Coherent nucleation

The characteristic feature of solid—solid reactions which controls, to some extent, the methods which can be applied to the investigation of their kinetics, is that the continuation of product formation requires the transportation of one or both reactants to a zone of interaction, perhaps through a coherent barrier layer of the product phase or as a monomolec-ular layer across surfaces. Since diffusion at phase boundaries may occur at temperatures appreciably below those required for bulk diffusion, the initial step in product formation may be rapidly completed on the attainment of reaction temperature. In such systems, there is no initial delay during nucleation and the initial processes, perhaps involving monomolec-ular films, are not readily identified. The subsequent growth of the product phase, the main reaction, is thereafter controlled by the diffusion of one or more species through the barrier layer. Microscopic observation is of little value where the phases present cannot be unambiguously identified and X-ray diffraction techniques are more fruitful. More recently, the considerable potential of electron microprobe analyses has been developed and exploited. 

Dehydration reactions are typically both endothermic and reversible. Reported kinetic characteristics for water release show various a—time relationships and rate control has been ascribed to either interface reactions or to diffusion processes. Where water elimination occurs at an interface, this may be characterized by (i) rapid, and perhaps complete, initial nucleation on some or all surfaces [212,213], followed by advance of the coherent interface thus generated, (ii) nucleation at specific surface sites [208], perhaps maintained during reaction [426], followed by growth or (iii) (exceptionally) water elimination at existing crystal surfaces without growth [62]. 

While it is possible that surface defects may be preferentially involved in initial product formation, this has not been experimentally verified for most systems of interest. Such zones of preferred reactivity would, however, be of limited significance as they would soon be covered with the coherent product layer developed by reaction proceeding at all reactant surfaces. The higher temperatures usually employed in kinetic studies of diffusion-controlled reactions do not usually permit the measurements of rates of the initial adsorption and nucleation steps. 

Nomura and Fujita (12), Dougherty (13-14), and Storti et al. (12). Space does not permit a review of each of these papers. This paper presents the development of a more extensive model in terms of particle formation mechanism, copolymer kinetic mechanism, applicability to intervals I, II and III, and the capability to simulate batch, semibatch, or continuous stirred tank reactors (CSTR). Our aim has been to combine into a single coherent model the best aspects of previous models together with the coagulative nucleation theory of Feeney et al. (8-9) in order to enhance our understanding of... 

Nucleation and growth processes of the metal lattice. Understanding of the nucleation and growth of surface nuclei, formation of monolayers and multilayers, and growth of coherent bulk deposit is based on knowledge of condensed-matter physics and physical chemistry of surfaces. 

Tanabe and Kamasaki (52) observed the nucleation growth mechanism in the deposition of Au on Fe(OOl) and Fe(l 10) single crystals. The population of nuclei (TDCs) of Au electrodeposited in the initial stages of deposition was 3 X 10 cm . In further deposition, micro-TDCs were connected one to another forming a network structure. Stable coherent deposits of Au were formed when the surface coverage was about 80%. 

The inflexion in curves (A) and ( ) occurs after a decomposition of about 30% of substance. The plots of the acceleratory period are approximately parabolic. The mechanism of the decomposition probably consists of nucleation of sub-grains at the edges and progression of the reaction into the grains with a non-coherent interface. 

Internal nucleation and growth can occur coherently or incoherently while the reaction volume can be negative or positive. The severe constraints which the matrix crystal exerts on the internal reaction can lead to the formation of metastable (or even unstable) phases, which do not exist outside the matrix. Often, heavy plastic flow and anisotropic growth has been found. 

In crystalline solutions, the developing interfaces are initially coherent—strains are continuous across interfaces. Unless defects such as anticoherency dislocations intervene, the interfaces will remain coherent until a critical stress is attained and the dislocations are nucleated. For small-strain fluctuations, the system can be assumed to remain coherent and the resulting elastic coherency energy can be derived.9... 

In crystalline solids, only coherent spinodal decomposition is observed. The process of forming incoherent interfaces involves the generation of anticoherency dislocation structures and is incompatible with the continuous evolution of the phase-separated microstructure characteristic of spinodal decomposition. Systems with elastic misfit may first transform by coherent spinodal decomposition and then, during the later stages of the process, lose coherency through the nucleation and capture of anticoherency interfacial dislocations [18]. 

An extensive formulation of classical and nonclassical models for homogeneous nucleation, as well as experimental tests of their validity, have been carried out for the Co-Cu precipitation system in which coherent Co-rich nuclei form [15]. 

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