Johnson Mehl Avrami Equation Research Articles

Determination of phase transformation kinetics under magnetic fields: Modeling based on magnetization and application in a Fe-1 wt.%Cu alloy

A phase transformation model based on magnetization is proposed in this paper, which accurately tracks the change in the phase transformation volume fraction with time/temperature f-T/t by analyzing phase transformation magnetization curves under a magnetic field. This allows for the determination of kinetic parameters related to the nucleation and growth processes such as the phase transformation rate df/dt-T/t and Avrami exponent n, enabling quantitative analysis of phase transformation kinetics under magnetic field effects. Additionally, the phase transformation magnetization under a magnetic field can be accurately fitted by combining the volume fraction calculation model with the Johnson–Mehl–Avrami equation, thus also obtaining the kinetics parameters. The aforementioned two models are applied to study the isothermal and isokinetic transformations of austenite (γ) to ferrite (α) in Fe-1 wt. %Cu alloys, demonstrating the effects of external conditions through variations in kinetic parameters.

Effective Reaction Temperatures of Irreversible Dust Chemical Reactions in a Protoplanetary Disk

Dust particles in protoplanetary disks experience various chemical reactions under different physicochemical conditions through their accretion and diffusion, which results in the radial chemical gradient of dust. We performed three-dimensional Monte Carlo simulations to evaluate the dust trajectories and the progress of fictitious irreversible reactions, of which kinetics is expressed by the Johnson–Mehl–Avrami equation. The distribution of the highest temperature that each particle experiences before the degree of reaction exceeds a certain level shows the lognormal distribution, and its mode temperature was used as the effective reaction temperature. Semi-analytical prediction formulas of the effective reaction temperature and its dispersion were derived by comparing a reaction timescale with a diffusive transport timescale of dust as a function of the reaction parameters and the disk parameters. The formulas reproduce the numerical results of the effective reaction temperatures and their dispersions within 5.5% and 24%, respectively, in a wide temperature range (200–1400 K). We applied the formulas for the crystallization of amorphous silicate dust and its oxygen isotope exchange with the H2O vapor based on the experimentally determined kinetics. For submicron-sized amorphous forsterite dust, the predicted effective reaction temperature for the oxygen isotope exchange was lower than that of crystallization without overlap even considering their dispersions. This suggests that the amorphous silicate dust in the protosolar disk could exchange their oxygen isotopes efficiently with the 16O-poor H2O vapor, resulting in the distinct oxygen isotope compositions from the Sun.

Kinetics of Austenite Decomposition in 54SiCr6 Steel during Continuous Slow Cooling Conditions

In this study, dilatometry and metallography were used to investigate the effect of silicon and copper alloying on the decomposition kinetics of 54SiCr6 steel during continuous slow cooling. It is different from the published literature for using the approach of the local activation energy of the austenite decomposition Ef and the local Avrami exponent n of the volume fraction of the transformed phase f to study the kinetics of austenite-pearlitic transformation in cooled 54SiCr steel at slow cooling rates. The Johnson–Mehl–Avrami equation was used to determine the dependence of the local activation energy for austenite decomposition Ef and the local Avrami exponent n on the volume fraction of the transformed phase f. The mechanism of the austenite decomposition was analysed based on the calculated values of n. Both the local and average activation energies were used to evaluate the alloying effect, and the results were compared with those obtained from other methods. The type of microstructure formed as a result of cooling at rates of 0.5 K/s, 0.3 K/s, 0.1 K/s and 0.05 K/s was determined. The effects of changes in the cooling rate and the content of silicon (1.5–2.5 wt.%) and copper (0.12–1.47 wt.%) on the dimension of nucleation and growth kinetics of the transformed phase were studied. It was revealed that the pearlite microstructure was formed predominantly in 54SiCr6 steel as a result of continuous cooling at slow cooling rates. It was also found that alloying this steel with copper led to a significant decrease in the value of Ef, as well as to a change in the mechanism of the kinetics of the austenite-pearlite transformation, which was realised in predominantly two- and three-dimensional nucleation and growth at a constant nucleation rate. At the same time, alloying this steel with silicon led only to a slight change in Ef. The results of the study of 54SiCr steel presented the dependence of the activation energy of transformation and the local Avrami exponent on the volume fraction of the transformed phase at a given cooling rate at different copper and silicon contents. In addition, the study provides insight into the mechanism of kinetics in cooled 54SiCr steel as a function of the cooling rate.

The Kinetics of Phase Transition of Austenite to Ferrite in Medium-Carbon Microalloy Steel

To reduce energy and resource consumption, high-strength hot-rolled rebars with yield strengths of ≥400 MPa (HRB500) and ≥500 MPa (HRB600) have been designed and produced in recent years. Optimizing the microstructure in the steel to improve strength necessitates determining the kinetics of the phase transition of austenite to polygonal ferrite. Therefore, in the study, the effect of temperature and holding time on the volume fraction of ferrite is investigated in HRB500 and HRB600 steels. Experimental results show that the ferrite percentage initially increases with an increase in temperature and then decreases as the temperature increases from 600 to 730 °C. The optimum temperature range is 680–700 °C for HRB500 steel and 650–680 °C for HRB600 steel. Based on the Johnson–Mehl–Avrami equation, phase transition kinetic models are established. Model predictions are consistent with the validation data. Thus, this study establishes a reference for studying ferrite formation during cooling.

Analysis of the Crystallization Kinetics and Thermal Stability of the Amorphous Mg72Zn24Ca4 Alloy.

The aim of this study was to analyze the crystallization of the Mg72Zn24Ca4 metallic glass alloy. The crystallization process of metallic glass Mg72Zn24Ca4 was investigated by means of the differential scanning calorimetry. The glass-forming ability and crystallization are both strongly dependent on the heating rate. The crystallization kinetics, during the isothermal annealing, were modelled by the Johnson–Mehl–Avrami equation. Avrami exponents were from 2.7 to 3.51, which indicates diffusion-controlled grain growth. Local exponents of the Johnson–Mehl–Avrami equation were also calculated. In addition, the Mg phase—being the isothermal crystallization product—was found, and the diagram of the time–temperature phase transformation was developed. This diagram enables the reading of the start and end times of the crystallization process, occurring in amorphous ribbons of the Mg72Zn24Ca4 alloy on the isothermal annealing temperature. The research showed high stability of the amorphous structure of Mg72Zn24Ca4 alloy at human body temperature.

Dynamics of Supramolecular Crystal Growth at the Liquid–Solid Interface Studied via Scanning Tunneling Microscope and the Avrami Equation

We report the study of supramolecular assembling from both experimental and theoretical points of view. A scanning tunneling microscope (STM) and the Johnson–Mehl–Avrami (JMA) equation were, respectively, used to reveal and to explain the “STM-directed” self-assembling of p-terphenyl-3,5,3′,5′-tetracarboxylic acid (TPTC) at the liquid–solid interface. The Avrami index helps in providing significant information regarding the surface supramolecular crystalline framework. It also helps us to calculate the domains of crystal growth, to distinguish the crystal development to be homogenous or heterogeneous, as well as to identify the dimension of the crystal growth. The JMA equation was also used to evaluate whether (i) the close-packing crystal of TPTC can develop into a single crystal or (ii) the porous networks of TPTC may hinder the close packing to form during its progression.

Metallurgical Coke Gasification by Carbon Dioxide under Nonisothermal Conditions: A Kinetic Study.

Metallurgical coke gasification by carbon dioxide was kinetically investigated through the use of thermogravimetric analysis under nonisothermal conditions. The results showed that the activation energy, gained by the Cai–Chen iterative model-free method, was estimated to be 183.15 kJ·mol–1. Notwithstanding, the mechanism function f(α) cannot be directly determined due to the fact that f(α) and the pre-exponential factor Aα were lumped together as [Aαf(α)]; this situation may be tackled by means of the master-plot methods. The most probable mechanism function, determined by the Málek master-plot method (based on Z(α) master plots), was discovered to be the Johnson–Mehl–Avrami equation. The usefulness of the compound kinetic calculation technique founded upon complemental application of the Málek master-plot and Cai–Chen model-free methods in estimating reaction kinetics of metallurgical coke gasification was verified. The comparison between original and reconstructed kinetic curves judged the accuracy of the gained kinetic parameters. By means of gained nonisothermal kinetic results, the forecasting of kinetic curves in isothermal as well as nonisothermal conditions was performed. In this work, new kinetic equations were presented and applied to reproducing and forecasting kinetic curves.

The precipitation behavior and its effect on mechanical properties of cold-rolled super-ferritic stainless steels during high-temperature annealing

The precipitation behavior, microstructure evolution and mechanical properties of a cold-rolled 27.6Cr–3.7Mo–2Ni ferritic stainless steel during high temperature annealing treatment were investigated. Experimental results demonstrated that the cold rolled microstructure was characterized by orientation-dependent heterogeneity, and many shear bands were found in the <111>//ND (normal direction) orientation grains. The elongated deformation microstructure gradually changed into equiaxed grains and three kinds of interphases including σ-phase, χ-phase and Laves phase were observed as the annealing temperature increased from 850 to 1000 °C. After annealing below 1000 °C, the σ-phase and χ-phase were observed to be located at grain boundaries, near the TiN particles as well as along with shear bands in grains, whereas the Laves phase distributed dispersedly in grains. After annealing at 1000 °C, both the σ-phase and χ-phase were almost completely dissolved, while the nanoscale Laves phases at grain boundaries were dominant. The grain boundary Laves phase precipitation at high temperature was attributed to the Nb segregation induced by cold rolling deformation. The σ-phase precipitation kinetics was calculated based the Johnson–Mehl–Avrami equation, and the fastest precipitation kinetics appeared at 850 °C with the activation energy of ~176.7 kJ·mol−1. The Vickers hardness, ultimate tensile strength and yield strength values decreased while the elongation value increased with increasing annealing temperature. The breakage pattern transformed from brittle to ductile fracture as the annealing temperature increases from 850 to 1000 °C.

Isothermal and non-isothermal crystallization kinetics of novel metalloid-bearing light rare-earth-based La64Al26Ga4C6 metallic glass with high thermal stability

The crystallization kinetics of a novel metalloid-bearing light rare-earth (RE)-based La64Al26Ga4C6 metallic glass (MG) under isothermal and non-isothermal conditions were systematically researched by Johnson-Mehl-Avrami (JMA), Arrhenius, Kissinger, Ozawa, Kissinger-Akahira-Sunose and Ozawa-Flynn-Wall approaches using differential scanning calorimeter. The present MG possesses higher thermal stability than other light RE-based MGs without metalloid. As the isothermal crystallization temperature increases, the Avrami exponent estimated by JMA equation ranges from 2.36 to 2.94, implying that the isothermal crystallization mechanism varies from a three-dimensional diffusion-governed growth with a decreasing nucleation rate to a three-dimensional diffusion-governed growth with an increasing nucleation rate. Meanwhile, the apparent activation energy determined by Kissinger and Ozawa methods for characteristic temperatures indicates that glass transition is more difficult than crystallization process. Additionally, the local Avrami exponents show various trends, implying a transformable crystallization mechanism with crystallization proceeding. Furthermore, the crystallization process becomes easier due to the decrease of local activation energy.

Coupling solidification kinetics with phase-behavior computations in hydrodynamic simulations of high-pressure, dynamic-compression processes

In this study, we report a numerical scheme to integrate models for the kinetics of solidification processes together with phase-behavior computations in the context of continuum-scale hydrodynamic simulations. The objective of the phase-behavior computations is to determine the pressure and temperature, given the following three sets of inputs: (1) an appropriate equation of state to describe our system, (2) the phase fraction(s) produced by the kinetic models, (3) and the volume and internal energy obtained by solving the conservation equations that govern the hydrodynamic behavior. The kinetics are assumed to be governed by the Kolmogorov–Johnson–Mehl–Avrami equation, and the nucleation and growth rates that enter into that equation are functions of the pressure and temperature produced by the phase-behavior computations. Our formulation allows for the fluid and solid phases to be at different temperatures (thermal nonequilibrium) and pressures (arising from surface-tension-induced Laplace contributions). The formulation is presented in a fairly general setting that is independent of any particular material, although we demonstrate it in some examples related to high-energy-density science applications where materials are rapidly compressed to pressures exceeding several gigapascals in less than a microsecond. We conclude with a critical evaluation of our approach and provide suggestions for future work to improve the predictive capabilities and generality of the models.

Viscosity and crystallisation behaviour of coal ash slag from the primary phase of anorthite

To achieve a stable slag-tapping process in entrained-flow coal gasifiers, the acceptable viscosity of coal ash slag is within 5–25 Pa·s in the temperature range 1200–1500 °C and the tapping temperature should be above the temperature of critical viscosity (Tcv) to avoid massive crystallisation. In general, coal slag from anorthite primary phase field can meet these requirements. In this work, we determined the viscosity, phase composition and crystallisation behaviour of synthetic coal slag from anorthite primary phase field using a high-temperature viscometer, thermodynamic modelling and microstructural analysis. On the basis of our results, we identified the optimal model for predicting the viscosity of fully liquid slag, and proposed a new empirical equation to predict Tcv. This has enabled us to develop a viscosity model for partially crystalline slag with the considered anorthite aspect ratio. Finally, we evaluated the isothermal crystallisation kinetics of anorthite using a modified Kolmogrorov–Johnson–Mehl–Avrami equation, and determined the effects of liquid viscosity, degree of supercooling, theoretical solid content, iron oxidation and alkali oxides on these kinetics. Based on the above results, we present here a comprehensive method for predicting the viscosity and crystallisation behaviour of slag from the anorthite primary phase field.

Development of Sheet Metal Forming Analysis Incorporating Phase-transformation Model for Hot Stamping

To predict the spring back after hot stamping of sheet metals, a user material routine incorporated with phase transformation effects has been developed and implemented in general-purpose commercial finite element software. The mechanical response of the metallographic structure incorporates variation of transformation plastic strain and transformation volume expansion. Additionally, the thermal response incorporates the dependencies of thermal properties and latent heat of phase transformation. The start timing of diffusive transformation was determined using Scheil’s law, and the Kolmogorov–Johnson–Mehl–Avrami equation was adopted for the progression of diffusive transformation. The Koistinen and Marburger equation was used for the progression of martensite transformation. Using the developed model, we considered the effects of phase transformation on shape fixability. We conducted experiments that focused on measuring the shape fixability of U-bend hot formed parts. In this study, we show that the spring back of the U-bend parts increases under conditions in which phase transformation occurs before formation has been completed. Furthermore, the spring back could accurately predict by using the developed model.

A Simple Mathematical Model for Establishing Isothermal Transformation Kinetics from Continuous Cooling Data

A simple mathematical model for establishing isothermal transformation kinetics from continuous cooling transformation data is presented. A new regression function of k, which is a reaction parameter of the Johnson–Mehl–Avrami equation, is proposed. The isothermal transformation kinetics of austenite-pearlite transformation in a eutectoid steel is converted from continuous cooling transformation data using the regression function in combination with the inverse additivity rule. The converted isothermal transformation kinetics excellently agrees with experimental results irrespective of temperature.

Morphology characterization of films from albumin and erythrosine dye: Effect of experimental procedures

In this study, we prepared layer-by-layer (LbL) films from erythrosine (ERY) dye alternated with bovine serum albumin (BSA). BSA was chosen because is a model protein, and due to ability to bind with organic and inorganic molecules and transport various substances in the blood. ERY is typically used in foodstuffs, cosmetics, textiles, and medicine. It has been associated with health problems such as hyperactivity, asthma, and thyroid cancer. Dyes and other bioactive molecules bind to albumin; consequently, they contribute significantly to dye–protein interactions. The adsorption of erythrosine was monitored by UV–Vis spectrophotometry. Adsorption kinetics was fitted with the Johnson–Mehl–Avrami equation and the surface morphology of the films was investigated by atomic force microscopy. The concentration, pH, and temperature of solutions, analyzed using scaling laws, are key factors affecting the morphology of the films. The morphology of the films depends on the preparation procedures, which changes the wettability of the films. The successful preparation of LbL films from BSA and ERY demonstrates the suitability of this technique for building films of biomolecules and dyes and its strong dependence on experimental factors.

Crystallization kinetics of Cu60Zr25Ti15 and (Cu60Zr25Ti15)95Ni5 bulk metallic glasses by differential scanning calorimetry (DSC)

Amorphous structures of the as-cast bulk metallic glass samples (BMGs) of Cu60Zr25Ti15 and (Cu60Zr25Ti15)95Ni5 alloys are confirmed by X-ray diffraction. Isothermal crystallization kinetics of these BMGs are investigated using differential scanning calorimetry. For both the alloys, the apparent activation energy (Ea) shows a strong dependency on crystallization volume fraction (x). Isothermal crystallization kinetic parameters are calculated by Arrhenius and Johnson–Mehl–Avrami equations. Avrami exponential factor (n) is also found to show clear correlation with the crystallization volume fraction (x). It is found that the crystallization process is easier in Cu60Zr25Ti15 BMG than in (Cu60Zr25Ti15)95Ni5 BMG as the Ea decreases constantly for the former alloy though in the case of second alloy, the Ea is almost unchanged up to x = 60%. For both the alloys, nucleation activation energy (Enucleation) is found to be higher than that of growth activation energy (Egrowth). This indicates that the growth of crystals during isothermal crystallization in these glasses is easier than nucleation, and the minor addition of Ni causes the higher thermal stability against crystallization in isothermal condition.

Minor alloying upon non-isothermal crystallization kinetics of a Cu-based bulk metallic glass: a comparative investigation

This paper reported the alloying effects in the non-isothermal crystallization of as-cast bulk metallic glasses. Three kinds of Al, Ni and Si elements with minor quantity of 0.5 at% were individually added into a base Cu55Zr37Ti8 bulk metallic glass. Differential scanning calorimetry was utilized to characterize the crystalline processes during heating, and Johnson–Mehl–Avrami equation was adopted to determine and evaluate the crystallization kinetic parameters. The results disclose that alloying processing with 0.5 at% of Al, Ni and Si elements altered the crystallization kinetic behaviors. Alloying with 0.5 at% of Ni performs more remarkable constraint on the nucleation and growth of the crystallization with regard to alloying with the same quantity of Al and Si elements in the base bulk metallic glass and favors the suppression of crystallization.

Study on the Influence of Prior Cold Work on Precipitation Behavior of 304HCu Stainless Steel During Isothermal Aging

The precipitation strengthening behavior of 304HCu austenitic stainless steel during isothermal aging at 650 °C is studied under 10 and 20 pct prior cold-worked conditions. The age hardening behavior under these cold-working conditions have been studied using hardness and electrical conductivity measurements. The analysis of electrical conductivity and hardness variation, during isothermal aging at 650 °C using the Johnson–Mehl–Avrami equation, indicates an increase in precipitation kinetics in the matrix, influenced by the dislocations formed during cold working. Further, XRD profiles of different cold-worked samples obtained from the INDUS-2 synchrotron are able to indicate the formation of very fine precipitates during thermal aging and these findings are corroborated with conductivity and hardness changes. The observed change in precipitation kinetics due to deformation is analyzed to evaluate an equivalent change in activation energy which is attributed to an equivalent of increase in aging temperature.

Numerical Simulation of Residual Stress for Laser Welding of Ti-6Al-4V Alloy Considering Solid-State Phase Transformation

In the present work, a thermal-metallurgical-mechanical model which considered the influence of phase transformation was used to predict the residual stress field of Ti-6Al-4V after laser welding. In this model, the Johnson–Mehl–Avrami equation was used to predict diffusional solid-state phase transformations: α phase to β phase during heating and β phase to α phase during cooling. The Koistinen–Marburger equation was used to predict diffusionless solid-state phase transformation of β phase to martensite during cooling. The properties of material were obtained using a mixing rule based on the phase fraction and the property of each pure phase. By applying this model, the effect of solid-state phase transformations of Ti-6Al-4V alloy on temperature field and stress field during laser welding was considered in the simulation. In addition, experiments were carried out for comparison, which significantly verified the accuracy of the applied model.

Crystallization, non-isothermal kinetics and structural analysis of nanocrystalline multiferroic bismuth ferrite (BiFeO3) synthesized by combustion method

The synthesis of bismuth ferrite (BiFeO3) in the nanocrystalline form is described in the present work with the help of self-combustion technique with DL-malic acid as fuel to obtain single-phase BiFeO3 nanopowders. The crystallization behavior for the formation of BiFeO3 was confirmed from the obtained powder diffraction pattern (p-XRD) and thermogravimetric analysis with simultaneous differential thermal analysis. Thermal measurements were carried out in the nitrogen atmosphere to determine the crystallization kinetics through various heating rates from simultaneous thermogravimetric–differential thermal (TG–DTA) analysis curve. The activation energies for the formation of BiFeO3 metal oxides formation were found to be around 124 kJ mol−1 and 113 kJ mol−1 from the phenomenological Johnson–Mehl–Avrami equation or in short JMA. The growth mechanism along three dimensions was observed for all heating rates. The formation of single-phase BFO in nanocrystalline nature was confirmed through microstructural investigations by the use of transmission electron microscopic analysis. The selected area electron diffraction pattern of nanostructure bismuth ferrite for the sample calcinated at 800 °C reveals the diffraction miller indices planes {104} and doublet peaks of {110}, {202} which is in good agreement with that of the present powder XRD pattern. The magnetization for the synthesized samples calcinated indicates that there exists the magnetic order and existence of room-temperature magnetic saturation for the multiferroic BiFeO3.

Microstructure and hydrogen storage properties of V48Fe12Ti15-xCr25Alx (x=0, 1) alloys

The microstructure and hydrogen storage characteristics of V48Fe12Ti15-xCr25Alx (x = 0, 1) alloys prepared by vacuum arc melting were studied by X-ray diffraction, scanning electron microscopy, transmission electron microscopy, and pressure–composition isotherm measurements. It was confirmed that all of the alloys comprise a BCC phase, a Ti-rich phase, and a TiFe phase. Al as a substitute for part of the Ti content caused an increase of lattice parameters of the BCC phase and of the equilibrium pressures of hydrogen desorption, but decrease of the hydrogen storage capacities. The kinetic mechanism of the hydrogenation and dehydrogenation of the alloys was investigated by the classical Johnson–Mehl–Avrami equation. The reaction enthalpies (ΔH) for the dehydrogenation of alloys without and with Al were calculated by the Van't Hoff equation based on the PCI measurement data, which are 30.12 ± 0.14 kJ/mol and 28.02 ± 0.46 kJ/mol, respectively. The thermal stability of the metal hydride was measured by differential scanning calorimetry. The hydrogen desorption activation energies were calculated using the Kissinger method as 79.41 kJ/mol and 83.56 kJ/mol for x = 0 and 1, respectively. The results suggest that the substitution of titanium with aluminum improves the thermodynamic properties of hydrogen storage and reduces the kinetic performance of hydrogen desorption.