Estimating carbon cluster binding energies from measured C sub n distributions, n <= 10.

Experimental data are presented for the cluster distribution of sputtered negative carbon clusters, C - over n, with n = 10 . Additionally, clusters have been observed with masses indicating they are CsC - over n, with n = 4 . The C - over n 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 sub n , using the universal relation, E sub n = (n-1) DELTA H sub n + RT sub e [ln(J sub n/J sub 1 ) + 0.5ln(n) - alpha - ( DELTA S sub n - DELTA S sub 1 )/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, J sub n is the observed current of n-atom clusters, DELTA H sub n is the heat of vaporization, DELTA H sub 1 = 7.41 eV, and T sub e approx 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, ( DELTA S sub n - DELTA S sub 1 )/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 deviation from thermodynamic equilibrium, shown by enhanced carbon atom emission, is represented by an empirically fit parameter, alpha approx 7, that is zero only for evaporation sources. Several possible mechanisms for the formation of clusters during sputtering are examined. One plausible mechanism is that the clusters form near the graphite surface by the recombination of a small fraction, e sup (-alpha) approx 10 sup (-3), of the energetic atoms created in a "collision cascade".