Difference between revisions of "Noncrystallographic symmetry"
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| + | <font color="blue">Symétrie non cristallographique</font> (''Fr''). <font color="red">Nichtkristallogtaphische Symmetrie</font> (''Ge''). <font color="black">Simmetria non cristallografica</font> (''It''). <font color="purple">非結晶的対称</font> (''Ja''). <font color="green">Simetría no cristalográfica</font> (''Sp''). | ||
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== Definition == | == Definition == | ||
| − | A symmetry | + | A symmetry operation that is not compatible with the periodicity of a [[crystal pattern]] (in two or three dimensions) is called a '''noncrystallographic symmetry'''. Rotations other than 1, 2, 3, 4, and 6 (in ''E''<sup>2</sup> and ''E''<sup>3</sup>) belong to this type of symmetry. Rotations 5, 8, 10 and 12 are compatible with a translation in higher-dimensional spaces, but they are commonly considered noncrystallographic. For example, in quasicrystals fivefold or tenfold rotational axes are incapable of tiling space through the application of three-dimensional lattice translations, but they act as normal symmetry axes in a higher-dimensional space. Continuous rotations, which give rise to the Curie groups contained in the [[cylindrical system]] and in the [[spherical system]], are noncrystallographic in any dimension. |
== Discussion == | == Discussion == | ||
| − | + | In [[:Category:biological crystallography|biological crystallography]], the term 'noncrystallographic symmetry' is often, but improperly, used to indicate a symmetry relationship between similar subunits within the crystallographic asymmetric unit. This use comes from the fact that the operation required to superimpose one subunit on another is similar to a [[space group]] operation, but it operates only over a local volume, and the superposition may be inexact because the subunits are in different environments. The 'subunit' can be a molecular aggregate, a single molecule, a monomer unit of an oligomeric molecule, or a fragment of a molecule. The superposition is inexact because protein subunits in different environments are never identical. At the very least, surface side chains are differently ordered, and solvation is different because of different interactions with adjacent subunits. | |
| − | + | This use of the term 'noncrystallographic symmetry' is improper for two reasons: | |
| − | + | #a symmetry operation acting on a subspace of the crystal space is called a [[local symmetry|local]] or [[partial symmetry]] operation; it is a space [[groupoid]] operation; | |
| + | #an operation that superposes two objects only approximately is called a [[pseudo symmetry]] operation. | ||
| − | + | ==See also== | |
| + | *Chapter 3.2.1.4 of ''International Tables for Crystallography, Volume A'', 6th edition | ||
| + | *Chapter 2.3.5 of ''International Tables for Crystallography, Volume B'' | ||
| + | *[http://www.degruyter.com/view/j/zkri.2008.223.issue-9/zkri.2008.1137/zkri.2008.1137.xml Nespolo, M., Souvignier, B. and Litvin, D. B. (2008). ''Z. Kryst. – Crystalline Mater.'' '''223''', 605–606]. ''About the concept and definition of “noncrystallographic symmetry"'' | ||
[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] | ||
[[Category:Biological crystallography]] | [[Category:Biological crystallography]] | ||
Latest revision as of 13:12, 16 November 2017
Symétrie non cristallographique (Fr). Nichtkristallogtaphische Symmetrie (Ge). Simmetria non cristallografica (It). 非結晶的対称 (Ja). Simetría no cristalográfica (Sp).
Definition
A symmetry operation that is not compatible with the periodicity of a crystal pattern (in two or three dimensions) is called a noncrystallographic symmetry. Rotations other than 1, 2, 3, 4, and 6 (in E2 and E3) belong to this type of symmetry. Rotations 5, 8, 10 and 12 are compatible with a translation in higher-dimensional spaces, but they are commonly considered noncrystallographic. For example, in quasicrystals fivefold or tenfold rotational axes are incapable of tiling space through the application of three-dimensional lattice translations, but they act as normal symmetry axes in a higher-dimensional space. Continuous rotations, which give rise to the Curie groups contained in the cylindrical system and in the spherical system, are noncrystallographic in any dimension.
Discussion
In biological crystallography, the term 'noncrystallographic symmetry' is often, but improperly, used to indicate a symmetry relationship between similar subunits within the crystallographic asymmetric unit. This use comes from the fact that the operation required to superimpose one subunit on another is similar to a space group operation, but it operates only over a local volume, and the superposition may be inexact because the subunits are in different environments. The 'subunit' can be a molecular aggregate, a single molecule, a monomer unit of an oligomeric molecule, or a fragment of a molecule. The superposition is inexact because protein subunits in different environments are never identical. At the very least, surface side chains are differently ordered, and solvation is different because of different interactions with adjacent subunits.
This use of the term 'noncrystallographic symmetry' is improper for two reasons:
- a symmetry operation acting on a subspace of the crystal space is called a local or partial symmetry operation; it is a space groupoid operation;
- an operation that superposes two objects only approximately is called a pseudo symmetry operation.
See also
- Chapter 3.2.1.4 of International Tables for Crystallography, Volume A, 6th edition
- Chapter 2.3.5 of International Tables for Crystallography, Volume B
- Nespolo, M., Souvignier, B. and Litvin, D. B. (2008). Z. Kryst. – Crystalline Mater. 223, 605–606. About the concept and definition of “noncrystallographic symmetry"