Kinetics of the peritectic phase transformation: In-situ measurements and phase field modeling

An experimental study has been conducted into the role of cooling rate on the kinetics of the peritectic phase transformation in a Fe−C alloy. The interfacial growth velocities of the peritectic phase transformation were measured in situ for cooling rates of 100, 50, and 10 K/min. In-situ observations were obtained using high-temperature laser scanning confocal microscopy (HTLSCM) in a concentric solidification configuration. The experimentally measured interface velocities of the liquid/austenite (L/γ) and austenite/delta-ferrite (γ/δ) interphase boundaries were observed to increase with higher cooling rates. A unique finding of this study was that as the cooling rate increased there was a transition point where the L/γ interface propagated at a higher velocity than the γ/δ interface, contrary to the findings of previous researchers. Phase field modeling was conducted using a commercial multicomponent, multiphase package. Good correlation was obtained between model predictions and experimental observations in absolute values of interface velocities and the effect of cooling rate. Analysis of the simulated microsegregation in front of the L/γ and γ/δ interfaces as a function of cooling rate revealed the importance of solute pileup. This microsegregation plays a pivotal role in the propagation of interfaces; thus, earlier modeling work in which complete diffusion in the liquid phase was assumed cannot fully describe the rate of propagation of the L/γ and δ/γ interfaces during the course of the peritectic transformation.     

Kinetics of the peritectic phase transformation: In-situ measurements and phase field modeling

An experimental study has been conducted into the role of cooling rate on the kinetics of the peritectic phase transformation in a Fe-C alloy. The interfacial growth velocities of the peritectic phase transformation were measured in situ for cooling rates of 100, 50, and 10 K/min. In-situ observations were obtained using high-temperature laser scanning confocal microscopy (HTLSCM) in a concentric solidification configuration. The experimentally measured interface velocities of the liquid/austenite (L/γ) and austenite/delta-ferrite (γ/δ) interphase boundaries were observed to increase with higher cooling rates. A unique finding of this study was that as the cooling rate increased, there was a transition point where the L/γ interface propagated at a higher velocity than the γ/δ interface, contrary to the findings of previous researchers. Phase field modeling was conducted using a commercial multicomponent, multiphase package. Good correlation was obtained between model predictions and experimental observations in absolute values of interface velocities and the effect of cooling rate. Analysis of the simulated microsegregation in front of the L/γ and γ/δ interfaces as a function of cooling rate revealed the importance of solute pileup. This microsegregation plays a pivotal role in the propagation of interfaces; thus, earlier modeling work in which complete diffusion in the liquid phase was assumed cannot fully describe the rate of propagation of the L/γ and δ/γ interfaces during the course of the peritectic transformation.     

Analysis of solute distribution in dendrites of carbon steel with δ/γ transformation during solidification

Solute distribution in dendrites during solidification of carbon steel was analyzed by unidirectional solidification experiments and mathematical analysis. The characteristic of the mathematical analysis is that diffusion of solutes in solid and redistribution of solutes at solid/liquid andδ/γ interfaces are taken into consideration. Based on the observed and calculated results, it was found that phosphorus was redistributed fromγ-phase toδ-phase, and that manganese was slightly redistributed fromδ-phase toγ-phase. Therefore the concentrated region of phosphorus can be separated from that of manganese duringδ/γ transformation in the case of slow cooling. Moreover, it was concluded that rapid diffusion inδ-phase and the redistribution duringδ/γ transformation played an important role in the variation of the interdendritic concentrations of solutes with lower carbon concentration.     

Kinetics of the peritectic phase transformation: In-situ measurements and phase field modeling

An experimental study has been conducted into the role of cooling rate on the kinetics of the peritectic phase transformation in a Fe−C alloy. The interfacial growth velocities of the peritectic phase transformation were measuredin situ for cooling rates of 100, 50, and 10 K/min.In-situ observations were obtained using high-temperature laser scanning confocal microscopy (HTLSCM) in a concentric solidification configuration. The experimentally measured interface velocities of the liquid/austenite (L/γ) and austenite/delta-ferrite (γ/δ) interphase boundaries were observed to increase with higher cooling rates. A unique finding of this study was that as the cooling rate increased there was a transition point where the L/γ interface propagated at a higher velocity than the γ/δ interface, contrary to the findings of previous researchers. Phase field modeling was conducted using a commercial multicomponent, multiphase package. Good correlation was obtained between model predictions and experimental observations in absolute values of interface velocities and the effect of cooling rate. Analysis of the simulated microsegregation in front of the L/γ and γ/δ interfaces as a function of cooling rate revealed the importance of solute pileup. This microsegregation plays a pivotal role in the propagation of interfaces; thus, earlier modeling work in which complete diffusion in the liquid phase was assumed cannot fully describe the rate of propagation of the L/γ and δ/γ interfaces during the course of the peritectic transformation.     

Precipitation behavior of MnS during δ/γ transformation in Fe−Si alloys

The precipitation behavior of MnS after solidification was analyzed with low-carbon Fe−Si alloys. This system was chosen since it has a wide temperature range for the δ/γ transformation. Experimental results showed that the amount of MnS precipitates increased drastically between 1300°C and 1100°C, and MnS precipitates were segregated almost entirely in the δ phase. This result was interpreted quantitatively by a mathematical model, taking into account the diffusion and the redistribution of solute elements and also the solubility product limit of Mn and S in both phases. Mathematical analysis shows that the precipitation of MnS starts first in the γ phase, but its growth will be very limited because of slow diffusion of Mn in the γ phase. The effects of some factors such as cooling rate and Si content of alloys on the rate of precipitation were discussed, and the degree of contributions of diffusion of Mn and the redistribution of S were estimated.     

Kinetics of peritectic reaction and transformation in Fe-C alloys

In situ dynamic observation of the progress of a peritectic reaction and transformation of Fe-(0.14 pct C)- and Fe-(0.42 pct C)-peritectic Fe-C alloys has been successfully made with a combination of a confocal scanning laser microscope and an infrared image furnace. The peritectic reaction is characterized by the formation of the γ-austenite phase at the junction of the liquid and the grain boundary of δ-ferrite crystals and subsequent propagation of the three-phase point, liquid/γ/δ, along the liquid/δ boundary, whereas the peritectic transformation occurs by the thickening of the intervening γ toward both the liquid side and the δ side. The rates of the peritectic reaction for the two peritectic alloys are found to be much faster than the rate that would be controlled by carbon diffusion, suggesting that either massive transformation to γ or solidification as γ controls the rate. This is also the case for the Fe-0.14%C transformation in the hypoperitectic alloy. However, the rate of the peritectic transformation in the Fe-0.42%C alloy is determined by carbon diffusion. This article is based on a presentation made in the “Geoffrey Belton Memorial Symposium,” held in January 2000, in Sydney, Australia, under the joint sponsorship of ISS and TMS.     

The Influence of Cr on the Solidification Behavior of Polycrystalline γ(Ni)/γ′(Ni3Al)-δ(Ni3Nb) Eutectic Ni-Base Superalloys

In the current investigation, the effect of Cr on the solidification characteristics and as-cast microstructure of pseudobinary γ-δ eutectic alloys based on a near-eutectic composition (Ni-5.5Al-13.5Nb at. pct) was investigated. It was found that Cr additions promote the formation of a higher volume fraction of γ-δ eutectic microstructure in the interdendritic region. Increasing levels of Cr also triggered morphological changes in the γ-δ eutectic and the formation of γ-γ′-δ ternary eutectic during the last stage of solidification. A detailed characterization of the as-cast alloys also revealed that Cr additions suppressed the liquidus, solidus, and γ′ precipitation temperature of these γ/γ′-δ eutectic alloys. A comparison of the experimental results with thermodynamic calculations using the CompuTherm Pandat database (CompuTherm LLC, Madison, WI) showed qualitative agreement.     

Microscopic modeling of fundamental phase transformations in continuous castings of steel

A model has been developed to describe the microscopic behavior of phase transformation of carbon steels in the range of cooling rate occurring in continuous casting. In the liquid-to solidphase transformation, this model simulates the phenomena of dendrite nucleation and growth during solidification. Both δ- and γ-dendrites are involved. The nucleation and growth model has been established on the basis of published experimental data and previous work. Also, a model of the peritectic transformation of carbon steels has been included. In the solid-to solidphase transformation, the model considers the δ→ γ, γ→ α, and γ→ α + Fe₃C phase transformations. The δ→ γ and γ→ α phase transformations have been modeled by using the Johnson-Mehl equation, also known as the Avrami equation. For the pearlite transformation, a nucleation law, as well as the growth kinetics, has been established. Good agreement has been found between the prediction of the model and the experimental data.     

Shear mechanisms of the γ′ phase in single-crystal superalloys and their relation to creep

The development of dislocation configurations in a single-crystal superalloy during creep and especially the shear mechanism of theγ′ phase is investigated by a transmission electron microscopy (TEM) study. Detailed analysis shows that at low strains and at coherent interfaces, shearing occurs by dissociation of matrix dislocations at theγ/γ′ interfaces, while at high strains and incoherent interfaces, cutting of theγ′ phase is achieved by antiphase boundary (APB) coupled dislocation pairs. The results are discussed in their connection to creep behavior.     

A thermodynamic analysis of the phase equilibria of the Fe-Ni system above 1200 K

A quasi-subregular solution model is used to describe the thermodynamic properties of the liquid phase; values of the solution parameters are obtained from extensive and consistent thermochemical data reported in the literature. For the fcc and bcc phases, the same model is used to account for the nonmagnetic part of the Gibbs energy and the magnetic contribution is taken from the previous paper. Again, the values for the quasi-subregular solution parameters for the fcc phase are obtained from extensive and consistent thermochemical data reported in the literature at high temperatures. The values of the solution parameters for the bcc phase are obtained from the thermodynamic values of the liquid and fcc phases and the known phase boundary data. The calculated phase equilibria are in good agreement with the available data. Based on the thermodynamic data, the metastablel + γ andl + δ phase boundaries as well as theT ₀ (γ + l) andT ₀(δ +l) curves are calculated.     

Examination of solidification pathways and the liquidus surface in the Nb-Ti-Al system

The solidification pathways, subsequent solid-state transformations, and the liquidus surface in the Nb-Ti-Al system have been examined as part of a larger investigation of phase equilibria in Nb-Ti-Al intermetallic alloys. Fifteen alloys ranging in composition from 15 to 40 at. pct Al, with Nb to Ti ratios of 4:1, 2:1, 1.5:1, 1:1, and 1:1.5, were prepared by arc melting and the as-cast microstructures were characterized by optical microscopy (OM), microhardness, X-ray diffraction (XRD), differential thermal analysis (DTA), backscattered electron imaging (BSEI), electron probe microanalysis (EPMA), and transmission electron microscopy (TEM). The results indicate that the range of primary β solidification is much wider than that indicated in previously reported liquidus surfaces, both experimental and calculated. Differential thermal analysis has identified the existence of a β to σ+γ transformation in three alloys where it was previously thought not to exist; confirmation was provided by high-temperature vacuum heat treatments in the single-phase β region followed by rapid quenching. The location of the boundary between the β, σ, and δ primary solidification fields has been redefined. A massive β → δ transformation, which was observed in the cast microstructure of a Nb-25Ti-25Al alloy, was repeatable through cooling following homogenization. A β → δ+σ eutectoid-like transformation in the 25 at. pct Al alloys, was detected by DTA and evaluated through microstructural analysis of heat-treated samples. Trends in the β phase with variations in composition were established for both lattice parameters and microhardness. As a result of this wider extent of the primary β solidification field, a greater possibility exists for microstructural control through thermal processing for alloys consisting of either σ+γ, β+σ, or β+δ phases. An erratum to this article is available at .     

Structure of phases in the δ-AI2O3 fiber studied by convergent beam electron diffraction

The phases in the δ-Al₂O₃ fibers were investigated using the methods of transmission electron microscopy (TEM): convergent beam electron diffraction (CBED) and high-resolution electron microscopy (HREM). A phaseγ′-Al₂O₃ discovered previously by Vewerly in oxide layers with an fcc structure was found and new atomic positions are proposed. A new structure ofδ-Al₂O₃ was also observed. It has aPmma space group and lattice parameters ofa _δ = 2a _γ′,b _δ = l.5a _γ′, andc _δ ≈a _γ′ The correlation of the observed A1₂O₃ lattices to the spinel lattice is discussed and translation of atom positions during theγ′ →γ →δ transformation is studied. All anions must change their positions by a small amount; one-third of the cation positions inγ′ and more than 90 pct of cation positions inδ experience a large translation during that transformation. This implies that for theγ′ it→γ} →δ transformation, the positions of cations in both lattices are important. The results are discussed in relation to the fiber-matrix interaction under spinel formation during thermal loading ofδ-Al₂O₃-fiber-reinforced aluminum piston alloys.     

An Investigation of the Massive Transformation from Ferrite to Austenite in Laser-Welded Mo-Bearing Stainless Steels

A series of 31 Mo-bearing stainless steel compositions with Mo contents ranging from 0 to 10 wt pct and exhibiting primary δ-ferrite solidification were analyzed over a range of laser welding conditions to evaluate the effect of composition and cooling rate on the solid-state transformation to γ-austenite. Alloys exhibiting this microstructural development sequence are of particular interest to the welding community because of their reduced susceptibility to solidification cracking and the potential reduction of microsegregation (which can affect corrosion resistance), all while harnessing the high toughness of γ-austenite. Alloys were created using the arc button melting process, and laser welds were prepared on each alloy at constant power and travel speeds ranging from 4.2 to 42 mm/s. The cooling rates of these processes were estimated to range from 10 K (°C)/s for arc buttons to 10⁵ K (°C)/s for the fastest laser welds. No shift in solidification mode from primary δ-ferrite to primary γ-austenite was observed in the range of compositions or welding conditions studied. Metastable microstructural features were observed in many laser weld fusion zones, as well as a massive transformation from δ-ferrite to γ-austenite. Evidence of epitaxial massive growth without nucleation was also found when intercellular γ-austenite was already present from a solidification reaction. The resulting single-phase γ-austenite in both cases exhibited a homogenous distribution of Mo, Cr, Ni, and Fe at nominal levels.     

Lattice misfits in four binary Ni-Base γ/γ1 alloys at ambient and elevated temperatures

High-temperature X-ray diffractometry was used to determine thein situlattice parameters,a _γ anda _γ′, and lattice misfits, δ = (a _γ′, -a _γ)/a _γ, of the matrix (γ) and dispersed γ′-type (Ni₃X) phases in polycrystalline binary Ni-Al, Ni-Ga, Ni-Ge, and Ni-Si alloys as functions of temperature, up to about 680 °C. Concentrated alloys containing large volume fractions of theγ′ phase (∼0.40 to 0.50) were aged at 700 °C to produce large, elastically unconstrained precipitates. The room-temperature misfits are 0.00474 (Ni-Al), 0.01005 (Ni-Ga), 0.00626 (Ni-Ge), and -0.00226 (Ni-Si), with an estimated error of ± 4 pct. The absolute values of the lattice constants of theγ andγ′ phases, at compositions corresponding to thermodynamic equilibrium at about 700 °C, are in excellent agreement with data from the literature, with the exception of Ni₃Ga, the lattice constant of which is much larger than expected. In Ni-Ge alloys, δ decreases to 0.00612 at 679 °C, and in Ni-Ga alloys, the decrease is to 0.0097. In Ni-Si and Ni-Al alloys, δ exhibits a stronger temperature dependence, changing to-0.00285 at 683 °C (Ni-Si) and to 0.00424 at 680 °C (Ni-Al). Since the times required to complete the high-temperature X-ray diffraction (XRD) scans were relatively short (2.5 hours at most), we believe that the changes in δ observed are attributable to differences between the thermal expansion coefficients of theγ andγ′ phases, because the compositions of the phases in question reflect the equilibrium compositions at 700 δC. Empirical equations are presented that accurately describe the temperature dependences ofa _γ,a _γ′, and δ over the range of temperatures of this investigation.     

A new criterion for internal crack formation in continuously cast steels

To estimate the cracking condition in continuously cast steels, a new model for critical fracture stress given from the measured critical strain has been proposed, which can take into account the brittle temperature range and strain rate. The effects of brittle temperature range and strain rate on critical strain for internal crack formation were analyzed. When the brittle temperature range and strain rate were increased, the possibility of internal crack formation increased due to the decreasing critical strain. To describe the thermomechanical property model of the mushy zone between zero strength temperature (ZST) and zero ductility temperature (ZDT), the yield criterion for porous metals, which can take into account δ/γ transformation, was used. Using the fitting equation for the measured critical strain and the microsegregation analysis, the thermomechanical behavior of the mushy zone could be successfully described by the proposed model, which incorporates the effects of microsegregation of solute elements and δ/γ transformation on hot tear during solidification at the given range of steel compositions and strain rates. A cracking criterion based on the difference of deformation energy in the brittle temperature range is proposed to explain the cracking phenomenon of whole carbon range.     

Effects of interstitial oxygen on microstructure and mechanical properties of Ti-48Al-2Cr-2Nb with fully lamellar and duplex microstructures

The effect of added oxygen in the range of 1000 to 4000 wt ppm on the microstructures of a Ti-48Al-2Cr-2Nb alloy has been investigated and compared to the microstructures for a high-purity alloy. For specimens cooled from theα phase, interstitial oxygen stabilizes the lamellar microstructure with respect toγ grains, with higher than equilibrium values for theα ₂ volume fraction. For specimens cooled from theα +γ phase field, the lamellar microstructure still tends to be favored by oxygen, but it is found that the phase volume fractions are not significantly different from equilibrium values. This suggests that interstitial O essentially reduces the kinetics of theα toα +γ transformation. Thus, interstitial oxygen will have a strong effect on microstructures obtained by continuous cooling fromα, but significantly less on those, such as the duplex microstructure, obtained by long treatment in theα +γ phase field. In general, increased O content is well correlated with reduced ductility. Finally, the role of interstitial oxygen on this phase transformation is discussed.     

Precipitation of the δ-Ni3Nb phase in two nickel base superalloys

The precipitation of the equilibrium δ-Ni₃Nb phase has been studied in two niobium bearing nickel base superalloys—INCONEL 718 and INCONEL* 625—both of which are hardenable by the precipitation of the metastableγ″-Ni₃Nb phase. The morphology and the distribution of precipitates have been examined and the crystallographic orientation relationship between the austenite and theδ phases has been determined. The nucleation of theδ phase at stacking faults within pre-existing δ" precipitates has been discussed.     

Nucleation and phase selection in undercooled Fe-Cr-Ni melts: Part II. Containerless solidification experiments

The solidification behavior of undercooled Fe-Cr-Ni melts of different compositions is investigated with respect to the competitive formation of δ-bcc (ferrite) and γ-fcc phase (austenite). Containerless solidification experiments, electromagnetic levitation melting and drop tube experiments of atomized particles, show that δ (bcc) solidification is preferred in the highly undercooled melt even at compositions where δ is metastable. Time-resolved detection of the recalescence events during crystallization at different undercooling levels enable the determination of a critical undercooling for the transition to metastable bcc phase solidifcation in equilibrium fcc-type alloys. Measurements of the growth velocities of stable and metastable phases, as functions of melt undercooling prior to solidification, reveal that phase selection is controlled by nucleation. Phase selection diagrams for solidification processes as functions of alloy composition and melt undercooling are derived from two types of experiments: X-ray phase analysis of quenched samples and in situ observations of the recalescence events of undercooled melts. The experimental results fit well with the theoretical predictions of the metastable phase diagram and the improved nucleation theory presented in an earlier article. In particular, the tendency of metastable δ phase formation in a wide composition range is confirmed.     

Solute redistribution during and after solidification of Ni-Al-Ta dendritic monocrystals

Dendritic Monocrystals of Ni-Al-Ta alloys were grown at 0.05, 0.25, and 2.00 m/h and in some cases at other intermediate rates, under thermal gradients of 8 × 10³ and 18 × 10³ K/m. The growth of such monocrystals provides a rapid and easy way for:a) establishing the distribution of solute during and after solidification, as well as its dependence on local cooling rate; b) determining the effect of dendritic coarsening on this distribution and; c) studying the solution kinetics of the nonequilibrium interdendritic γ′ phase. Back-diffusion in the solid rather than dendritic coarsening was found to control the evolution of the solute distribution profile across the dendritic structure during solidification. With increasing local cooling rate the maximum solute concentration,C _M, remained practically unchanged, the minimum solute concentration,C _m, slightly decreased, the segregation ratio,S = C _M/C_m, increased and so did the volume fraction of nonequilibrium interdendritic γ′ phase. This phase dissolved during crystal pulling much faster at higher crystal growth rates. Solution kinetics were found to depend on the dimensionless parameterDθ/L ², whereD is diffusivity of solute at a given temperature at which a given transverse cross-section of the crystal remains for a timeθ andL is half the primary dendrite arm spacing.     

Effect of heat treatments on phase chemistry of the Nickel-Base superalloy SRR 99

The average phase composition of the single-crystal nickel-base alloy SRR 99 after solution treatment, single and double stage annealing, and overaging has been determined by energy dispersive X-ray spectrometry (EDX) (HPGe detector) in a transmission electron microscope (TEM). Calculations of hypothetical nominal compositions for the alloy, using measured compositions ofγ′ phase and matrix as a function of the volume fraction ofγ′ phase, allow determination of the volume fraction ofγ′ phase at the minimum error between nominal composition and hypothetical nominal composition. After single-stage annealing, theγ′ concentrations of W, Al, and Co are higher, and those of Cr, Ta, Ti, and Ni are lower near the phase boundary compared to the average concentration of a precipitate. These concentration gradients and the integral concentrations of element in theγ′ phase are interpreted by the temperature-dependent solubility of elements in theγ′ phase.