ESTIMATING CARBON CLUSTER BINDING-ENERGIES FROM MEASURED CN DISTRIBUTIONS, N LESS-THAN-OR-EQUAL-TO 10

Experimental data are presented for the cluster distribution of sputtered negative carbon clusters, Cn-, with n<10. Additionally, clusters have been observed with masses indicating they are CsC 2n-, with n<4. The Cn- data are compared with the data obtained by other groups, for neutral and charged clusters, using a variety of sources such as evaporation, sputtering, and laser ablation. The data are used to estimate the cluster binding energies E n, using the universal relation, En = (n - 1)ΔH n + RTe[ln(Jn/Jl) + 0.5 ln(n) - α - (ΔSn - Δ5l)/R], derived from basic kinetic and thermodynamic relations. The estimated values agree astonishingly well with values from the literature, varying from published values by at most a few percent. In this equation, Jn is the observed current of n-atom clusters, ΔHn is the heat of vaporization, ΔHl = 7.41 eV, and Te ≈ 0.25 eV (2900 K) is the effective source temperature. The relative change in cluster entropy during sublimation from the solid to vapor phase is approximated to first order by the relation (ΔSn - ΔSl)/R = 3.1 + 0.9(n - 2), and is fit to published data for n between 2 and 5 and temperatures between 2000 and 4000 K. The parameter α is empirical, obtained by fitting the data to known binding energies for Cn≤5 clusters. For evaporation sources, a must be zero, but α∼7 when sputtering with Cs+ ions, indicating the sputtered clusters appear to be in thermodynamic equilibrium, but not the atoms. Several possible mechanisms for the formation of clusters during sputtering are examined. One plausible mechanism is that atoms diffuse on the graphite surface to form clusters which are then desorbed by energetic, recoil atoms created in subsequent sputtering events. © 1990 American Institute of Physics.