Kinetics Of Solid-state Reactions Research Articles

Geometrical probabilities in heterogeneous kinetics: 60 years of side by side development

In developing the theory of heterogeneous chemical kinetics, the use of ideas and methods of geometrical probabilities provided the explanation of the universal kinetic regularities inherent in solid state reactions conjugated with first-order phase transitions. But in the course of time it is becoming clearer and clearer that the other side of the universality of the conventional geometric-probabilistic approach in terms of coverings is the set of discrimination issues which find no adequate resolution within this phenomenology. Meanwhile another mathematical language, the language of tessellations, had been worked out in the framework of the theory of geometrical probabilities and, later, stochastic geometry. It is more promising with respect to deeper interpretation and chemical differentiation of models. The interplay between these two languages is discussed from the angle of essential issues concerning the mathematical description of solid state reaction kinetics.

Enhancement of Ionic Diffusion by Microwave-Field-Induced Ponderomotive Forces at Physical Interfaces

ABSTRACTNumerous observations have been reported in the literature of enhanced mass transport and solid-state reaction rates during microwave heating or processing of a variety of ceramic, glass, and polymer materials. Recent research reveals that these phenomena are probably the result of a previously-unknown driving force for ionic mass transport. The driving force--termed a “ponderomotive” (mass-moving) force--results from the application of intense, high-frequency electric fields near physical interfaces (e.g., free surfaces, grain boundaries). Experiments, theory, and numerical simulations all demonstrate that this driving force can influence solid state reaction kinetics by enhancing mass transport rates.

Kinetics in solids.

The kinetics of solid state reactions generally cannot be assumed to follow simple rate laws that are applicable to gas-phase reactions. Nevertheless, a widely practiced method for extracting Arrhenius parameters from thermal analysis experiments involves force fitting of experimental data to simple reaction-order kinetic models. This method can produce significant errors in predicted rates outside the experimental range of temperatures, and it is of limited utility for drawing mechanistic conclusions about reactions. In this review, we discuss how an alternative "model-free" approach to kinetic analysis, which is based on the isoconversional method, can overcome some of these limitations.

The Prout-Tompkins rate equation in solid-state kinetics

Abstract In more than 50 years since its publication, a paper in the Transactions of the Faraday Society by Prout and Tompkins has been extensively cited in the literature. The paper dealt with the kinetics of the thermal decomposition of crystals of potassium permanganate, and suggested a rate equation, which has become known within the field as the Prout-Tompkins equation, for use in the kinetic analysis of solid-state reactions. This equation and its applications in a variety of different fields, including general kinetics of solid-state reactions; continuing work on KMnO 4 ; irradiation effects; pharmaceutical stability studies, and colloid and interfacial chemistry, are discussed.

Isothermal and Nonisothermal Reaction Kinetics in Solids: In Search of Ways toward Consensus

Thermogravimetric data for the decomposition of ammonium dinitramide (ADN) have been obtained under isothermal and nonisothermal conditions in order to determine the efficacy of different methods for analyzing the kinetics of solid-state reactions. A widely used model-fitting method gives excellent fits to the experimental data but yields highly uncertain values of the Arrhenius parameters when applied to nonisothermal data because temperature and extent of conversion are not independent variables. Therefore, comparison of model fitting results from isothermal and nonisothermal experiments is practically meaningless. Conversely, model-free isoconversional methods of kinetic analysis yield similar dependencies of the activation energy on the extent of conversion for isothermal and nonisothermal experiments. Analysis of synthetic data generated for a complex kinetic model suggests that, in the general case, the identical dependencies are unlikely to result from experiments obtained under isothermal and nonisothermal conditions.

Physico-geometric kinetics of solid-state reactions by thermal analyses

The physico-geometric kinetics for the solid-state reactions by thermoanalytical (TA) measurements were reexamined by focusing some fundamental aspects: (1) the fundamental kinetic equation, (2) the kinetic model function, (3) the fractional reaction α, and (4) the apparent kinetic parameters. It was pointed out that some pitfalls in the practical kinetic study are originated by the disagreement between the kinetic information from the TA measurements and the theory of the physico-geometric kinetics. In order to increase the degree of coordination between the theory and practice, several attempts were made from both the theoretical and experimental points of views. The significance of the apparent kinetic parameters was discussed with a possible orientation for obtaining the reliable kinetic parameters.

Polychronous kinetics with nonstationary rate constants. Effect of a medium

Characteristic features of the kinetics of solid-state cage reactions with distributed parameters of the relaxing matrix were considered. Depending on the ratio of the constants of the reaction rate and relaxation of environment, the kinetics of chemical conversions can be either exponential or nonexponential. Plausible reasons for the unsteady-state character of the kinetics of the processes of two types,viz., the reactions of alkyl radicals in amorphous alcohol matrices and conversions in biological systems, were discussed. The main reason for the unsteady-state character of the reactions of the first type is a dispersion of the equilibrium distances between the reagents. Kinetics of the reactions of the second type, such as rebinding of the ligands in the heme-containing proteins (e.g., in myoglobin), is determined by the distances in the pairs of reagents and the relaxation transitions.

DEXAFS — a new technique to investigate the kinetics of high temperature solid state reactions in situ

Three types of solid state reactions — namely the precipitation formation (dissolution) of spinel or metal particles, both in (A 1 − x B x ) 1 − δO solid solutions, and the oxidation of metal foils to the corresponding oxide BO n — were studied first by means of DEXAFS spectroscopy. This technique allows us to follow the different solid state reactions in situ and time resolved, after changing the oxygen activity at elevated temperature (770 < T < 1450 K).

The effect of layer thickness and composition on the kinetics of solid state reactions in the niobium-selenium system studied using superlattice reactants

The ability to form an amorphous reaction intermediate by the low temperature interdiffusion of a modulated elemental reactant is shown to be a function of the overall composition as well as elemental layer thicknesses in the niobium-selenium system. For niobium-rich reactants, an amorphous reaction intermediate was observed to form upon low temperature annealing of reactants with modulation thicknesses less than 60 Å. Further annealing of the amorphous intermediates led to the crystallization of Nb 2Se, Nb 5Se 4 or Nb 3Se 4 depending upon the overall composition of the amorphous intermediate. Modulated elemental reactants with overall compositions containing more than two-thirds selenium were found to heterogeneously nucleate NbSe 2 at the reacting interfaces. The formation of the thermodynamically expected compounds Nb 2Se 3, NbSe 3, and Nb 2Se 9 at their respective compositions required extended high temperature annealing to react the dichalcogenide with the remaining elemental reactants. A striking difference between the evolution of the low angle diffraction patterns in these two composition regimes suggests the differences in the reaction kinetics result from a composition dependence of the diffusion coefficients.

Theoretical solutions for mixed control of solid state reactions

The kinetics of solid state reactions has been reexamined to include solutions for mixed control by an interfacial process and diffusion. The Valensi-Carter, Ginstling-Brounshtein, and other quasi steady state models have been extended to include mixed control. Solutions were obtained for planar, cylindrical and spherical particles. Mixed control may occur at either the inner or outer interface for cylindrical or spherical particles, for which significantly different solutions are valid. Mixed control at the outer interface usually gives faster reaction than mixed control at the inner interface. The kinetics of these solid state reactions with mixed control is usually nearly independent of the product to reagent volume ratio.

Magnetothermal analysis of the amorphous to nanocrystal transformation

Nanocrystalline phases can be formed during crystallization of amorphous alloys annealed isothermally below the crystallization temperature. We present magnetic susceptibility data on this transformation. Magnetic measurements are able to detect the onset of the transformation of amorphous Ni-P alloys much earlier than differential scanning calorimetry. The transformation kinetics are analyzed by means of the Avrami plot based on the Johnson-Mehl-Avrami equation. The kinetics of further solid state reactions in the nanostructured material can be investigated similarly.

Solid-State Reactions in Model Oxide Systems

AbstractThe kinetics of thin-film solid-state reactions have been investigated in two model spinel forming oxide systems, NiO/Al2O3 and MgO/Fe2O3. In the NiO/Al2O3 system, thin-films of epitactic NiO were reacted with (0001), , and orientated Al2O3 (corundum). The kinetics of the spinel forming reaction for this system were found to be linear-parabolic in nature. Additionally, it was found that the kinetics of the spinel-forming reaction varied by nearly two orders of magnitude between the fastest and slowest diffusion couples. The substrate determines the orientation of the overlayers and thereby the structure of the phase boundaries. In the MgO/Fe-oxide system, thin films of epitactic Fe oxide were reacted with {001} MgO. The kinetics of this spinel forming reaction were parabolic in nature, indicative of diffusion control. In contrast to the N1O/Al2O3 system, the movement of phase boundaries are not the step controlling the reaction rate, but rather the diffusion of one of the cations across the reaction layer. In comparing the reaction rates for the two systems the activation energy for the formation of the spinel product in the MgO/Fe-oxide system was found to be almost a factor of 4 lower in comparison to the NiO/Al2O3 system.

Reconciliation of Arrhenius and iso-conversional analysis kinetics parameters of non-isothermal data

Calculations pertaining to nth order analyses of various solid state reaction kinetics models have been extended to consider iso-conversional Arrhenius (i.e. Friedman) analyses. Non-isothermal extent and rate of reaction data for several models, with the same kinetics parameters, generated over a wide heating rate range, are subjected to both Arrhenius and Friedman nth order analyses over the entire extent of reaction range. A necessary model correction for the Friedman preexponential factors is presented and discussed. Calculated extent of reaction as a function of temperature data at a desired heating rate is compared with the original model data and analogous data generated using the single heating rate Arrhenius analyses parameters. Essentially complete agreement is obtained despite the widely disparate values of the Arrhenius and Friedman derived kinetics parameters. Application of this procedure to the analysis of experimental data is discussed.

Kinetic aspects of the formation of lead zirconium titanate

The kinetics of the second calcination step in the formation of PZT solid solution (with perovskite ABO 3 lattice) has been investigated by using two different particle sizes of the B-site precursor (1.91 and 5.08 μm), the finer size being obtained by prolonged milling. In-situ analysis performed by high-temperature X-ray diffractometry in a non-isothermal mode (20–800 °C) revealed a reduction of the calcination temperature by 100 °C with a decrease in particle size of the precursor. In order to clarify the mechanism of the solid-state reaction to PZT, isothermal heat treatment of the mixtures was performed in the temperature range 540–700 °C. The activation energies for the fine and the coarse powders were estimated as 150 and 210 kJ mol −1 respectively, and the reaction was found to follow the Jander model for diffusion-controlled solid-state reaction kinetics.

A theoretical justification for the application of the Arrhenius equation to kinetics of solid state reactions (mainly ionic crystals)

Although the Arrhenius equation has been widely and successfully applied to innumerable solid state reactions, this use lacks a theoretical justification because the energy distribution amongst the immobilized constituents of a crystalline reactant is not represented by the Maxwell-Boltzmann equation. The present analysis focuses attention on the role of the reactant-product interface, the active zone within which chemical changes preferentially proceed in many solid state rate processes. We identify interface energy levels, that are the precursors to the bond redistribution step, as extensions to the band structure of the solid into the structurally less-regular reaction zone. These interface energy levels are analogous to impurity levels. Electron reorganization requires a locally high energy so that interface levels are appreciably above the Fermi level of the crystalline reactant (and product). Occupancy is determined by energy distribution functions based on Fermi-Dirac statistics for electrons and Bose-Einstein statistics for phonons. For the highest energies, necessary for reaction, both distributions approximate to the exponential energy term, thereby providing a theoretical justification for the application of the Arrhenius equation to reactions of solids. The treatment given here has been largely developed from the theory applicable to ionic solids and the conclusions are most directly relevant to reactions of this class of substance. It is intended, however, that the approach should be of value in extending theoretical understanding of all rate processes involving solids which require the preinvestment of energy in an electron reorganization step.

Solid State Interfacial Reactions Between Tic Thin Films and Ti3AI Substrates

ABSTRACTThe products and kinetics of solid state reactions between TiC and Ti3Al have been investigated using X-ray diffractometry (XRD) and Auger electron spectroscopy (AES) with Ar ion beam sputtering. Diffusion couples were prepared by sputtering TiC thin films onto polished Ti3AI substrates, and then isothermally annealed in vacuum in the temperature range of 800 to 1000°C for 0.25 to 2.25 hours. The thickness of the interfacial reaction layer was obtained from AES elemental concentration depth profiling, while the reaction products were identified from XRD spectra. In the TiC/Ti3Al system, the reaction product was primarily P(Ti3AlC) phase. The growth-rate of the reaction product was fitted to a parabolic growth law (dZ/dt = k1/Z) and the activation energy of the rate constant was about 36.16 kcal/mole. The reaction mechanism will be discussed on the basis of thermodynamical equilibrium in Ti-Al-C ternary system.

The general utility of the nth order model in solid state reaction kinetics

Computerized kinetics analysis of simulated solid state reaction data has been used to demonstrate how the empirical nth order model may be employed as a diagnostic tool in thermoanalytical research. The characteristic shape of the curves of the extent and rate of reaction as a function of temperature, generated under non-isothermal conditions, together with the magnitude of the kinetics parameters when this data is subjected to nth order Arrhenius analysis, can be utilized to postulate a solid state reaction mechanism, and to calculate the pertinent activation energy and pre-exponential factor. This approach has been employed to analyze the non-isothermal thermogravimetric data characterizing the three stages in the thermal degradation of calcium oxalate monohydrate, postulated to conform to the D4, R3 and D4 mechanisms, respectively. Although the second stage appears to be essentially a single contracting-volume-controlled reaction, the variation of the activation energies and pre-exponential factors with heating rate for the first and third stages implies multiple diffusion-controlled reactions. The procedure has also been used to generate the kinetics parameters of the crystallization of an amorphous form of a candidate drug compound (A2 mechanism) from non-isothermally monitored differential scanning calorimetric data.

Thermophysical characterization studies of pharmaceutical hydrates

The use of both differential scanning calorimetry and thermogravimetry to study the solid state dehydration of hydrated pharmaceutical compounds, and the subsequent behavior of the anhydrous drug is discussed. Three compounds, each with differing thermal behavior serve as examples. Emphasis is placed on applying current solid state reaction kinetics theory to analyze non-isothermal data and ascribe possible mechanisms for the various physicochemical transformations and physical transitions monitored. Solvent removal from a final product can effect partial or total dehydration. It is necessary to ascertain the dehydration temperature limits, and, of equal importance to examine the ability of the compound to rehydrate. The dehydration/rehydration behavior of a drug candidate is described as a practical demonstration of the utility of thermal analysis in pharmaceutical process development.

A new approach to the study of solid-state reactions in oxide ceramics

Thin-film reactions have potential applications for the production of buffer layers in heterojunctions and for the reaction bonding of materials. The main drawback to these applications at present isthat the effect of interface morphology on the initial kinetics of solid-state reactions is not well understood. In order to study the kinetics and mechanisms of thin-film reactions in oxide ceramics, a new method has been developed. The approach relies on the production of a well characterized high-quality oxide thin film on a single-crystal oxide substrate which makes up the idealized reaction couple-a ‘single-crystal’ thin film in intimate contact with a single crystal substrate. The thin-film approach localizes the reaction near the surface of the specimen so that conventional cross-sectioning techniques can be utilized. Additionally, the scale of the reaction is of the order of tens of nanometers or less which is ideally suited to high-resolution SEM or conventional TEM.NiO/α-Al2O3 is a model system for the study of solid-state reactions.

Spectroscopicin situstudies of defect-dependent properties of transition metal oxides Defects, diffusion, and reaction kinetics

Abstract Results are reviewed of high-temperature in situ investigations of transition metal oxides using Mossbauer and optical spectroscopy. Emphasis is placed on the characteristic features of in situ experiments, which are discussed and illustrated by examples taken from studies of defect dependent crystal properties. Studies of ionic disorder in spinels and of the nature of electronic lattice defects in transition metal monoxides demonstrate the potential of optical spectroscopy and of the in situ approach in these fields. Ionic migration processes in complex structures, providing distinct sites for diffusion, have been detected and analysed exploiting the site selectivity of Mossbauer spectroscopy. The kinetics of solid-state oxidation and formation reactions has been investigated by means of time-resolved in situ Mossbauer experiments.