Quantum-size effects in the thermodynamic properties of metallic nanoparticles

Abstract

THE properties of nanometre-scale metallic particles differ from those of the same material1,2 in bulk. Conduction electrons, because of their wave-like nature, can have only certain discrete values of kinetic energy or wavelength. Such 'quantum-size' effects have been observed in two-dimensional electron gases in semiconductors3,4, and in atomic-scale metallic point contacts5. Also present are 'Coulomb-charging' effects: these are purely classical in origin, and occur when the energy required to add one electron to a conducting sphere exceeds the mean thermal energy kBT. Thermal fluctuations in the total charge on the particle are then suppressed6. In theory, the combination of quantum-size and Coulomb-charging effects should cause the properties of small metallic particles to depend sensitively on whether they have an odd or even number of electrons7. Odd–even effects have been observed in experiments on tunnelling between discrete electronic levels of single metal particles8, but their influence on thermodynamic properties remains to be demonstrated. Here we report measurements of the heat capacity and electronic magnetic susceptibility of small metallic clusters. Our results show definitive evidence for odd–even effects, thus confirming that quantum and classical size effects strongly influence the thermodynamic properties of small particles.