Application of the paracrystal model to GISAXS analysis of the 3D self-assembled nanoparticle crystals

Abstract

An original diffraction model for the evaluation of the grazing‐incidence small‐angle X‐ray scattering (GISAXS) of the three‐dimensional (3D) supported self‐assembled nanoparticle crystals is presented. The model utilizes the formalism of traditional crystallography that is applied to nanoparticles as scattering entities. The infinite paracrystal concept was adopted in order to include cumulative disorder that is typical for the self‐assembled nanoparticle structures. Azimuthal averaging around a chosen crystallographic direction allows incorporation of texture effects. A transformation of the SAXS paracrystal equations to comply with the GISAXS geometry was employed to describe the scattering process in the limit of the kinematical approximation which facilitates calculations. The model was developed for the face‐centered cubic (FCC) symmetry, however, its extension to any other cubic symmetry is straightforward. The model was tested on a 3D nanoparticle assembly formed on silicon from a dried drop‐cast colloidal solution of monodisperse silver nanoparticles of 5.8 ± 0.6 nm diameter. Presence of the FCC nanoparticle crystal with the [111] texture along the substrate normal was evidenced from evaluation of the synchrotron GISAXS data. The degree of paracrystal disorder is 2.5% and 3.6% parallel and perpendicular to the substrate, respectively, suggesting the anisotropic character of the self‐assembling process. A SAXS measurement of the nanoparticle crystal formed from the same solution in a capillary revealed a randomly oriented FCC structure with a slightly larger paracrystal disorder of 4%. Obviously, different conditions of the nanoparticle crystal formation affect its azimuthal and translational disorder.

Propagation of Structural Disorder in Epitaxially Connected Quantum Dot Solids from Atomic to Micron Scale

“…S3.2. For more detailed developement of these models, the reader is referred to the work of Hosemann [4,5], Guinier [6], and others [7,8,9,10].…”

“…Though the polydispersity of QD building blocks used here was only ∼6%, which represents approximately a single lattice plane spacing, any polydispersity should in principle result in paracrystallinity (see Supporting Information S3), and recent GISAXS studies have concluded that unconnected colloidal crystal thin films are paracrystalline. 25 However, the superiority of the real paracrystal model has not yet been demonstrated in either unconnected or connected colloidal crystals and is essential to understanding the relationship between short and long-range SL order. These structural distinctions may have dramatic implications for electronic transport in CBCs.…”