Clusters growth principles

In 1985 Car and Parrinello invented a method [111-113] in which molecular dynamics (MD) methods are combined with first-principles computations such that the interatomic forces due to the electronic degrees of freedom are computed by density functional theory [114-116] and the statistical properties by the MD method. This method and related ab initio simulations have been successfully applied to carbon [117], silicon [118-120], copper [121], surface reconstruction [122-128], atomic clusters [129-133], molecular crystals [134], the epitaxial growth of metals [135-140], and many other systems for a review see Ref. 113. 

A metal surface that is uniformly flat offers no sites for further growth. In this case a new nucleus, or center of growth, must be formed. Since small clusters of metal atoms consist mainly of surface atoms, they have a high energy content, and their formation requires an extra energy. The basic principles of the formation of new nuclei can be understood within a simple model. We consider a small three-dimensional cluster of metal atoms on a flat surface of the same material, and suppose that the cluster keeps its geometrical shape while it is growing. A cluster of N atoms has a surface area of ... 

METAL CLUSTER NUCLEATION AND GROWTH 2.1. Principles of Metal Atom Formation... 

Probably the least-known aspect of the CD process is what determines the nucle-ation on the substrate and the subsequent film growth. In considering this aspect, we will treat the ion-by-ion and hydroxide cluster mechanisms separately, although there will be many features in common. The principles discussed should be the same for both the free chalcogenide and the complex-decomposition mechanisms. 

The topochemical model, however, describes the origination and growth of macrostructures. In principle one could construct kinetic models accounting for the kinetics of cluster (or nucleate) formation as a model for the system or reverse consecutive reactions [114, 121]. 

The clusters transform into the crystal nuclei having ability for the growth under certain conditions. Only clusters with some critical size r = 2 Oct/Ap can become potential centers of crystallization (here Cl is the specific volume of an atom or molecule involved into the cluster, a is the specific surface energy of interphase boundary and Ap is the difference in chemical potentials for the phases) [10]. There are two main possible ways to transform the clusters into the critical crystal nuclei as a result of fluctuations [1] (1) attachment of individual atoms (molecules) to the cluster and (2) coalescence of clusters with each other. It should be noted that in principle the critical nuclei formation as a result of coalescence of individual atoms (molecules) with each other is possible too. In all these cases the clusters must grow to the size r > r, in order the start a crystal growth process. 

The validity of this relationship is expected to be limited to droplet radii not to small. In principle the surface tension is a decreasing function of the radius r for small clusters. Hence, the result of Eq. (3) are corrected by Tolmans formula (see Ref. [14]) with 6 = lO- o m, the intermolecular distance in the liquid, see Fig. 1 - right. If the droplet radius is small compared with the mean free path X, the molecular growth is described by the Hertz Knudsen formula... 

Teo BK, Zhang H (1995) Polyicosahedricity icosahedron to icosahedron of icosahedra growth pathway for bimetallic (Au-Ag) and trimetallic (Au-Ag-M M=Pt, Pd, Ni) supra-clusters synthetic strategies, site preference, and stereochemictil principles. Coord Chem Rev 143 611-636... 

In principle, many chemical approaches exist for the preparation of quantum dot clusters. Qassical preparative methods include wet colloidal techniques, growth in dielectric glass matrices, and growth in polymers. In these materials, however, cluster or particle sizes are usually nonuniform, and agglomeration of... 

---