Johnson Mehl Avrami Kolmogorov Model Research Articles

Non-isothermal nanocrystallization of Fe83.3Si4B8P4Cu0.7 (NANOMET®) alloy: modeling and the heating rate effect on magnetic properties

The kinetics of the nanocrystallization of a Fe83.3Si4B8P4Cu0.7 amorphous alloy by using differential scanning calorimetry has been investigated by non-isothermal annealing in a wide heating rate range from 10 °C min−1 to 200 °C min−1. The amorphous alloy was prepared by melt-spinning and showed a two-stage crystallization. In the first crystallization stage, α-Fe nanocrystals are formed. This phase is responsible for the good soft magnetic properties. The activation energy during the crystallization of the α-Fe nanocrystalline phase was determined from an isoconversional approach, and was found to be distinctively varying during the crystallization. An attempt was made to model the crystallization in an interval where the activation energy is relatively constant. The Malek criterion indicated that the Kolmogorov–Johnson–Mehl–Avrami model is not appropriate, whereas the Sestak–Berggren model meets the criterion. The acquired model shows good agreement with the experimental results. The magnetic properties of annealed ribbons at different heating rates show an initially steep decrease of the coercivity (Hc) from 82 A m−1 at a heating rate of 10 °C min−1 to 20 A m−1 above 100 °C min−1, whereas saturation magnetization (Ms) is practically invariant at ca 175 Am2 kg−1. This dependence is explained as due to diminishing grain size with higher heating rates, which is further supported by x-ray diffraction measurements.

Sinter-crystallisation kinetics of a SiO2–Al2O3–CaO–MgO–SrO glass-ceramic glaze

This paper examines the microstructural development and kinetics of the sintering and crystallisation processes of a SiO2–Al2O3–RO (R = Ca, Mg, Sr) glass-ceramic glaze. Crystallisation and sintering kinetics were studied by DTA and HSM, respectively, at different heating rates. The kinetic parameters of crystallisation were determined by the usual methods (Kissinger, Kissinger-Akahira-Sunose, Ozawa and Augis-Bennet methods), and the Johnson–Mehl–Avrami–Kolmogorov (JMAK) model, with an Avrami index of n = 3, characteristic of the surface crystallisation of very fine glass particles, was found to describe crystallisation kinetics very well. Sintering could also be described by the JMAK model, but with n < 1. Assuming the effect of temperature on the sintering rate to be the same as that of this variable on the inverse of glass matrix viscosity, a model was developed, based on the JMAK model, which only required a single fitting parameter. As the heating rate increased, the degree of overlap between the sintering and crystallisation processes was verified to decrease.

Crystallization kinetics of gehlenite glass microspheres

The glass of gehlenite composition was prepared by flame synthesis in the form of microspheres. The powder precursor was synthesised by standard solid-state reaction method using SiO2, Al2O3 and CaCO3. The prepared glasses were characterized from the point of view of surface morphology, phase composition and thermal properties by optical microscopy, scanning electron microscopy (SEM), X-ray diffraction (XRD) and differential scanning calorimetry (DSC), respectively. The prepared samples contained only completely re-melted spherical particles. SEM did not reveal any features indicating the presence of crystalline phases. However, traces of crystalline gehlenite were detected by XRD. The high-temperature XRD measurements (HT XRD) were carried out to identify the phase evolution during glass crystallization. In the studied temperature range, gehlenite phase was identified as the main crystalline phase. Non-isothermal DSC analysis of prepared glass microspheres was carried out from room temperature up to 1200 °C at five different heating rates: 2, 4, 6, 8 and 10 °C/min to determine the thermal properties of microspheres. In order to study the crystallization kinetics, the DSC curves were transformed into dependence of fractional extent of crystallization (α) on temperature. The Johnson–Mehl–Avrami–Kolmogorov model was found to be suitable for description of crystallization kinetics. Frequency factor A = 5.56 × 1029 ± 1.73 × 1029 min−1, apparent activation energy Eapp = 722 ± 3 kJ mol−1 and the Avrami coefficient m = 2 were determined. In the studied system, the linear temperature dependence of nucleation rate, diffusion controlled crystal growth interface and a 2D crystal growth were confirmed.

Growth behavior of the δ-Ni3Nb phase in superalloy 718 and modified KJMA modeling for the transformation-time-temperature diagram

The δ-Ni3Nb phase is indispensable in achieving the uniform microstructure containing refined grains during the hot-forging process of superalloy 718. The growth behavior of the δ-Ni3Nb phase at temperatures ranging from 1213 to 1283 K was investigated. The heat-treatments were performed in the argon atmosphere, and annealing time for the precipitation of the δ-Ni3Nb phase varies from 10.8 to 93.6 ks. The measurement of the δ-Ni3Nb phase was performed on the backscattered electron (BSE) image. The positive influence of small grain size on accelerating the precipitation process of the δ-Ni3Nb phase was confirmed. The δ-Ni3Nb phase was found to nucleate at grain boundary preferentially, and the evaluation of the δ-Ni3Nb phase strongly depends on the grain size. A grain-size-dependent Kolmogorov-Johnson-Mehl-Avrami (KJMA) equation, ξ=1−exp[−K(T)ρlm∫0tnt1n−1(t−t1)32dt1] where ξ is the transformed phase fraction over the equilibrium fraction, K(T) is the temperature-dependent term, ρl is the length of the grain boundary per unit area, m is a constant, t is the time in second, and n is a nucleation index, was used by considering proper nucleation and growth behaviors. The predicted TTT curve agrees well with the reported experimental data. The presently proposed KJMA model and plotted TTT curve provide the valuable information for the microstructure control of superalloy 718, accelerating the development of superalloy 718.

Inverse identification of tungsten static recrystallization kinetics under high thermal flux

Understanding of recrystallization phenomenon is essential to apprehend damage process of tungsten armored plasma facing components and to optimize their use in tokamak environment. In ITER, plasma facing components will reach extreme surface temperature value up to 2000 °C. Up to now, recrystallization kinetics of ITER tungsten grade were investigated from 1150 °C to 1350 °C. In order to understand tungsten recrystallization process on the wider relevant temperature range, kinetics have to be investigated at higher temperature and on several tungsten grades. Usually, kinetics are investigated by performing successive isothermal annealings on tungsten samples. Due to number of ITER tungsten grades and large temperature range (from 500 °C to 2000 °C), an important amount of tungsten samples have to be prepared to investigate recrystallization kinetics on ITER representative conditions. In this paper, an innovative way is proposed to obtain recrystallization kinetics of ITER tungsten grade based on the use of small-scale plasma facing component tested under high heat flux. Thanks to the use of this inverse method, tungsten recrystallization kinetics are identified at 1348 °C±29, 1480 °C±29, 1586 °C±28 and 1696 °C±27 by using experimental measurements and Johnson–Mehl–Avrami–Kolmogorov model. Then, obtained kinetics are used as input data in numerical post-treatments to obtain tungsten recrystallization gradients after 500 thermal cycles at 20 MW/m2.

Study of AlSi7Mg0.6 Alloy by Selective Laser Melting: Mechanical Properties, Microstructure, Heat Treatment

This study presents a panorama of the AlSi7Mg0.6 (A357) aluminum alloy in additive manufacturing by selective laser melting. The document is mainly interested in the metallurgical tempers obtained after manufacture and after heat treatment; it quickly cover the process. The results concerning the material integrity (porosity), mechanical properties, microstructures, residual stresses, etc., are presented in order to best define the technological capacities of these metallurgical tempers: as-built, soft annealed, T6, and artificial aging. Some information on the mechanisms and kinetics of precipitation is also presented using the Johnson–Mehl–Avrami–Kolmogorov model. Finally, the conclusion proposes an inventory (advantages/disadvantages) of the metallurgical tempers obtained to better understand the industrial applications.

Study of AlSi7Mg0.6 Alloy by Selective Laser Melting: Mechanical Properties, Microstructure, Heat Treatment

This study presents a panorama of the AlSi7Mg0.6 (A357) aluminum alloy in additive manufacturing by selective laser melting. The document is mainly interested in the metallurgical tempers obtained after manufacture and after heat treatment; it quickly cover the process. The results concerning the material integrity (porosity), mechanical properties, microstructures, residual stresses, etc., are presented in order to best define the technological capacities of these metallurgical tempers: as-built, soft annealed, T6, and artificial aging. Some information on the mechanisms and kinetics of precipitation is also presented using the Johnson–Mehl–Avrami–Kolmogorov model. Finally, the conclusion proposes an inventory (advantages/disadvantages) of the metallurgical tempers obtained to better understand the industrial applications.

Experimental and numerical study on the temperature sensitivity of the dynamic recrystallization activation energy and strain rate exponent in the JMAK model

The temperature dependency of the dynamic recrystallization (DRX) activation energy and strain rate exponent, which are major material properties in the Johnson–Mehl–Avrami–Kolmogorov (JMAK) model affecting the DRX phenomenon, are quantitatively presented in experimental and numerical ways. A finite element analysis-based optimization method was used to acquire the material properties of the JMAK model. The first and second stages of a three-stage hot forging process for a bearing outer race were used to obtain and verify all of the material properties, including the DRX activation energy and the strain rate exponent of the JMAK model, which were assumed to be constants or functions of temperature. The predicted grain size after the third stage obtained with the optimized material properties was compared with the experimental values to validate the acquired material properties and reveal the dependence of the two major material properties on temperature. The comparison showed that the difference between the measured and predicted grain sizes was significantly smaller for temperature-dependent material properties, indicating that the DRX activation energy and strain rate exponent are highly temperature-dependent.

Modeling and Simulation of Nucleation and Growth Transformations with Nucleation on Interfaces of Kelvin Polihedra Network

Nucleation is a phenomenon associated to the start of the new phase, from a primary phase, named matrix. Growth is the increase in size of this new phase over time. In metallic materials, the nucleation may take place on the grain boundaries of the primary phase. A network of Kelvin polyhedra was used in this paper to represent the grains. A computer simulation was performed in which nucleation took places at the faces, edges and vertices of this polyhedral network. The Causal cone method was employed in the simulations. The results of the present computational simulations were compared with the classical Johnson Mehl-Avrami-Kolmogorov (JMAK) as well as with Cahn model for nucleation at the grain boundaries. JMAK theory considers nuclei to be uniform randomly located within the matrix. Cahn analytical model specifies that nucleation takes place on random planes. For a small number of nuclei, the simulations approached the JMAK model whereas as the number of nuclei increased the simulation results agree with Cahn's theory. Reasons for this are fully discussed.

On the possible generalization of JMAK-type kinetic functions

The Johnson-Mehl-Avrami-Kolmogorov (JMAK) kinetic equation is generally used for describing the progress of solid state diffusion-controlled transformations. The traditional JMAK model is applicable for modeling only monophase decomposition (precipitation) processes. This paper deals with possible generalizations of the classical JMAK kinetic model by taking into consideration the simultaneous occurrence of more parallel transformations. It is revealed that the Jones-Bhadeshia kinetic model belonging to the family of the strongly coupled multiphase models has only a limited practical application because it contains only few fitting parameters. Moreover, it has been shown and demonstrated that for predicting decomposition processes it is more advantageous to use a multiphase kinetic model including a finite set of ordinary autonomous differential equations.

Mesoscopic Phase Transition Kinetics in Secondary Particles of Electrode-Active Materials in Lithium-Ion Batteries

Many compounds used as battery storage electrodes undergo large composition changes during use that are accompanied by a first-order phase transition. Most studies of these phase transitions have focused on the unit cell to single-crystallite scale, whereas real battery electrodes are typically composed of mesoscopic assemblies of nanocrystallites, for which phase transformation mechanisms are poorly understood. In this work, a systematic study is conducted of the potentiostatic (constant driving force) kinetics of phase transition in secondary particles of representative intercalation compounds: LiFePO4, LiMn1–xFexPO4, and Li4Ti5O7. Storage kinetics are studied as a function of overpotential, material composition, primary particle size, and temperature. We find that in regimes where phase transformation occurs, the results can be self-consistently explained as nucleation and growth kinetics within the framework of the Johnson–Mehl–Avrami–Kolmogorov model. This implies that despite the common secondary particle topology, the electrochemically driven phase transformations occur by nucleation and growth with little apparent resistance to phase propagation across the grain boundaries. Growth appears to be one-dimensional in nature, consistent with a hybrid growth model in which rapid surface propagation is followed by slower growth into particles.

Dynamic Analysis of Recalescence Process and Interface Growth of Eutectic Fe82B17Si1 Alloy

By employing the glass fluxing technique in combination with cyclical superheating, the microstructural evolution of the undercooled Fe82B17Si1 alloy in the obtained undercooling range was studied. With increase in undercooling, a transition of cooling curves was detected from one recalescence to two recalescences, followed by one recalescence. The two types of cooling curves were fitted by the break equation and the Johnson–Mehl–Avrami–Kolmogorov model. Based on the cooling curves at different undercoolings, the recalescence rate was calculated by the multi-logistic growth model and the Boettinger–Coriel–Trivedi model. Both the recalescence features and the interface growth kinetics of the eutectic Fe82B17Si1 alloy were explored. The fitting results that were obtained using TEM (SAED), SEM and XRD were consistent with the changing rule of microstructures. Finally, the relationship between the microstructure and hardness was also investigated.

Modeling of dissolution kinetics of rare earth crystals in a borosilicate glass melt

The novelty of this work is the comparison of two methods to determine the dissolution kinetics in order to evaluate the applicability of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model for the crystals dissolution in silicate melts. For this, this work focuses on the dissolution of rare earth (RE) silicates (Ca2RE8(SiO4)6O2 where RE=Nd) with an apatite structure in a sodium-borosilicate glass melt. The first approach consists in the characterization of the dissolution kinetics by following the crystalline area fraction by image analysis as a function of time and temperature. Then, a model based on the generalized JMAK equation is proposed to fit the experimental data. This model enables to determine both the mechanism limiting the dissolution (i.e. the diffusion) and the activation energy of crystals dissolution in the studied glass system (496kJ/mol). To support these results, a second and most common approach is the measure of the chemical profiles at the crystal/melt interfaces by microprobe. The conclusions obtained by this last method are in agreement with the conclusions based on JMAK model. All these results allowed to confirm that the JMAK model is well suited to model crystals dissolution in silicate melts.

Turning induced residual stress prediction of AISI 4130 considering dynamic recrystallization

ABSTRACTMachining-induced residual stress distribution is strongly influenced by the machining process condition, tool geometry and workpiece material mechanical properties. The high temperature, large strain and high strain rate environment will promote the material micro-structural attribute changes. The material micro-structural attribute changes could directly affect the material mechanical properties. An analytical model is proposed for the residual stress prediction in the orthogonal turning by considering the material dynamical recrystallization induced grain growth effect. The grain size effect on the material flow stress behavior is included by adding a grain size dependent term into the traditional Johnson–Cook model. The Johnson–Mehl–Avrami–Kolmogorov model calculates the recrystallized volume fraction and grain size as a function strain, strain rate and time. The average grain size is calculated with a rule of mixture by volume. Then the modified Johnson–Cook model is embedded into a classic residual stress prediction model for the machining induced residual stress profile prediction on the machined workpiece surface. Experimental tests are conducted for the model validation. The predicted residual stress shows good approximation with the measurement in both the trend and magnitude of the residual stress. Also, the effects of cutting speed and feed rate on the residual stress profile are investigated.

Crystallization kinetics of glass microspheres with yttrium aluminium garnet (YAG) composition

A combination of sol–gel Pechini method and flame synthesis was used to prepare yttrium aluminate glass microspheres with the garnet composition (YAG, 62.5 mol% aluminium oxide, 37.5 mol% yttrium oxide). Prepared glass microbeads were studied by optical microscopy, SEM, X-ray diffraction (XRD), differential scanning calorimetry (DSC) and high-temperature (HT) XRD analysis. Formation of YAG as the only crystalline phase was observed during HT XRD experiment in the temperature interval (750–1200 °C), with the onset of YAG phase crystallization in the temperature interval 860–870 °C and most prominent increase in the YAG phase content between 905 and 910 °C. The experimental data obtained by DSC analysis and the Johnson–Mehl–Avrami–Kolmogorov model were used for determination of crystallization behaviour of the studied system. The frequency factor A = 5.2 × 1048 ± 9.6 × 1048 min−1, apparent activation energy E app = 1100 ± 10 kJ mol−1 and the Avrami coefficient m = 4 were determined. The linear temperature dependence of nucleation rate, reaction-controlled crystal growth interface and a 3-D crystal growth were confirmed in the studied system.

Residual stress prediction for turning of Ti-6Al-4V considering the microstructure evolution

An analytical model for residual stress prediction considering the effects of material dynamic recrystallization under process-induced mechanical and thermal stresses is proposed. The effect of microstructure evolution on residual stress generation during the turning process is considered. The Johnson–Mehl–Avrami–Kolmogorov model is used to calculate grain size evolution due to thermal mechanical effects in the machining process. A modified Johnson–Cook flow stress model is developed by introducing a material grain growth–induced softening term. The classic Oxley’s cutting mechanics theories are implemented for machining forces calculation. A hybrid algorithm accounting for thermal, mechanical, and microstructure evolution effects is used to predict the residual stress profile on a machined workpiece surface. The proposed method is implemented for the orthogonal turning of Ti-6Al-4V material. Comparison is conducted between the model prediction and the literature measurement residual stress data. The general trend of the machining-induced residual stress on the machining surface is accurately captured by the proposed model. Also, the parametric study is conducted to investigate the effect of rake angle and depth of cut on the residual stress profile.

A revisited Johnson–Mehl–Avrami–Kolmogorov model and the evolution of grain-size distributions in steel

Abstract The classical Johnson–Mehl–Avrami–Kolmogorov approach for nucleation and growth models of diffusive phase transitions is revisited and applied to model the growth of ferrite in multiphase steels. For the prediction of mechanical properties of such steels, a deeper knowledge of the grain structure is essential. To this end, a Fokker–Planck evolution law for the volume distribution of ferrite grains is developed and shown to exhibit a log-normally distributed solution. Numerical parameter studies are given and confirm expected properties qualitatively. As a preparation for future work on parameter identification, a strategy is presented for the comparison of volume distributions with area distributions experimentally gained from polished micrograph sections.

Predicting the Morphology of Perovskite Thin Films Produced by Sequential Deposition Method: A Crystal Growth Dynamics Study

We performed a kinetic analysis of the sequential deposition method (SDM) to investigate how to form perovskite (CH3NH3PbI3) phases, and the effects of processing conditions on the final perovskite morphology. The reaction was found to consist of two periods with distinct kinetics. During the first period, perovskite crystals nucleated on the lead iodide (PbI2) surface, and the reaction proceeded until the surface was completely converted to perovskites. The reaction during this period determined the surface morphology of the perovskites. We were able to extract the value of the rate of the phase transformation during the first period by applying the Johnson–Mehl–Avrami–Kolmogorov model, in which the rate r is related to the average grain size R by R ∝ r–1/3. In this way, r was used to predict the surface morphology of the perovskite under certain processing conditions. During the second period, the remaining lead iodide under the top perovskite layer was converted. Methylammonium iodide (CH3NH3I, MAI) mo...

Phase transformation kinetics of Voronoi cells in space tessellation governed by the Kolmogorov–Johnson–Mehl–Avrami model

On the basis of the Kolmogorov–Johnson–Mehl–Avrami (KJMA) method for space tessellation the kinetics of Voronoi cell filling, by central grain growth, has been studied as a function of the cell size. This is done by solving an integral equation for which a class of solutions is obtained in closed form, where the cell-size probability density is the Gamma distribution function. The computation gives the time evolution of the mean grain size, as a function of cell volume, which is further employed for describing the grain-size probability density function. The present approach is applied to determine, analytically, the exact grain-size distribution function in 1D and the size distributions in 2D and 3D through approximation.

Understanding the isothermal growth kinetics of cdse quantum dots through microfluidic reactor assisted combinatorial synthesis

With the use of a microfluidic-assisted combinatorial reactor, the synthesis of CdSe quantum dots was optimized by varying one parameter at a time, and the isothermal growth kinetics of CdSe quantum dots using various models was analyzed. To understand precisely the nucleation and growth characteristics of CdSe quantum dots (QDs), we synthesized the CdSe QDs using various experimental conditions. Different model equations, like acceleratory growth-time curves, sigmoidal growth-time curves or Johnson-Mehl-Avrami-Kolmogorov (JMAK), acceleratory growthtime curves based on diffusion, geometric model growth-time curves, and nth order growth-time curves were fitted. Among all growth models, the JMAK model with \(\alpha = 1 - {e^{ - {{(kt)}^n}}}\), and n = 1 was the best fitting model with the MATLAB interactive curve-fitting procedure were used. Errors associated with the best-fitting model and statistics for the goodness of fit were analyzed. Most of the models were not as good as the other than the proposed model. The errors associated with the proposed model were minimal, and the growth kinetics and other associated statistical factors are very similar, for all the variables investigated. The minimal error associated with the reproducibility and the similar data for growth kinetics for all studied parameters indicated that microfluidic-assisted combinatorial synthesis can be used in the industrial production of QDs. By using the proposed model to obtain an understanding of growth of QDs, their size and properties can be managed and simulated.