# 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''.''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 is typically accompanied by a contraction or expansion of the unit cell, which makes the above assumption no longer valid.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. | + | 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 is typically accompanied by a contraction or expansion of the [[unit cell]], which makes the above assumption no longer valid.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 === |

## Revision as of 04:57, 3 March 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

- Section 3.4.2.5 in
*International Tables for Crystallography*, Volume D.