Structure and Morphology of Crystalline Metal Nanoparticles: Polyhedral Cubic Particles

TL;DR

This paper analyzes the structure and morphology of crystalline metal nanoparticles with polyhedral shapes based on cubic lattice models, providing formulas and visualizations to estimate real nanoparticle shapes.

Contribution

It introduces a detailed analytical and numerical framework for understanding the shape and surface facets of cubic lattice-based nanoparticles, aiding experimental shape estimation.

Findings

Derived geometric formulas for nanoparticle shapes

Visualized characteristic nanoparticle examples

Provided tools for experimental shape estimation

Abstract

We examine nanoparticles (NPs) forming polyhedral sections of the ideal cubic lattice, simple (sc), body centered (bcc), and face centered (fcc) cubic, which are confined by facets characterized by densest and second densest {h k l} monolayers of the lattice. Together with the constraint that the NPs exhibit the same point symmetry as the ideal cubic lattice, i.e. Oh, different types of generic NPs serve for the definition of general polyhedral cubic NPs. Their structural properties, such as shape, size, and surface facets, are discussed in analytical and numerical detail with visualization of characteristic examples. The geometric relationships of the model particles expressed by corresponding formulas and numerical tables can be used to estimate shapes and sizes of real compact metal nanoparticles observed by experiment.