Small rings and amorphous tetrahedral carbon

We apply first-principles density-functional calculations to study strain i n dense amorphous tetrahedral carbon(a-tC). While the large strain present in small-ring structures? particularly three-member rings, could argue agai nst their existence in a-tC, we demonstrate, based on energetic arguments, that strained small (three- and four-member) rings are plausible topologica l microstructural elements. We present two bulk carbon structures made up e ntirely of fourfold-coordinated atoms: the first with every atom in one thr ee-member ring, the second with every atom in one four-member ring. Calcula tions show these bulk ring structures are relatively low in energy, only 0. 37 and 0.23 eV/atom above diamond, respectively. This computed strain energ y is much less than that present in recent models for a-tC. We examine prop erties of these structures with the intention to provide benchmark calculat ions for more approximate models, and to investigate the impact small rings might have on the properties of a-tC. We use a recently developed linear-r esponse algorithm to compute phonon spectra for these ring structures. [S01 63-1829(99)02901-X].