Thermodynamical stability of carbon-based defects in α boron from first principles

We report an exhaustive study of the formation enthalpy and charge states of carbon-based defects in rhombohedral α boron within the density functional theory (DFT) that enables us to derive rules about the formation of complex carbon defects. We have accounted for one and two interstitial carbon atoms, eventually combined with one substitutional carbon atom and/or one interstitial boron atom and varied several geometric parameters. We find that when positioned in the plane perpendicular to the [111] rhombohedral axis, two carbon atoms turn out to preferentially form a graphite-like hexagon with four boron atoms. When positioned instead along the [111] axis, the distance between them strongly affects the defect thermodynamic stability, and we find in particular that additional negative charges strongly stabilize the diatomic carbon–carbon chains.