Small rings and amorphous tetrahedral carbon

We apply first-principles density-functional calculations to study strain in dense amorphous tetrahedral carbon (Formula presented) While the large strain present in small-ring structures, particularly three-member rings, could argue against their existence in (Formula presented) we demonstrate, based on energetic arguments, that strained small (three- and four-member) rings are plausible topological microstructural elements. We present two bulk carbon structures made up entirely of fourfold-coordinated atoms: the first with every atom in one three-member ring, the second with every atom in one four-member ring. Calculations show these bulk ring structures are relatively low in energy, only 0.37 and 0.23 eV/atom above diamond, respectively. This computed strain energy is much less than that present in recent models for (Formula presented) We examine properties of these structures with the intention to provide benchmark calculations for more approximate models, and to investigate the impact small rings might have on the properties of (Formula presented) We use a recently developed linear-response algorithm to compute phonon spectra for these ring structures.