From space to superspace and back: Superspace Group Finder
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In the present paper, we study the spatialization of the soundfield in a room, in particular the evolution of room impulse responses as function of their spatial positions. The presented technique allows us to completely characterize the sound field in any ...
The room temperature structure (a-form) of the organic compound p-chlorobenzamide, C7H6ClNO, can be described as a classical three-dimensional periodic superstructure (alpha(s)) and also as a commensurately modulated structure (alpha(m)) in (3 + 1)-dimensi ...
An X-ray study of three phase transitions (PTs) at 86, 78 and 72 K has been carried out for the trigonal modification of the Cs3Sb2I9 crystal (space group P-3m1, a = 8.460 Angstrom, c = 10.398 Angstrom). The T-c1 = 86 K PT preserves the trigonal symmetry a ...
The structure of aperiodic crystals which includes incommensurate, quasi- and composite crystals is usually described in spaces of higher dimension, the so called superspace. The main advantage of the superspace formalism is that an aperiodic structure in ...
The low temperature (LT) modification of Cs3Bi2I9 has been refined to R(F) = 0.055 on the basis of X-ray diffraction measurements at T = 130 K from a twin crystal with six fractions connected by 3-fold axis and m-planes symmetry operations. Data were colle ...
The high- and low-temperature forms, i.e., phase I (stable above 328 K) and phase II (stable below 328 K), of Cu8GeSe6 have been investigated by the powder X-ray diffraction method. Cu8GeSe6 II is hexagonal with A = 12.6438(2), C = 11.7570(1) Angstrom, Z = ...
The superspace concept is a new crystallographic approach for the generalisation of symmetry, structural models and structure dependent properties. Although the original motivation for the superspace was intended to describe symmetry of aperiodic crystals, ...
The mathematical facet of modern crystallography is essentially based on analytical geometry, linear algebra as well as group theory. This study endeavours to approach the geometry and symmetry of crystals using the tools furnished by differential geometry ...
We announce results on the structure of CAT(0) groups, CAT(0) lattices and of the underlying spaces. Our statements rely notably on a general study of the full isometry groups of proper CAT(0) spaces. Classical statements about Hadamard manifolds are estab ...
Differential geometry provides a useful mathematical framework for describing the fundamental concepts in crystallography. The notions of point and associated vector spaces correspond to those of manifold and tangent space at a given point. A space-group o ...