Superspace finder: behind the interface
Ivan S. Orlov, Lukáš Palatinus, G. Chapuis · Acta Crystallographica Section A Foundations of Crystallography · 2007
in higher dimensonsApperiodic structures do not exhibit three-dimensionnal translation symmetry.However, in, higker-dimensional translation space symmetry can be restored in the so-called superspace.Commensurately modulated structures and therfore, their symmetry may be described in two ways: by the (3+1)D superspace groups, when they are considered as usual 3D periodic superstructures.Such dualism suggests, that we are capable to find relations between (3+1)D superspace groups and the 3D ones and vice versa.The Superspace Finder is a Web-application, providing such transformations and conditions for corresponding commensurate cuts.A dedicated database stores a complete set of data for (3+1) to 3D group relations obtained for the first time.Along with its fundamental value this net provides vats ground for investigations both in theoretical and practical fields, for ewample, allowed space group sequences for phase transitions.Another question is for example what can we learn from a statistical study of all possible (3+1) to 3D relations?[1] http://superspace.epfl.ch/finder