Noncubic symmetry in garnet structures studied using extended x-ray-absorption fine-structure spectra

Abstract

The noncubic symmetry appearing in garnets that can be represented by ${\mathit{A}}_{3}$${\mathit{B}}_{5}$${\mathrm{O}}_{12}$ is investigated. Extended x-ray-absorption fine-structure (EXAFS) spectra about Fe, Ga, and Y K-edge and Gd and Er ${\mathit{L}}_{\mathrm{III}}$-edge absorptions of ${\mathrm{Y}}_{3}$${\mathrm{Fe}}_{5}$${\mathrm{O}}_{12}$, ${\mathrm{Gd}}_{3}$${\mathrm{Ga}}_{5}$${\mathrm{O}}_{12}$, ${\mathrm{Y}}_{3}$${\mathrm{Ga}}_{5}$${\mathrm{O}}_{12}$, ${\mathrm{Y}}_{3}$${\mathrm{Al}}_{5}$${\mathrm{O}}_{12}$, and ${\mathrm{Er}}_{3}$${\mathrm{Al}}_{5}$${\mathrm{O}}_{12}$, respectively, are measured and analyzed. It is first confirmed from the results that about 10% of the A atoms exchange their sites with about 5% of the B atoms. This means, in garnet structure, 10% of the A atoms enter the (a) sites, which should be occupied by B atoms according to the crystallographic data; at the same time, those 5% of B atoms replaced by A go into the (c) sites. It is estimated that about two A and two B atoms exchange their sites with each other in a unit cell. This site exchange can be interpreted as an intrinsic characteristic of the garnet structure.Combining EXAFS results with other experimental ones on noncubic symmetry in garnets, a heuristic structural model is proposed to explain the noncubic symmetry in garnet structure tentatively, in which the atomic positions of atoms at (a) sites in four-body diagonals are shifted by small displacements and two B atoms at (a) sites in the [111] axis are assumed to be replaced by A atoms in a unit cell. Calculations of the x-ray-diffraction relative intensity are carried out with this model. The calculated results on the relations of intensities between {222} diffraction peaks, which are forbidden in cubic symmetry, are in agreement with the experimental ones for ${\mathrm{Y}}_{3}$${\mathrm{Fe}}_{5}$${\mathrm{O}}_{12}$ and ${\mathrm{Gd}}_{3}$${\mathrm{Ga}}_{5}$${\mathrm{O}}_{12}$. It is recognized that the site exchange between A and B atoms and the small displacement of atomic positions are mainly responsible for the noncubic symmetry in garnets. This noncubic symmetry can be described in R3\ifmmode\bar\else\textasciimacron\fi{}; i.e., the lowering of space-group symmetry from Ia3\ifmmode\bar\else\textasciimacron\fi{}d into R3\ifmmode\bar\else\textasciimacron\fi{} occurs for the garnet structure.