Polyhedral Metal Nanoparticles with Cubic Lattice: Theory of Structural Properties

TL;DR

This paper develops a theoretical framework to describe the structural properties of polyhedral metal nanoparticles with cubic lattice structures, highlighting how shape and surface features depend on lattice type and parameters.

Contribution

It introduces a model using three integer parameters to characterize nanoparticle shape, size, and surface facets, providing analytical tools and visualization for understanding their structural details.

Findings

Structural fine details differ between fcc and bcc lattice types.

Microfacets and narrow facet strips depend on lattice type.

The model can classify shapes and estimate sizes of real nanoparticles.

Abstract

We examine the structure of compact metal nanoparticles (NPs) forming polyhedral sections of face centered (fcc) and body centered (bcc) cubic lattices, which are confined by facets characterized by highly dense {100}, {110}, and {111} monolayers. 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 compact polyhedral cubic NPs. Their structural properties, such as shape, size, and surface facets, can be described by only three integer valued polyhedral NP parameters N, M, K. Corresponding analytical details are discussed with visualization of characteristic examples. While the overall NP shapes are quite similar between the different cubic lattice types, structural fine details differ. In particular, monolayer planes of adjacent NP facets can join at corners and edges which are not occupied by atoms of the ideal lattice. This gives rise to microfacets and narrow facet strips depending on the lattice type. The discussion illustrates the complexity of seemingly simple nanoparticles in a quantitative account. The geometric relationships of the model particles can also be used to classify shapes and estimate sizes of real compact metal nanoparticles observed by experiment.