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: https://zoom.us/j/97815974015?pwd=NW9nWFRSSFAycVdBd05OUEkrYW0rZz09
Room: Meeting ID: 978 1597 4015 | Passcode: 063543
Host: TH Department

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.