Vacancies in Self-Assembled Crystals: An Archetype for Clusters Statistics at the Nanoscale

Complex systems involving networks have attracted strong multidisciplinary attention since they are predicted to sustain fascinating phase transitions in the proximity of the percolation threshold. Developing stable and compact archetypes that allow one to experimentally study physical properties around the percolation threshold remains a major challenge. In nanoscale systems, this achievement is rare since it is tied to the ability to control the intentional disorder and perform a vast statistical analysis of cluster configurations. Here, a self-assembly method to fabricate perfectly ordered structures where random defects can be introduced is presented. Building binary crystals from two types of dielectric nanospheres and selectively removing one of them creates vacancies at random lattice positions that form a complex network of clusters. Vacancy content can be easily controlled and raised even beyond the percolation threshold. In these structures, the distribution of cluster sizes as a function of vacancy density is analyzed. For moderate concentrations, it is found to be homogeneous throughout the structure and in good agreement with the assumption of a random vacancy distribution.