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Nanomaterials 2016, 6(2), 27; doi:10.3390/nano6020027

Extended Superspheres for Shape Approximation of Near Polyhedral Nanoparticles and a Measure of the Degree of Polyhedrality

Department of Materials Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta, Yokohama 226-8502, Japan
Academic Editor: Helmut Cölfen
Received: 15 January 2016 / Accepted: 27 January 2016 / Published: 2 February 2016
View Full-Text   |   Download PDF [5186 KB, uploaded 2 February 2016]   |  

Abstract

Crystalline nanoparticles or nanoprecipitates with a cubic structure often have near polyhedral shapes composed of low-index planes with {100}, {111} and {110}. To consider such near polyhedral shapes, algebraic formulas of extended superspheres that can express intermediate shapes between spheres and various polyhedra have been presented. Four extended superspheres, (i) {100} regular-hexahedral; (ii) {111} regular-octahedral (iii) {110} rhombic-dodecahedral and (iv) {100}-{111}-{110} rhombicuboctahedral superspheres are treated in this study. A measure ∏ to indicate the degree of polyhedrality is presented to discuss shape transitions of the extended superspheres. As an application of ∏ superspherical coherent precipitate is shown. View Full-Text
Keywords: particle; precipitate; elastic-strain energy; equilibrium shape; polyhedron; supersphere particle; precipitate; elastic-strain energy; equilibrium shape; polyhedron; supersphere
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Onaka, S. Extended Superspheres for Shape Approximation of Near Polyhedral Nanoparticles and a Measure of the Degree of Polyhedrality. Nanomaterials 2016, 6, 27.

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