Concentration asymmetry and carbon enrichment in titanium carbide and silicon carbide clusters

Abstract

The mass spectra of metal clusters obtained by gas aggregation and laser vaporization techniques show variations of the abundance with cluster size, and the best-known manifestation is the magic numbers. The case of nanoalloys adds structural and chemical richness, and asymmetry in the atomic concentrations is sometimes observed. This is the case with ${\mathrm{Ti}}_{x}{\mathrm{C}}_{y}$ and ${\mathrm{Si}}_{x}{\mathrm{C}}_{y}$ clusters, for which the experiments performed until now reveal an enrichment of the clusters in carbon. The structure of the mass spectrum arises when hot clusters evaporate atoms to cool down. By performing density functional calculations, complemented by a thermochemical formalism to obtain Gibbs free energies, we have found that for each cluster in the families ${\mathrm{Ti}}_{x}{\mathrm{C}}_{y}$ and ${\mathrm{Si}}_{x}{\mathrm{C}}_{y}$ with $x$ = 1--4 and $y$ = 1--4, it is easier to remove titanium or silicon atoms as compared to removing carbon atoms, and this explains the carbon enrichment systematically observed in the experiments. The conclusion is that the broad compositional trends expected in the formation of alloy nanoclusters can be anticipated from calculations of the evaporation energies of the alloy components, and this may be particularly interesting in the field of catalysis.