Kinetics of Solid-state Reactions

This topic is a large one and cannot be covered fully in this book. There are very many research papers on the subject, and also reviews of the topic, which should be consulted. An outline only of the techniques and problems will be given here. 

The starting point for examining kinetic data is to write the differential equation, as in conventional kinetics. 

Integral equation g(a) = kt Differential equation da/dt = kf(a) Notation Name 

In this a is the fraction reacted, t is time, k is the rate constant, and /(a) is the particular kinetic function, for example taken from those in Table 4. 

The experiment could be carried out isothermally or non-isothermally. These methods will be considered separately. 

In solution chemistry it is customary to express the reaction rates in terms of concentrations if the reactants and products are dissolved and well mixed and if the reactions are not diffusion-limited. This cannot be done in solids because solids are never perfectly stirred reactors. Reaction rates in solids do not have the same or similar relationships to the concentrations as reactions in liquids but they are diffusion-limited. Solid state reactions have other types of reaction order than reactions in liquid solution and the kinetic rules in solid state chemistry are different from those of reactions between molecules. The reaction rates depend on morphologies, the geometry of the reaction front, the diffusivities of the reacting species, the possibilities of nucleation, and the anisotropy of crystallites. In summary  

Reactions occur mainly on surfaces or grain boundaries, the state and form of the surfaces affect the rates, and the kinetics are heterogeneous. 

Diffusion in solids is less easy than in liquids and the reaction rates in solids are usually limited by the diffusion, which dominates not only the overall formation rates but also the morphology of the solid product of the reaction. 

The conversion can also be described by the Johnson-Mehl-Avrami equation  

1 Homogeneous nucleation at the beginning and continuous heteronucleation on the grain surfaces 

---

Young, D. A. (1966). Decomposition of Solids. Pergamon Press, Oxford, UK. An excellent book that discusses reactions of many inorganic solids and principles of kinetics of solid-state reactions. 

Kinetics of Solid State Reactions from Single Velocity Experiments... 

The examples illustrate the strong points of XRD for catalyst studies XRD identifies crystallographic phases, if desired under in situ conditions, and can be used to monitor the kinetics of solid state reactions such as reduction, oxidation, sulfidation, carburization or nitridation that are used in the activation of catalysts. In addition, careful analysis of diffraction line shapes or - more common but less accurate-simple determination of the line broadening gives information on particle size. 

Describe in brief, the kinetics of solid state reactions. 

The technique is also referred to as NEXAFS, although this acronym appears to be used increasingly for X-ray absorption at low energies and in light elements [36, 48]. Like QEXAFS, XANES spectra can be recorded in fast mode, to monitor the kinetics of solid-state reactions in real time [49]. 

The extent of non-stoichiometry, i.e. the extent to which a compound can partly be reduced or oxidized, strongly depends on the kind of cation. In Coj or Sn02 8 can be of the order of one percent and in several oxides such as Ce02 s and Mni- O even several percent are possible in AI2O3 or MgO, on the other hand, the degree of non-stoichiometry is extremely small [78, 80-82], Nevertheless, even very small -values can determine the charge carrier concentration in a solid, and thus effects such as the kinetics of solid state reactions. 

The summary of the theory of kinetics of solid-state reactions given here is applicable to TG investigations and also equally to rate measurements by other methods of thermal analyses. For more extensive treatments and further background information see References 4,5,10,29,71,76,103. 

Books and reviews dealing with the kinetics of solid-state reactions (e.g., [1-3]) usually pay little attention to the analysis and comparison of the metrological characteristics of the methods employed in TA measurements although a correct choice of the method to be used in measurement and calculation of the quantity of interest determines the reliability of the results obtained. This chapter addresses these points. 

Table 13.2 Contribution of flame and electrothermal AAS and QMS to the kinetics of solid-state reactions...

Introduction Dehydrations of metal hydroxides are attractive model reactions for basic studies of the kinetics of solid-state reactions and these reactions are widely used for the commercial production of metal oxides [45]. However, as shown in the recent paper by L vov and Ugolkov [55], available data on the reaction mechanisms and kinetics are inconsistent. For example, the parameter E for the dehydration of Mg(OH)2, reported in different papers, varies from 53 to 372 kJ mol One of the factors responsible for the large scatter of the E values estimated from Arrhenius plots is the low precision and accuracy of this method, especially as applied to decomposition to gaseous and solid products. The results obtained in [55[ by the third-law method, as indicated below, are much more reliable. 

Introduction Hydrates of metal salts undoubtedly played a leading part in the history of the kinetics of solid-state reactions. Particularly noteworthy are the first observations of the dehydration of crystalline hydrates, made by Faraday after scratching the crystal surface (Chapter 1), and the anomalous acceleration of the dehydrations of some crystalline hydrates in the presence of water vapour, discovered by Topley and Smith (Chapter 7). 

The correctness of new ideas and theories in scientific research is commonly evaluated by their fruitfulness in interpretation of problems accumulated in one or another field and by their capability to predict unknown trends and effects. The other general criteria that are applied to new theories are simplicity, internal consistency, experimental reliability (verifiability), and compliance with previous theories. The thermochemical approach to the kinetics of solid-state reactions used in this study meets these criteria. 

Some aspects of the kinetics of solid-state reactions in the context of polymorphism are encountered again in die next section, vdiich deals with the characterization of organic solvates and their desolvation. 

Galway, A.K. Brown. M.E. A theoretical justification for the application of the Arrhenius equation to kinetics of solid state reactions (mainly ionic crystals). Proc. R. Soc. Lond.. A 1995. 450. 501-512. 

We need to understand what controls the rate of a phase transformation. We can monitor both chemical and structural changes to address the sometimes subtle question— which change (chemistry or structure) occurs first The answer depends on why the phase change itself occurs. The experimental techniques we use are those given in Chapter 10, so we just give some specific illustrations here. The classical approach used to study the kinetics of solid-state reactions between two ceramic oxides is to react a bulk diffusion couple in much the same way as, for example, when studying the Kirkendall effect in metals. 

Riickenstein, E. Vavanellos, (1975). Kinetics of solid state reactions. AIChEJ., 21, 756-763. 

---