Wulff-Based Approach to Modeling the Plasmonic Response of Single Crystal, Twinned, and Core–Shell Nanoparticles

Abstract

The growing interest in plasmonic nanoparticles and their increasingly diverse applications is fuelled by the ability to tune properties via shape control, promoting intense experimental and theoretical research. Such shapes are dominated by geometries that can be described by the kinetic Wulff construction such as octahedra, thin triangular platelets, bipyramids, and decahedra, to name a few. Shape is critical in dictating the optical properties of these nanoparticles, in particular their localized surface plasmon resonance behavior, which can be modeled numerically. One challenge of the various available computational techniques is the representation of the nanoparticle shape. Specifically, in the discrete dipole approximation, a particle is represented by discretizing space via an array of uniformly distributed points-dipoles; this can be difficult to construct for complex shapes including those with multiple crystallographic facets, twins, and core–shell particles. Here, we describe a standalone user-friendly graphical user interface (GUI) that uses both kinetic and thermodynamic Wulff constructions to generate a dipole array for complex shapes, as well as the necessary input files for DDSCAT-based numerical approaches. Examples of the use of this GUI are described through three case studies spanning different shapes, compositions, and shell thicknesses. Key advances offered by this approach, in addition to simplicity, are the ability to create crystallographically correct structures and the addition of a conformal shell on complex shapes.

Approaches to modelling the shape of nanocrystals

“…Since interest in crystal shape started gaining momentum, initially to model minerals and later nanoparticles, an increasing variety of computational tools have been developed to implement Wulff-like constructions. The list of available tools is quite large and includes both web-based and desktop applications such as Wulffman [ 90 ], WinXMorph [ 91 ], Wulffmaker [ 53 ], BCN-M [ 92 ], NanoCrystal [ 57 ] and Crystal Creator [ 93 ] as well as open source codes such as Wulffpack [ 94 ] and SOWOS [ 95 ]. These can construct a variety of crystal shapes based on user input that typically involves defining the crystal structure, the exposed facet orientations (denoted or i) in the form of Miller indices, and their associated surface energies (or growth velocities) .…”

“…Analytical calculations of the resulting shape involve a convexification process of , achieved by means of constructing a dual Wulff shape or by closest vertex identification techniques. A numerical approach, adopted in Crystal Creator [ 93 ], has also been reported, where the shape construction is based on the calculation of growth velocities over discretized space. Further, the increasing applicability of Wulff approaches in nanoparticle modelling has prompted an interest in tools that overlay atomic structure to Wulff-derived shapes, such as BCN-M [ 92 ] and NanoCrystal [ 57 ].…”

First-principles study of the surface structure and stability of BC5

“…Despites much of the previous theoretical work has focused on the structure and properties of bulk BC 5 , research on the surface structures (atomic and electronic) and morphology, which plays an essential part of understanding fundamental physical properties and potential applications, has not been found yet. It has been clearly proved that a DFT-based Wulff construction is a reliable tool for identifying the single crystal shape under equilibrium conditions [17][18][19][20][21]. In the present work, we will explore the surface structures and present the equilibrium crystal shape of BC 5 using Wulff construction.…”

Selective suppression of {112} anatase facets by fluorination for enhanced TiO2 particle size and phase stability at elevated temperatures

“…By using XRD diffraction patterns from thermally treated nanoparticles, in a wide range of temperature, we have used Wulff construction, to extract meaningful information about facet growth on the TiO2 particles. [34,35,36]…”