Nucleation atomic processes

Video microscopy with crossed polarizers permits the direct and non-invasive observahon of the nucleahon and growth process for many substances, and thus the study of the hme evoluhon of the spherulite radius R t). When the growth is controlled by diffusion the radius of the spherulites increases as R t) a while when the growth is determined by a nucleation-controlled process (incorporahon of atoms or molecules to the surface of the crystalline part) the radius increases linearly with hme, R t) a t. 

Despite the fact that the atomic processes and micromechanisms that are occurring during each of these phenomena are quite different, there is a commonality among them. In each case, a nucleated or preexisting flaw grows with time, leading to the eventual failure of the part, usually with disastrous consequences. In other words, the ceramic now has a lifetime that one has to contend with. 

The elementary atomic processes governing the growth of nanostructures on surfaces under ultrahigh vacuum (UHV) conditions are summarized in Fig. 8. They include diffusion processes on terraces, at edges, between layers and across steps, as well as nucleation and coalescence. Each of these processes i is temperature dependent and can be described by a simple Arrhenius-type kinetic equation (12) ... 

Nucleation of a thin film is usually described in terms of classical nucleation theory resulting from coalescence of clusters from a random collection of atoms on a surface. The basic energetics and macroscopic kinetics of nucleation was described in some detail in Section 4.4.2 and will not be repeated here. However, it is useful to look more closely at the atomic processes that are involved in the phenomena described in Chapter 4. 

A molten metal alloy would normally be expected to crystallize into one or several phases. To form an amorphous, ie, glassy metal alloy from the Hquid state means that the crystallization step must be avoided during solidification. This can be understood by considering a time—temperature—transformation (TTT) diagram (Eig. 2). Nucleating phases require an iacubation time to assemble atoms through a statistical process iato the correct crystal stmcture... 

Because of the possibility of focusing laser beams, tlrin films can be produced at precisely defined locations. Using a microscope train of lenses to focus a laser beam makes possible tire production of microregions suitable for application in computer chip production. The photolytic process produces islands of product nuclei, which act as preferential nucleation sites for further deposition, and tlrus to some unevenness in tire product film. This is because the subsuate is relatively cool, and therefore tire surface mobility of the deposited atoms is low. In pyrolytic decomposition, the region over which deposition occurs depends on the drermal conductivity of the substrate, being wider the lower the thermal conductivity. For example, the surface area of a deposit of silicon on silicon is nanower dran the deposition of silicon on silica, or on a surface-oxidized silicon sample, using the same beam geomeU y. 

A pre-factor 1/r contains a time scale r or a frequency which for instance corresponds to the hard phonon or to an atomic frequency. The growth rate of the crystal is proportional to this rate (23). As will be shown later, the nucleus once formed expands in a time scale shorter than the one necessary for nucleation. If the process consists of a series of sequential subprocesses, the global velocity is governed by the slowest one. Therefore, this nucleation process determines the growth rate of a faceted surface. 

Single-step nucleation, (ii) above, requires the unsatisfactory assumption that the generation of a single molecule (atom, ion-pair, etc.) of product constitutes the establishment of a nucleus. (It would seem to be more realistic to regard this as the outcome of several distinct chemical steps.) The mathematical treatment expressing the probability of the occurrence of this unimolecular process is... 

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