Decomposition of a single solid

The term recrystallization in Table 2 can include sintering but may also occur during decomposition. Sintering processes are very often studied as 

Sintering Melting Sublimation Decomposition I Melting with l decomposition 

Decomposition of a single solid J- Nucleation - Growth Interface phenomena. Geometric control 

Reaction of a solid] with a gas J L Reaction at immobile A surface l Interface control or Diffusion control No barrier layer Interface phenomena Geometric control 

Reaction of a solid with a liquid (or solute) As with solid and gas Diffusion in the liquid may be important, particularly where no barrier layer is formed 

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The kinetic principles operating during the initiation and advance of interface-controlled reactions are identical with the behaviour discussed for the decomposition of a single solid (Chaps. 3 and 4). The condition that overall rate control is determined by an interface process is that a chemical step within this zone is slow compared with the rate of arrival of the second reactant. This condition is not usually satisfied during reaction between solids where the product is formed at the contact of a barrier layer with a reactant. Particular systems that satisfy the specialized requirements can, however, be envisaged for example, rate processes in which all products are volatilized or a solid additive catalyzes the decomposition of a solid yielding no solid residue. Even here, however, the kinetic characteristics are likely to be influenced by changing effectiveness of contact as reaction proceeds, or the deactivation of the catalyst surface. 

These sigmoid-type curves can be identified with thermal decomposition of a single solid in an autocatalytic-type reaction having an initial (a<0.2) induction period and an intermediate (0.2normal growth stage with the final (a>0.9) decay or deceleratory stage absent [8,9]. 

The rate of decomposition of a single solid material is governed by the formation of nuclei. The Prout-Tompkins rate equation, ln[a/(l-a)] = kt + C, which is based on the chain theory of nucleation and allows for branching interference, was applied to our data in Fig. 1, and gave remarkable linearity over the range 0 <0.8, as shown in Fig. 2. 

Decomposition of a single pure solid substance A may be represented as ... 

Figure 1. Typical a vs. time curves for the thermal decomposition of P HMX at 3.6 GPa for the various temperatures indicated. Sigmoid curves such as those shown here are characteristic of autocatalytic decomposition reactions of a single solid.

Here in 2007, we can now handle data in the form of discrete named landmark points, curves and surfaces from a wide variety of geometric data sources (photographs, solid medical images, surface scans) in two or three dimensions. We can accommodate the special cases, quite common in practice, for which landmark points arise from curves, or landmark curves from surfaces. Indeed, this approach, the simplicial decomposition of a single form, has become the most common way of building a coherent geometric representation (see Bookstein, 2004) that compromises between the enormous over-representation by surface meshes and the equally severe under-representation by conventional discrete point schemes. 

In the case of a single solid as product (which excludes the reactions of double decompositions that we will approach in section 14.4.2.4), we can write the reaction between two solids in the general form ... 

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. 

Kinetic Expressions. In this study, we have analyzed nonisothermal TGA data using the Chen-Nuttall equation, the widely accepted Coats-Redfern equation, and the Anthony-Howard equation. These equations are derived from simple rate expressions. The basic single reaction kinetic equation for the decomposition of a solid has been presented by Blazek (24) as... 

An interesting theory of promoter action is based on the belief that interfaces are the seat of catalytic activity—the active centers.1,2 It is apparent that new boundaries will be provided and existing ones altered when one solid is incorporated with another, and the enhanced activity may reside in specific configurations produced at boundaries of the two solids. That boundaries between surfaces can be the seat of activity is supported by the fact that a decomposition or combination may be difficult to start on a solid surface consisting entirely of a single component. Overburnt lime does not hydrate readily because water does not combine except where hydration has already begun.22 Faraday found that hydrated salts do not commence to effloresce unless the surface is scratched. The action of manganese dioxide on the decomposition of potassium... 

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