Entropy of Nanostructures: Topological Effects on Schottky Vacancies Concentration in Graphenic Bidimensional HC(N) Lattices

Introduction

The graphene basal plane, which is made by sp² carbon atoms chemically bonded through π-π orbital interactions, is definitely a stable 2D network, with high in-plane stiffness, where vacancy defects spontaneously occur at quite low concentration. Vacancies formation in a honeycomb lattice made of N atoms HC(N) in fact is normally achieved by ion bombardment (Cataldo et al. 2002; 2003; 2009), neutron bombardment (Cataldo et al. 2013; 2014a; 2014b), high energy processing (Cataldo, 2000a; 2000b) or after reaction with oxygen gas (this latter method is preferred for its relative simplicity). Such an imperfection of the atom network due to vacancy is known as Schottky defect. It is created by transferring an atom/ion from the original correct site normally to the surface of the sample.

The possibility to use atomic-scale defects to tailor graphene properties finds its ground in the defect-induced modifications of graphene band structure, such as for example the appearance of sharp peaks in the density of states (localized states) near the Dirac point in the case of vacancies.

Irradiation with high-energy ions creates defects in the honeycomb system whose atomic structure (as well the electronic structure) remains debated. Some observations on the magnetic behavior of proton-irradiated graphene suggest that the majority of irradiation defects consist in reconstructed monovacancies (via Jahn-Teller mechanisms) rather than divacancies or other more complex defects. On the contrary, in case the dangling bonds remain unsaturated, monovacancies are generally believed to group and evolve into divacancies or more complex 555-777 defects. Experimentally, graphene layers show in fact various types of structural (vacancies, grain boundaries, dislocations) and topological (Stone-Wales, dislocation dipoles) defects which vary graphene electronic, magnetic and mechanical properties, vacancies being the most common defects. Typical defective regions with diameters of 20 nm are generated in fact in the graphene basal plane exposed to oxygen/argon flow at 723 K, being the threshold temperature for the reaction of graphene with oxygen gas in the range 473 - 573 K (Liu et al, 2008). A related investigation (Yamada et al. 2010), still using Raman spectroscopy, has shown the existence of temperature-related size effect on vacancy density, suggesting that the size of the vacancy defects becomes smaller when the oxidation temperature lowers. Therefore, a graphene oxidation temperature in the onset region favors the creation of subnanometer vacancy defects in the graphenic mesh. Recently and for the very first time a Japanese-North American team (Yamada et al. 2014), by adopting various oxidation temperatures in the 493 - 573 K interval, has directly observed subnanometer vacancies in graphenic layers detected by High-resolution TEM microscopy (HRTEM) and those defective structures were simulated ab-initio to determine their relative stabilities by density functional theory (DFT) computations. Direct observations of the structures of the vacancy defects in the basal plane including functional groups have been obtained via HRTEM images that show the tendency of graphene oxidized at 533 K to form subnanometer vacancy stable defects with an average density of 1 defect/100 nm². The presence of C=O bonds, proven by XPS spectroscopy, demonstrates that the vacancy defects introduced in the basal plane of graphene were generated by oxygen gas upon heating. Typical defective structure involve a few hexagonal rings in different configurations with 0.5 nm size (see next section). Moreover, according to the authors the experimental observation of subnanometer vacancies underline the stabilization role played by oxygen-containing functional groups such as C=O and C−O−C.