page shows potential transformations of (3+1)D Bravais classes into 3D classes for commensurate modulation, listing possible options for q-vector components and orientation of consequent superstructures.

    • Rational approximator

      How far from a rational expression is your incommensurate q-value?
      This applet converts real numbers into the closest rational number with the smallest denominator e.g. 0.85714285 => 6/7. 

Superspace playground

This part contains interactive Flash simulations intended for teaching and introducing the superspace concept.

Most web browsers have the Flash plug-in already incorporated. However, if you see nothing, click here to install. Installation takes less than a minute with a 56.6K modem.

  • Real family embedding: hexagonal ferrites

    Hexagonal ferrites, a group of ferromagnetic layered structures of exceptional diversity can be derived by stacking three building blocks S, R and T, with 2, 3 and 4 oxygen layers respectively. This applet reproduces the superspace embedding of a (TS)nT subfamily for both cases: periodic structures with integer n and non-periodic sequences with single composition-dependent parameter.

    Click button to launch the model after the first introductory slide. The button creates an intersecting line, from which you will immediately see the corresponding cha≤nges in the 4D construction and its 3D cut. As in the models above, you can control the q-vector with the mouse or type its value in a special window.

    Applet 1: Level of rigid T and S blocks.
    Note the crenel size dependence on q-vector.

    Applet 2: Level of atomic layers.
    Colour depth underlines block shifts in XY plane. You may thus see how the R-centred Bravais lattice comes into existence.