Kinetics Of Solid-state Reactions Research Articles

The kinetics of solid state reactions accompanied by fracture: I. Reaction of ion exchange in lime-soda glass

Reaction of Na + to Li + ion exchange in lime-soda glass was investigated as an example of a solid state reaction accompanied by fracture. The reaction proceeds at contact between the glass and lithium-containing melted salts and causes cracking of the glass and formation of combined reaction-fracture front. It is shown that both disordered and ordered pattern of cracking can be observed in different conditions. Results of the experimental investigation are compared with the existing models describing the stationary propagation of the combined reaction-fracture front. It turned out that the models describe satisfactorily only the case of disordered morphology of fracture. We suppose that the phenomenon of ordered fracture is connected with some factors providing a stable propagation of ordered system of cracks which have not been considered in the existing models yet. It is shown that the ordered fracture in the case under consideration can be caused by the effect of spatial separation of the diffusion and fracture fronts due to local crystallization of the reaction melt occurring near the reaction zone in definite conditions.

Kinetic study on solid state reaction for synthesis of LiBOB

The process of preparing lithium bis(oxalato)borate (LiBOB) was studied by TG/DTA and XRD methods. Five DTA plots were obtained at five different heating rates. According to the DTA plots, the Ozawa integral method and the Kissinger differential method were employed in the study on kinetics of solid state reaction. The result showed that to increase the heat preservation time at 100–120 °C was advantageous to the synthesis of LiBOB. The stages of solid state reaction for preparing LiBOB were analyzed by XRD method. The optimum conditions of synthesis LiBOB were first heat preservation at 100–120 °C, and then heat preservation at 240–280 °C.

Improved version of Doyle integral method for nonisothermal kinetics of solid-state reactions

An improved version of Doyle integral method for the determination of the kinetic parameters from nonisothermal thermoanalytical data has been presented. The relative errors involved in the activation energy and frequency factor determined from Doyle integral method and its improved integral method have been estimated. The results have shown that the precision of the improved version of Doyle integral method for the determination the kinetic parameters (including the activation energy and frequency factor) is much higher than that of Doyle integral method.

The single-step approximation

Mechanisms of the processes in condensed phase tend to occur in multiple steps that have different rates. Their kinetics is very often described by the single-step approximation. The first attribute of the approximation is the substitution of a generally complex set of kinetic equations describing the complex process by the sole single-step kinetic equation. The other attributes of the approximation are the separability of the temperature and conversion functions and the additivity. The temperature function for the best fit of experimental data may not be the Arrhenius relationship. The main strength of the single-step approximation is that it enables a mathematical description of the kinetics of solid-state reactions without a deeper insight into their mechanism. The low trustworthiness of far extrapolation is a weak point.

Synthesis of Bulk Nano-Al2O3 Dispersed Cu-Matrix Composite Using Ball Milled Precursor

Kinetics of solid-state reduction reaction during ball milling of CuO-Al and CuO-prealloyed Cu(Al) powder blends in dry and wet condition has been investigated by using X-ray diffraction (XRD), differential scanning calorimetry (DSC), and transmission electron microscopy (TEM) techniques. Direct reduction of CuO by Al has resulted into Al2O3 dispersed Cu-matrix composite through a self-propagating reaction only during milling in dry condition. However, indirect reduction of CuO by prealloyed Cu(Al) resulted into formation of nano-Al2O3 dispersed Cu-matrix composite either by continued ball milling in dry condition or by subsequent thermal treatment of wet milled powder precursor. The influence of milling conditions, that is, milling speed, and milling media, on the occurrence of reduction of CuO by elemental Al or Al in prealloyed Cu(Al) during ball milling have been explained by considering their effects on the rise of powder temperature due to collisions between balls and powder particles, and the rate of reduction of ignition temperature of the reaction due to microstructural refinement. TEM investigation has revealed that the size of Al2O3 particles in the composite power blend formed by the indirect reaction route (CuO-prealloyed Cu(Al)) is much finer than the same in case of direct reaction route (CuO-Al). It is suggested that the kinetics of the reduction reaction in the indirect reaction route is relatively sluggish in nature and amenable to processing of large amount of nano-Al2O3 dispersed Cu-matrix composite powder for industrial purpose.

Investigation of the Multi-Step Dehydration Reaction of Theophylline Monohydrate Using 2-Dimensional Powder X-ray Diffractometry

(i) To study the dehydration kinetics of theophylline monohydrate using 2-dimensional (2D) powder X-ray diffractometry (XRD), and (ii) to investigate the effect of polyvinylpyrrolidone (PVP) on the dehydration pathway and kinetics. Theophylline monohydrate (C(7)H(8)N(4)O(2).H(2)O; M) was recrystallized from aqueous PVP solutions of different concentrations. Dehydration kinetics was studied isothermally, at several temperatures, from 35 to 130 degrees C. The experimental set-up comprised of a high intensity X-ray source (synchrotron radiation or 8 kW rotating anode), a heating chamber, and a 2D area detector. Diffraction patterns were collected continuously, with a time resolution ranging from 40 ms to 30 s, over the angular range of 3 to 27 degrees 2theta. Dehydration of M resulted in either the stable (C(7)H(8)N(4)O(2); A), or the metastable anhydrate (A*), with the latter having a tendency to transform to A. The XRD technique allowed simultaneous quantification of M, A* and A during the dehydration reaction. The rate constants for individual reaction steps (M-->A*; M-->A and A*-->A) were determined by fitting the data to solid-state reaction models. In presence of PVP, there was a decrease in the magnitude of the rate constant associated with the M-->A transition, resulting in an increased build-up of A* in the product. The inhibitory effect of PVP on M-->A transition was more pronounced at lower dehydration temperatures, and was proportional to the concentration of PVP. Two dimensional powder X-ray diffractometry, using a high intensity source, is a powerful technique to study kinetics of rapid solid-state reactions. The inhibitory effect of excipients can have profound effect on phases formed during pharmaceutical processing.

Nanostructure and Phases Formation under Mechanical Alloying of Bynary Powder Mixtures of Fe and sp-Element (M); M = C,B,Al,Si,Ge,Sn

The processes of mechanical alloying of iron and sp-elements (C, B, Al, Si, Ge, Sn) under identical conditions of mechanical treatment have been studied. General regularities and differences in the mechanisms and kinetics of solid state reactions have been ascertained. A microscopic model of mechanical alloying in these systems is suggested.

Investigation on solid-state polymerisation reaction mechanism of Nylon-6

Solid-state polymerisation (SSP) is a convenient method of producing high molecular weight polymers at relatively low temperatures. In this work the SSP of nylon-6 was examined in a fixed-bed reactor. The solid-state polymerisation reaction kinetics of Nylon-6 was investigated in connection with the relative viscosity (RV) of the initial starting materials. The changes in the molecular weight and other properties were monitored as a function of the reaction times at solid-state temperatures of 130–200 °C. Starting materials with higher initial molecular weights exhibited higher rates of SSP than those with lower initial values. Activation energies decreased at temperatures above 170 °C, and this indicated a change in the SSP reaction mechanism. At temperatures of 170–200 °C similar activation energies were required for the polymerisation of all samples.

Simple Chemical Reactions in the Solid State: Towards Elaborating a Conception

In contrast to the conventional homogeneous kinetics, there is no conception of a simple reaction in the solid-state reaction kinetics. The geometric-probabilistic phenomenology currently in use is not adequate for describing the interplay between the chemical mechanism and the observed kinetic behaviour. An attempt is made to formulate a conception of simple reaction in the solid state as a basis for constructing kinetic models of involved reactions.

Considerations on the single-step kinetics approximation

Mechanism of the processes in condensed phase are very often unknown or too complicated to be characterised by a simple kinetic model. They tend to occur in multiple steps that have different rates. To describe their kinetics, the single-step kinetics approximation is often applied which resides in substituting a generally complex set of kinetic equations by the sole single-step kinetics equation. The main contribution of the single-step kinetics approximation is that it enables a mathematical description of the kinetics of solid-state reactions without a deeper insight into their mechanism. The single-step kinetics approximation is based on the assumption that the temperature and conversion functions are separable. In the paper, some consequences originating from ignoring the function separability are discussed.

Role of isoconversional methods in varying activation energies of solid-state kinetics: II. Nonisothermal kinetic studies

The concept of variable activation energy in solid-state reaction kinetics has caused considerable debate. Activation energy variation has been detected by isoconversional or “model-free” calculation methods, which generate activation energy as a function of reaction progress. The relationship between calculation methods and artifactual variation in activation energy was investigated in this work by employing model-fitting and isoconversional methods to analyze both simulated and experimental nonisothermal data. The experimental data was for nonisothermal sulfameter-dioxolane solvate desolvation by TGA. We show that variable activation energy in simple reactions could be an artifact resulting from the incorrect application of isoconversional methods.

The theory and practice of thermoanalytical kinetics of solid-state reactions

on kinetics have become a feature of ICTAC Congresses and are generally well-attended and result in lots of useful discussion. The Workshop at ICTAC 13 continued the tradition with about 50 attendees. The workshop was chaired by Haruhiko Tanaka and Michael Brown. Six introductory presentations were made on the subject, followed by the discussion summarized below. The six introductory speakers were: (1) Ranjit K. Verma; (2) Mike Reading; (3) Crisan Popescu; (4) Erwin Kaiserberger; (5) Mike Brown; (6) Haruhiko Tanaka.

Kinetics of solid state reactions under isothermal and non-isothermal conditions

An attempt has been made to review various theoretical and practical aspects of the kinetics of solid state reactions. A very wide range of models developed so far for the study of the kinetics of such reactions by both isothermal and non-isothermal methods have been documented and their applicability has been critically examined. Though hundreds of literatures are available on this subject, only very relevant ones have been cited to avoid lengthy bibliography.

Effect of gas composition on the kinetics of iron oxide reduction in a hydrogen production process

Fe 2 O 3 is a suitable oxygen transfer agent for converting CO present in syngas to CO 2 for its eventual separation from H 2 . However, H 2 also reacts with iron oxide to form H 2 O . In order to evaluate the reactions for hydrogen enrichment, investigations into Fe 2 O 3 to FeO reduction kinetics in the presence of syngas constituents were conducted. The reaction kinetic parameters were estimated based on the thermogravimetric data. Hancock and Sharp method of comparing the kinetics of isothermal solid-state reactions, based on Johnson–Mehl–Avrami–Erofe’ev equation describing nucleation and growth processes, was applied. The experimental results indicate that the reduction is initially a surface-controlled process, but once a thin layer of lower iron oxides (magnetite, wüsite) is formed on the surface, the mechanism shifts to diffusion control. It was concluded that this initial stage of the reaction process could be interpreted as a both phase-boundary-controlled reaction and the two-dimensional nucleation and growth (transformation of the crystallographic lattices of higher oxide to lattices of lower oxide) at the gas/iron oxide interface. Comparison of the reaction courses for both the reducing agents ( H 2 , CO) independently and for their mixture was performed. It was found, that the reaction rate increases with, both, temperature and the hydrogen content in inlet gas. The activation energy values were estimated and compared.

Mechanical alloying in binary Fe-M (M = C, B, Al, Si, Ge, Sn) systems

The processes of mechanical alloying of iron and sp-elements (C, B, Al, Si, Ge, Sn) under identical conditions of mechanical treatment have been studied. General regularities and differences in the mechanisms and kinetics of solid state reactions have been ascertained. A microscopic model of mechanical alloying in these systems is suggested.

The kinetic study of the synthesis of magnesium aluminate spinel from mechanochemically treated mixtures of oxide-hydroxide

The kinetics of solid-state reaction of magnesium aluminate (MA) spinel formation from the mechanically activated mixtures of both Mg and Al oxides and hydroxides was studied in situ by high-temperature X-ray diffraction at elevated temperatures. The degree of conversion α of the MA spinel formation was determined by the Rietveld method. The dependence of the conversion degree of the MA spinel formation on the time of isothermal heating of the particular mixtures was studied. Time dependence α(t) of the crystalline MgAl2O4 formation at the temperature T was analysed by the equation corresponding to the first order kinetics α(t) = P1 · [1 − P2 · exp(−k · t)], where P1, P2, and k are the parameters. The rate constants k and the activation energies of the crystalline MgAl2O4formation for the selected mixtures were calculated by the fitting the kinetic data. Comparison of acquired data shows that the most beneficial results for MA spinel synthesis were obtained from the mechanically activated hydroxide mixture Mg(OH)2 + Al(OH)3.

Comparative analysis of mechanisms and kinetics of mechanical alloying in Fe–Al and Fe–Si systems

A detailed study of the mechanical alloying processes in the Fe–32 at.% Al system was carried out using X-ray diffraction, Mössbauer spectroscopy, Auger spectroscopy, magnetic and chemical composition measurements. The results are compared with those for the Fe–32 at.% Si system obtained under the same milling conditions. Differences in the kinetics of solid state reactions are found, which do not depend on the differences in the individual properties (structure, melting temperature, mechanical properties, etc.) of Al and Si.

Numerical exploration of diffusion-controlled solid-state reactions in cubic particles

The characteristics of diffusion-controlled solid-state reactions in cubic particles are explored in this study. In order to capture the three-dimensional reaction front, the diffusion equation, subject to an interfacial chemical reaction in cubic particles, is solved in a transient form using the finite volume method. How the unreacted core is shrunk with time is clearly revealed. In addition, the concentration distributions of reactants and products are numerically predicted. A comparison of reacted zones advancing along different directions from the particle surface to the center is also made. The simulated kinetic curves at different conversion constants are shown to be useful to evaluate the conversion kinetics of diffusion-controlled solid-state reactions in cubic particles.

Synthesis of Ba(Mg1/3Ta2/3)O3 microwave dielectrics by solid state processing

Synthesis and formation of Ba(Mg1/3Ta2/3)O3 (BMT) from BaCO3, MgO and Ta2O5 was examined by thermal and X-ray diffraction analyses using quenching technique. Several reactions take place during heating process. BaCO3 can react with Ta2O5 to form BaTa2O6 (BT2) and B4T2 .B T 2 as an intermediate product was found at the first stage of the reaction, and then BaTa2O6 or B4T2 react with MgO to form BMT. The reaction of BMT formation was not complete until it was sintered at 1350 � C for 60 min. An intermediate reproduce cycle keeps company with the BMT formation in calcinations and sintering processing. The kinetics of solid-state reaction between powdered reactants for the reaction of BaTa2O6 formation was diffusion mechanism controlled, which can be described by Jander’s model for three-dimensional diffusion. The activation energy was determined to be 235.6 kJ/mol. The BMT powders were sintered to � 96% of relative density after 3 h at 1650 � C. The final sintered ceramics exhibited a dielectric constant of 24.5, a Q.f of 120,000 GHz, and a temperature coefficient of resonant frequency of 6 ppm/ � C.

Experiment vs. theory in solid-state reaction kinetics: A discrete model for NH4HCO3 thermal decomposition

A discrete model has been constructed for the thermal decomposition of NH4HCO3 single crystals according to the mechanism of nucleation and growth to impingement. The rate-time curve has been computed in terms of the crystal structure of ammonium hydrocarbonate proceeding from microscopic assumptions. This illustrates previously suggested discrete approach to solid-state reaction kinetics in terms of Dirichlet tessellations.