Parent clamping approximation
From Online Dictionary of Crystallography
Revision as of 09:37, 17 November 2017 by BrianMcMahon (Added German and Spanish translations (U. Mueller))
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 is typically accompanied by a contraction or expansion of the unit cell, which makes the above assumption no longer valid.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.
- Chapter 184.108.40.206 of International Tables for Crystallography Volume D