A measurement of the temperature dependent work functions of alkali metal clusters and implications of the scaling law

The photo ionization yield curves for nanometer-sized clusters of Li, Na and K has been measured as a function of temperature. The data can be fitted very well by a finite-temperature Fowler plot, originally derived for bulk surfaces. The zero-temperature ionization thresholds extracted from the data match precisely the literature work function values, confirming that large nanometer-sized clusters of alkali metals exhibit bulk-like metal behavior.;The measured temperature derivatives of the work functions are in excellent agreement with the predictions from a recent semi-empirical model derived for bulk surfaces. The semi-empirical model, which is derived from classical electro-statics, is generalized to all cluster sizes. The resulting scaling law is shown to be able to fit the atomic first ionization potential and the bulk work function for all metallic elements in the periodic chart to within ∼10%. For intermediate sizes, the scaling law is shown to fit the majority of all available data on metallic clusters. The fit depends only on one material dependent property, the atomic polarizability. There are no other adjustable parameters.;An empirical relationship connecting the atomic polarizability to the nearest neighbor distance is presented. The similarities between this relationship and a geometric hard sphere packing formula is discussed. Finally, the intimate correlation between the atomic; polarizability, nearest neighbor distance, ionization potential, work function and hard sphere packing is explored. It is shown that all of these seemingly unrelated properties are correlated to each other in a simple manner via the scaling law.