Johnson Mehl Avrami Kolmogorov Model Research Articles

Preform design to reduce forging load and grain size simultaneously in disk forging of IN718

In this study, we propose a new methodology for designing preform shapes for turbofan blisk and disk forgings of IN718 superalloy using a CNN (Convolutional Neural Network). The objective function of the preform design model is set to minimize grain size and reduce forging load. Various preform shape candidates were generated using NURBS (Non-Uniform Rational B-Splines) curves, defined by points on the target shape outline, and the grain size was calculated through FE (Finite Element) analysis based on the JMAK (Johnson-Mehl-Avrami-Kolmogorov) model to train the CNN model. The preform shapes derived from the proposed load and grain size-aware CNN model were compared and validated against those from previous studies regarding grain size and load reduction. An objective function f, which is capable of quantitatively expressing the load and grain size improvement, was developed for comparison and validation. The results showed an improvement of 19.64% for the blisk and 18.96% for the disk compared to previous studies. This research is expected to significantly contribute to the forging of aerospace components.

The recrystallization behavior of cryo- and cold-rolled AlCoCrFeNiTi high entropy alloy

The present work was conducted on the non-equiatomic Al0·2Co1·5CrFeNi1·5Ti0.3 high entropy alloy (HEA), which was separately subjected to 50% cold- and cryo-rolling. Subsequent annealing was performed within the temperature range of 800–1000 °C to investigate their recrystallization behavior. A partial recrystallization was achieved up to 900 °C for the cold-rolled material, while the cryo-rolled one had shown nearly fully recrystallized microstructure after 800 °C. A significant reduction in grain size from the solution-treated state (∼784 μm) to fully recrystallized state (∼71 μm for cold-rolled and ∼6 μm for cryo-rolled) was observed. A combined XRD and TEM analysis confirms that the cryo-rolled sample exhibits higher dislocation density than the cold-rolled sample, which resulted in faster recrystallization kinetics observed in the former than in the latter. Additionally, the Johnson–Mehl–Avrami–Kolmogorov model was employed to understand the recrystallization behavior.

Kinetic analysis of 2D Mo2C crystal growth via CVD

We investigated the growth mechanism of 2D Mo2C crystals by chemical vapor deposition (CVD) under various time and temperature conditions. The growth kinetics and mechanism of Mo2C on Cu via chemical vapor deposition (CVD) were investigated using a modified Johnson–Mehl–Avrami–Kolmogorov (JMAK) model. To analyze the surface coverage, we employed scanning electron microscopy (SEM) and applied the modified JMAK model to determine the growth rate and activation energy. The growth rate of Mo2C exhibited temperature-dependent behavior, described by the Arrhenius relationship, with an apparent activation energy of 4 eV. The Avrami plot exhibited an exponent of 3 indicating a complex process with nucleation and growth.

(Invited) Operando Observation of Fast Charging in Li-Ion Cells

Fast charging (<15 min) of lithium-ion batteries (LIBs) for electrical vehicles (EVs) is widely seen as the key factor that will greatly stimulate the EV markets, and its realization is mainly hindered by the sluggish diffusion of Li+. To have a mechanistic understanding of Li+ diffusion within LIBs, in this study, structural evolutions of electrodes for a Ni-rich LiNi0.6Mn0.2Co0.2O2 (NMC622) || graphite cylindrical cell with high areal loading (2.78 mAh cm−2) are developed for operando neutron powder diffraction study at different charging rates. Via sequential Rietveld refinements, changes in structures of NMC622 and Li x C6 are obtained during moderate and fast charging (from 0.27 C to 4.4 C). NMC622 exhibits the same structural evolution regardless of C-rates. For phase transitions of Li x C6, the stage I (LiC6) phase emerges earlier during the stepwise intercalation at a lower state of charge when charging rate is increased. It is also found that the stage II (LiC12) → stage I (LiC6) transition is the rate-limiting step during fast charging. The LiC12 → LiC6 transition mechanism is further analyzed using the Johnson–Mehl–Avrami–Kolmogorov model. It is concluded as a diffusion-controlled, 1D phase transition with decreasing nucleation kinetics under increasing charging rates.

Insights into Perovskite Film Formation Using the Hybrid Evaporation/Spin-Coating Route: An In Situ XRD Study

The hybrid evaporation/spin-coating route has been widely used for fabrication of highly efficient fully textured perovskite silicon tandem solar cells and is a promising route for upscaling. Nevertheless, fundamental aspects of the fabrication process such as the kinetics of perovskite crystallization and the influence of the environmental conditions remain uncertain. In this work, we investigate the individual stages of tandem-relevant 1.66 eV bandgap perovskite formation and map the structural evolution from the precursor to the perovskite phase until the degradation phase. We find that the kinetics of these transitions can be tuned by varying the humidity or the temperature during the annealing treatment. Specifically, increasing the relative humidity up to 50% elevates the reaction rate and results in improved perovskite quality. This is directly reflected in the solar cell power conversion efficiency with a 3%abs increment on average. While high annealing temperatures are found to promote large grain size growth and enhanced crystallinity, we observe that above 150 °C the remnant PbI2 precursor compromises film quality. Furthermore, the perovskite formation kinetics is fitted using the Johnson–Mehl–Avrami–Kolmogorov model. The Avrami constant is found in the range 0.66–0.87, indicating a diffusion-controlled one-dimensional growth process with an associated activation energy of 54.49 kJ/mol. Using in situ XRD, this work gives insights on key process parameters to ensure reproducible synthesis of high-quality perovskite films.

Direct comparison of surface crystal growth kinetics in chalcogenide glass measured by microscopy and DSC

AbstractSurface crystallization in fine powder Se70Te30 chalcogenide glass was studied by differential scanning calorimetry (DSC) and optical microscopy. A complex kinetic analysis of these experimental data reveals that the contracting sphere mechanism (R3 model) is the rate determining step of crystal growth, and the conventional Johnson–Mehl–Avrami–Kolmogorov model cannot be used in this case. Moreover, it is clearly shown that the particle size distribution should be considered in crystallization studies. Actually, when the particle size effect is taken into account, the simulated DSC curves for the R3 model agree very well with the experimental data over the entire temperature range. The crystallization kinetics determined from the nonisothermal DSC data are consistent with previously reported isothermal crystallization data for the same powder fraction. The crystal growth rate calculated from isothermal and nonisothermal DSC data agrees very well with the microscopically measured surface and bulk crystal growth rate.

Promotion of thermomechanical processing of 2-GPa low-alloyed ultrahigh-strength steel and physically based modelling of the deformation behaviour

A low-alloyed ultrahigh-strength steel comprising CrNiMoWMnV was designed based on thermodynamic calculations and by controlling the microalloying elements to promote various strengthening mechanisms upon processing. The hot deformation behaviour and mechanism were correlated with the processing parameters, that is, strain rate and temperature. The fine features of the deformed microstructures were analysed using electron backscatter diffraction (EBSD) and MATLAB software, combined with the MTEX texture and crystallographic analysis toolbox. The flow stress behaviour at high temperatures was modelled using the dislocation density-based Bergström's model, which could be applied up to the peak strain. However, the diffusional transformation (i.e. recrystallisation)-based Kolmogorov–Johnson–Mehl–Avrami model has been applied to fit the flow stress over a wide deformation strain. The effective grain size (EGS) of martensite and prior austenite grain size (PAGS) were correlated with the deformation temperature and strain rate. Because the PAGS was significantly refined from 16 μm in the initial microstructure to 6 μm after processing at 850 °C/0.01 s−1, the corresponding martensite EGSs were 1.38 and 1.01 μm, respectively. Therefore, these fine-controlled characteristics of the processed microstructures at high temperatures help to enhance the mechanical properties, such as the strength and toughness, of the designed ultrahigh-strength steel.

Numerical simulation of the nickel alloy microstructure formed in the process of hot fogging

The paper presents a comprehensive analysis of the deformation and thermal states of the Waspaloy alloy billet heated to different initial temperatures of 1100°C and 1150°C and subjected to free upsetting to an average diameter of ~1060 mm at the deformation rate of 100 mm/s. The thermodynamic forces acting on the billet trigger the process of dynamic recrystallization, which is associated with the appearance and growth of low-defect nuclei of new grains instead of the deformed ones. To describe the material microstructure evolution, the phenomenological approach implemented in the DEFORM-2D/3D software package was applied. The simulation was based on the modified Johnson - Mehl - Avrami - Kolmogorov (JMAK) model, whose equations allow calculating the volume fraction of recrystallized material and describing the grain structure transformation of metal alloys. The results of solution of the non-stationary temperature problem are used to construct the temperature fields in the Waspaloy alloy billet during its transportation through air from the furnace to the deforming equipment within 45 seconds and during the subsequent upsetting process. For the latter, the force and strain characteristics, including the force required to complete this process, are determined in the framework of the plastic flow theory, and the characteristics of the grain structure of the nickel alloy, such as the average size of recrystallized grains and their volume fraction, are determined in the framework of the JMAK model. The results obtained by numerical simulation make it possible to substantiate an optimal selection of parameters of billet deformation ensuring the formation of the required material structure.

Growth Mechanism of High-Quality hBN Monolayers on Cu through Chemical Vapor Deposition with Inductively Coupled Plasma

The growth mechanism associated with the nucleation and growth kinetics of hexagonal boron nitride (hBN) on Cu through chemical vapor deposition (CVD) has been studied. A fully covered hBN film with a large grain size has been obtained by lowering the density of the grain boundary during the thermal CVD. The Cu substrate is first annealed under the H2 ambiance in order to efficiently reduce the copper oxide on the surface and promote the Cu surface with the (111) plane. Next, the nucleation and growth kinetics of CVD hBN are investigated by the analysis of scanning electron microscopy (SEM) images and the Johnson–Mehl–Avrami–Kolmogorov model. The hBN growth is overall dominated by nucleation under a low flow rate of H2, while it is initially dominated by grain growth under a high flow rate of H2 and the grain size of hBN can be larger than 25 μm. The competition between nucleation and grain growth is reversed at higher temperatures, resulting from the wavier Cu surface. Furthermore, the hBN film is grown by the inductively coupled plasma-enhanced CVD (ICP-CVD) and its growth mechanism is compared with that of CVD hBN. The growth rate of ICP-CVD hBN is 50 times faster than that of CVD hBN due to more energetic B and N species caused by plasma. The growth mechanism of ICP-CVD hBN without a long incubation time is dominated by nucleation.

Kinetics of the isothermal A2 to sigma phase transformation in Fe-Cr alloy

The transition of the A2 phase with random Fe and Cr atoms distribution to the sigma (σ) phase in Fe-46 wt%Cr alloy during isothermal annealing near 655 and 700 °C is investigated both in the bulk material by in situ neutron diffraction and on the surface of a sample by X-ray diffraction method. Kinetics of the σ-phase formation is quantitatively described with the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model. According to neutron data, the A2 phase fully transformed to σ-phase at 655 °C for 5 h. In X-ray diffraction experiments, the partial A2 to σ transition and subsequent reverse transformation of the σ-phase into the A2 phase are observed, and the probable reason for this phenomenon is discussed. • A2 to σ-phase transition in the Fe-46Cr alloy is studied. • A2 phase completely transformed into the σ-phase in the bulk alloy. • Kinetics of the σ-phase formation is analyzed by JMAK model.

(Digital Presentation) Understanding of Fast Charging in Li-Ion Batteries, an Operando Neutron Diffraction Study

Fast charging (<15 min) of lithium-ion batteries (LIBs) for electrical vehicles (EVs) is widely seen as the key factor that will greatly stimulate the EV markets, and its realization is mainly hindered by the sluggish diffusion of Li+. To have a mechanistic understanding of Li+ diffusion within LIBs, in this study, structural evolutions of electrodes for a Ni-rich LiNi0.6Mn0.2Co0.2O2 (NMC622) || graphite cylindrical cell with high areal loading are developed for operando neutron powder diffraction study at different charging rates. Via sequential Rietveld refinements, changes in structures of NMC622 and Li x C6 are obtained during moderate and fast charging (from 0.27 C to 4.4 C). NMC622 exhibits the same structural evolution regardless of C-rates. For phase transitions of Li x C6, the stage I (LiC6) phase emerges earlier during the stepwise intercalation at a lower state of charge when charging rate is increased. It is also found that the stage II (LiC12) → stage I (LiC6) transition is the rate-limiting step during fast charging. The LiC12 → LiC6 transition mechanism is further analyzed using the Johnson–Mehl–Avrami–Kolmogorov model. It is concluded as a diffusion-controlled, 1D phase transition with decreasing nucleation kinetics under increasing charging rates.

A note on the kinetics of non-isothermal crystallization of polymers

On the kinetics of non-isothermal crystallization of polymers, the reinterpreted Ozawa method proposed in a previous report is studied further to generate valuable information. The Ozawa method is used to investigate the crystallization kinetics with constant temperature scanning rates β and is concerned with the basic formula for apparent crystallinity, from which the true crystallinity is derived using the concept of an extended volume of the Kolmogorov–Johnson–Mehl–Avrami model. The formula is expressed by the temperature scanning rate β and a function of temperature T, βOz(T). This study investigates the temperature derivative of βOz(T), which represents the crystal growth rate in the presence of athermal nucleation from foreign heterogeneities including nucleating agents; this case is applicable to most polymer crystallization processes. The validity of this relationship was verified by comparing it directly to the crystal growth rate in numerical simulations and by comparing it to the crystallization peak and half times of isothermal crystallization for experimental results of poly(butylene terephthalate). This evaluation provides basic information on the crystal growth rate, which is necessary for understanding polymer crystallization. As is well known, the temperature derivative of βOz(T) also corresponds to the function required to derive Nakamura et al. model's suggested equation for polymer processing.

Evaluation of static recrystallization and grain growth kinetics of hot-rolled AZ31 alloy

The static recrystallization/grain growth kinetics of the AZ31 (Mg-3Al-1Zn, wt%) alloy were investigated employing Vickers microhardness and electron backscatter diffraction (EBSD) measurements. The AZ31 alloy was subject to a hot-rolling for 70% of thickness reduction and then annealed at various temperatures (150°C, 250°C, and 350°C) from 5 min to 24 h. First, the static recrystallization kinetics were analysed by means of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model. The results showed that the recrystallization occurred under two regimes both involving their own Avrami exponent/ activation energy. In regime I, the Avrami exponent was found in the range of 1.5-0.35 depending on the annealing temperature and activation energy of 74.1±5.7 kJ×mol-1. In regime II, an identical value of Avrami exponent was found (0.1-0.2) and a very low activation energy of 14.8±0.7 kJ×mol-1 was found for all annealing conditions. Non-random nucleation sites such as shear bands were considered as the main factor responsible for the deviation from the JMAK model. Moreover, the grain growth kinetics was well fitted by the general equation where . Accordingly, Qg = 109± 0.2 kJ×mol-1 which is median between grain boundary diffusion and bulk diffusion values for Mg and its alloys. The derived activation energies were discussed in terms of influencing factors such as solute drag, formation of basal texture, and microstructural heterogeneities like shear bands and twinning.

Advances in Laser Additive Manufacturing of Cobalt-Chromium Alloy Multi-Layer Mesoscopic Analytical Modelling with Experimental Correlations: From Micro-Dendrite Grains to Bulk Objects.

This study presents two analytical models for the laser powder bed fusion (LPBF) process. To begin, the single layer’s dimensions were measured using principal operating conditions, including laser power, laser scanning speed, powder layer thickness, and hatch distance. The single-layer printing dimensions were transformed into multi-layer printing using the hatch distance. The thermal history of the printed layers was used as an input to the Johnson–Mehl–Avrami-Kolmogorov model to estimate the average dendrite grain size. LPBF experiments were conducted for a Cobalt–chromium (Co–Cr) alloy to validate the developed model. The average dendrite grain size was estimated using a scanning electron microscope (SEM) combined with “Image J” software. The Vickers hardness test was performed to correlate the average dendrite grain size and operating conditions. A 10–15% mean absolute deviation was presented between experiments and simulation results. In all samples, a Co-based γ-FCC structure was identified. An inverse correlation was established between the laser power and smaller average dendrite grain, while a direct relationship has been determined between laser scanning speed and average dendrite grain size. A similar trend was identified between hatch distance and average dendrite grain size. A direct link has been determined between the average dendrite grain size and hardness value. Furthermore, a direct relationship has connected the laser volume energy density and hardness value. This study will help experimentalists to design operating conditions based on the required grain size and corresponding mechanical characteristics.

Structural Evolution and Transition Dynamics in Lithium Ion Battery under Fast Charging: An Operando Neutron Diffraction Investigation.

Fast charging (<15 min) of lithium‐ion batteries (LIBs) for electrical vehicles (EVs) is widely seen as the key factor that will greatly stimulate the EV markets, and its realization is mainly hindered by the sluggish diffusion of Li+. To have a mechanistic understanding of Li+ diffusion within LIBs, in this study, structural evolutions of electrodes for a Ni‐rich LiNi0.6Mn0.2Co0.2O2 (NMC622) || graphite cylindrical cell with high areal loading (2.78 mAh cm−2) are developed for operando neutron powder diffraction study at different charging rates. Via sequential Rietveld refinements, changes in structures of NMC622 and Li x C6 are obtained during moderate and fast charging (from 0.27 C to 4.4 C). NMC622 exhibits the same structural evolution regardless of C‐rates. For phase transitions of Li x C6, the stage I (LiC6) phase emerges earlier during the stepwise intercalation at a lower state of charge when charging rate is increased. It is also found that the stage II (LiC12) → stage I (LiC6) transition is the rate‐limiting step during fast charging. The LiC12 → LiC6 transition mechanism is further analyzed using the Johnson–Mehl–Avrami–Kolmogorov model. It is concluded as a diffusion‐controlled, 1D phase transition with decreasing nucleation kinetics under increasing chargingrates.

Isothermal crystallization kinetics of an industrial-grade Zr-based bulk metallic glass

Bulk metallic glasses (BMGs), due to their amorphous structure, exhibit remarkable mechanical properties, and there is an increasing interest in their commercialization. For the industrial fabrication of BMG, knowledge about the isothermal crystallization kinetics of industrial-grade BMG is required. Previous investigations on isothermal crystallization kinetics are mainly based on high-purity samples with very good glass forming ability and/or mainly limited to the low temperature regime. In the present study, a systematic investigation on the isothermal crystallization kinetics of an industrial-grade Zr-based BMG (Zr59.3Cu28.8Al10.4Nb1.5 at.%, trade name: AMZ4) has been performed using conventional and flash differential scanning calorimetry.We report the time-temperature-transformation (TTT) diagrams of the AMZ4 with two different oxygen levels. The diagrams cover the temperature range from glass transition temperature up to liquidus temperature, that have the typical “C-shaped” noses. Faster crystallization of the higher oxygen level AMZ4 was observed, and the underlying mechanisms were investigated. The universal isothermal Johnson-Mehl-Avrami-Kolmogorov (JMAK) model was employed to model the isothermal crystallization kinetics. Satisfactory match was achieved between the experimental facts and the JMAK model, and the interfacial energies between the crystalline phase and liquid were determined as ∼0.04 J/m2 for the industrial-grade AMZ4. The crystallization fraction dependence of Avrami index and activation energy is studied and found to be neglectable in the JMAK modeling. The critical casting thicknesses were estimated based on the TTT diagrams.

A new approach of predicting dynamic recrystallization using directly a flow stress model and its application to medium Mn steel

We present a new approach of predicting the dynamic recrystallization (DRX) of an alloy steel during hot compression testing with an emphasis on higher solution accuracy and practicability than the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model approach. We use not only an accurate closed-form function (CFF) flow stress model which allows to exclude modelling of the strain at 50% recrystallization but also an Avrami kinetics model with improved parameters formulated as the CFFs of state variables; this enhances generality, flexibility, and accuracy. Comparisons of the fitted and experimental flow stresses revealed that accuracy is excellent; the average and maximum errors are less than 2.83% and 4.61%, respectively. The average error of the fitted DRX volume fraction (Xdrx) values in our approach is 5.15% (standard deviation of 2.35%), which is considerably low. The comparison of the grain sizes predicted by the new approach with those by the JMAK model approach also showed that the former is closer to the experimental data than the latter.

Molecular Engineering of Organic Spacer Cations for Efficient and Stable Formamidinium Perovskite Solar Cell

AbstractLow dimensional (LD) perovskite materials generally exhibit superior chemical stability against ambient moisture and thermal stress than that of 3D perovskites. Recently, LD perovskite has been used as a passivation layer on the surface of 3D perovskite grains. Although various LD perovskites have been developed focusing on their hydrophobicity, the impact of crystal structure of LD perovskite on the photovoltaic performance of perovskite solar cell (PSC) is still uncertain. In this work, the effects of the structural characteristics of LD perovskites on the crystal formation of formamidinium lead triiodide (α‐FAPbI3) and on the optoelectrical properties of PSCs are elucidated. The phase‐transformation kinetics of FAPbI3 mixed with LD perovskites is studied using the Johnson–Mehl–Avrami–Kolmogorov model. It is found that the arrangement of PbI6 octahedra in the LD perovskite changes the rate of α‐FAPbI3 formation. Facilitated nucleation of α‐FAPbI3 at the LD/FAPbI3 interface results in minimal structural disorder and prolonged charge‐carrier lifetimes. As a result, the PSC with the optimized LD perovskite structure exhibits a power conversion efficiency of 21.25% from a reverse current–voltage scan, and stabilized efficiency of 19.95% with excellent ambient stability without being encapsulated.

Effect of particle size distribution on the sinter-crystallisation kinetics of a SiO2–Al2O3–CaO–MgO–SrO glass-ceramic glaze

Sinter-crystallisation kinetics of a glaze with an average particle size of 9.6µm, 4.0µm and 0.65µm, which devitrified anorthoclase and diopside, were studied by non-isothermal techniques. It was confirmed that the crystallisation kinetics could be described by the Johnson–Mehl–Avrami–Kolmogorov model, assuming the Avrami index and activation energy to be independent of particle size. To describe the sintering kinetics, a kinetic model was developed, based on the Johnson–Mehl–Avrami–Kolmogorov model, assuming the effect of temperature on the process rate to be the same as its effect on the inverse viscosity of the glass matrix, and introducing a correction that took into account the difference between the heating rate of the kiln and that of the test piece. The pre-exponential factor of the developed model was confirmed to be proportional to the inverse of glaze average particle size. Glaze sinterability was observed to increase as the heating rate rose and/or average particle size decreased.

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.