Diffusion-controlled Transformation Research Articles

Phase transformation kinetics in Ti 575 titanium alloy during heat treatment: Role of the initial microstructure during ageing

Phase transformation kinetics were studied of Ti-575 titanium alloy during cooling from solution annealing and subsequent ageing using in-situ high energy X-ray diffraction. Cooling rates of 1.7, 10 and 30 °C·s−1 were applied from Tβ-60 °C therefore generating several microstructures with different size, morphologies or spatial distribution of α precipitates. Isothermal ageing at 500 °C for 1 h on these three microstructures allowed the study of the influence of the initial microstructural state upon phase transformation during ageing. For this purpose, the combined analysis of mass fraction, aβ mean lattice parameter and full width at half maximum is carried out for both cooling and ageing segment and is presented in this study. Displacive and diffusion-controlled transformations were recorded and seem to be cooling rate dependent, particularly with the precipitation of the α″ orthorhombic phase. The chemical and mechanical evolution of these transformation products will influence the phase transformation kinetics during cooling and following ageing hence conditioning the final microstructure and mechanical properties of this alloy.

Multi-phase-field modeling of the dissolution behavior of stoichiometric particles on experimentally relevant length scales

The dissolution of stoichiometric particles within a melt plays a crucial role in various material processes. This study presents a comprehensive phase-field model to analyze the dissolution behavior of these stoichiometric particles under experimental conditions. Our approach addresses the classical phase-field challenges related to modeling stoichiometric compounds and scaling to experimentally relevant lengths in a multi-phase, multi-component context. To overcome the difficulties posed by stoichiometric compounds, we rederive the classical phase-field evolution equations for a multi-phase system, adopting a composition-independent free energy expression for the stoichiometric compound. Additionally, we extend Feyen’s high driving force model [Feyen and Moelans, Acta Materialia, 256 (2023)] to multi-component systems, allowing us to perform quantitative simulations for technologically relevant material systems at experimental length scales within a reasonable computing time. The model’s precision in capturing diffusion-controlled transformations, including dissolution, growth, and the Gibbs–Thomson effect, is validated against analytical solutions for a hypothetical system. The quantitative nature of the model is validated by applying it to the dissolution of Al2O3 particles in CaO–Al2O3–SiO2 slags. We break new ground by conducting three-dimensional simulations for a system size of 875μm×875μm×875μm, directly comparable to confocal scanning laser microscopy experiments, where previous models were limited to two-dimensional simulations and a system size of 2μm×2μm. This validation underscores the model’s proficiency to quantitatively describe the diffusion-controlled dissolution of Al2O3 at the experimentally relevant length scales.

Temperature dependence of tensile mechanical properties and work hardening behavior in direct laser deposited austenitic stainless steel 316L

Austenitic stainless steel 316 L is widely used in various industries due to its good mechanical properties at elevated temperatures (up to 600 °C), excellent corrosion resistance, and relatively low cost. However, there is lack on investigations of high-temperature properties of direct laser deposited (DLD) 316 L alloy. In the present investigation, tensile tests were performed at temperatures ranging from 20 to 1000 °C to study the effect of temperature on mechanical properties and work hardening behaviour. It was found that DLD-processed 316 L alloy has minor anisotropy of mechanical properties and work hardening behaviour at elevated temperatures higher than 200 °C. A gradual decrease in yield stress accompanied by a slight altering of ductility in the temperature range between 200 °C and 700 °C is caused by the dynamic strain ageing effect. At higher temperatures, a rapid decrease in mechanical properties is observed. Strength properties of the DLD alloy are lower in comparison with selective laser melted alloy but higher than those of wrought alloy up to 900 °C. Stress-strain curves of the material has shown stage-by-stage work hardening behaviour, depending on the test temperature. Dilatometric tests revealed a linear increase in the coefficient of thermal expansion (CTE) during heating up to 670 °C for the longitudinal sample and up to 770 °C for the transverse one. Then a non-linear growth of the CTE was observed due to diffusion-controlled transformation of the delta-ferrite to austenite.

Microstructure evolution of Inconel 625 alloy during single-track Laser Powder Bed Fusion

Elemental microsegregation and precipitate formation are inevitable during solidification of Additive Manufacturing (AM) parts. In this study, single-track Laser Powder Bed Fusion (LPBF) has been combined with optical and electron microscopy, as well as thermodynamic (CALPHAD) simulations, to evaluate the solidified microstructure and also the formation of the precipitates in an as-built LPBF microstructure of Inconel625 (IN625). It is shown that the microstructure consists mainly of columnar Nickel–Chromium ( γ -FCC) cell-like dendrites which grew epitaxially from the substrate. Utilizing Scanning Transmission Electron Microscopy (STEM) with Energy-Dispersive X-ray Spectroscopy (EDS) and High-Angle Annular Dark-Field Scanning Transmission Electron Microscopy (HAADF-STEM), we have detected NbC, γ ′ ′ -Ni 3 Nb, and laves precipitates embedded into the interdendritic regions. The level of microsegregation and the microsegregation patterns during the solidification of primary arms are obtained by STEM-EDS, and calculated using the Scheil–Gulliver (with solute trapping) and DIffusion-Controlled TRAnsformations (DICTRA) methods. Good agreement is seen between the Scheil–Gulliver predictions and STEM-EDS observations of microsegregation, however the level of elemental microsegregation was overestimated in DICTRA simulations as compared to the experimental result. The formation of precipitates was also evaluated computationally by calculation of driving force for the nucleation of the precipitates from the last solidified liquid where the composition and thermal information for the last solidified liquid extracted from the Scheil solidification simulation. The precipitates predicted via CALPHAD were compared with the precipitates identified via HAADF-STEM analysis inside the interdendritic region.

On the mechanism of Mn partitioning during intercritical annealing in medium Mn steels

To understand how solute Mn in the reverted austenite is able to rapidly partition to near-equilibrium concentration values during the typically short intercritical annealing (IA) of medium Mn steels (MMS), reverse transformation kinetics were simulated numerically. We applied a variety of assumptions both for the diffusivity of Mn in austenite and martensite/ferrite and for the interface mobility. These simulation results were compared with measurements of the Mn concentration gradient near the interface as measured by atom probe tomography. Our inclusion of an interface mobility term, with physical origins from the interfacial dissipation energy, reduced the interphase interface migration rate, resulting in much higher values of the interfacial Mn concentration than in the scenario whereby diffusion-controlled transformation kinetics dominate. These results have led us to propose that the austenite/ferrite interface exhibits a fluctuational interface mobility during IA. This new phenomenological description of the interface migration achieves the best fit to the measured fluctuations of the Mn concentration gradients near the interface. We suggest that the fluctuational mobility arises from encounters between the interface and the regions of crystal containing precipitates and/or microstructural defects.

Diffusivity and Atomic Mobility in fcc Ni-Fe-V System: Experiment and Modeling

In this work, the ternary diffusion behavior in fcc Ni-Fe-V system has been investigated by means of solid-state diffusion couple technique at 1000, 1100 and 1200 °C. The composition-dependent ternary interdiffusion coefficients were determined via Whittle-Green method, in which the uncertainties were calculated by error propagation and the reliability was validated via thermodynamic constraints. The ternary main interdiffusion coefficients of $$\tilde{D}_{\text{FeFe}}^{\text{Ni}}$$ and $$\tilde{D}_{\text{VV}}^{\text{Ni}}$$ were compared with the ones in binary Fe-Ni and Ni-V systems in the literature, respectively. The obtained interdiffusion coefficients combined with the thermodynamic description were employed to evaluate the atomic mobilities in fcc Ni-Fe-V system through the DICTRA (DIffusion-Controlled TRAnsformations) software package. A comprehensive comparison between the model-predicted diffusion behaviors and the experimental ones, including concentration/interdiffusion-flux distribution and diffusion path, confirms the reliability of the present atomic mobility. Besides, based on the presently obtained atomic mobilities, three-dimensional surfaces for the diagonal interdiffusivity at 1000, 1100 and 1200 °C were plotted. Furthermore, three-dimensional planes of the activation energy and frequency-factor of main interdiffusivities were evaluated using the Arrhenius equation. This work is part of our work to build a general kinetic database for soft magnetic alloys and cemented carbides.

Effect of welding speed on microstructure and mechanical properties of laser-welded transformation induced plasticity (TRIP) steels

The weldability of 0.28C–2.0Mn–0.93Al–0.97Si (wt.%) transformation induced plasticity (TRIP) steels was investigated using a 2.5 kW CO2 laser at the welding speeds of 2, 2.5 and 3 m/min. The welded joints were characterized in terms of hardness, tensile properties and microstructure. High-quality welded joints of TRIP steels with the carbon equivalent of 0.7 were obtained. Lower loss of ductility, nearly unvaried hardness of the fusion zone (FZ) and tensile strength equal to the base metal were observed with increasing welding speed. Lath martensite and lower bainite formed in FZ and the microstructure of FZ varied little with welding speed. Weld thermal simulations of heat-affected zone (HAZ) were carried out using a quenching dilatometer, and the microstructures of dilatometric samples revealed the carbon diffusion-controlled transformations in HAZ. The microstructure distribution of HAZ could be influenced by the welding speed due to the significant temperature gradient over the narrow HAZ.

Investigation of the Peritectic Phase Transition in a Commercial Peritectic Steel Under Different Cooling Rates Using In Situ Observation

In situ studies of two separate events of the peritectic phase transition during continuous casting, the peritectic reaction and the peritectic transformation, were performed using high-temperature confocal scanning laser microscopy (HTCSLM). The interface migration velocities during the peritectic transformation at different cooling rates were analyzed in situ by measuring the migration distance of the interface vs time. Moreover, the solute distributions near the moving liquid/solid interface during the peritectic reaction and the peritectic transformation were predicted using the commercial software package diffusion-controlled transformation. The results revealed that the images of HTCSLM clearly recorded these two separate events: the peritectic reaction (L + δ → γ) and the peritectic transformation (L → γ and δ → γ). In the initial stage of the peritectic reaction, the austenite (γ) phase was observed to nucleate at the liquid/δ-ferrite (L/δ) interface and then grow along the periphery of primary δ phases. Upon further cooling, these emerging γ phases gradually isolated the liquid and primary δ phases. Subsequently, the laterally growth of the γ phase was regarded as the peritectic transformation. The growth rate of the γ phase was governed by the liquid to γ and δ to γ phase transformations. As the cooling rate increased, the peritectic reaction was observed to occur at lower temperature. Higher cooling rates enhanced the migration rates of the L/γ and γ/δ interfaces during the peritectic transformation. Meanwhile, an interesting massive transformation of δ into γ phase was observed to occur at a cooling rate of 60 °C/min. All primary δ phases were quickly covered by wrinkled γ phases in a short time. Based on the assumption of the solute incomplete diffusion in the liquid phase, the predicted results revealed that the enrichment of carbon near the L/δ, L/γ, and γ/δ interfaces increased as the cooling rate increased. An increase in the cooling rate exacerbated the carbon segregation of the interface during continuous solidification, causing a nucleation suppression of the γ phase. In turn, the increasing carbon enrichment accelerated the interface migration with the diffusion of large amounts of solute across the interface, causing an increase in the driving force for the peritectic transformation.

Computational Efficient Modeling of Sintering in Multi-component Alloys for ICME Applications

The major challenge while using sintering models for simulation of densification in multi-component alloys is finding the correct transport parameters, which are affected by not only temperature but also chemical composition and phase dispersion. A novel approach for determining the effective self-diffusivity and hence modeling the densification of engineering alloys during sintering is proposed. The approach integrates computational thermodynamics and simulation of diffusion-controlled transformations in multi-component alloys together with a low-order model for solid-state sintering. Computational thermodynamics, using the CALPHAD method, is used to predict microstructural phase stability, which is then used by diffusion simulation models to evaluate the effective transport properties for the sintering model. The modeling approach is validated by comparing results for densification of precipitation-hardened and austenitic stainless-steel alloys during an iso-rate sintering schedule with data from the literature. It is shown that the model can capture experimental observations very well. The modeling approach can thus be used in the development of an efficient search methodology for particulate materials within the context of an integrated computational materials engineering (ICME) frameworks.

Microstructural evolution during cyclic oxidation of a Ni-based singe crystal superalloy at 1100 °C

The effect of cyclic oxidation on the evolution of alloying elements and microstructure was investigated at 1100 °C in a Ni-based single crystal superalloy. The changes of composition and microstructure suffered from oxidation damage were monitored using multiply microscopic techniques. An approach coupling deterministic interfacial cyclic oxidation spalling model (DICOSM) and the homogenization model was employed to simulate these changes, with the help of diffusion-controlled transformations (DICTRA) software. Our results showed a good agreement between experiment and simulation, revealing the fast diffusion of aluminum outward to form alumina layer dominated the evolution of composition and phase.

Atomic mobilities in fcc Ni–rich Ni−X (X=Rh, Ta, W, Re, and Ir) systems

In this paper, a critical review of all the experimental diffusivities in fcc Ni−X (X = Rh, Ta, W, Re, and Ir) systems available in the literature was first performed. The four end-member parameters corresponding to self- and impurity diffusivities in fcc Rh, Ta, W, Re and Ir in Ni−X (X = Rh, Ta, W, Re, and Ir) systems were then evaluated based on the literature data, first-principles results and semi-empirical equations. After that, the atomic mobilities for fcc Ni−X (X = Rh, Ta, W, Re, and Ir) systems were assessed by using DICTRA (DIffusion-Controlled TRAnsformations) software package on the basis of the critically reviewed diffusivities and the corresponding thermodynamic descriptions. The excellent agreement between various calculated diffusion properties, including impurity/tracer diffusivities and interdiffusivities, and the experimental data was obtained. Finally, the reliability of the currently obtained atomic mobilities in fcc Ni−X (X = Rh, Ta, W, Re, and Ir) alloys were validated by comparing the model-predicted concentration profiles of 24 groups of fcc Ni/Ni−X (X = Rh, Ta, W, Re, and Ir) diffusion couples with the experimental data. The presently obtained atomic mobility descriptions for fcc Ni−X (X = Rh, Ta, W, Re, and Ir) systems are to be merged into the atomic mobility database for nickel-based superalloys.

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.

Effect of Ultra-Fast Heat Treatment on the Subsequent Formation of Mixed Martensitic/Bainitic Microstructure with Carbides in a CrMo Medium Carbon Steel

The current work focuses on complex multiphase microstructures gained in CrMo medium carbon steel after ultra-fast heat treatment, consisting of heating with heating rate of 300 °C/s, 2 s soaking at peak temperature and subsequent quenching. In order to better understand the microstructure evolution and the phenomena that take place during rapid heating, an ultra-fast heated sample was analyzed and compared with a conventionally treated sample with a heating rate of 10 °C/s and 360 s soaking. The initial microstructure of both samples consisted of ferrite and spheroidized cementite. The conventional heat treatment results in a fully martensitic microstructure as expected. On the other hand, the ultra-fast heated sample shows significant heterogeneity in the final microstructure. This is a result of insufficient time for cementite dissolution, carbon diffusion and chemical composition homogenization at the austenitization temperature. Its final microstructure consists of undissolved spheroidized cementite, nano-carbides and martensite laths in a ferritic matrix. Based on EBSD and TEM analysis, traces of bainitic ferrite are indicated. The grains and laths sizes observed offer proof that a diffusionless, massive transformation takes place for the austenite formation and growth instead of a diffusion-controlled transformation that occurs on a conventional heat treatment.

Possible Mechanisms of the Formation of Bainitic Colonies

The possible mechanisms of bainitic transformation in steels are discussed. According to the known models of the growth of Widmanstatten ferrite, an acicular shape of bainitic lathes is due to anisotropy in the surface energy. However, the lath replication mechanisms in upper and lower bainite presumably differ from each other. Upper bainite results from the diffusion-controlled transformation, at which the pearlitic autocatalysis due to the formation of cementite at the interface with ferrite takes place. Lower bainite is formed at a smaller temperature via the diffusionless mechanism, when the branching of precipitates or the autocatalysis of lathes can be provided by a decrease in the system energy due to the disposition of structural defects at the interfaces of precipitates, so the existence of a characteristic lath size is energetically stipulated (Weissmuller effect). The combined effect of different autocatalysis mechanisms leads to a variety of possible bainite modifications.

Возможные механизмы формирования бейнитных колоний

AbstractThe possible mechanisms of bainitic transformation in steels are discussed. According to the known models of the growth of Widmanstatten ferrite, an acicular shape of bainitic lathes is due to anisotropy in the surface energy. However, the lath replication mechanisms in upper and lower bainite presumably differ from each other. Upper bainite results from the diffusion-controlled transformation, at which the pearlitic autocatalysis due to the formation of cementite at the interface with ferrite takes place. Lower bainite is formed at a smaller temperature via the diffusionless mechanism, when the branching of precipitates or the autocatalysis of lathes can be provided by a decrease in the system energy due to the disposition of structural defects at the interfaces of precipitates, so the existence of a characteristic lath size is energetically stipulated (Weissmüller effect). The combined effect of different autocatalysis mechanisms leads to a variety of possible bainite modifications.

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.

Interdiffusion and Atomic Mobilities of fcc Co-V-Mo Alloys: Measurement and Modeling

Based on 18 bulk diffusion couples, the composition-dependent interdiffusion coefficients in the fcc Co-V-Mo alloys at 1273, 1373 and 1473 K were obtained from the intersection points of the diffusion couples by means of EPMA technique coupled with the Whittle and Green method. With the experimentally determined interdiffusion coefficients and the critically reviewed experimental diffusivities available in the literature, the atomic mobilities of fcc Co-V-Mo alloys were assessed by means of Diffusion Controlled Transformation (DICTRA) software. The quality of the assessed atomic mobilities was confirmed by the comprehensive comparisons between various DICTRA-calculated diffusion behaviors and the experimental ones, including concentration profiles and diffusion paths.

Assessment of atomic mobilities for fcc Co–Ti–V alloys

Based on the experimental interdiffusion coefficients from our previous work and the critically reviewed experimental diffusivities available in the literature, the atomic mobilities of Co, Ti and V in fcc Co–Ti–V alloys were assessed by means of DICTRA (DIffusion Controlled TRAnsformation) software. Askill's empirical relations were utilized to assess the self-diffusion coefficients of fcc Ti and fcc V. Comprehensive comparisons between the DICTRA-calculated diffusivities and the experimental data indicate that the presently obtained atomic mobilities can reproduce most of the diffusivities in binary and ternary systems. In addition, a further verification on the obtained atomic mobilities was carried out through comparing the DICTRA-simulated concentration profiles/diffusion paths of the diffusion couples with the corresponding experimental ones. This work contributes to the establishment of a kinetic database for multi-component cemented carbide.

Kinetic study of hydrogen-induced direct phase transformation in Y2Fe17 magnetic alloy on the basis of Kolmogorov’s model

The kinetics of the hydrogen induced direct phase transformation in Y2Fe17 magnetic alloy has been analysed within the framework of Kolmogorov’s kinetic model. It is established that the transformation can be classified as a diffusion-controlled transformation, which occurs by a mechanism of nucleation and growth with a decreasing nucleation rate of new phases, namely α-Fe and YH2. A kinetic equation has been obtained that well describes the isothermal kinetic curves of the phase transformation in Y2Fe17 as a function of the transformation temperature.

Interdiffusion and atomic mobility in bcc Ti–rich Ti–Nb–Zr system

Accurate interdiffusion information is the necessity for the control of the production of homogeneous biomedical alloys. Ternary interdiffusivities in bcc Ti–rich Ti–Nb–Zr alloys at 1273K were determined by using the combination of the diffusion couple technique and the Matano–Kirkaldy method. Subsequently, on the basis of the presently obtained interdiffusivities together with the diffusivity and mobility parameters of sub–binary Ti–Nb–Zr system and the thermodynamic descriptions for bcc Ti–Nb–Zr system, the atomic mobilities of Ti, Nb and Zr in bcc Ti–Nb–Zr alloys were assessed by means of DICTRA (DIffusion Controlled TRAnsformation) software package. Moreover, the comprehensive comparisons between the experimental diffusion properties (i.e., interdiffusivities, composition profiles, interdiffusion fluxes and diffusion paths) and the calculated/model–predicted data due to the present atomic mobilities were conducted in order to verify the reliability of the mobilities. The present atomic mobilities for bcc Ti–Nb–Zr system can provide the accurate interdiffusivity matrix over the wide composition range.