Atomistic nucleation

Nucleation — Atomistic theory of nucleation — Figure 1. Dependence of the nucleation work AG (ft) on the cluster size n (a) and dependence of the critical nucleus size nc on the supersaturation Ap (b) according to the atomistic nucleation theory (a schematic representation)... 

Apart from the purely thermodynamic analysis, the description of the -> electro crystallization phenomena requires special consideration of the kinetics of nucleus formation [i-v]. Accounting for the discrete character of the clusters size alteration at small dimensions the atomistic nucleation theory shows that the super saturation dependence of the stationary nucleation rate /0 is a broken straight line (Figure 2) representing the intervals of Ap within which different clusters play the role of critical nuclei. Thus, [Ap, Apn is the supersaturation interval within which the nc -atomic cluster is the critical nucleus formed with a maximal thermodynamic work AG (nc). 

Interrelation between the classical and the atomistic nucleation theories... 

The question "How are the classical and the atomistic nucleation theories interrelated " arose simultaneously with the Walton s theoretical model [2.56] but was successfully settled 12 years later, in the framework of... 

It is well known presently that under certain conditions self-assembled nanocrystal QDs may nucleate spontaneously when a material is grown by an atomistic... 

Atomistic theory of nucleation — The theory applies to very small clusters, the size n of which is a discrete variable and the process of nucleus formation must be described by means of atomistic considerations. Thus, the thermodynamic barrier AG ( ) that has to be overcome in order to form an n-atomic nucleus of the new phase is given by the general formula [i-v]... 

Consider an example from nucleation and growth of thin films. At least three length scales can be identified, namely, (a) the fluid phase where the continuum approximation is often valid (that may not be the case in micro- and nanodevices), (b) the intermediate scale of the fluid/film interface where a discrete, particle model may be needed, and (c) the atomistic/QM scale of relevance to surface processes. Surface processes may include adsorption, desorption, surface reaction, and surface diffusion. Aside from the disparity of length scales, the time scales of various processes differ dramatically, ranging from picosecond chemistry to seconds or hours for slow growth processes (Raimondeau and Vlachos, 2002a, b). 

The first term in this partial differential equation describes the temporal change of the population tj the second term describes the atomistic growth of the particles (which assumes that G is independent of particle size r), and finally the last two terms account for the birth and death of particles of size r by an aggregation mechanism. The birth fimction describes the rate at which particles enter a particle size range r to r + Ar, and the death function describes the rate at which the particles leave this size range. In the case of continuous nucleation, an additional birth rate term is used for the production of atoms (or molecules) of product by chemical reaction. In this case, the size of the nuclei are the size of a single atom (or molecule) and the rate of their production is identical to the rate of chemical reaction, kfi, where C is the reactant concentration, giving... 

Table 4.1 Gibbs free energies of 3D nucleation and nucleus size in the deposition of different metals on Pt as estimated from the classical and atomistic treatment of the experimental results.

For a small number of Me atoms in a critical cluster, the strain of a 2D UPD Meads overlayer can be inherited by the nucleus. Using the atomistic approach [4.13], the rate of nucleation on top of a strongly compressed and internally strained 2D UPD Meads overlayer can be expressed by [4.54-4.57] (cf. Section 4.2) ... 

Under the specific conditions of electrochemical metal deposition, the critically sized clusters of the new phase have been found to consist of only a few atoms, where classical thermodynamic bulk quantities cannot be applied. Therefore, the original kinetic theory of Becker and Doering was further developed to an atomistic theory of nucleation. 

The atomistic theory becomes of additional significance for the transition from 2D Me phase formation in the UPD range to 3D Me phase formation in the OPD range. Experimental results obtained using modern in situ techniques with lateral atomic resolution showed that the transition phenomena can only be interpreted on the basis of atomistic approaches. The UPD surface modification turns out to be a more general phenomenon affecting not only the nucleation processes but also the growth mode and epitaxy of 3D metal phases. 

Thin-film formation is described as a sequential process which includes nucleation, coalescence and subsequent thickness growth, whereby all states can be influenced by deposition parameters, such as temperature, pressure, gas flow rate, etc. [3,4], For physical vapour deposition (PVD) processes, significant works have been published and progess made in understanding the microstructure evolution of the films. In the atomistics of growth processes, there exists much in common bewteen CVD and PVD. Theories from PVD processes can thus be used to analyse the microstructure evolution of CVD processes [5, 6],... 

It is difficult to deduce what gold particle morphologies arise from heterogeneous chemical reduction of HAuCU. Understanding of the model catalysts is much easier. In brief, a) nucleation of gold clusters occurs at surface defects that act as traps b) on AI2O3, there are two kinds of traps at <0.8 and >1.6eV c) the defect density is ca. 3 x 10 sites per cm (10 monolayer) and d) when the clusters grow to >600 atoms, they leave the traps. This can explain the bimodal size distribution of the clusters. Atomistic definition of these traps is needed. 

In addition to the questions that can be raised about kink motion, the type of atomistic analysis being described here has also been used to examine the propensity for nucleation of kinks themselves. Though plausible mechanisms for... 

The pre-exponential factor A 1p is independent of potential as long as Ncrjt is potential independent, and the factor 3 depends on the mechanism of attachment. Equation [7] reduces to a classical Volmer-Weber type model for nucleation if Ncrjt 3- The total potential dependence of the nucleation rate in an overpotential range where Ncrit is constant according to the atomistic model is thus given by ... 

Classical nucleation theory may be not well suited to describe the nucleation kinetics of diamond in CVD, since the critical nucleus size under the typical CVD conditions may be on the order of a few atoms. The surface energy contribution may cause a reverse effect on the phase stability and the GFobs free-energy of the formation of a critical nucleus may be negative, a case referred to as nonclassical nucleation. In such a case, atomistic theory should be employed as the starting point of theoretical analyses. 

---