Johnson Mehl Avrami Equation Research Articles

A Novel Approach for Analytical Description of the Isothermal Bainite Transformation in Alloyed Steels

Abstract A novel approach for modeling the bainite transformation in alloyed steels during isothermal quenching is presented. The approach is based on the application of the logistic function with the logarithmic argument of the isothermal holding time. The proposed model involves two time-independent fitting parameters, a and b, where are specified for the given isothermal quenching temperature and other conditions (e.g., steel grade, austenite grain size, etc.). The adequacy of the modeling results is estimated using the sum of squared differences between the experimental and calculated bainite fraction formed at every time step Δτ during isothermal quenching. The logistic function was found to provide a fit between the experimental and calculated bainite transformation kinetics that was up to ten times better than that of the conventionally applied Kolmogorov–Johnson–Mehl–Avrami equation. An excellent agreement is achieved between the modeling results and the experimental data for commercially produced high-strength alloyed steels 300M, HY-TUF, and D6AC isothermally quenched in the temperature range of the bainite transformation. The obtained temperature dependences of the model parameters a and b reveal the potential for further theoretical investigation and verification of their physical meaning.

Effect of Co on the microstructure evolution of modified HR3C austenitic heat-resistant steels during long-term ageing

ABSTRACTThe modified HR3C austenitic heat-resistant steels were aged at 650°C and 700°C for up to 3000 h. The effect of Co on microstructure evolution during long-term ageing was investigated using scanning electron microscope and transmission electron microscope. The experimental results showed that a large amount of σ phase precipitated within the grain during long-term ageing. The growth and coarsening of the σ phase were greatly influenced by the temperature. The variation of micro-hardness can be well understood in terms of volume fraction of the σ phase. The activation energy of forming σ phase was calculated by the Johnson–Mehl–Avrami equation and Arrhenius equation. It was found that Co addition can suppress the precipitation of the σ phase. The related mechanism of Co effect is discussed.

Kinetics of anatase phase transformation of TiO2 NPs synthesized using controlled hydrolysis technique

Thermal kinetics of TiO2 NPs at varying time and at different temperatures for anatase–rutile phase transition was investigated by Powder XRD diffraction analysis. Decrease in the diffraction intensities of XRD peaks of anatase phase (101) was observed from 900 °C onwards, which substantiates the evolution of rutile phase. Isothermal curves of transformed rutile mass fraction as a function of varying time were investigated at 925 °C and 950 °C and the data were fitted using Johnson–Mehl–Avrami equation. Thermal behavior of nanostructured TiO2 was characterized using thermogravimetry and differential analyses. In addition, specific heat capacities of the synthesized TiO2 NPs at higher temperature range were reported. By recapitulating the results, we indicate that TiO2 NPs synthesized by controlled hydrolysis technique prolongs the transition state and it can be concluded that interfacial nucleation and growth site improvements are accomplished by activation energy. Activation energy calculated for varying time derivatives was found to be 39 kcal/mol, 64 kcal/mol and 175 kcal/mol.

Correlation Between the Pitting Potential Evolution and $$\varvec\sigma$$ σ Phase Precipitation Kinetics in the 2205 Duplex Stainless Steel

The aim of this work is to correlate the pitting potential (Epit) evolution with the kinetics of σ phase precipitation in the 2205 duplex stainless steel aged at 850 °C after solution treatment at 1150 °C. The potentiodynamic polarization curves indicate a reduction of the pitting corrosion resistance with the aging time, which is revealed by a decrease in the Epit values from 0.65 to 0.40 VSCE. Thus, Epit values are used to determine the kinetics parameters of the σ phase precipitation. The experimental transformed fraction agrees well with the one calculated by using the modified Kolmogorov–Johnson–Mehl–Avrami equation with an impingement parameter c = 0.6.

Prediction of properties distribution of 7B50 alloy thick plates after quenching and aging by quench factor analysis method

In the present work, continuous cooling curves were accurately measured by the modified Jominy specimen of 7B50 alloy during water-spray quenching tests. Besides, the time–temperature–properties (TTP) curves of this alloy were obtained during isothermal treatments. Based on the accurate cooling curves and TTP curves, the hardness distribution along the thickness direction of 7B50 alloy thick plates was predicted by quench factor analysis method. It is found that the quench sensitive temperature range of 7B50 alloy is 240–410 °C, the nose temperature is 335 °C, and the incubation period at the nose temperature is about 0.87 s. When 7B50 alloy was isothermal treated at 180–400 °C after solid solution treatment (470 °C for 1 h followed by 483 °C for 2 h), the exponent (n) in the Johnson–Mehl–Avrami equation is close to 1 until transformed fraction of new precipitates is up to 60%, indicating that new precipitates first grow into rodlike shape and then coarsen or thicken. When the distance is less than 65 mm from the spray quenching surface of the modified Jominy specimen, the deviation between the predicted and measured hardness is less than 2.7%, confirming the quench factor analysis method as the feasible way to predict the hardness distribution along the thickness direction of 7B50 alloy thick plates. When the distance from the spray quenching surface is 25 mm, the average cooling rate in quench sensitive temperature range is 9.93 °C·s−1, while the quench factor (τ) is 9.89 and the corresponding predicted hardness is HV 185.1 equivalent to 97.3% of the maximum measured hardness of 7B50 alloy in T6 temper.

Non-isothermal crystallization kinetics and fragility of Zr56Co28Al16 and Zr56Co22Cu6Al16 bulk metallic glasses

The role of substitution of Cu for Co on the non-isothermal crystallization kinetics and fragility of Zr56Co28Al16 and Zr56Co22Cu6Al16 bulk metallic glasses (BMGs) were evaluated by differential scanning calorimetry (DSC). The X-ray diffraction, transmission electron microscopy and microhardness test were used to investigate the glassy alloys structure. DSC results exhibited two crystallization processes for both BMGs. All the characteristic temperatures except glass transition temperature of parent alloy were more sensitive to heating rate than those of Cu containing alloy. The activation energies of characteristic temperatures were obtained by Kissinger and Ozawa methods. The results showed that the activation energy of glass transition decreased and the other activation energies increased with Cu addition. Also, the local Avrami exponents at various heating rates were calculated by the Johnson–Mehl–Avrami equation. The n value variations for each crystallization process were in almost similar trends for both BMGs. The results demonstrated that the transformation kinetics is dominated by diffusion-controlled three-dimensional growth with increasing nucleation rate for the first crystallization process and also for initially stage of the second crystallization process. However, the crystallization is dominated by interface-controlled three-dimensional growth with increasing nucleation rate at final stage of the second crystallization processes. In addition, both BMGs were classified into “strong glasses”, depending on the calculated values of fragility index.

The effect of Fe doping on the crystallization kinetics of Ni-Mn-Sn free-standing alloy thin films

The exploration of Fe doping on crystallization behavior of Ni-Mn-Sn alloy thin films is crucial for its application, but remains unknown. Here, we investigated the effect of Fe doping on the crystallization kinetics of Ni-Mn-Sn free-standing alloy thin films by differential scanning calorimetry (DSC) in the mode of non-isothermal and isothermal conditions. In the case of non-isothermal crystallization, it is found that the crystallization peak temperatures of Ni50−xMn39Sn11Fex (x = 0, 0.5, 2, 4) free-standing alloy thin films increase with increasing Fe content. The apparent activation energy from the amorphous state to crystallization which determined by Kissinger's method increase with increasing Fe content. The local activation energy is determined by Doyle method. In the case of isothermal crystallization, the crystallization kinetics was modeled by the Johnson–Mehl–Avrami equation. The Avrami exponents were calculated to be in the range of 1 to 1.5. The local Avrami exponents indicating that the crystallization mechanism of Ni50−xMn39Sn11Fex (x = 0, 0.5, 2, 4) free-standing thin films is all from diffusion-controlled one-dimensional growth to diffusion-controlled two-dimensional and three-dimensional growth.

Bake hardening behavior and precipitation kinetic of a novel Al-Mg-Si-Cu aluminum alloy for lightweight automotive body

The natural aging (NA) phenomena and its negative effect on bake hardening (BH) response, and a wide temperature/time range of pre-aging (PA) treatment on a novel Al-Mg-Si-Cu automotive aluminum alloy were investigated systematically by micro-hardness measurement, tensile test, transmission electron microscopy (TEM) and differential scanning calorimetry (DSC) analysis. The precipitation kinetic of main strengthening β″ phase was calculated according DSC curves based on JMA (Johnson-Mehl-Avrami) equation. The results indicate that artificial aging (AA) immediately after solution treatment is helpful to achieve good BH response, while aging temperature and time determine the value and arrival time of peak hardness. BH value is decreased with increase of NA time. BH value is ranging from 40 MPa to 110 MPa after different PA treatment, and the optimal one is obtained while PA at 160 °C for 10 min. The precipitation activation energy of β″ phase of T4P state (160 °C/10 min) is reduced about 42 kJ/mol compared to T4 state, which is attributed to the increase of GP region size during PA treatment.

Kinetics of Glass Transition and Crystallization of a Zr40Hf10Ti4Y1Al10Cu25Ni7Co2Fe1 Bulk Metallic Glass with High Mixing Entropy

The kinetics of glass transition and crystallization of a novel Zr40Hf10Ti4Y1Al10Cu25Ni7Co2Fe1 bulk metallic glass (BMG) with high mixing entropy have been studied by differential scanning calorimetry (DSC) and X-ray diffraction (XRD). The continuous DSC curves show five stages of crystallization at lower heating rates (≤ 20 K/min). The activation energies of glass transition were determined by Moynihan and Kissinger methods, while the activation energies of crystallization were calculated utilizing Kissinger, Ozawa, and Boswell models. The crystalline phases corresponding to each crystallization step have been found out. The kinetic fragility of Zr40Hf10Ti4Y1Al10Cu25Ni7Co2Fe1 BMG has also been evaluated. Based on the isothermal DSC curves, the Avrami exponent, evaluated from the Johnson–Mehl–Avrami equation, has been analyzed in detail. The current study reveals that the crystallization behavior of Zr40Hf10Ti4Y1Al10Cu25Ni7Co2Fe1 BMG exhibits characteristics of both the high entropy BMGs and traditional BMGs with a single principal element, leading to its high glass-forming ability.

Kinetics of conversion of brushite coatings to hydroxyapatite in alkaline solution

This work describes the kinetics of conversion of brushite coatings, produced by chemical deposition, to hydroxyapatite. The conversion was performed in alkaline solution at three temperatures: 50°C, 55°C, and 60°C. The evolution of the transformation was assessed by X-ray diffraction, and the phase fractions were determined by Rietveld refinement. The Johnson–Mehl–Avrami equation was applied to the data in order to describe the conversion mechanisms. The value of 42kJ/mol obtained for the conversion activation energy is of the same order as found in similar surface-controlled dissolution processes. The Avrami exponent was n=3.5, which is consistent with an interface-controlled growth of three-dimensional HA crystals with decreasing nucleation rate.

Thermal and structural investigations of xLi2O‐(1−x)Bi2O3 (0.25 ≤ x ≤ 0.35) glasses

AbstractIn this paper, we have studied the nonisothermal and isothermal crystallization kinetics of xLi2O‐(1−x)Bi2O3 (0.25 ≤ x ≤ 0.35) glasses, using differential scanning calorimetry. Both the energies of glass transition and crystallization are estimated, using the Ozawa and Kissinger methods for nonisothermal crystallization. The modified Johnson‐Mehl‐Avrami (JMA) equation is used to estimate the nature of nucleation and crystal growth during the nonisothermal crystallization. The nature of nucleation and crystal growth is also determined by the Sestak‐Berggren model for the non‐isothermal crystallization. On the other hand, the JMA equation describes the diffusion controlled growth of crystallites for isothermal crystallization. Nature of crystal growth is identified by scanning electron micrographs both non‐isothermally and isothermally. In situ low frequency Raman spectra are analyzed to determine the degree of amorphous nature below onset of crystallization temperature for the glasses. Transition from local ordering to high range ordering of BiO6 octahedral units after crystallization is also identified, using Raman susceptibility spectra.

The effect of Ag addition on the non-isothermal crystallization kinetics and fragility of Zr56Co28Al16 bulk metallic glass

The non-isothermal crystallization kinetics and fragility of Zr56Co28Al16 and Zr56Co24Ag4Al16bulk metallic glasses (BMGs) were studied by differential scanning calorimetry (DSC). The X-ray diffraction (XRD), transmission electron microscopy (TEM) and microhardness test were used to investigate the glassy alloys structure. DSC traces exhibited two crystallization processes for both alloys. The activation energies of characteristic temperatures were obtained by Kissinger and Ozawa methods. Also, the heating rate sensitivity of characteristic temperatures was determined. The Ag-bearing Zr-based BMG presented higher activation energies and lower heating rate sensitivity in regard to characteristic temperatures, indicating a higher stabilization of the supercooled liquid, which can be correlated with the existence of strong icosahedral short range order (ISRO) clusters in the structure. In addition, the local Avrami exponents at various heating rates were calculated by the Johnson–Mehl–Avrami equation. The n value variations for each crystallization process pursued almost similar trends for both alloys with n>2.5, revealing that the transformation kinetics is dominated by a diffusion-controlled three-dimensional growth, as well as an increase in the nucleation rate. Moreover, both BMGs were classified into “strong glasses”, depending on the fragility index calculated values.

Recrystallization-Induced Surface Cracks of Carbon Ions Irradiated 6H-SiC after Annealing.

Single crystal 6H-SiC wafers with 4° off-axis [0001] orientation were irradiated with carbon ions and then annealed at 900 °C for different time periods. The microstructure and surface morphology of these samples were investigated by grazing incidence X-ray diffraction (GIXRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). Ion irradiation induced SiC amorphization, but the surface was smooth and did not have special structures. During the annealing process, the amorphous SiC was recrystallized to form columnar crystals that had a large amount of twin structures. The longer the annealing time was, the greater the amount of recrystallized SiC would be. The recrystallization volume fraction was accorded with the law of the Johnson–Mehl–Avrami equation. The surface morphology consisted of tiny pieces with an average width of approximately 30 nm in the annealed SiC. The volume shrinkage of irradiated SiC layer and the anisotropy of newly born crystals during annealing process produced internal stress and then induced not only a large number of dislocation walls in the non-irradiated layer but also the initiation and propagation of the cracks. The direction of dislocation walls was perpendicular to the growth direction of the columnar crystal. The longer the annealing time was, the larger the length and width of the formed crack would be. A quantitative model of the crack growth was provided to calculate the length and width of the cracks at a given annealing time.

Effect of Fe2O3 on the crystallization behavior of glass-ceramics produced from naturally cooled yellow phosphorus furnace slag

CaO–Al2O3–SiO2 (CAS) glass-ceramics were prepared via a melting method using naturally cooled yellow phosphorus furnace slag as the main raw material. The effects of the addition of Fe2O3 on the crystallization behavior and properties of the prepared glass-ceramics were studied by differential thermal analysis, X-ray diffraction, and scanning electron microscopy. The crystallization activation energy was calculated using the modified Johnson–Mehl–Avrami equation. The results show that the intrinsic nucleating agent in the yellow phosphorus furnace slag could effectively promote the crystallization of CAS. The crystallization activation energy first increased and then decreased with increasing amount of added Fe2O3. At 4wt% of added Fe2O3, the crystallization activation energy reached a maximum of 676.374 kJ·mol−1. The type of the main crystalline phase did not change with the amount of added Fe2O3. The primary and secondary crystalline phases were identified as wollastonite (CaSiO3) and hedenbergite (CaFe(Si2O6)), respectively.

Numerical simulation of solute evolution during laser cladding with nickel superalloy powder injection

A transient 3‐D numerical model including heat transfer, solute transport and phase change kinetics is developed for laser cladding with coaxial injection of nickel superalloy powders. The evolution of the temperature and composition distributions of the built‐up layer is investigated. The modified Kolmogorov–Johnson–Mehl–Avrami equation is used for phase change modeling considering non‐homogeneous temperature distribution of the melt pool. The influence of self-consistent heat conduction and phase change kinetics as well as of substrate boundary and soluble impurity atoms on the phase change process is analyzed. The results indicate the influence of solute concentration on the rapid crystallization process and can be used for the clad layer dimensions and microstructure estimation in laser cladding with nickel superalloy powder injection.

Preparation of Al72Ni8Ti8Zr6Nb3Y3 amorphous powders and bulk materials

Amorphous Al72Ni8Ti8Zr6Nb3Y3 powders were successfully fabricated by mechanical alloying. The microstructure, glass-forming ability, and crystallization behavior of amorphous Al72Ni8Ti8Zr6Nb3Y3 powders were investigated by X-ray diffraction (XRD), transmission electron microscopy (TEM), and differential scanning calorimetry (DSC). The isothermal crystallization kinetics was analyzed by the Johnson–Mehl–Avrami equation. In the results, the supercooled liquid region of the amorphous alloy is as high as 81 K, as determined by non-isothermal DSC curves. The activation energy for crystallization is as high as 312.6 kJ·mol−1 obtained by Kissinger and Ozawa analyses. The values of Avrami exponent (n) imply that the crystallization is dominated by interface-controlled three-dimensional growth in the early stage and the end stage and by diffusion-controlled two- or three-dimensional growth in the middle stage. In addition, the amorphous Al72Ni8Ti8Zr6Nb3Y3 powders were sintered under 2 GPa at temperatures of 673 K and 723 K. The results show that the Vickers hardness of the compacted powders is as high as Hv 1215.

Monitoring of cocrystallization of ethenzamide–saccharin: Insight into kinetic process by in situ Raman spectroscopy

In situ monitoring in cocrystallization processes is of great significance in controlling the quality of crystalline active pharmaceutical ingredients. In this work, a mechanism for cocrystallization through solution-mediated phase transformation is revealed whereby ethenzamide (EA) and saccharin (SAC) were selected to study the cocrystallization process in water as well as kinetics by in situ Raman spectroscopy. It is observed that the formation of cocrystal nucleus required a long time, yet the growth time was short. Therefore, we concluded that this solution-mediated phase transformation process is mainly controlled by the nucleation rate. Furthermore, kinetic parameters of the transformation process at different temperatures obtained by using the Johnson–Mehl–Avrami equation indicated that high temperature would increases the nucleation and growth rate K and decrease the induction time. The influence of different operating factors on the transformation process was also studied to better understand the process. Meanwhile, in situ Raman spectroscopy was proved as an effective approach for exploring the mechanism of cocrystallization.

Determination of the Final Microstructure during Processing Carbon Steel Hardening

Numerical analysis of thermal treatment processes is an important issue to be considered by contemporary laboratories dealing with industrial designing in general. Phenomena associated with heat treatment are complex and not yet adequately explained. Improvement in this field of numerical solutions is particularly forced by industry which, striving for deployment of state of the art technologies and reduction of costs, is demanding continuous enhancement of tool thermal treatment. Phase transformations, in particular in cooling processes, involve considerable changes in kinetics that are not always associated with external thermal impact. Analyses of experimental data allowed developing many mathematical models to measure volume fractions of phase transformations in solid state. The Johnson-Mehl Avrami equation and generalised Kolmogorov equation are the two primary models applied in almost all tests evaluating transformation of austenite into ferrite, bainite and martensite. In order to calculate the martensitic phase volume fraction, usually the Koistinen-Marburger equation, or any of its modified formulas, are used.

Non-isothermal phase-transformation kinetics model for evaluating the austenization of 55CrMo steel based on Johnson–Mehl–Avrami equation

In order to attain the distribution of hardness and austenite volume fraction in the induction hardening by the numerical simulation, the dilatometric curves of phase-transformation for 55CrMo steel were tested by the Gleeble-1500D thermal–mechanical simulator at the different heating rates. The volume fraction of austenite was evaluated using the level principle according to these curves. The regression analysis is performed to evaluate some parameters in the non-isothermal Johnson–Mehl–Avrami (JMA) equation. For 55CrMo steel, the phase-transformation activation energy Q=7.264×105J/mol, the phase-transformation kinetic parameters n=1.2303, lnk0=78.7087. Using the JMA equation and the user subroutine developed in the paper, the distribution of austenite volume fraction and the hardness in the surface of the ball screw were obtained by the numerical simulation. The comparison of the calculation results and the experiment results shows that, the simulation results are consistent with the experiment results, the JMA equation and the user subroutine are valid, and the JMA equation can well describe the austenitization of 55CrMo steel.

Isothermal kinetic analysis of the effects of high-energy ball milling on solid-state reaction of Li4Ti5O12

The effects of high-energy ball milling on the solid-state reaction were determined by X-ray diffractometry, scanning electron microscopy, and activation energy calculation, respectively. Isothermal kinetic analysis of solid-state reaction of Li4Ti5O12 was studied using an isothermal thermogravimetric tests. The results indicate that the anatase to rutile transformation of TiO2 and formation of Li4Ti5O12 occur at a lower temperature, because the particle size of raw materials reduced by high-energy ball milling. In contrast to Jader equation, the model based on Johnson–Mehl–Avrami equation shows better linear fitting within temperature interval from 450 to 550°C. The value of the kinetic parameter m is approximate to 0.4, indicating that the formation of products could be a diffusion controlled mechanism. Meanwhile, the activation energy of solid-state reaction decreases from 119.4 to 95.2kJ/mol after high-energy ball milling. Electrochemical tests show that Li4Ti5O12 samples synthesized by high-energy ball milling exhibit better rate capacity and cycle performance.