Structure analysis of Zn-Mg-Ho icosahedral quasicrystal by modified Rietveld method using ellipsoid and sphere windows

TL;DR

This study used a modified Rietveld method with ellipsoid and sphere models to analyze the structure of Zn-Mg-Ho icosahedral quasicrystals, revealing a near-perfect Penrose tiling and atomic occupation patterns.

Contribution

It introduces a modified Rietveld analysis approach with simplified models for icosahedral quasicrystals, demonstrating its effectiveness and limitations.

Findings

Identified a near-perfect Penrose tiling with edge length 5.20 Å.

Revealed atomic occupation patterns with Zn, Mg, and Ho.

Achieved good agreement between measured and calculated diffraction intensities.

Abstract

A structure analysis of Zn-Mg-Ho icosahedral quasicrystal was carried out by the powder X-ray diffraction method using synchrotron radiation (Lambda=0.73490 A) at SPring-8. The intensity distribution was analyzed by the Rietveld method modified for an icosahedral quasicrystal, in which simplified models were assumed: ellipsoid and spherical windows were assumed at five crystallographic sites in a F-type hypercubic unit cell. The analysis revealed the presence of an almost perfect Penrose tiling with edge length 5.20 A. The vertices are occupied alternatively by Zn and Mg, and almost all of the edge centers of the Penrose rhombohedra are occupied by 0.8Zn and 0.2Mg. Ho and Mg atoms tend to be present on the body diagonal of the prolate rhombohedra. Good agreement between the measured and calculated intensity distribution using the simplified model suggests the applicability and the limitation of structure analysis using the powder X-ray diffraction method.