In our recent works [1,2], we analyzed the structural diversity of nanoparticles and the fragmentariness of their structure and formulated the statement that the structural inhomogeneity is a fundamental property of the nanostate. This statement was experimentally confirmed for a number of materials.In particular, reasoning from the results of neutron diffraction and X-ray diffraction investigations of ZrO 2 nanoparticles, Burkhanov et al. [3] proposed a twophase model allowing for the difference between the central and peripheral regions of a particle and their pseudomorphic conjugation. Palosz et al. [4] also used a two-phase model to interpret their diffraction data for SiC, GaN, and diamond nanoparticles. The concept of an "apparent lattice parameter" clearly indicates strong deviations of the position of Bragg peaks (especially at small angles) from the predicted crystallographic positions. The inference was made that a unique lattice parameter for microcrystallites cannot be determined by standard powder diffractometry. The behavior of nanocrystalline powders under pressure cannot be satisfactorily explained in terms of a unique compressibility coefficient. This also counts in favor of the twophase structure of nanoparticles.Earlier [5][6][7], structurally inhomogeneous zirconia nanoparticles that consist of interpenetrating fragments with different symmetries and are characterized by the orientational relationships "incompatible" from the standpoint of classical crystallography were experimentally found for the first time. Regularly oriented fragments with different symmetries, for which the requirements of classical crystallography are not satisfied (the interface need not be a plane, so that the orientational relationships do not necessarily correspond to the Miller indices and the fragments themselves need not be crystals), were referred to as centaurs [5]. The boundaries of fragments are coherent, and, therefore, these particles can be defined as nanostructures with coherent boundaries.Alok Singh and Tsai [8] revealed that the cubic and icosahedral phases in metal alloys can intergrow in a regular oriented manner. It was found that the threefold axes of the cubic phase coincide in direction with the twofold axes of the icosahedral phase and the cubic twofold axes are almost parallel to the icosahedral fivefold axes. The interface is not a plane, and the orientational relationships do not correspond to rational ratios of the corresponding Miller indices and are inconsistent with the assumption that this cubic phase is a quasicrystalline approximant of the icosahedral phase.The structural inhomogeneity of nanoparticles has become evident owing to widespread use of high-resolution electron microscopy [7,9]. Of special interest are materials prepared by ultrafast solidification, because extreme conditions often lead to the formation of vitreous or unstable crystalline structures and quasicrystals. Specifically, it has been demonstrated that fragments of cubic crystals can intergrow to form a hierarchic st...
Methyl radicals react with Pt0NPs suspended in aqueous solutions in fast reactions. The major product is stable methyl coated Pt0NPs, (Pt0NPs)(CH3)n. C2H6, C2H4 and some polymerization products are also formed (see scheme).
In this work, we proceed with the concept of developing nanoclusters (fundamental configurations), which are the basic building blocks of certain crystal structures, allowed us to propose a universal algorithm for crystal self-assembly structure, and hence to elaborate a uniform approach to the analysis of the essentially hierarchic structure of natural objects under the nanoscale. It should be noted that we use the conception, where the configuration of points on the single sphere that minimize potential energy for broad class of potential functions (with the characteristic quadric function of potential versus distance between points) has been studied. The model is not connected both with the undefined isolated from structure nets (like diamond net) and polyhedra (like Friauf polyhedra), which are the basis of clusters, but is hierarchically constructed on local polyhedral structure's searching according to universal algorithm. Crystal structure can explicitly store the information on the structure of the particles that formed it. These particles, geometrically distorted in some extent, can remain in parts of fundamental nanoclusters, coherently grow into them, and emerge as clusters-centaurs.
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 ZrO 2 with coherent boundaries between their constituent fragments are treated as cross sections of this praphase by three-dimensional Euclidean hyperplanes. The monoclinic, tetragonal, and orthorhombic zirconia structures are assembled from the capped octahedra Z 7 and the Bernal polyhedra Z 8 and Z 9 that are geometrical structural complexes (building blocks) of fluorite-like structures. The interrelated constructions of finite projective geometries are determined. These constructions make it possible to specify graphs of the Z 7, Z 8, and Z 9 polyhedra and to simulate the corresponding ZrO 2 phases as fiber bundles associated with one principal fiber bundle, namely, the ZrO 2 praphase. A priori possible mutual transformations in zirconia are considered, and new structural forms of nanoparticles assembled from the Z 7, Z 8, and Z 9 polyhedra are predicted.
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