Photon Factory Activity Report 2005 #23 Part B (2006)
Crystallography

4B2/2004G058,2004G256,2005G157,2005G158

Crystal structures and the oxygen deficiency of tetragonal and monoclinic
zirconium oxide nanoparticles
Masatomo YASHIMA1,* and Shin TSUNEKAWA2
Department of Materials Science and Engineering, Interdisciplinary Graduate School of Science andEngineering, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa,
226-8502, Japan; 2Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku,Sendai, Miyagi, 980-8577, Japan
1Introduction
Phase stability and particle size dependence in purezirconium oxides have extensively been studied bynumerous researchers. Recently, Tsunekawa et al. (2005)
indicated that the valence of Zr ions in the zirconiumoxide nanocrystallites decrease with decreasing particle
size, suggesting the occurrence of oxygen deficiency δ in
ZrO2-δ (0<δ≤1), where the δ is the vacancy concentration.
Although the nanocrystallites include both the tetragonal
and monoclinic phases, the oxygen deficiency of eachphase has not been directly determined yet. The purposeof the present work is to determine the oxygen
deficiencies in the both tetragonal and monoclinic phasesof a nanocrystalline sample from precise diffraction
experiments.
Furthermore
weinvestigate
theelectron-density distribution of the nano-sized tetragonal
ZrO2-δ. (Yashima & Tsunekawa, Acta Crystallogr., B61(2005) 161-164).
Experiments
We performed synchrotron X-ray powder diffraction
experiments of a zirconium oxide nanocrystalline sample
using the multiple-detector system installed at the BL-4B2
experimental station of the Photon Factory, High Energy
Accelerator Research Organization (KEK), Japan.
Powder diffraction data from the sample at 298 K in air
were collected in asymmetric flat-specimen reflection
geometry with a fixed incident angle of 7.0 deg. Scanningparameters were as follows: step interval of 0.010 deg.,counting time of 4.5 s step-1, and diffraction angle 2θ
range from 8° to 140°. The crystal structures of thezirconium oxide nanocrystallites were refined by theRietveld method with a computer program RIETAN-2000(Izumi & Ikeda, 2000). Electron-density distribution of
the tetragonal zirconium oxide nanocrystallites wasinvestigated by a maximum-entropy method (MEM). The
calculations were done using a computer program
PRIMA.
Results and discussion
All the reflections were indexed with the tetragonal(Space group, P 4 2 / nmc ) and monoclinic (Space group,P 21 / c ) phases. In a preliminary Rietveld analysis, theoccupancy factors of oxygen atoms in the tetragonal andmonoclinic phases were refined independently. The
occupancy factor of oxygen atoms of monoclinic phasewas 1.12(4), thus it was fixed at 1.00 in the final

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Users' Reportrefinement. This suggests that the monoclinic phase hasno oxygen deficiency. Figure1(A) shows the refined
crystal structure of the tetragonal phase. The occupancy
factor of oxygen atom in the tetragonal phase was refined
to be 0.984(4). This suggests that the tetragonal ZrO2-δ
has oxygen deficiency (δ=0.031(7)). Corresponding
chemical formula of the tetragonal phase was ZrO2-δ(δ=0.031(7)). On the contrary, the monoclinic phase did
not have oxygen deficiency within the experimental error.
The MEM electron-density map shown in Fig. 1(B) is
consistent with the refined crystal structure of thetetragonal phase. The electrons are located at thepositions of Zr and O atoms. No extra peaks are observedin the MEM electron-density map. The MEM density
map also suggests the anisotropic distribution of thecation, which could be ascribed to the thermal motion or
static disorder. There exist larger and smaller
distributions of electron around the cation along thelonger and shorter Zr-O bonds, respectively. The MEM
density map in Fig. 1(C) indicates a covalent bonding
between Zr and O atoms. The bond with shorter Zr-O
length r has stronger bonding, while the bond with longer
distance R has weaker bonding.

Fig. 1. (A) Refined crystal structure andequi-electron-density surfaces (B) at 10 and (C) at 1
Å-3 of the tetragonal zirconium oxide nanoparticles.
Two bond lengths between the cation and anion are R= 2.3562(6) Å and r = 2.0805(5) Å. Arrows stand forthe displacements of oxygen atoms along the c axis
(0.237(1) Å). Figures were drawn with the VENUS
program made by Drs. R. A. Dilanian and F. Izumi.

*yashima@materia.titech.ac.jp