This web page is maintained by joint effort of the SIG3 and CAC. CAC is the Commission on Aperiodic Crystals established in April 1991 by International Union of Crystallography (IUCr). SIG3 is the Special Interest Group on Aperiodic Crystals established in August 1998 by European Crystallographic Association (ECA).
According to IUCr [Acta Cryst. A48(1992), p. 928] by "crystal" we mean any solid having an essentially discrete diffraction diagram, and by "aperiodic crystal" we mean any crystal in which three dimensional lattice periodicity can be considered to be absent. The mission of both SIG3 and CAC is promotion of experimental and theoretical research on aperiodic crystals, including quasicrystals, modulated crystals, composite crystals, magnetic systems, and polytypes.
The triannual flagship conferences Aperiodic are organized by CAC since 1994. Because the web pages of old Aperiodic conferences are vanishing we would like to conserve here memories about these nice and important events.
Aperiodic2015, 30 August - 4 September 2015, Prague, Czech Republic
Aperiodic2012, 2-7 September 2012, Cairns, Australia
Aperiodic2009, 13-18 September 2009, Liverpool, UK
Aperiodic2006, 17-22 September 2006, Zao, Japan
Aperiodic2003, 8-13 September 2003, Belo Horizonte, Brasil
Aperiodic2000, 5-8 July 2000, Nijmegen, The Netherlands
Aperiodic1997, 27-31 August 1997, L'alpe D'huez, France
Aperiodic1994, 18-22 September 1994, Les Diablerets, Switzerland
The international Schools on Aperiodic Crystals (ISAC) are organized triannually by CAC and SIG3 since 2010.
The 2nd School on Aperiodic Crystals, 2 - 12 April 2013, Bayreuth, Germany
The 1st School on Aperiodic Crystals, 26 September - 2 October 2010, La Valerane-Carqueiranne, France
|P S Q||REMOS,PREMOS,MODPLT and PRJMS|
|P S Q||Crystallographic computing system for standard, modulated and composite crystals|
|P S Q||Rietveld refinement. See also.|
|P S Q||Full Powder Pattern Fitting Program|
|P S Q||Simultaneous Rietveld Refinement|
|P S Q||Program written by Eugenio Durand, at the Geometric Center, for drawing Penrose tilings and its generalizations. The page contains also an introduction to the geometry of quasicrystals. QuasiTiler is implemented as a HTML fill-out form.|
|P S Q||Many JAVA applets and applications.|
|P S Q||See Superspace Tools in this table.|
|P S Q||Calculates phonon dispersion relations and phonon density of states of crystals from force constants or Hellmann Feynman forces found by an ab initio program|
|P S Q||Program for refinement of q vectors up to 6 dimensions from CCD and Imaging plate data.|
|P S Q||The program generates Ammann-Beenker and Penrose quasicrystal structures with various parameters.|
|P S Q||Ab-initio direct-method phasing of diffraction data from incommensurately modulated/composite crystals|
|P S Q||Visual computing in Electron Crystallography, including structure-solving programs DIMS and MIMS for incommensurately modulated/composite crystals|
|P S Q||Two programs for Mathematica to obtain quasiperiodic tilings using the generalized grid method (GDM). See also Z. Kristallogr. 218,(2003)|
|P S Q||On line tools concerning mostly the superspace symmetry.
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.
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.
Superspace group finder. This database provides all potential transformations of (3+1)D superspace groups into 3D space groups for commensurate modulation, listing possible options for q-vector components, t-values and origin shifts of consequent superstructures. The method is based on 3-dimensional rational cuts and enables a common (3+1)D superspace group between different members of a structural family to be found. Alternatively, you may explore 3D space groups resulting from a (3+1)D superspace group. The project has been conceived in order to exploit possibilities offered by the superspace concept with the aim of finding a common denominator in a series of structures based on a limited number of structural blocks, i.e. modular structures.
List of (3+1) dimensional superspace groups. According International Tables for Crystallography (1999) nomenclature, Volume C, Table 126.96.36.199.
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 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 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.
|P S Q||Program for solution of three or more dimensional structures by the charge flipping method.|
|P S Q||An interactive molecular dynamics JAVA applet to demonstrate self-assembly of identical particles to a decagonal quasicrystal in two dimensions.|
Links to any interesting software for aperiodic structures are welcome!
|China||Beijing||at the Institute of Physics, Chinese Academy of Sciences||M Q|
|Czech Republic||Prague||Institute of Physics,||M Q|
|France||Caen||- (CRISMAT)||M Q|
|France||Nancy||at the||M Q|
|France||Nantes||CNRS -,||M Q|
|France||at at||M Q|
|Germany||Bayreuth||at the||M Q|
|Germany||Mainz||- Institute of Geosciences -||M Q|
|Germany||Tubingen||- Institute of Theoretical Physics. .||M Q|
|Germany||Stuttgart||- .||M Q|
|Japan||(National Institute for Materials Science), .||M Q|
|Mexico||Ciudad Universitaria||University of Mexico,,||M Q|
|Netherlands||Nijmegen||Theoretical Solid State Physics at theat||M Q|
|Russia||Moscow||at Moscow state university||M Q|
|Spain||Bilbao||- -||M Q|
|Sweden||Stockholm||at the||M Q|
|Switzerland||Zurich||at the||M Q|
|USA||Pasadena||. See also .||M Q|
|USA||Ames||, - - -||M Q|
Any update or additional information are welcome!
- at Iowa State University and Ames Laboratory
- , Zurich, Switzerland
- at Universidad Nacional Autonoma de Mexico.
- by Ben Chaffin
- by James P. Sethna
- by A. P. Tsai
- maintained by Dr. Cynthia Jenks, Iowa-State University
- Textbooks on the subject of aperiodic crystals:
Aperiodic Crystals: From Modulated Phases to Quasicrystals
This book written by Ted Janssen, Gervais Chapuis & Marc de Boissieu will be published by Oxford in the series "International Union of Crystallography Texts on Crystallography" in June 2007.
This book written by Sander van Smaalen will be published by Oxford in the series "International Union of Crystallography Texts on Crystallography" in Aug. 2007.
- IUCr Crystallography Journals
- John Huesman's of crystallography papers using the Fourier-space derived by Mermin and collaborators from a 1962 paper of Bienenstock and Ewald
- by Ivan Orlov. Complete list of 3+1 superspace groups from International Tables C and various tools.
Mailing list of the special interest group SIG3 is used to announce occassionally news which we consider to be important. To be included in such list please send a request to Michal Dusek, firstname.lastname@example.org .
Please send any information, comments or suggestions concerning this web page to Michal Dusek, email@example.com