Cohesive energy of small metallic particles

The cohesive energy of sodium microparticles is calculated using the density functional formalism. The model particles are formed by a central atom surrounded by successive coordination shells of first neighbours, second neighbours, etc. Maxima in the cohesive energy per atom are obtained for particles with filled coordination shells. The sublimation energy is also studied. Insight is gained on the nature of “magic numbers” observed in the experimental size distribution.     

Electronic properties of small metallic particles

Metallic particles with linear dimensions d small compared with other characteristic lengths (like the wavelength of electromagnetic radiation, the de Broglie wavelength of the conduction electrons, the coherence length or the penetration depth in the superconducting state, etc.) show interesting effects which are usually unobservable in bulk metals. The electronic properties of these particles with diameters of a few nm can be analysed by considering the microcrystals not as “giant molecules” but as “small solids”, i.e. by using the familiar methods of solid state physics with some properly defined boundary conditions. Due to the smallness of the particles, the customary quasi-continuous electronic excitation spectrum splits up into discrete energy levels with an average energy splitting δ of a few meV. If then the relevant energies (like the thermal energy kT, the Zeeman energy μ₀μ_BH, the electrostatic energy edE, the photon energy $\text{h}\text{?}\text{ω}$, the condensation energy for the superconducting state Δ, etc.) are comparable with δ, novel effects are to be expected, called “quantum size effects” (QSE). In an ensemble of small particles, it is expected that the discrete energy levels are statistically distributed; therefore, methods of level statistics can be employed to calculate the different electronic properties of small particles.In this report, the more phenomenological aspects of the physics of small particles are discussed, where e.g. the interaction of the electromagnetic radiation with the particle is described by a dielectric constant, also characteristic for the bulk metal. The more microscopic quantum size effects in small particles are then analysed theoretically, mainly from the point of view of the statistics of discrete energy levels, and the existing experimental results are discussed. Superconductivity in small metallic particles is reviewed with emphasis on the critical fields in small particles, the magnetic field dependence of their microscopic properties (e.g. density of states), the problem of a lower size limit of a superconductor, and fluctuations in small superconductors. Finally, the most commonly used experimental methods to produce small particles are described.     

Electronic properties of metallic small particles

The electronic properties of very small metallic particles are reviewed. The emphasis is placed on the experimental work done by the author's group using nuclear magnetic resonance. The anomalies in the properties such as the spin susceptibility and the nuclear spin lattice relaxation arising from the discreteness of the orbital energies are discussed. For superconducting particles, the fluctuation of the order parameter and the critical magnetic field are also discussed.     

Optical absorption by small metallic particles

We study theoretically the dependence of absorption by small metallic particles on particle shape and wave polarization in the IR frequency range. We examine the electric and magnetic absorption by small particles. The particles may be either larger or smaller than the electron mean free path. We show that for asymmetric particles smaller than the mean free path the light-induced conductivity is a tensor. We also show that the total absorption and the electric-to-magnetic absorption ratio are strongly dependent on particle shape and wave polarization. Finally, we construct curves representing the dependence of the ratio of the electric and magnetic contributions to absorption on the degree of particle asymmetry for different wave polarizations. Similar curves are constructed for the ratio of the components of the light-induced conductivity tensor. Zh. éksp. Teor. Fiz. 112, 661–678 (August 1997)     

Impurity atoms in small metallic particles

The effect of self-purification has been discovered in small metallic particles containing impurity atoms. Due to small dimension of the particles impurities were shown to get out of the particles and to reach its surface in relatively short times. The phenomenon has been studied for small particles of Li containing Na atoms as impurities and for NiCu alloy particles. The distribution of atoms in lithium particles was studied by the ESR method and the information about the distribution of Ni atoms within CuNi alloy particles was obtained by comparing the structure date with magnetic properties.     

Third-order optical susceptibility of small metallic particles

Summary We present a tight-binding model for the linear and non-linear optical properties of small metal particles, which takes into account both size and matrix effects. We show that the surface states and the dielectric medium embedding the particles determine the properties of the microcrystals; in particular, we prove that the shallow-lyingd-band plays a crucial role in noble-metal particles. As an example, we calculate the third-order susceptibility and the phase-conjugated signalfor gold clusters made of several hundred atoms. A good agreement with experimental results is obtained.     

Mechanism for far infrared absorption of small metallic particles

A mechanism for far infrared absorption of small particles of noble metals is described. The electric double layer formed at the particle surface allows excitation of the resonant low frequency mode in which the metal core oscillates rigidly with respect to the shellof adsorbed atoms. The model is capable of explaining the large magnitude and the anomalous frequency dependence recently reported for Pt particles.     

Generalized bond-energy model for cohesive energy of small metallic particles

A generalized bond-energy model has been developed to calculate the cohesive energy of nanoparticles by considering the different contributions of face-, edge- and corner-atoms. The model is adapted for metallic particles in a large size range from several atoms to infinity, studying their morphology, phase stability and melting point, etc.     

Ultraviolet laser removal of small metallic particles from silicon wafers

Laser removal of small 1 μm sized copper, gold and tungsten particles from silicon wafer surfaces was carried out using ultraviolet radiation at 266 nm generated by Nd:YAG harmonic generation. Successful removal of both copper and gold particles from the surface was achieved whereas tungsten particles proved to be difficult to remove. The cleaning efficiency was increased with an increase of laser fluence. The optimum processing window for safe cleaning of the surface without any substrate damage was determined by measuring the damage threshold laser fluence on the silicon substrate and the required fluence for complete removal of the particles. The different cleaning efficiencies with particle type are discussed by considering the adhesion force of the particle on the surface and the laser-induced cleaning force for the three different particles.     

Density functional calculation of the ionization potentials of small metallic particles

A Density Functional Pseudopotential method is used to compute the ionization potential IP of Sodium, Aluminium and Lead microparticles as a function of particle size. The model particles are formed by a central atom surrounded by successive coordination shells of first neighbours, second neighbours, etc. Maxima in IP are obtained for particles with filled coordination shells. The magnitude of IP correlates with the magnitude of the electron density in the region where the electron is extracted.     

The new mechanism of surface-enhanced second harmonic generation in small metallic particles

A surface enhancement factor growth over 4 orders of magnitude is observed for the second harmonic generation from metallic particles of 10 Å radius. The effect can be explained by a specific mechanism, originating from the irregular distortions of the shapes of the particles.     

Lattice defects in small metallic particles and their influence on size effects

Several systems of isolated silver particles have been produced by different methods and have been analysed by electron microscopy. Their optical absorption spectra in the region of the spherical plasma resonance were recorded and compared with calculated spectra. The experimental plasmon band width was found to differ markedly from the predictions of size effect theories in several particle systems, while in other systems correspondence was observed. These discrepancies are attributed to different concentrations of lattice defects in the particles. Electron-lattice defect relaxation frequencies determined from the optical spectra differ by more than one order of magnitude in differently prepared particles. It is further shown that extended defects such as grain boundaries in regular particles may cause size dependencies of the dielectric constant of the particle material, in addition to those induced by the particle surface.     

Toward the existence of monatomic small metallic particles of a nearly dodecahedral habit

The arguments for the existence of monatomic small metallic particles of a nearly dodecahedral habit have been considered. The results of the corresponding experiments on electrodeposition of silver have been reported and discussed. It has been shown that the manufacturing of the above objects is mainly hindered by large plastic stresses accompanying their formation.