Characterization of large vacancy clusters in diamond from a generational algorithm using tight binding density functional theory

Abstract

Point defects and pores in diamond affect its optical and electrical properties. We generated and evaluated a large number of vacancy V_n clusters representing nanosized voids in diamonds for n up to 65. Our generational algorithm spawns the new generation n + 1 from the list of the most stable structures in the previous generation n. With energy as the only criterion, we generate a large structural diversity that allows their unbiased analysis. Since π-electron delocalization is important for carbon, we used quantum mechanical tight-binding density functional theory (TBDFT). Adamantane-like globular shapes are preferred for n up to ∼22. Beginning around n ≈ 35, the most stable structures show overall oblate shapes with some irregularities. These novel structures have not been seen before because hitherto only highly regular structures were considered. We see local graphitization in these relaxed structures providing an atomistic justification for the widely used “slit pore” model. The preference for structures with minimum number of cut bonds diminishes as n increases. There are no particularly stable “magic” sizes for vacancy clusters larger than n = 22 indicating that these larger voids can easily incorporate small vacancies and vacancy clusters. Radial distribution analysis shows that unusual contact or bond distances in the 1.6 to 2.8 Å range appear in the vicinity of the internal surfaces of the vacancy clusters. Extremely long C–C bonds emerge as a result of structural relaxation of the dangling bonds in the vicinity of the vacancy clusters that cannot be simply described by ordinary sp²/sp³ hybridization.