Publication

Incommensurate phases

Gervais Chapuis
2024
Book Chapters

Abstract

Incommensurately modulated crystalline phases are part of a more general family called aperiodic crystals. Their symmetry is treated within the theoretical framework of superspace groups that is a generalization of the 3D space groups that are used for conventional crystalline structures. Aperiodic structures are conveniently embedded in superspace with dimensions varying from (3+1) to (3+3)D. They do occur in all types of material, organic and inorganic, metal and alloys, minerals and macromolecules under various pressure and temperature. Some examples of incommensurate structures are presented along with their chemical and physical properties.

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https://infoscience.epfl.ch/entities/publication/d7948b33-4668-4ac1-aee8-fb26664222b1

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Gervais Chapuis
2024
Book Chapters

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/d7948b33-4668-4ac1-aee8-fb26664222b1

About this result

Related concepts (23)

Tessellation

A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner identically arranged.

Space group

In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that leave it unchanged. In three dimensions, space groups are classified into 219 distinct types, or 230 types if chiral copies are considered distinct. Space groups are discrete cocompact groups of isometries of an oriented Euclidean space in any number of dimensions.

Superspace

Superspace is the coordinate space of a theory exhibiting supersymmetry. In such a formulation, along with ordinary space dimensions x, y, z, ..., there are also "anticommuting" dimensions whose coordinates are labeled in Grassmann numbers rather than real numbers. The ordinary space dimensions correspond to bosonic degrees of freedom, the anticommuting dimensions to fermionic degrees of freedom. The word "superspace" was first used by John Wheeler in an unrelated sense to describe the configuration space of general relativity; for example, this usage may be seen in his 1973 textbook Gravitation.

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