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.
Conferences Aperiodic
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     Report
Aperiodic2009, 13-18 September 2009, Liverpool, UK     Report
Aperiodic2006, 17-22 September 2006, Zao, Japan     Report
Aperiodic2003, 8-13 September 2003, Belo Horizonte, Brasil     Report
Aperiodic2000, 5-8 July 2000, Nijmegen, The Netherlands     Report
Aperiodic1997, 27-31 August 1997, L'alpe D'huez, France
Aperiodic1994, 18-22 September 1994, Les Diablerets, Switzerland     Report     Gallery
Schools on aperiodic crystals
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     Conference web
The 1st School on Aperiodic Crystals, 26 September - 2 October 2010, La Valerane-Carqueiranne, France     Conference web
Table of Software available for aperiodic crystallography
(P=Powder,S=Single crystals,Q=Quasicrystals)
Name Material Comment
Yamamoto's software P S Q REMOS,PREMOS,MODPLT and PRJMS
JANA P S Q Crystallographic computing system for standard, modulated and composite crystals
XND P S Q Rietveld refinement. See also CPD newsletter.
SIMPRO P S Q Full Powder Pattern Fitting Program
SIMREF P S Q Simultaneous Rietveld Refinement
QuasiTiler 3.0 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.
S. Weber's programs P S Q Many JAVA applets and applications.
CSECM P S Q See Superspace Tools in this table.
Phonon Software 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
Nada P S Q Program for refinement of q vectors up to 6 dimensions from CCD and Imaging plate data.
tilings.exe P S Q The program generates Ammann-Beenker and Penrose quasicrystal structures with various parameters.
DIMS P S Q Ab-initio direct-method phasing of diffraction data from incommensurately modulated/composite crystals
VEC P S Q Visual computing in Electron Crystallography, including structure-solving programs DIMS and MIMS for incommensurately modulated/composite crystals
Tiling P S Q Two programs for Mathematica to obtain quasiperiodic tilings using the generalized grid method (GDM). See also Z. Kristallogr. 218, 397 (2003)
Superspace Tools in Lausanne 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
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.
Superflip P S Q Program for solution of three or more dimensional structures by the charge flipping method.
INJAVIS P S Q An interactive molecular dynamics JAVA applet to demonstrate self-assembly of identical particles to a decagonal quasicrystal in two dimensions.
See also: CCP4 - software for incommensurate/modulated structures
Links to any interesting software for aperiodic structures are welcome!
Research groups in the field of Aperiodic Crystallography
(M=Modulated structures,Q=Quasicrystals)
Country City Name Scope
Australia Canberra Solid State Inorganic Chemistry at Research School of Chemistry M Q
China Beijing Research group on methods of solving crystal structures at the Institute of Physics, Chinese Academy of Sciences M Q
Czech Republic Prague Institute of Physics, Laboratory of Crystallography M Q
France Bordeaux Magnetic Materials and Structural Determinations at ICMCB M Q
France Caen ISMRA - Laboratory of Crystallography and material Science (CRISMAT) M Q
France Nancy LSG2M at Ecole des Mines de Nancy M Q
France Nancy LCM3B at the University Henri Poincare M Q
France Nantes CNRS - IMN, Inorganic materials for optics and storage (MIOPS) M Q
France Chatillon Laboratory of Microstructures
France   Quasicrystals at Metal Physics at LTPCM M Q
Germany Bayreuth Laboratory of Crystallography at the University of Bayreuth M Q
Germany Kiel University of Kiel - Crystallography M Q
Germany Mainz University of Mainz - Institute of Geosciences - Crystallography M Q
Germany Tubingen University of Tubingen - Institute of Theoretical Physics. Peter Kramers's page. M Q
Germany Stuttgart University of Stuttgart - Institute for Theoretical and Applied Physics. M Q
Japan   NIMS (National Institute for Materials Science), Quasicrystals research. M Q
Mexico Ciudad Universitaria University of Mexico, Institute of Physics, Gerardo Garcia Naumis M Q
Netherlands Nijmegen Theoretical Solid State Physics at the Institute for Theoretical Physics at Radboud University Nijmegen M Q
Russia Moscow Inorganic crystal chemistry laboratory at Moscow state university M Q
Spain Bilbao UPV - LAMA - Dep. of the Physics of the Condensed Matter M Q
Sweden Stockholm Inorganic Chemistry at the Stockholm university M Q
Switzerland Lausanne Laboratory of Crystallography at EPFL M Q
Switzerland Zurich Crystallography at the ETH Zurich M Q
USA Pasadena California Institute of Technology. See also Ron Lifshitz's page. M Q
USA Ames Iowa State University, Ames Laboratory - Xray physics - Quasicrystal research - group of Patricia A. Thiel M Q
Any update or additional information are welcome!
Miscellaneous Links and Information
Mailing list
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, .
Contact Information
Please send any information, comments or suggestions concerning this web page to Michal Dusek,
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