Growth of nuclei

The uniformity of film thickness is dependent upon temperature and pressure. The nucleation rate rises with pressure, such that at pressures above atmospheric the high rate of nucleation can lead to comparatively uniform oxide films, while increase in temperature reduces the density of oxide nuclei, and results in non-uniformity. Subsequently, lateral growth of nuclei over the surface is faster than the rate of thickening until uniform coverage is attained, when the consolidated film grows as a continuous layer ... 

This behaviour has been identified from microscopic measurements for growth of nuclei during the dehydration of crystalline hydrates [431], the... 

If the initial rate of growth of nuclei is slower than the constant value subsequently attained, the above expression remains applicable [28] provided that appropriate subtraction from the measured time is included, viz. 

Torkar et al. [702,706—708] identified nucleation as an autocatalytic process at the (hk0) planes of hexagonal platelets of NaN3. The decelera-tory reaction fitted the first-order equation [eqn. (15)]. Values of E tended to be irreproducible for the pure salt E was about 180 kJ mole 1 but this was reduced to about half by doping. This influence of an additive and the observed similarities in magnitudes of E for decomposition and for diffusion were interpreted as indicating that growth of nuclei was controlled by a diffusion process. 

Singh and Palkar [726] identified an initial deceleratory reaction in the decomposition of silver fulminate. This obeyed first-order kinetics (E = 27 kJ mole-1) and overlapped with the acceleratory period of the main reaction, which obeyed the power law [eqn. (2), n = 2] with E = 119 kj mole-1. The mechanism proposed included the suggestion that two-dimensional growth of nuclei involved electron transfer from anion to metal. 

Isothermal a—time curves for the decomposition of U02(CH3C02)2 in air (513—573 K) [1018] showed two approximately linear regions, 0.0 < a < 0.2 and 0.2 < a < 0.9, for which the values of E were 107 and 165 kJ mole-1, respectively. In nitrogen, the earlier portion of the curve was not linear and E = 151 kJ mole-1 for the later interval. The zero-order kinetic behaviour was explained by growth of nuclei in thin, plate-like crystals, which were shown by microscopic and surface area measurements to fragment when a > 0.85. The proposed initial step in the decomposition was fission of bonds between the U02+ and the (OCO CH3) species [1018]. 

Although we have covered mechanisms relating to solid state reactions, the formation and growth of nuclei and the rate of their growth in both heterogeneous and homogeneous solids, and the diffusion processes thereby associated, there exist still other processes zifter the particles have formed. These include sequences in particle growth, once the particles have formed. Such sequences include ... 

Let us now reconsider our nucleation models of 4.4.1., specifically Models B, D and E. These are examples of phase-boundary controlled growth involving random nucleation. We now assume an exponential embryo formation law (see 4.4.7), with isotopic growth of nuclei in three dimensions and k2 as the rate constant. By suitable manipulation of 4.4.6.,... 

We note that the growth of nuclei is associated with the motion of a phase boundary. 

A3 Avrami-Erofeev three-dimensional growth of nuclei [— in(1 - a)],/3... 

Growth of nuclei by surface diffusion of atoms to form a continuous layer. 

When the charge-transfer step in an electrodeposition reaction is fast, the rate of growth of nuclei (crystallites) is determined by either of two steps (I) the lattice incorporation step or (2) the diffusion of electrodepositing ions into the nucleus (diffusion in the solution). We start with the first case. Four simple models of nuclei are usually considered (a) a two-dimensional (2D) cylinder, (b) a three-dimensional (3D) hemisphere, (c) a right-circular cone, and (d) a truncated four-sided pyramid (Fig. 7.2). 

The overall current-time relationships for the simultaneous nucleation and growth of nuclei are of the form ioc where is a variable depending primarily on the model of... 

Agl crystals grow in aqueous solution via four steps (I) formation of molecules and complexes, (2) formation and growth of nuclei, (3) aggregation, and (4) ripening. These reaction scheme can be written as... 

Growth of Nuclei to Metal Nanoparticles. If the elemental cluster of 13 atoms is the nucleus, the growth of nuclei to metal nanoparticles could proceed by deposition of atoms or microclusters on the surface of nuclei. This process is understandable based on the consideration of the formation of monodispersed nanoparticles. However, structural analysis has often proposed the aggregation of elemental clusters to form fundamental clusters (64). A similar idea is discussed for the structural analysis of bimetallic nanoparticles with cluster-in-cluster structure (40,61). 

Formation and growth of nuclei have been observed microscopically in single crystals in several decomposition and dehydration reactions. 

The conventional theory of the decomposition of solids distinguishes between formation and growth of nuclei in a very real way by ascribing different rate constants kf and kg to these two processes. This is a realistic procedure if a nucleus can be formed as a result of a single reaction step because the first molecular decomposition at a nucleus-forming site is clearly occurring in a different environment from that for subsequent ones. 

Zhdanov (1) describes the mechanism of zeolite crystallization in terms of a quasiequilibrium between the solid and liquid phase in gels and emphasizes that the formation and growth of nuclei occurs in the liquid phase. 

The overall recrystallization process, consisting of the initial nucleation and the subsequent growth of nuclei, can be modelled by the basic equations describing these respective processes. The rate of formation of nuclei as developed is ... 

Figure 7. Particle size distributions measured with the SEMS showing the formation and growth of nuclei in the 1-octene photooxidation. The distributions are shown (A) without S02 and (B)with added S02. (Reproduced from reference 49. Copyright 1991 American Chemical Society.)...

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