A simple circularity-based approach for nanoparticle size histograms beyond the spherical approximation

Conventional Transmission Electron Microscopy (TEM) is widely used for routine characterization of the size and shape of an assembly of (nano)particles. While the most basic approach only uses the projected area of each particle to infer its size (the "circular equivalent diameter" corresponding to the so-called "spherical approximation"), other shape descriptors can be determined and used for more elaborate analyses. In this article we present a generic model of particles, considered to be made of a few individual grains, and show how the equivalent size (i.e. a particle volume information) can be reliably deduced using only two basic parameters: the projected area and the perimeter of a particle. We compare this simple model to the spherical and ellipsoidal approximations and discuss its benefits. Then, partial coalescence of grains in a particle is also considered and we show how a simple analytical approximation, based on the circularity parameter of each particle, can improve the experimental determination of a particle size histogram. The analysis of experimental observations on nanoparticles assemblies obtained by mass-selected cluster deposition is presented, to illustrate the efficiency of the proposed approach for the determination of particle size just from conventional TEM images. We show how the presence of multimers offers an excellent opportunity to validate our improved and simple procedure. In addition, since the circularity plays a central role in this approach, attention is attracted on the perimeter determination in a pixelated image.