Nucleation of small silicon carbide dust clusters in AGB stars

Silicon carbide (SiC) grains are a major dust component in carbon-rich AGB stars. The formation pathways of these grains are, however, not fully understood.\ We calculate ground states and energetically low-lying structures of (SiC)$_n$, $n=1,16$ clusters by means of simulated annealing (SA) and Monte Carlo simulations of seed structures and subsequent quantum-mechanical calculations on the density functional level of theory. We derive the infrared (IR) spectra of these clusters and compare the IR signatures to observational and laboratory data.\ According to energetic considerations, we evaluate the viability of SiC cluster growth at several densities and temperatures, characterising various locations and evolutionary states in circumstellar envelopes.\ We discover new, energetically low-lying structures for Si$_{4}$C$_{4}$, Si$_{5}$C$_{5}$, Si$_{15}$C$_{15}$ and Si$_{16}$C$_{16}$, and new ground states for Si$_{10}$C$_{10}$ and Si$_{15}$C$_{15}$. The clusters with carbon-segregated substructures tend to be more stable by 4-9 eV than their bulk-like isomers with alternating Si-C bonds. However, we find ground states with cage ("bucky"-like) geometries for Si$_{12}$C$_{12}$ and Si$_{16}$C$_{16}$ and low-lying, stable cage structures for n $\ge$ 12. The latter findings indicate thus a regime of clusters sizes that differs from small clusters as well as from large-scale crystals. Thus, and owing to their stability and geometry, the latter clusters may mark a transition from a quantum-confined cluster regime to crystalline, solid bulk-material. The calculated vibrational IR spectra of the ground-state SiC clusters shows significant emission. They include the 10-13 $\mu$m wavelength range and the 11.3 $\mu$m feature inferred from laboratory measurements and observations, respectively, though the overall intensities are rather low.