The influence of shells, electron thermodynamics, and evaporation on the abundance spectra of large sodium metal clusters

Abstract

Measurements of the mass abundance spectra of sodium clusters containing up to 600 atoms are presented. The clusters are produced in a seeded supersonic expansion of Ar or Kr gas, and the spectra are obtained by a time-of-flight technique. The sawtooth features in the spectra are interpreted as evidence of a regular spherical shell structure with magic numbers, N O , scaling approximately with the cube root of the number of sodium atoms. Altogether twelve shell closings are observed, N o = 2, 8, 20, 40, 58, 92, 138, 196, 260, 344, 440 and 558. There is also a pronounced odd-even staggering all the way up to N = 70. The experimentally observed intensity changes for the clusters around the magic numbers are discussed in terms of the electronic free energy, F(N), calculated at finite temperature, and the second differences of the free energy A2F(N ) = F(N -1) -2F(N) + F(N + 1). The processes behind the non-uniform abundance distributions, and the thermodynamics of finite electron systems with non-uniform level spacings are discussed on this basis.

Thermal properties of the valence electrons in alkali metal clusters

“…A semi -quantitiative comparison of observed abundance spectra with preliminary results of our calculations has been quite encouraging [6]. A more detailed comparison would necessitate the inclusion of deformation effects for clusters in the regions between the filled spherical shells.…”

Selfconsistent calculation of electronic supershells in metal clusters

“…Expanding for large temperatures and using hu oc TV"" 1 / 3 , this gives a temperature with Ailn [7,9], the agreement of the two curves is striking. This demonstrates that the finite temperature of the valence electrons which alone contribute to the quantities shown here -the ionic parts of the free energies practically cancel in the differences A2F(N) and Ai In INplays an essential role in the mass yields and can be correctly taken into account in selfconsistent KS calculations even in the simple jellium model.…”

“…Much remains, however, to be understood -in particular the value of the factor c which, using the above harmonic oscillator estimates, is too large for the estimated temperatures [1,7] of ~ 400 -500 K. A more realistic study of the evaporation mechanism and, more generally, a non-equilibrium treatment of the ions' dynamics would be desirable to this aim.…”

“…The experimental observation of supershell structure in cluster expansion sources is inhibited by the fact that the clusters so produced have, at least initially, a finite temperature which tends to reduce the shell effects [7,8,9]. Nevertheless, in the newest sodium vapour expansion experiments of the Copenhagen -Orsay -Stuttgart collaboration [1], a supershell beating in the mass abundance spectrum of sodium clusters has been put into evidence.…”

“…The Wigner-Seitz radius of bulk sodium, ra = 3.96 a.u., is used; otherwise our calculations are com- The quantity A2E(N) = A2F(N)(T = 0) has often been taken as a measure for the stability of the cluster: since it represents the curvature of the total binding energy as a function of TV, it is particularly large for the 'magic' systems which have a strongly negative shell correction. It has furthermore been argued [7] that if the evaporation process, which takes place immediately after the adiabatic expansion, is responsible for enhancing the most stable clusters in the final mass yield,…”