Growth of a Solid Phase

We propose to examine the growth of a sohd phase B starting from a nucleus on the surface of another solid phase A, The description of the various modes of growth of a nucleus and their modeling makes it possible to clarify relations that are then necessary to model the total reaction (involving growth and nucleation) of a powder. 

We assume that the new phase starts to grow at time r and that its size at this moment is negligible compared with that reached at time t, which is higher than r. This means that there will be no delay over the initial moments of the growth. 

Moreover, various models are based on the following two simplifying assumptions  

The growth of a nucleus (formed on the surface), even if it obeys the same balance equation as that of nucleation, is a different process being held according to its own mechanism that takes into account the necessary presence of solid B located at the surface of the initial solid A and between this last phase and the third phase if 

To define the zones, we distinguish two categories of transfonnations according to whether the initial solid A is a single reactant or whether it reacts with another phase. 

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A proper thermodynamic description of electrochemical phase formation is necessarily complicated by the need to consider the changes in energy and entropy associated with the process as a whole. Fortunately, electrocrystallisation has many features in common with the growth of a solid phase from its supersaturated vapour, and it is useful to examine this simpler process first. In the case where two phases but only one component are present, phase formation involves the incorporation of atoms or molecules into a pre-existing surface of the solid, and the enthalpy change is therefore related to the transition... 

For the growth of a solid phase with variable composition, or to control macroscopic dopant or impurity distribution, the classical works on crystal growth apply a distribution coefficient term. The difference between a solid solution and a doped crystal is that the term solid solution is restricted to members of an isostractural series whereas dopants may differ a great deal in structure from the host. If polythermal methods are used, the resulting crystals will normally be inhomogeneous, and exceptions to this rule require rather unusual conditions. 

We saw in Chapter 6 that diffusive transformations (like the growth of metal crystals from the liquid during solidification, or the growth of one solid phase at the expense of another during a polymorphic change) involve a mechanism in which atoms are attached to the surfaces of the growing crystals. This means that diffusive transformations can only take place if crystals of the new phase are already present. But how do these crystals - or nuclei - form in the first place ... 

A bioslurry phase system consists of the suspension of a solid phase in water or other liquid medium to a concentration typically between 5% and 40% (w/v) and kept under agitation conditions to allow the microbial growth of the indigenous microbiota or a particular inoculated microorganism [114], Bioslurry systems for bioremediation purposes have been mostly conducted with bacterial cultures [146, 147], although in the last few years WRF were also successfully applied to soil bioremediation of PAHs, hexachlorocyclohexane and pentachlorophenol [110, 113, 114],... 

Crystal growth is the process of the birth and development of a solid phase with a regular structure out of a disordered and irregular state, and thus it can be regarded as a first-order phase transition. 

Let us begin an analysis of the process of formation of chemical compounds in heterogeneous systems with the simplest case of growth of a solid layer between elementary substances A and B which form, according to the equilibrium phase diagram of the A-B binary system, only one chemical compound ApBq, p and q being positive numbers (Fig. 1.1). The substances A and B are considered to be solid at reaction temperature 7, and mutually insoluble. 

This is a technique frequently used for the preparation of both support precursors and catalyst precursors and takes place when two or more solutions are mixed by a suitable method [7], The growth of nanometersized materials, in some cases, involves the process of precipitation of a solid phase from the solution. In this regard, for nanoparticle formation, the solution has to be supersaturated by directly dissolving the solute at a higher temperature and then cooling to low temperatures, or by the addition of the needed reactants to generate a supersaturated solution during the reaction. 

Reactions of KI with Cl2 and of NaCl and KC1 with F2 have been studied [92, 93, 103, 104] and a variety of properties have been measured as a function of the extent of reaction in the conversion of CuCl to CuCl2 by reaction with Cl2 [89, 105, 106]. A consistent feature of all these studies is that, together with or sometimes preceding nucleation and growth of new solid phases, the solid reactant is damaged by electron withdrawal, leading to the formation of various types of electronic defect of the trapped-hole or V-centre type. Studies of electrical conductivity, electron spin resonance spectra and UV absorption are useful in elucidating the behaviour of these defects. 

The deposition-precipitation of Ni(II) shows the typical pH versus time behaviour found in high surface area Ni/SiOz systems [8-11]. The pH-curve displays a maximum after this value the nucleation and growth of the solid phase start up rapidly and the rate of generation of hydroxyl ion is lower than its consumption leading to a temporary decrease in the pH value (Fig. 1). 

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