Energetics of metal slabs and clusters: the rectangle-box model

TL;DR

This paper develops a finite-depth potential well model to analyze the energetics of metal slabs and clusters, examining size-dependent properties like work function and Coulomb stability, with applications to gold, sodium, and silver clusters.

Contribution

It introduces an expanded energy model for metal slabs and clusters using the free-electron approximation, providing new insights into size effects and Coulomb instability mechanisms.

Findings

Work function of low-dimensional metals is always smaller than semi-infinite metals.

Calculated critical sizes for charged clusters match experimental data.

Proposed a new mechanism for Coulomb instability differing from Rayleigh's theory.

Abstract

An expansion of energy characteristics of wide thin slab of thickness L in power of 1/L is constructed using the free-electron approximation and the model of a potential well of finite depth. Accuracy of results in each order of the expansion is analyzed. Size dependences of the work function and electronic elastic force for Au and Na slabs are calculated. It is concluded that the work function of low-dimensional metal structure is always smaller that of semi-infinite metal sample. A mechanism for the Coulomb instability of charged metal clusters, different from Rayleigh's one, is discussed. The two-component model of a metallic cluster yields the different critical sizes depending on a kind of charging particles (electrons or ions). For the cuboid clusters, the electronic spectrum quantization is taken into account. The calculated critical sizes of Ag_{N}^{2-} and Au_{N}^{3-} clusters are in a good agreement with experimental data. A qualitative explanation is suggested for the Coulomb explosion of positively charged Na_{\N}^{n+} clusters at 3<n<5.