The activities of the Commission were focused on the organization of
international conferences and the coordination of activities between
the different communities working on quasicrystals and incommensurate
structures. The organization of the congress Aperiodic 2003 by Prof.
Nivaldo Speziali proceeded. The dates for this meeing have been fixed
to the period 8 through 13 September 2003. Aperiodic 2003 will take
place at the Federal University of Minas Gerais in Belo Horizonte
(Brasil). The web site of Aperiodic 2003 is
http://agora.grude.ufmg.br/QuickPlace/aperiodic2003/Main.nsf/h_Toc/
The Commission continued to promote activities on the
crystallography of aperiodic crystals at national and international
meetings. Two microsymposia on aperiodic crystals were organized at the
XIX Congress of the IUCr in Geneva (6 -15 August 2002). One
microsymposium on "diffraction and symmetry aspects of aperiodic
crystals" was chaired by M. Ohmasa and M. De Boissieu. The second
microsymposium on "diffraction by non-periodic structures" was chaired
by G. Chapuis and T. Janssen. Hot topic was the still unsolved problem
of the atomic structures of quasicrystals. Presentations included
discussions on diffuse scattering, dynamics and non-ordered aspects of
the structures of quasicrystals. The crystal structures of modulated
compounds were discussed in the non-harmonic regime.
At the XIX Congress of the IUCr an Open Commission Meeting was
organized around the question "What is a crystal?" Although seemingly a
simple question it requires careful consideration of the properties we
want to assign to crystalline materials. One property that does not
characterize the crystalline state is a periodic atomic structure.
Aperiodic crystals are crystals that lack 3-dimensional (3D)
translational symmetry. A property that can be assigned to an ideal
crystal structure is that it will have infinitely sharp Bragg peaks in
the diffraction. For aperiodic crystals these Bragg reflections cannot
be indexed on the basis of a 3D reciprocal lattice. In 1993 "an
essentially discrete diffraction diagram" was used by the IUCr as
definition of the crystalline state [The 1991 annual report of the
Executive Committee, Acta Cryst. A48, 922-946 (1992)]. A problem with
this definition is that it requires the understanding of diffraction. A
motivation for the discussion thus was to try to develop a definition
that generalizes the notion of a periodic array of atoms towards
aperiodic crystals, and that can be made easily understandable for non
specialists. At the Open Commission Meeting these questions were
introduced by Sander van Smaalen, Walter Steurer and Dhananjai Pandey.
Subsequently they were discussed with many contributions from the
audience. An agreement on one particular definition was not obtained,
but the discussion lead to three statements, that each by itself might
characterize the crystalline state:
The n-dimensional periodic structure refers to the superspace
description of the crystal structures of aperiodic crystals. Long-range
order is defined through the autocorrelation function of the electron
or atomic density function. It can be simplified to the statement that
crystalline structures are structures for which knowledge of the
positions of a few atoms enables one to exactly compute the positions
of all atoms, including those at large separations, e.g. 1 meter.
Advantages of and problems with each of these definitions were
discussed.
Following previous work, the CIF dictionary for modulated structures
was completed in February 2002. Based on this new CIF dictionary a
database of incommensurately modulated structures and composite
crystals was developed. Both projects evolved under the direction of G.
Madariaga (Bilbao) in cooperation with the Committee for the
Maintenance of the CIF standard. The CIF standard is available at the
IUCr Web site. The database is available at the Bilbao Crystallography
Server at http://www.cryst.ehu.es/icsdb/index.html.
The Commission on Aperiodic Crystals maintains internet pages at the
web site of the IUCr at http://www.iucr.org/iucr-top/comm/capd/index.html.
A web site on all aspects of the crystallography of aperiodic crystals
is maintained by the special interest group (SIG) on aperiodic crystals
of the European Crystallography Association. It is maintained by M.
Dusek (Prague, Czech Republic), and it can be found at http://www-xray.fzu.cz/sgip/aphome.html.
| Bayreuth, 18 February 2003 | Sander van Smaalen |