Geometrical Structural Complexes of ZrO₂ Nanoparticles

V. Ya. Shevchenko*, M. I. Samoilovich**, A. L. Talis***, A. E. Madison*, and V. E. Shudegov*

* Grebenshchikov Institute of Silicate Chemistry, Russian Academy of Sciences,
ul. Odoevskogo 24/2, St. Petersburg, 199155 Russia

** OAO Central Research Technological Institute “Tekhnomash,” ul. Ivana Franko 4, Moscow, 121108 Russia

*** All-Russia Research Institute of Synthesis of Mineral Raw Materials,
Institutskaya ul. 1, Aleksandrov, Vladimirskaya oblast, 601650 Russia

Received October 27, 2004

Abstract—It is demonstrated that the structural inhomogeneity of the nanostate is a fundamental property and
can be adequately explained in terms of the algebraic geometry when the four-dimensional fiber space is chosen
as a hypothetical praphase of a nanoparticle. Zirconia nanoparticles ZrO₂ with coherent boundaries between
their constituent fragments are treated as cross sections of this praphase by three-dimensional Euclidean hyper-
planes. The monoclinic, tetragonal, and orthorhombic zirconia structures are assembled from the capped octa-
hedra Z7 and the Bernal polyhedra Z8 and Z9 that are geometrical structural complexes (building blocks) of
fluorite-like structures. The interrelated constructions of finite projective geometries are determined. These con-
structions make it possible to specify graphs of the Z7, Z8, and Z9 polyhedra and to simulate the corresponding
ZrO₂ phases as fiber bundles associated with one principal fiber bundle, namely, the ZrO₂ praphase. A priori
possible mutual transformations in zirconia are considered, and new structural forms of nanoparticles assem-
bled from the Z7, Z8, and Z9 polyhedra are predicted.

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