Diffusional Transformations Research Articles

Rapid precipitation of intermetallic phases during isothermal treatment of duplex stainless steel joints produced by friction stir welding

The propensity of duplex stainless steels to form secondary phases that harm their main properties is a metallurgical problem that continues to be studied. Friction stir welding has shown excellent results when applied to duplex stainless steels, enabling the formation of joints that maintain the austenite-ferrite balance, without the presence of secondary phases. Welding processes cause significant microstructural reformulation in the joint microstructure, so the properties and metallurgical behavior of welded joints differ significantly from those of the corresponding base metals. The formation of secondary phases in duplex stainless steels occurs by diffusional transformation processes that are dependent on the transformation time, with the kinetics being influenced by the previous microstructure. Although friction stir welding makes it possible to obtain joints free from secondary phases, it is important to study the propensity of welded joints to subsequently form secondary phases, in order to be able to understand the behavior of these joints when they are subjected to hot operations, such as weld repairs. In this work, friction stir welded joints were treated isothermally at 850 °C and were analyzed using scanning electron microscopy, energy-dispersive X-ray spectroscopy, Ferritoscope measurements, and X-ray diffractometry. The results revealed that the friction stir welded joints presented much faster formation of intermetallic phases, compared to the base metals, with the appearance of regions showing advanced stages of intermetallic phase precipitation after only 5 min exposure at 850 °C.

Diffusional transformation in Ti6Al4V alloy during isothermal compression

Abstract Thermodynamic calculation of the two-phase Ti alloy was completed using CompuTherm Pandat™ and Ti data base, followed by isothermal compression of Ti6Al4V (Grade 5), with an initial colony lamellar structure that was performed in the (α+β) and β-phase field. Microstructural evolution and phase transformation were investigated using X-ray diffraction, scanning and transmission electron microscopy. The presence of the Ti3Al or α2 (hcp), the phase stability and transition temperatures were predicted by the Gibbs free energy−temperature and phase fraction−temperature diagrams. The isothermal compression in the (α+β)-phase field is characterized by reorientation and localized kinking of α/β lamellae, and cracking at α/β interphase regions. While in the α→β-phase transformation area, deformation in β-phase and at α/β interphase boundaries, extensive transformation of α into β-phase, martensitic transformation and spheroidization of α-laths mainly characterize this isothermal compression. A complete transformation of α into β single phase occurs in the β-phase field. Ti3Al or α2 (hcp), β (bcc) and α (hcp)-phase, and additional hcp α' and orthorhombic α” phases in a deformed Ti6Al4V are revealed. The flow stress level, the dynamic recovery and dynamic globularization are affected by deformation temperature.

(Invited) Atomistic Simulations of Hydrogen Storage Materials

Solid state hydrogen storage materials possess good volumetric and gravimetric hydrogen storage densities and can be more attractive hydrogen storage media for hydrogen fuel cell vehicles. However, the current hydrogen storage materials are limited by their slow hydrogen storing and releasing kinetics. Understanding thermodynamic and kinetic foundations that limit the current storage materials is critical for accelerated material improvement. To achieve this understanding, we have been developing and applying atomistic simulation tools to study various classes of hydrogen storage materials. Here we present three cases. First, we have developed a series of molecular dynamics methods to study diffusional phase transformation hydrides, such as PdHx. This allows us to analytically quantify bulk and interfacial diffusivities, surface and interfacial energies, surface segregation, lattice constants, Gibbs free energy, and elastic constants, all as a function of temperature and composition. We then implemented all these properties in phase field codes and directly simulated the hydrogenation and dehydrogenation of PdHx at the engineering scale. Second, we have developed a high-fidelity Mg-H bond order potential to study the structural phase transformation hydrides, such as MgH2. We demonstrate that this potential not only captures the property trends for a variety of selected phases, but also ensures direct molecular dynamics simulation of formation and decomposition of the crystalline MgH2 phase. This new capability, not demonstrated in the past, opens up opportunities to explore in great details mechanisms of hydrogenation and dehydrogenation processes. Finally, we discuss our recent progress on developing a Mg-B-H ternary potential that can be used in atomistic simulations to study thermodynamics and kinetics behaviour of complex metal hydrides based on magnesium and boron. Acknowledgement - Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. A portion of this work was performed under the auspices of Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. The authors gratefully acknowledge research support through the Hydrogen Storage Materials—Advanced Research Consortium (HyMARC), from the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Fuel Cell Technologies Office, under Contract Numbers DE-AC04-94AL85000 and DE-AC52-07NA27344. The views expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights.

Acceleration of diffusional transformation in a high-carbon steel layer composed of a sandwich-like clad steel sheet

The thermomechanical interactions between two different regions with different carbon contents during cooling from the austenite single phase condition was studied with a sandwich-like clad sheet. The clad steel with a layered structure where a 0.65%C high-carbon steel sheet was sandwiched by 0.05%C low-carbon steel sheets was prepared. The benefit of this clad structure for this study is that any fraction of the composed layers can be fabricated artificially with the constant carbon content in both component layers. In the experiments, the clad sheets were prepared by plain strain compression at 900 °C for welding, followed by gas quenching. The microstructural observation revealed that the fraction of the martensite structure in the high-carbon steel layer decreased and, alternatively, a pearlite structure evolved as the fraction of the low-carbon steel layers was increased; whereas the low-carbon steel layers showed ferrite and pearlite structures with any construction of the clad steel. Consequently, the hardness of the high-carbon steel layer decreased in the sheet with the higher fraction of low-carbon steel layers. The reason for this change is due to both the elastic strain and the plastic deformation of the high-carbon steel layer induced by phase transformation in the low-carbon layers.

Heat flow model based on lattice Boltzmann method for modeling of heat transfer during phase transformation

PurposeA fundamental principle of materials engineering is that the microstructure of a material controls the properties. The phase transformation is an important phenomenon that determines the final microstructure. Recently, many analytical and numerical methods were used for modeling of phase transformation, but some limitations can be seen in relation to the choice of the shape of growing grains, introduction of varying grain growth rate and modeling of diffusion phenomena. There are also only few comprehensive studies that combine the final microstructure with the actual conditions of its formation. Therefore, the objective of the work is a development of a new hybrid model based on lattice Boltzmann method (LBM) and cellular automata (CA) for modeling of the diffusional phase transformations. The model has a modular structure and simulates three basic phenomena: carbon diffusion, heat flow and phase transformation. The purpose of this study is to develop a model of heat flow with consideration of enthalpy of transformation as one of the most important parts of the proposed new hybrid model. This is one of the stages in the development of the complex model, and the obtained results will be used in a combined solution of heat flow and carbon diffusion during the modeling of diffusion phase transformations.Design/methodology/approachDifferent values of overheating/overcooling affect different values in the enthalpy of transformation and thus the rate of transformation. CA and LBM are used in the hybrid model in part related to heat flow. LBM is used for modeling of heat flow, while CA is used for modeling of the microstructure evolution during the phase transformation.FindingsThe use of LBM and CA in one numerical solution creates completely new possibilities for modeling of phase transformations. CA and LBM in comparison with commonly used approaches significantly simplify interface and interaction between different parts of the model, which operates in a common domain. The CA can be used practically for all possible processes that consist of nucleation and grains growth. The advantages of the LBM method can be well used for the simulation of heat flow during the transformation, which is confirmed by numerical results.Practical implicationsThe developed heat flow model will be combined with the carbon diffusion model at the next stage of work, and the new complex hybrid model at the final stage will provide new solutions in numerical simulation of phase transformations and will allow comprehensive modeling of the diffusional phase transformations in many processes. Heating, annealing and cooling can be considered.Originality/valueThe paper presents the developed model of heat flow (temperature module), which is one of the main parts of the new hybrid model devoted to modeling of phase transformation. The model takes into account the enthalpy of transformation, and the connection with the model of microstructure evolution was obtained.

Phase transformation effect in distortion and residual stress of thin-sheet laser welded Ti-alloy

To overcome the detrimental effect of residual stress and distortion in a welded structure, there is continued interest on the assessment of stress field and deformation pattern. Phase transformation has pronounced effect on the generation of residual stress and distortion which is often neglected in thermo-mechanical analysis. To investigate the same for dual phase (α+β) Ti-alloy, a finite element based sequentially coupled thermal-metallurgical-mechanical model is developed for pulse laser welding condition. More degree of mechanical constraint restricts the deformation, but induces plastic strain which in turn increases the effective residual stress. Different phases evolved during welding are qualitatively estimated as a function of temperature or transient temperature change by allowing volumetric expansion or contraction induced by β-transformation or α′-martensitic transformation. The influence of non-isothermal diffusional transformation during heating and non-diffusional transformation in cooling cycle on residual stress and deformation pattern is evaluated. Understanding the influence of phase transformation on residual stress and distortion play a decisive role to minimize the deleterious effect. It is advantageous if the evolved plastic strain is kept low and its distribution is restricted to confined area. Stable α → β transformation leads to uniform non-diffusional transformation during cooling cycle. At martensitic start temperature, the magnitude of effective tensile stress decreases due to volumetric expansion of β→α′ transformation.

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.

Effect of iron content on β → α phase transformation behavior of Ti-5Al-xFe (x = 1, 2.5, 4) alloys during continuous cooling

We investigated the effect of Fe content on the β→α phase transformation behavior of Ti-5Al-xFe (x=1, 2.5, 4) alloys during continuous cooling. The presence of Fe delayed long-range diffusional phase transformation, thus facilitating diffusionless transformation even at low cooling rates. This effect was explained by the extremely low solubility of Fe atoms in the α phase, so that they must be significantly redistributed before the precipitation of the equilibrium α phase. Fe also reduced the phase-transformation start temperature by lowering the β-transus temperature. Differences in the β-transus temperature of the alloys accounted for the differences in the phase-transformation start temperature at a low cooling rate. However, as the cooling rate increased, the difference in the phase-transformation start temperature greatly increased, which could no longer be explained by the difference in the β-transus temperature. It was reasoned that Fe significantly stabilized the β phase; hence, the effective β-transus temperature decreased as the cooling rate increased. This reduction was intensified by an increase in the Fe content. The strong dependence of the β→α phase transformation behavior on the Fe content led to the development of different microstructures in the alloys. Hardness was strongly dependent on the resulting microstructure, which differed with the Fe content and cooling rate. Our results provide a clear understanding of the β→α phase transformation behavior of these alloys and would be useful for designing appropriate solution heat treatment.

In Situ Time-Resolved Phase Evolution and Phase Transformations in U-6 Wt Pct Nb

In situ time-resolved synchrotron X-ray diffraction experiments were conducted to study the fine-scale phase evolution of U-6Nb. Upon rapid heating from 125 °C to 400 °C, a reverse martensitic transformation sequence, α″ → γo → γs, was observed in less than 4 seconds, which represents the first direct observation of the γo → γs transformation in diffraction-based measurements. Consistent with previous ex situ metallography experiments, our isothermal hold experiments at 526 °C, 530 °C and 565 °C reveal two distinct reactions for the phase separation, γs → α-U + γ1 (general precipitation) followed by (α-U + γ1) → α-U + γ1-2 (discontinuous precipitation). For the first-stage precipitation, the incubation time is determined to be ~ 50 and 100 seconds, respectively, for the isothermal aging at 526-530 °C and 565 °C. At this stage, the phase transformation is characterized by the simultaneous growth of α-U and γ1 at the expense of γs. As expected from the Arrhenius equation for the reaction rate, the determined times (~ 23 minutes) for the completion of the first-stage reaction at 526 ± 3 °C and 530 ± 3 °C are nearly twice longer than that at 565 ± 4 °C (~ 13 minutes). Over these periods of time, the Nb contents derived from a Vegard’s-type relationship for γ1 are in the 30.2 to 32.1 and 29.2 to 30.6 at. pct ranges, and the kinetics of the precipitation at 565 ± 4 °C can be described by the classic Avrami rate equation and one-dimensional growth of a surface or grain-boundary nucleation. During the second-stage precipitation, the γ1 phase continues to enrich in Nb as it gradually evolves toward the α + γ1-2 metastable state (up to 47 at. pct over a period of 172 minutes at 530 °C). These new and time-resolved measurements can be used to better constrain the time–temperature–transformation diagram, solute (Nb) redistribution, and transformation kinetics during the early stages of the diffusional phase transformation.

Two-dimensional simulations and experiments of homogenization and Kirkendall effect in single-phase diffusion triples

A fully discrete local discontinuous Galerkin (LDG) method has been successfully adopted to simulate two-dimensional (2D) homogenization in single-phase diffusion triples controlled by diffusion process. Two Co-Ni and Co-Fe-Ni diffusion triples were prepared and analyzed to verify the simulation results at 1473 K. In areas far away from the triple conjunction of a diffusion triple, there exists composition gradient in only one direction, which can be efficiently predicted by one-dimensional (1D) sharp-interface diffusion simulations (for example, DICTRA: DIffusion-Controlled TRAnsformation simulation software). It has been extensively adopted in the study of diffusional phase transformations readily supported by multi-component multi-phase thermodynamics and full diffusion matrix establishing an integrated thermodynamics-kinetics simulation platform for engineering materials and industrial applications. However, there are composition gradients in two independent directions in the vicinity of triple conjunction (i.e. triple diffusion zone), which cannot be handled on this platform. In the present work, the LDG method combining with alloy thermodynamics and diffusion kinetics was demonstrated to tackle this 2D homogenization problem very well and the effectiveness of this method has been proved from the aspect of numerical analysis by realizing it with a standalone C++ code. In addition to the composition and flux evolutions during 2D homogenization processes, one can reasonably simulate the shift of the Kirkendall plane in the 2D single-phase diffusion zone. This standalone code serves as a solid basis to further consider 2D diffusional multi-phase transformations assuming sharp interfaces in between.

A Gibbs Energy Balance Model for Growth Via Diffusional Growth-Ledges

Growth ledges are commonly observed on interphase boundaries during diffusional phase transformations and are of great importance for understanding inter-sheet spacing of interphase precipitates. A simple model based on Gibbs Energy Balance (GEB) for describing growth kinetics via diffusional growth-ledges of height λ is presented for the case of ferrite growth into austenite. The model is validated against the case of austenite to ferrite transformation involving interphase precipitation in a V, Mn, Si alloyed HSLA steel where, λ is assumed to be equal to the inter-sheet spacing of interphase carbide precipitates. The presented model provides a computationally efficient and versatile method for predicting the ledge height, λ, and the growth kinetics of ferrite from initial nucleation through to final soft impingement considering the evolution of solute drag at growth ledge risers. It is suggested that the intrinsic mobility of growth ledge risers is: M_{m}^{aR} = 0.58(exp\frac{-140x10^{3}{RT})mmol.J^{-1}s^{-1}, with R the gas constant and T the absolute temperature in K.

Nonequilibrium Diffusional Phase Transformations in Alloys Induced by Migration of Grain Boundaries and Dislocations

The main scenarios of nonequilibrium diffusional transformations induced by moving defects (dislocations, grain boundaries) in alloys under severe plastic deformation are considered. It has been shown that the phase state locally changes in the area of a defect where thermodynamic properties of alloy are locally changed, and the attained state is frozen after the displacement of a defect due to the difference between the rates of bulk diffusion and diffusion on a defect. For this reason, an alloy shifts from the state of its thermodynamic equilibrium under treatment, thus different nonequilibrium states, such as the disordering of alloy, the dissolution of equilibrium phase precipitates, the appearance of nonequilibrium phases, and the formation of regular structures, are possible depending on the type of the system. These effects may take place if the treatment of an alloy is performed at moderate temperatures, when diffusion is frozen in the bulk and rather active on defects. The phenomena of phase and structural instability developing under severe plastic deformation at moderate temperatures are considered within the framework of the proposed model.

Неравновесные диффузионные фазовые превращения в сплавах, обусловленные миграцией границ зерен и дислокаций

AbstractThe main scenarios of nonequilibrium diffusional transformations induced by moving defects (dislocations, grain boundaries) in alloys under severe plastic deformation are considered. It has been shown that the phase state locally changes in the area of a defect where thermodynamic properties of alloy are locally changed, and the attained state is frozen after the displacement of a defect due to the difference between the rates of bulk diffusion and diffusion on a defect. For this reason, an alloy shifts from the state of its thermodynamic equilibrium under treatment, thus different nonequilibrium states, such as the disordering of alloy, the dissolution of equilibrium phase precipitates, the appearance of nonequilibrium phases, and the formation of regular structures, are possible depending on the type of the system. These effects may take place if the treatment of an alloy is performed at moderate temperatures, when diffusion is frozen in the bulk and rather active on defects. The phenomena of phase and structural instability developing under severe plastic deformation at moderate temperatures are considered within the framework of the proposed model.

Modeling and experiment on microstructure evolutions and mechanical properties in grade 600 MPa reinforcing steel rebar subjected to TempCore process

In this study, finite element (FE) modeling of the microstructure evolutions and resultant mechanical properties in the grade 600 MPa steel bar subjected to the TempCore process, a thermo-mechanically controlled process involving quenching and self-tempering, and related experiments are presented. The phase transformation kinetics based on the Johnson–Mehl–Avrami–Kolmogorov (JMAK) and Koistinen–Marburger equations were implemented in the user-defined subroutine of FE software to consider diffusional and martensitic transformations, respectively. Moreover, a robust simulation approach for solving complex thermo-mechanical problems induced by the quenching (i.e., external water cooling), internally generated heat due to phase transformations, and heat transfers between core and surface were addressed. The developed model can also simulate deformations associated with temperature change, phase transformations, and mechanical plasticity. The developed model was validated by estimating evolutions of various phase fractions and hardness in steel bars produced by both TempCore and normal air-cooling, which were compared with corresponding experimental results. Finally, prediction of flow stress curves and their experimental validation were also performed.

On the influence of the heat treatment on microstructure formation and mechanical properties of near-α Ti-Fe alloys

We study the microstructure formation and mechanical properties of Ti-1Fe (wt%) and Ti-3Fe (wt%) alloys for different heat treatments in the β-phase and α + β-phase regions. By applying different heat treatment routes, we observe different microstructure formation mechanisms causing a wide range of mechanical properties from high strength (1.3 GPa) and low ductility (2%) to intermediate strength (700 MPa) and high ductility (30%) in these simple binary alloys.We performed microstructure characterizsation using scanning electron microscopy, transmission electron microscopy and atom probe tomography to show that the alloying content and heat treatment significantly affect the local martensitic and / or diffusional phase transformations causing the substantial changes in the mechanical behavior.

Improved accessibility of porous carbon electrodes with surfactant ionic liquids for supercapacitors

Ionic liquids (ILs) are promising electrolytes for supercapacitors due to their wide electrochemical window. However, most ILs are viscous in nature and require diffusional and rotational transformations to access the pore space of common supercapacitor electrodes. In this study, novel anionic surfactant ILs (ASILs) are synthesized to lubricate the electrode surface to improve pore accessibility by IL ions. ASIL composition (0–10 wt%) and temperature (22–150 °C)-dependent capacitances, as a measure of pore accessibility and wettability, are determined by cyclic voltammetry. 10 wt% 1-butyl-1-methylpyrrolidinium docusate, [PYR14][AOT], in the base IL 1-propyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide, [PYR13][TFSI], exhibits the highest specific capacitance (202 F g−1 at 150 °C and 10 mV s−1), compared to [PYR13][TFSI] (160 F g−1). Electrochemical impedance spectroscopy measurements indicate resistive charging for ASIL/IL electrolyte compared to the base IL at 22 °C due to reduced conductivity—a consequence of larger non-polar domains. However, at elevated temperatures (> 100 °C), electrolyte resistance is circumvented as the viscosity is reduced. The wide voltage window of ILs and improved wettability by ASILs can be coupled to maximize energy storage capability of supercapacitors for high-temperature power applications.

Temperature invariable magnetization in Co-Al-Fe alloys by a martensitic transformation

Recently, it was reported that in a dual-phase ferromagnetic Fe-Ga alloy, highly thermally stable magnetization is achieved by a diffusional transformation between the two phases with different magnetizations, which compensates for the inevitable magnetization reduction. Contrasting with the compensation mechanism through a diffusional transformation, here we report that a diffusionless martensitic transition can also be used as a compensation mechanism for achieving nearly temperature invariable magnetization. We found that ferromagnetic Co-Al-Fe alloys with a non-thermoelastic martensitic transformation exhibit almost unchanged magnetization up to 830 K (about 81% TC). In-situ heating transmission electron microscopy reveals that the gradual transformation from a hexagonal close-packed (hcp) martensite phase with lower magnetization into a face-centered-cubic (fcc) parent phase with higher magnetization occurs over a wide temperature range, giving rise to such temperature invariable magnetization. The electrical resistivity measurement reveals that the fcc → hcp transformation can be repeated during heating-cooling cycles, which can be used to design temperature invariable magnets with a long cycling life.

Kinetic Model for the Phase Transformation of High-Strength Steel Under Arbitrary Cooling Conditions

To meet the demands of energy conservation and security improvement, high-strength steel (HSS) is widely used to produce safety-related automotive components. In addition to fully high-strength parts, HSS is also used to manufacture components with tailored properties. In this work, a computational model is presented to predict the austenite decomposition into ferrite, pearlite, bainite and martensite during arbitrary cooling paths in HSS. First, a kinetic model for both diffusional and martensite transformations under isothermal or non-isothermal with constant cooling rate cooling conditions is proposed based on the well-known Johnson–Mehl–Avrami–Kolmogorov and Kamamoto models. The model is then modified for arbitrary cooling conditions through the introduction of the effects of the cooling rate, and the influence of diffusional transformations on martensite transformation is considered. Next, the detailed kinetics parameters are identified by fitting experimental data from BR1500HS steel. The model is further verified by several experiments conducted outside of the fit domain. The results obtained by calculation are found to be in good agreement with the corresponding experimental data, including the transformation histories, volume fraction microconstituents and Vickers hardness. Additionally, the model is also implemented as a subroutine in ABAQUS to simulate a tailored-strength hot stamping process of HSS, and the results are consistent with the test data. Thus, this computational model can be used as a guideline to design manufacturing processes that achieve the desired microstructure and material properties.

Crystallography of phase transformation during quenching from β phase field of a V-rich TiAl alloy

Well-developed $$ \alpha_{2}^{{\prime }} $$ -martensitic laths were formed in a Ti–40Al–10V (at.%) alloy after a homogenization treatment within the β phase field followed by brine quenching. The morphology and crystallography of martensite were examined by electron backscatter diffraction. It was found that the martensitic transformation was incomplete and about 35 vol% β phase was retained to room temperature. No diffusional or massive transformation has been detected in the β grain interior. All the 12 martensite variants were formed according to the Burgers orientation relationship (BOR) with the parent β grain. While global variant selection has not been detected, local variant selection occurred so that three self-accommodant variants which shared a common 〈11.0〉 axis were predominant in local regions. Based on the traces of the variants, the habit plane was determined to be close to {679}β by using a simply geometrical method. Besides, $$ \alpha_{2}^{{\prime }} $$ plates were frequently observed along the β grain boundaries, which accorded to a strict BOR with one of the adjacent β grains, but tended to grow into the other β grain and hence resulted in serrated interface. Such features were an indication of massive transformation. Moreover, an apparent variant selection criterion for the grain boundary $$ \alpha_{2}^{{\prime }} $$ plates was noted. That is, if a $$ \alpha_{2}^{{\prime }} $$ variant has, in addition to an exact BOR with one of the two adjacent β grains, a near BOR with the other β grain, this $$ \alpha_{2}^{{\prime }} $$ plate would be very large and even extends along the entire grain boundary.

Thermodynamic and kinetic analysis of the melt spinning process of Fe-6.5 wt.% Si alloy

Abstract The microstructural evolution of Fe-6.5 wt.% Si alloy during rapid solidification was studied over a quenching rate of 4 × 104 K/s to 8 × 105 K/s. The solidification and solid-state diffusional transformation processes during rapid cooling were analyzed via thermodynamic and kinetic calculations. The Allen-Cahn theory was adapted to model the experimentally measured bcc_B2 antiphase domain sizes under different cooling rates. The model was calibrated based on the experimentally determined bcc_B2 antiphase domain sizes for different wheel speeds and the resulting cooling rates. Good correspondence of the theoretical and experimental data was obtained over the entire experimental range of cooling rates. Along with the asymptotic domain size value at the infinite cooling rates, the developed model represents a reliable extrapolation for the cooling rate > 106 K/s and allows one to optimize the quenching process.