# Parent clamping approximation

### From Online Dictionary of Crystallography

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+ | <font color="red">Urklammernäherung</font> (''Ge''). <font color="green">Aproximación de la abrazadera precursora</font> (''Sp''). | ||

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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. | ||

## Latest revision as of 09:37, 17 November 2017

Urklammernäherung (*Ge*). Aproximación de la abrazadera precursora (*Sp*).

**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field *etc.*) is typically accompanied by a contraction or expansion of the unit cell, which makes the above assumption no longer valid.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*