Polyhedron Distortion and Site-Specific Rigidity in Garnet-Type Compounds

Abstract

Rigidity of a crystal structure has a simple and imaginable meaning, although its quantitative expression has not been established. A widely accepted approach is to select the Debye temperature as a measurement of rigidity, yet it overlooks the site differences within a unit cell. In this work, the correlation between polyhedron distortion and rigidity of the corresponding crystallographic site is explored in a series of garnet-type compounds. The polyhedron distortion is characterized by determining to what extent the real polyhedron differs from its best fitted ideal one. The smaller octahedron and tetrahedron are much closer to the ideal shapes than the larger dodecahedron. Nevertheless, the dodecahedron has the least variation percentage change, indicating that the 24c site has the smallest deformation on component changing. This observation could explain the excellent thermal luminescence resistance in Ce 3+ -doped garnet phosphors, in which Ce 3+ is accommodated in the dodecahedral site. This new interpretation sheds light on understanding the rigidity of crystal structure and will promote its quantitative characterization for wider applications.