Solid-state Transformation Kinetics Research Articles

Strong d-π Orbital Coupling of Co-C4 Atomic Sites on Graphdiyne Boosts Potassium-Sulfur Battery Electrocatalysis.

Potassium-sulfur (K-S) batteries are severely limited by the sluggish kinetics of the solid-phase conversion of K2S3/K2S2 to K2S, the rate-determining and performance-governing step, which urgently requires a cathode with facilitated sulfur accommodation and improved catalytic efficiency. To this end, we leverage the orbital-coupling approach and herein report a strong d-π coupling catalytic configuration of single-atom Co anchored between two alkynyls of graphdiyne (Co-GDY). The d-π orbital coupling of the Co-C4 moiety fully redistributes electrons two-dimensionally across the GDY, and as a result, drastically accelerates the solid-phase K2S3/K2S2 to K2S conversion and enhances the adsorption of sulfur species. Applied as the cathode, the S/Co-GDY delivered a record-high rate performance of 496.0 mAh g-1 at 5 A g-1 in K-S batteries. In situ and ex situ characterizations coupling density functional theory (DFT) calculations rationalize how the strong d-π orbital coupling of Co-C4 configuration promotes the reversible solid-state transformation kinetics of potassium polysulfide for high-performance K-S batteries.

The interplay of dissolution, solution crystallization and solid-state transformation of amorphous indomethacin in aqueous solution

Supersaturation profiles of amorphous indomethacin in aqueous solution containing 0.4 wt% and 4 wt% of isopropanol were predicted by combining separately-determined kinetics for dissolution, solution crystallization, and solid-state transformation. The kinetics of solid-state transformation were measured and compared to various data from the literature. The proposed kinetic model accounts for dissolution, solution crystallization and amorphous-to-crystalline solid-state transformation. It was validated for different initial amounts of amorphous and crystalline material and systems with different isopropanol contents. Furthermore, the influence of polyethylene glycol on the supersaturation behavior was investigated. The results clearly show the robustness of the model and give insight into the interplay of dissolution, solution crystallization, and solid-state transformation of. In particular, the influence of solid-state transformation on the overall supersaturation profile was elucidated in a quantitative manner. An amorphicity function φ(t) is proposed to account for the kinetics of the solid-state transformation. Its general form could be derived consistently from different sets of experimental data and seems to be independent of the particle size of the amorphous material and hydrodynamic conditions. This work is among the first of its kind to successfully integrate dissolution, crystallization from solution and solid-state transformation in a model that shows good predictability.

On-line monitoring of vacuum drying of theophylline using NIR spectroscopy: solid-state transitions, water content and semi-empirical modeling

The aim of this work was to monitor in-line and at a real time, the solid-state forms during pharmaceuticals manufacturing. It concerns the dehydration behavior and the solid-state transitions of theophylline in an agitated vacuum contact dryer. First, a near infrared spectroscopy (NIRS) method was performed using a reflectance diffuse probe to measure the in-line and in-situ exact composition of the mixture of different forms of theophylline and water content during drying. A multivariate modeling has been investigated to build a robust model which can predict four components at the same time during drying process. The XRPD analysis was used as a reference method in the process of calibration of NIRS. The indicators of the accuracy in quantitative spectral analysis confirm the robustness of the model and the efficiency of the method of calibration. Second, the kinetics of solid state transformations were investigated. It was shown that the dehydration advanced first by the formation of the metastable anhydrate and after a lag time of the stable one. Once the stable form appeared, formation of the metastable form came to an end. The temperature was found out to be the main factor controlling the overall process rate but also the final contents of the stable and metastable anhydrates for the considered dryer and operating conditions range. Finally, a semi-empirical drying model was proposed and significant quantitative differences were found, particularly at the product temperature which was probably caused by the excessive simplicity of the model.

A multiscale perspective on the kinetics of solid state transformations with application to bainite formation

We give an excerpt of recent developments in the experimentally benchmarked modeling of bainite formation in the press hardening process. As the press hardening process poses a heavily multi-parameter dependent modeling challenge, we focus on three main branches which complement each other. We emphasise the combination of basic sharp interface and phase field models with pragmatically adapted multi phase field models and experimentally parametrized implementations of the Johnson-Mehl-Avrami model. In the basic thermodynamic modeling part, we review fundamental aspects of displacive and diffusional-displacive transformations to predict dominant transformation morphologies. These results provide a link to multi-phase-field implementations which allow to simulate isothermal bainitic transformations, supported by available material data from thermodynamic databases. Excellent agreement with experiments, e.g. scanning electron microscopy for the transformed bainite in the high-carbon steel 100Cr6 shows the value of these model implementations. The further connection to Johnson-Mehl-Avrami models offers to extend the understanding to transformation plasticity for the press hardening steel 22MnB5.

New approach to the novel synthesis of boehmite (γ-AlOOH) by microwave irradiation of gibbsite: Kinetics of solid-phase reactions and dielectric properties of the reactants

Microwave irradiation of gibbsite is suggested as a method of obtaining crystalline boehmite. The kinetics of solid-state transformations of gibbsite under microwave radiation has been investigated, and the dielectric properties of the initial and microwave-activated gibbsite samples have been determined. Extending the gibbsite irradiation time leads to an increase in tanδ. This indicates that microwave-activated gibbsite has a stronger capacity for dissipating microwave energy owing to the formation of an amorphous component containing a variable amount of weakly bound molecular water. The general chemical formula of the amorphous component can be represented as Al2O3 · xH2O (0.5 < x < 3.0). The results of this study can provide a basis for developing new, low-waste, resource- and energy-saving methods for the synthesis of crystalline boehmite and for converting it into γ-Al2O3 with acid-base and textural properties that are atypical of the known low-temperature modifications of Al3+ oxides.

Mechanism and Kinetics of Solid-State Transformation in High-Temperature Processed Linepipe Steel

A relatively new class of linepipe steels with yield strength greater than 500 MPa created for thermomechanical processing at temperatures in excess of 1473 K (1200 °C) has established a firm foothold in the market for modern, large diameter, and high-pressure gas transmission systems. The design concept for the steels takes advantage of the enhanced role which higher levels of niobium can play in very low carbon steels, during the plate manufacturing process. The transformation products observed after cooling have been interpreted in conflicting ways in the literature, using ambiguous terms which are not established rigorously. Revealing characterization experiments have therefore been conducted to establish that the principal transformation product grows by a displacive transformation mechanism, and that it is properly identified as bainite. The implications of this, on both the interpretation of microstructure and on the processing of the steel, are discussed.

Monitoring of theophylline dehydration in a vacuum contact dryer by near-infrared spectroscopy

This study is a contribution for development of in-line monitoring of solid-state forms during pharmaceuticals manufacturing. It concerns the dehydration behaviour of theophylline monohydrate by stirred bed vacuum contact drying. First it was demonstrated that NIRS coupled with PLS regression enabled to measure in-line and in situ the exact composition of the mixture of different forms of theophylline (and water) during drying. Second, the influence of operating parameters (temperature and water activity) on the kinetics of solid state transformations was investigated. It was shown that the dehydration advanced first by the formation of the metastable anhydrate and after a lag time of the stable one. Once the stable appeared, formation of the metastable form came to an end. The temperature was found out to be the main factor controlling the overall process rate but also the final contents of the stable and metastable anhydrates for the considered dryer and operating conditions range.

Evaluation of Kinetic Parameter Calculation Methods for Non-Isothermal Experiments in Case of Varying Activation Energy in Solid-State Transformations / Neizotermisko Eksperimentu Kinētisko Parametru Noteikšanas Metožu Izvērtēšana Mainīgas Aktivācijas Enerģijas Gadījumā Cietfāžu Pārvērtībām

Simulations of solid-state transformation kinetics were carried out calculating temperature and conversion degree for non-isothermal experiments with different heating rates. Simulations were divided in two parts: with constant and with variable activation energy. Simulations were analyzed with widely used model-based and model-free activation energy determination methods, frequency factor and kinetic model determination methods. Much of the attention was devoted to the calculation of kinetic models and frequency factors, as a more difficult and less developed step. For simulations where activation energy did not change all activation energy determination methods were found to give correct results. However, much attention should be devoted to frequency factor determination, because incorrect results would lead to problems in determination of kinetic models. For simulations where activation energy changes, correct activation energy can be determined only by differential methods or integral methods using numerical integration over small intervals. Isokinetic relationship coefficients b and c were more accurately determined with the average linear integral method. Correct kinetic model determination was possible only when coefficients b and c were accurate, and only by analyzing results of all available methods.

Impact of anisotropic growth on kinetics of solid-state phase transformation

Based on the statistical analysis of blocking effect arising from anisotropic growth, the anisotropic effect on the kinetics of solid-state transformation was investigated. The result shows that the blocking effect leads to the retardation of transformation and then a regular behavior of varying Avrami exponent. Following previous analytical model, the formulations of Avrami exponent and effective activation energy accounting for blocking effect were obtained. The anisotropic effect on the transformation depends on two factors, non-blocking factor γ and blocking scale k, which directly acts on the dimensionality of growth. The effective activation energy is not affected by the anisotropic effect. The evolution of anisotropic effect with the fraction transformed is taken into account, showing that the anisotropic effect is more severe at the middle stage of transformation.

Predicting Solid-State Phase Transformations during Welding of Ferritic Steels

The current work presents the numerical analysis of solid-state transformation kinetics relating to conventional welding of ferritic steels, with the aim of predicting the constituent phases in both the fusion zone and the heat affected zone (HAZ) of the weldment. The analysis begins with predictions of isothermal transformation kinetics using thermodynamic principles, such that the chemical composition of the parent metal is the sole user-defined input. The data is then converted to anisothermal transformation kinetics using the Scheil-Avrami additive rule, including the effects of peak temperature and austenite grain growth. Subroutines developed for the Abaqus finite element package use the semi-empirical approach described to predict phase transformations in SA508 Gr.3 Cl.1 steel. To study the effect of the cooling rates and the ability of the current model to predict the final microstructure, two weld samples were subjected to autogenous beam TIG welds under a fast (TG5-F, 5.00 mm/s) and slow (TG5-S, 1.25 mm/s) torch speed. Model validation is carried out by direct comparison with microstructural observations and hardness measurements (via nanoindentation) of the fusion and heat affected zones in both welds. Excellent agreement between the measured and predicted hardness has been found for both weld samples. Additionally, it is shown that the correct identification of the partial austenisation region is a crucial input parameter.

Effect of 4 GPa pressure treatment on the solid state transformation kinetics of T8 steel in heating process

The transformation temperatures and durations of solid state transformation in T8 steel before and after 4 GPa pressure treatment are measured using differential scanning calorimetry, and the transformation activation energy and Avrami exponent are also calculate. Then the effects of 4 GPa pressure treatment on solid state transformation kinetics in T8 Steel are investigated based on the kinetic parameters and the observation of microstructure. The results show that the solid state transformation in T8 steel shifts toward the low temperature region after 4 GPa pressure treatment. The high pressure treatment can reduce the phase transformation time and Avrami exponent and enhance the phase transformation activation energy, which is favorable for refining the grains but has little effect on the phase transformation mechanism.

Kinetics of solid-state transformation subjected to anisotropic effect: Model and application

In the present work, a growing particle subjected to anisotropic effect, if not influenced by other particles, is assumed to be an isotropically growing particle with constant volume. Accordingly, how to describe the anisotropic growth just becomes how to solve the blocking effect arising from the anisotropic growth. Following the statistical description of Johnson–Mehl–Avrami–Kolmogorov kinetics, the blocking effect was investigated further. Consequently, a series of analytical models for solid-state transformation, where a particle undergoes 1-scale blocking, k-scale blocking and infinite-scale blocking, were developed. On this basis, it was analytically proved for the first time that the classical phenomenological equation accounting for the anisotropic effect ( f = 1 - [ 1 + ( ξ - 1 ) x e ] - 1 / ξ - 1 ) corresponds to an extreme case where a particle encounters infinite-scale blocking. From the model analysis, the anisotropic effect on the transformation depends on two factors: the non-blocking factor γ and the blocking scale k. From the model calculations, the Avrami exponent, subjected to the anisotropic effect, changes as a function of the transformed fraction, whereas the effective activation energy is not affected by the anisotropic effect. The present models were adopted to describe isothermal crystallization of amorphous Fe 33Zr 67 ribbons; good agreement with the published results was achieved.

A Kinetic Model for Dissolution of Second Phases in Die-Cast Mg Alloy AM50

Dissolution of secondary phases during thermal treatment in cast magnesium alloys influences their engineering properties. In this study, a kinetic model based on a Kissinger-type method has been developed for describing dissolution of secondary phases in the high pressure die cast magnesium alloy AM50 during a thermally activated heating process. Also, differential scanning calorimetry (DSC) was effectively used for investigating the dissolution kinetics of secondary phases in the AM50 alloy. By fitting a kinetic model to the DSC results, the activation energy of the dissolution of the secondary phases can be determined. In parallel, the microstructure of the alloy was analyzed by scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (EDS). It was found that the distribution of secondary phases and the concentration of alloying elements both at the grain boundaries and in the grains play an important role in the solid-state transformation kinetics of die cast magnesium alloy AM50.

Formation of single-phase supersaturated solid solution upon solidification of highly undercooled Fe–Cu immiscible system

Applying glass fluxing combined with cyclic superheating and rapid quenching after recalescence, the solidification of undercooled immiscible Fe–Cu alloy melts was studied. Subjected to low undercooling, a coarse dendritic pattern results, where both Cu precipitation and dot substructure can be observed. For sufficiently high undercooling, a typical granular structure forms, where the dot substructure still exists because of the effect of post-recalescence. Only if both sufficiently high undercooling and rapid quenching immediately after recalescence are satisfied, a single-phase supersaturated solid solution can be obtained, where the Cu precipitation and the dot substructure are suppressed. Therefore, the formation of single-phase supersaturated solid solution can be attributed to a combination of an absolute solute trapping occurring upon rapid recalescence and a selection of rapid quenching point after recalescence, which suppresses the dot substructure through δ/γ massive transformation. This has been qualitatively interpreted using an extended steady-state dendritic growth model and the classical solid-state transformation kinetics, e.g., temperature–time–transformation (TTT) diagram.

Accelerated bainitic transformation during cyclic austempering

Austempering is an important thermal processing operation, where strong and tough bainitic steel is produced in a single heat treatment [1, 2]. During the austempering process, the steel is first austenitized and then cooled rapidly just above the martensite start temperature until bainite nucleates and grows, usually until the transformation stops and then it is cooled to room temperature. Due to the sluggish solid-state transformation kinetics, industrial austempering necessitates isothermal holds of 2–24 h, depending on the size and composition of steel. In contrast to conventional isothermal processing, cyclic thermal processing has been shown to accelerate the kinetics of several phase transformations [3–5], with a significant beneficial impact on productivity and energy consumption of these energy intensive operations. This was attributed to the non-isothermal effects resulting from cyclic treatment. The non-isothermal effect on phase transformations has also been utilized to enhance the productivity of a modern batch annealing operation [6]. In the present work, the effect of cyclic processing on austempering kinetics has been compared with conventional isothermal processing for 1080 steel. Furthermore, the effect of cyclic frequency on the austempering kinetics has been studied. Austempering kinetics experiments were performed on 6 mm diameter cylindrical samples of a 1080 steel using a Gleeble 3500 thermo-mechanical simulator (DSI Poestenkill, NY). A diametrical dilatometer was mounted on the specimen to measure the diameter change during the thermal processing. The austempering experiments were performed in two cycles, where the first cycle provides the same initial microstructure prior to each experiment. After completing the first cycle, the cylindrical specimens were heated to the austenitizing temperature (850 C), held for 5 min and then cooled to different austempering temperatures, where the bainite transformation was monitored for the desired period of time, followed by cooling to room temperature. The cooling rate was sufficiently fast to avoid any transformation occurring before reaching the austempering temperature (Fig. 1). The isothermal experiments were carried out at austempering temperatures of 260 and 300 C, whereas the cyclic experiments were carried out between 260 C and 300 C at two different heating/ cooling rates of 1 and 5 C/min. The percentage of bainitic transformation as a function of time was computed from the dilation curve [2] in conjunction with the microstructural examination by optical microscopy and SEM. The normalized dilatation curves for isothermal austempering at 260, 300 C, and cyclic austempering between 260 C and 300 C for 1 C/min and 5 C/min are shown in Fig. 2. In this figure, only the portion of the curve corresponding to austempering is shown and the dilatation curve has been offset to start at zero. The plateau of the dilatation curve with respect to the time represents the end of the transformation to bainite. It must be noted that the end of the bainite transformation does not necessarily correspond to 100% volume fraction of bainite [1]. Previously, using the same type of Gleeble experiments, it was shown that the end of the transformation corresponds closely to the austenite carbon content corresponding to a T0 equal to the austempering temperature [2, 7]. Furthermore the transformation dilatation at the end of the V. Sista P. Nash (&) Thermal Processing Technology Center, IIT, 10 W 32nd St., Chicago, IL 60616, USA e-mail: philip.nash@iit.edu

Enhanced Phenomena in Metals with Electric and Magnetic Fields: I Electric Fields

The effects of an externally-applied electric field on the equilibria and kinetics of solid state transformations in metals and alloys are reviewed. Regarding equilibria, electric fields have been found to affect the solubility of solutes and the composition as well as volume fraction of phases present. Regarding kinetics, electric fields have been shown to affect recovery and recrystallization, precipitation, phase coarsening, hardenability and sintering. Electric fields thus offer an additional means of controlling microstructure and in turn properties. Our understanding of the effects of an electric field on solid state transformations in metals and alloys is very meager. It appears that most of the observed effects on kinetics are through its influence on vacancies.

Use of isothermal microcalorimetry in pharmaceutical preformulation studies, Part I. Monitoring crystalline phase transitions

Solid-state transformation kinetics of two crystal forms of a synthetic tetrapeptide was monitored by isothermal microcalorimetry and complementary solid-state analytical techniques. Form B, the crystal form obtained from the synthetic process transformed to Form D upon exposure to higher relative humidity conditions (>60% RH). The transformation occurred rapidly at higher temperature, and relative humidities. An intermediate phase of very low crystallinity (amorphous-like phase) was observed when transformation was slow. Form D was observed to be physically stable at higher relative humidities and thus the preferred crystal form for development. Exposure of Form B to high relative humidity was the only process through which Form D was obtained. Optimal conditions for transformation of Form B to Form D were determined by microcalorimetric experiments and were used for larger scale processing of Form B to Form D.

Solid state transformation kinetics of high nodule count ductile Iron

This work focuses on the study of the kinetics of solid state transformations of thin wall ductile iron (TWDI). The aim is to identify the effect of the nodule count and the matrix homogeneity on the rate of transformation. The study is carried out on samples taken from sand cast plates of thickness ranging from 1.5 to 4mm, which show nodule counts up to 1700 per square millimetre. The results are compared to those obtained on samples taken from 12.5 mm thick Y-blocks, having approximately 300 nodules per square millimetre. Kinetics of ferritising, austenitising, austempering and cementite dissolution are studied.The results show that solid state transformations involving carbon transport from the matrix to the nodules or vice versa, such as subcritical ferritising and austenitising, show faster kinetics as the nodule count increases. The kinetics of the austempering transformation, which does not involve changes in the carbon content of the matrix, is not affected by the nodule count. The dissolution of the cementite present in unalloyed TWDI, also takes place at a very fast rate, ranging between 3 and 5 % per minute.

The effect of geometrical assumptions in modeling solid-state transformation kinetics

In the quest for the ideal transformation model describing the austenite decomposition in steel, emphasis shifts from empirical to physical models. This has resulted in the widely used description of the transformation by means of the interface velocity between the parent phase and the newly formed phase, a description which yields reliable predictions of the transformation behavior only when combined with a realistic austenite geometry. This article deals with a single-grain austenite geometry model applied to transformations in which the interface velocity is constant throughout the transformation, e.g., certain types of massive transformations. The selected geometry is a regular tetrakaidecahedron, combining topological features of a random Voronoi distribution with the advantages of single-grain calculations. The simulations show the influence of the ferrite-nucleus density, the relative positions of the ferrite nuclei inside the austenite grain, and the grain-size distribution. From simulations with a constant interface velocity, the transformation behavior for a tetrakaidecahedron is in agreement with transformation kinetics in terms of the Johnson-Mehl-Avrami (JMA) model. Using the tetrakaidecahedron geometry, one can simulate transformation curves that can be experimentally obtained by calorimetry or dilatometry, in order to study the quantities affecting the transformation behavior.

Nucleation and growth transformation kinetics.

As a result of the reassessment of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory for the kinetics of nucleation and growth transformations, an integral-equation formulation has been developed instead of the well-known and widely used Avrami equation. The presented formulation considers interfacial and diffusional growths, in one, two, and three dimensions, with both time-dependent and time-invariant nucleation and growth rates. The integral-equation model corrects reported inadequacies of the KJMA theory when applied in numerous experiments and various solid-state transformations. It is shown that in the example cases examined in this paper, crystallization from the amorphous state in melt-spun ribbons, isothermal aging of CuAlZn, pearlitic transition in an eutectoid steel, and crystallization in a PEKK polymer, the thermodynamic and kinetic interpretation and parameters extracted from best fits of the Avrami equations to the experimental data are erroneous. The KJMA formulation is a simplification of the real physical conditions. The main limitation of the new model is that almost all the integral equations representing the kinetics of solid-state transformations have no analytical solutions.