# Difference between revisions of "Parent clamping approximation"

### From Online Dictionary of Crystallography

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'''Parent clamping approximation''' (PCA), or '''high-symmetry approximation''', is a term indicating the suppression of all distortions of the unit cell in a [[phase transition]] with group-subgroup relation. | '''Parent clamping approximation''' (PCA), or '''high-symmetry approximation''', is a term indicating the suppression of all distortions of the unit cell in a [[phase transition]] with group-subgroup relation. | ||

− | Let G be the [[space group]] of the parent (higher-symmetry) phase, and H the space group of daughter (low-symmetry) phase. The group-subgroup relation is fulfilled if the translation [[subgroup]] T(H) of H is a (proper or trivial) subgroup of the translation subgroup T(G) of G, ''i | + | Let ''G'' be the [[space group]] of the parent (higher-symmetry) phase, and ''H'' the space group of daughter (low-symmetry) phase. The group-subgroup relation is fulfilled if the translation [[subgroup]] ''T''(''H'') of ''H'' is a (proper or trivial) subgroup of the translation subgroup ''T''(''G'') of ''G'', ''i.e.'' if the lengths of the basis vectors of ''H'' are commensurate with those of the basis vectors of ''G''. A phase transition occurring under a change of external conditions (temperature, pressure, applied field ''etc.'') is typically accompanied by a contraction or expansion of the [[unit cell]], which makes the above assumption no longer valid. The parent clamping approximation is adopted precisely to assure the validity of translational symmetry descents. |

=== See also === | === See also === | ||

− | * | + | * Chapter 3.4.2.5 of ''International Tables for Crystallography Volume D'' |

[[Category: Fundamental crystallography]] | [[Category: Fundamental crystallography]] | ||

[[Category: Physical properties of crystals]] | [[Category: Physical properties of crystals]] |

## Revision as of 12:16, 16 May 2017

**Parent clamping approximation** (PCA), or **high-symmetry approximation**, is a term indicating the suppression of all distortions of the unit cell in a phase transition with group-subgroup relation.

Let *G* be the space group of the parent (higher-symmetry) phase, and *H* the space group of daughter (low-symmetry) phase. The group-subgroup relation is fulfilled if the translation subgroup *T*(*H*) of *H* is a (proper or trivial) subgroup of the translation subgroup *T*(*G*) of *G*, *i.e.* if the lengths of the basis vectors of *H* are commensurate with those of the basis vectors of *G*. A phase transition occurring under a change of external conditions (temperature, pressure, applied field *etc.*) is typically accompanied by a contraction or expansion of the unit cell, which makes the above assumption no longer valid. The parent clamping approximation is adopted precisely to assure the validity of translational symmetry descents.

### See also

- Chapter 3.4.2.5 of
*International Tables for Crystallography Volume D*