Nanoparticles with Cubic Symmetry: Classification of Polyhedral Shapes

  • TH Department Seminar
  • Date: Nov 23, 2023
  • Time: 02:00 PM (Local Time Germany)
  • Speaker: Prof. Klaus Hermann
  • Fritz-Haber-Institut der MPG, Theorie Department, Berlin, Germany
  • Location:
  • Room: Meeting ID: 978 1597 4015 | Passcode: 063543
  • Host: TH Department
Nanoparticles with Cubic Symmetry: Classification of Polyhedral Shapes
The detailed characterization of polyhedral bodies, while a subject of mathematical research since ancient times, has attracted new interest in connection with crystalline nanoparticles (NP).

This can help to analyze geometric details of observed NPs where we consider compact polyhedra of cubic point symmetry as simple models. Here we focus on polyhedra with facets of families {100}, {110}, and {111}, suggested for metal and oxide NPs with cubic lattices. Resulting generic polyhedra with one facet type have been observed in a few cases as NP shapes by electron microscopy. They can serve for a complete description of non-generic polyhedra as intersections of corresponding generic species, not studied by experiment so far. In particular, all corresponding polyhedral shapes can be systematically classified, leading to a novel phase diagram for easy identification. Structural details of the polyhedra, such as shape, size, and facet geometry, are discussed in analytical and numerical detail with visualization of typical examples.

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