Macrosegregation caused by thermosolutal convection during directional solidification of Pb-Sb alloys

Pb-2.2 and 5.8 wt pct Sb alloys were directionally solidified with a positive thermal gradient of 140 K cm⁻¹ at growth speeds ranging from 0.8 to 30 μm s⁻¹, and then quenched to retain the mushyzone morphology. Chemical analysis along the length of the directionally solidified portion and in the quenched melt ahead of the dendritic array showed extensive longitudinal macrosegregation. Cellular morphologies growing at smaller growth speeds are associated with larger amounts of macrosegregation as compared with the dendrities growing at higher growth speeds. Convection is caused, mainly, by the density inversion in the overlying melt ahead of the cellular/dendritic array because of the antimony enrichment at the array tip. Mixing of the interdendritic and bulk melt during directional solidification is responsible for the observed longitudinal macrosegregation.     

Macrosegregation in ternary systems

The paper presents a theoretical approach to the macrosegregation in ternary systems caused by mixing in the liquid bulk melt. Contrary to binary alloys, at least two concentration gradients exist in the heterogeneous solid-liquid zone of solidifying ternary alloys. The corresponding temperature gradients are called the partial temperature gradients. The concept of these partial temperature gradients permits to calculate the segregation of the dissolved elements. Experiments were carried out with iron-carbon-manganese and iron-carbon-sulphur alloys in a unidirectional solidification device. The results are in good agreement with the theoretical calculations if the additional mass transfer from the interdendritic melt into the bulk liquid is taken into account in the same way as was done with binary alloys. The way by which the dissolved elements mutually influence each other is discussed.     

Modeling of globular equiaxed solidification with a two-phase approach

A two-phase volume averaging model for globular equiaxed solidification is presented. Treating both liquid and solid (disperse grains) as separated but highly coupled interpenetrating continua, we have solved the conservation equations for mass, momentum, species mass fraction, and enthalpy for both phases. We also consider the conservation of grain density. Exchange or source terms take into account interactions between the melt and the solid, such as mass transfer (solidification and melting), friction and drag, solute redistribution, release of latent heat, and nucleation. An ingot casting with a near globular equiaxed solidification alloy (Al-4 wt pct Cu) is simulated. Results including grain evolution, melt convection, sedimentation, solute transport, and macrosegregation formation are obtained. The mechanisms producing these results are discussed in detail.     

Macrosegregation of Impurities in Directionally Solidified Silicon

Directional solidification of molten metallurgical-grade Si was carried out in a vertical Bridgman furnace. The effects of changing the mold velocity from 5 to 110 μm seconds^–1 on the macrosegregation of impurities during solidification were investigated. The macrostructures of the cylindrical Si ingots obtained in the experiments consist mostly of columnar grains parallel to the ingot axis. Because neither cells nor dendrites can be observed on ingot samples, the absence of precipitated particles and the fulfillment of the constitutional supercooling criterion suggest a planar solid–liquid interface for mold velocities ≤10 μm seconds^–1. Concentration profiles of several impurities were measured along the ingots, showing that their bottom and middle are purer than the metallurgical Si from which they solidified. At the ingot top, however, impurities accumulated, indicating the typical normal macrosegregation. When the mold velocity decreases, the macrosegregation and ingot purity increase, changing abruptly for a velocity variation from 20 to 10 μm seconds^–1. A mathematical model of solute transport during solidification shows that, for mold velocities ≥20 μm seconds^–1, macrosegregation is caused mainly by diffusion in a stagnant liquid layer assumed at the solid–liquid interface, whereas for lower velocities, macrosegregation increases as a result of more intense convective solute transport.     

Formation of macrosegregation by multicomponent thermosolutal convection during the solidification of steel

The formation of macrosegregation by multicomponent thermosolutal convection during the solidification of steel is simulated by simultaneously solving macroscopic mass, momentum, energy, and species conservation equations with full coupling of the temperature and concentrations through thermodynamic equilibrium at the solid/liquid interface. The flow field, solid fraction evolution, and macrosegregation patterns for four cases are presented. The results show both the formation of channel segregates and the formation of islands of mush surrounded by bulk melt. In examining the solidification of a ten-element steel, the global extent of macrosegregation of an element is found to be linearly dependent on its partition coefficient (more severe segregation for small partition coefficient), although such scaling is not possible locally. Results for the solidification of a binary Fe-C alloy (with the same carbon content as the ten-element alloy) are similar to those for the ten-element alloy due solely to the large contribution of carbon to buoyancy driven flow in the ten-element steel chosen for study. While including only those elements that make significant contributions to buoyancy driven flow reproduces the global extent of macrosegregation seen in the ten-element alloy, local differences in the predictions are visible. Finally, comparison of results for the solidification of the same ten-element steel using two different sets of data to describe the partition coefficients and change in liquidus temperature with concentration of the elements shows completely opposite behavior,i.e., upward flow through the mushy zone for one case and downward flow for the other. Thus, the need to have accurate phase-equilibrium data when modeling multicomponent macrosegregation is illustrated. Together, the results give an indication of what areas require more careful examination if accurate modeling of multicomponent solidification is to be accomplished.     

Simulation of convection and macrosegregation in a large steel ingot

Melt convection and macrosegregation in casting of a large steel ingot are numerically simulated. The simulation is based on a previously developed model for multicomponent steel solidification with melt convection and involves the solution of fully coupled conservation equations for the transport phenomena in the liquid, mush, and solid. Heat transfer in the mold and insulation materials, as well as the formation of a shrinkage cavity at the top, is taken into account. The numerical results show the evolution of the temperature, melt velocity, and species concentration fields during solidification. The predicted variation of the macrosegregation of carbon and sulfur along the vertical centerline is compared with measurements from an industrial steel ingot that was sectioned and analyzed. Although generally good agreement is obtained, the neglect of sedimentation of free equiaxed grains prevents the prediction of the zone of negative macrosegregation observed in the lower part of the ingot. It is also shown that the inclusion of the shrinkage cavity at the top and the variation of the final solidification temperature due to macrosegregation is important in obtaining good agreement between the predictions and measurements.     

Modeling of macrosegregation caused by volumetric deformation in a coherent mushy zone

A two-phase volume-averaged continuum model is presented that quantifies macrosegregation formation during solidification of metallic alloys caused by deformation of the dendritic network and associated melt flow in the coherent part of the mushy zone. Also, the macrosegregation formation associated with the solidification shrinkage (inverse segregation) is taken into account. Based on experimental evidence established elsewhere, volumetric viscoplastic deformation (densification/dilatation) of the coherent dendritic network is included in the model. While the thermomechanical model previously outlined (M. M’Hamdi, A. Mo, and C.L. Martin: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 2081–93) has been used to calculate the temperature and velocity fields associated with the thermally induced deformations and shrinkage driven melt flow, the solute conservation equation including both the liquid and a solid volume-averaged velocity is solved in the present study. In modeling examples, the macrosegregation formation caused by mechanically imposed as well as by thermally induced deformations has been calculated. The modeling results for an Al-4 wt pct Cu alloy indicate that even quite small volumetric strains (≈2 pct), which can be associated with thermally induced deformations, can lead to a macroscopic composition variation in the final casting comparable to that resulting from the solidification shrinkage induced melt flow. These results can be explained by the relatively large volumetric viscoplastic deformation in the coherent mush resulting from the applied constitutive model, as well as the relatively large difference in composition for the studied Al-Cu alloy in the solid and liquid phases at high solid fractions at which the deformation takes place.     

The rate of absorption of hydrogen into iron and of nitrogen into Fe-Cr and Fe-Ni-Cr alloys containing sulfur

The rate of absorption of hydrogen into liquid iron and of nitrogen into liquid Fe-Cr alloys containing various levels of sulfur was measured by using a constant-volume Sieverts apparatus employing a sensitive pressure transducer. The rate for the absorption of hydrogen was measured by using H2 containing a small amount of H₂S(<0.2 pct) such that the activity of sulfur on the surface of the melt was the same as in the bulk metal. The hydrogen-absorption rate for Fe-S melts containing up to 0.72 pet sulfur was virtually independent of sulfur content and controlled by liquid-phase mass transfer. The liquidphase mass-transfer coefficient for hydrogen in liquid iron, calculated from the results, was comparable to that for nitrogen transfer in liquid iron. The rate of absorption of nitrogen into Fe-Cr melts with low-sulfur contents was controlled by liquid-phase mass transfer. For melts containing significant amounts of sulfur it was controlled by both mass transfer and the chemical rate of the dissociation of nitrogen on the surface in series. Equations were developed to calculate the chemical rate from the measured rate, correcting for mass transfer. The chemical rate decreased with increasing sulfur content as expected, because sulfur is strongly adsorbed on the surface and increased with chromium content at constant sulfur activity, possibly because available Cr sites promote nitrogen dissociation. Formerly with United States Steel Corporation, Monroeville, PA     

Principles of macrosegregation caused by mixing flow in the liquid bulk melt

A theoretical model is presented describing the macrosegregation caused by mixing flow in the liquid bulk melt for the case where the melt solidifies with formation of a heterogeneous solid-liquid zone. The model is based on the boundary layer concept applied to the plane of the dendrite tips combined with the condition , a condition necessary to remove the constitutional supercooling. On this basis the enrichment of the solute in the liquid bulk melt during solidification is calculated. In order to obtain the distribution of the solute in the solid phase the concentration profile within the interdendritic melt is calculated. This allows to determine the solute distribution in the solid. Three cases, namely those of complete, partially, and no equalization of the solute within the dendrites during solidification are treated seperately. The thickness of the heterogeneous layer for the three cases and the percentage of eutectic crystallisation are also determined.     

Redistribution of second phase particles in solidifying alloy melts—entrapment and microsegregation within dendritic networks

Particles disperesed in a melt get redistributed during solidifacation due to buoyant motion and interactactions between the particles and the solidification front. In alloy melts the distortion of the concentration field by the particle leads to entrapment of the particle within the dendritic network. The particles are forced to be confined to the interdenritic eutectic thereby causing a “microsegregation” of the particles in addition to the “macrosegregation” brought about by buoyant motion. In this paper a computer model which simulates the movement and segregation of particles in solidifying alloy melts, is described. The effect of particle size, particle volume fraction and heat extraction rate on the segregation is demonstrated for SiC particles in solidifying Al−4.5% Cu melts. The model can be used for predicting the particle distribution in cast metal matrix composites.     

The kinetics of S35 exchange between SO2/CO/CO2 gas mixtures and copper sulfide melts at 1523 K

The kinetics and mechanisms of oxidation of copper sulfide melts have been investigated using a radioisotope exchange technique. Copper sulfide melts were doped with S³⁵. The transfer of the radioisotope between the melt and SO₂/CO/CO₂ gas mixtures in chemical equilibrium with the melt was monitored by analyzing the changes in radioactivity of the gas. Analysis of the results indicates that the rate-limiting chemical reaction involves the formation of an activated complex SO, and the rate of exchange of the sulfur isotope at 1523 K is described by the relationshipR = 6.4(±2) (P _CO /P _CO2 )P _SO2 g atom S m⁻² s⁻¹. formerly Research Assistant, University of Queensland formerly Postdoctoral Fellow, University of Queensland     

Mathematical modeling of macrosegregation of iron carbon binary alloy: Role of double diffusive convection

During alloy solidification, macrosegregation results from long range transport of solute under the influence of convective flow and leads to nonuniform quality of a solidified material. The present study is an attempt to understand the role of double diffusive convection resulting from the solutal rejection in the evolution of macrosegregation in an iron carbon system. The solifification process of an alloy is governed by conservation of heat, mass, momentum, and species and is accompanied by the evolution of latent heat and the rejection or incorporation of solute at the solid liquid interface. Using a continuum formulation, the goverming equations were solved using the finite volume method. The numerical model was validated by simulating experiments on an ammonium chloride water system reported in the literature. The model was further used to study the role of double diffusive convection in the evolution of macrosegregation during solidification of Fe 1 wt pct C alloy in a rectangular cavity. Simulation of this transient process was carried out until complete solidification, and the results, depicting the influence of flow field on thermal and solutal field andvice versa, are shown at various stages of solidification. Under the given set of parameters, it was found that the thermal buoyancy affects the macrosegregation field globally, whereas the solutal buoyancy has a localized effect.     

A mathematical approach for the mass transfer between liquid steel and an ascending bubble

A mathematical model which is adaptable to practical conditions has been put forward to deseribe adequately the purging of liquid steel with an inert gas. The mass transfer between liquid steel with varying C, O, H, N, and S contents and an ascending argon bubble has been investigated. The simultaneous mass transfer of all possible gaseous compounds is considered as a function of the initial bubble mass, height of the steel bath, the bulk concentrations in the melt, and the external pressure. The model takes into account the change in size and form of the bubble resulting from its rise and the mass transfer between the bubble and the melt, and also the influence of surface active agents such as sulfur and oxygen. The following general conclusions can be drawn: 1) the gases flushed (out of the melt) by the bubble can be related to the amount of argon injected into the bath. 2) Increase in the initial bubble size and the content of the gas in the bath to be purged, and decrease in the external pressure result in more pronounced deviations from equilibrium saturation within the bubble. 3) Lower external pressure, increasing supersaturation of CO, and greater amounts of purging gas at higher dispersion are the chief factors responsible for increasing, purging efficiency for H, N₂, CO in steel melts. 4) Surface-active agents decrease the purging ratio for nitrogen in a carbon-free melt, but, in carbon-containing melts, increasing amounts of oxygen alone lead to a considerable increase in the purging ratios for nitrogen due to the high mass transfer of CO to the bubble. In the latter case, the effect of increasing sulfur content on the purging ratios is of no significance. KAZUO OKOHIRA, formerly Graduate Student at the Institut für Eisenhüttenkunde at Aachen HERMANN SCHENCK, Dr.-Ing., Dr.-Ing. E.h., Dr.h.e., formerly Director of the Institut für Eisenhüttenwesen, President of the German Iron and Steel Institute (VDEh) from 1950 to 1968 This paper is based in part on a thesis submitted by KAZUO OKOHIRA in partial fulfillment of the requirements for degree of Doktor-Ingenieur at the Technische Hochschale, Aachen.     

Macrosegregation in Rotated Remelted Ingots

A computer model is presented for predicting macrosegregation in rotated electroslag or vacuum arc remelted ingots. Sample calculations of segregation are carried out for ingots of the model alloy Sn-12 pet Pb in which the liquid density increases during solidification and for two hypothetical alloys; in one, the liquid density decreases during solidification, and in the other, liquid density first increases and then decreases during solidification. In alloys such as Sn-Pb in which liquid density increases during solidification, segregation is positive at the ingot centerline and if solidification is sufficiently slow, “freckles” form near the centerline. Positive segregation and freckles are found at the outer periphery of the ingot when liquid density decreases during solidification. Positive segregation and freckles are found at midradius when liquid density first increases and then decreases during solidification, and when the solidus isotherm changes shape abruptly at midradius (with density increasing during solidification). Ingot rotation, by introducing a radial component to the force field, alters interdendritic flow behavior and therefore macrosegregation. Modest rotation speeds eliminate “freckles” and reduce macrosegregation in all modeling studies conducted. Greater rotational speeds can accentuate the segregation. Experiments were conducted on simulated remelted ingots of Sn-Pb alloy. The ingots were 8 cm diam, rotated at speeds up to 119 rpm and solidified at rates from 5.3 × 10^?3 to 1.36 × 10^?2 cm/s. Segregation behavior obtained agrees qualitatively and quantitatively with theory.     

Modeling of marangoni-induced droplet motion and melt convection during solidification of hypermonotectic alloys

A two-phase volume averaging approach to model Marangoni-induced droplet motion of the minority liquid phase and the convection in the parent melt during solidification of the hypermonotectic alloys is presented. The minority liquid phase decomposed from the parent melt as droplets in the miscibility gap was treated as the second-phase L ₂. The parent melt including the solidified monotectic matrix was treated as the first phase L ₁. Both phases were considered as different and spatially interpenetrating continua. The conservation equations of mass, momentum, solute, and enthalpy for both phases, and an additional transport equation for the droplet density, were solved. Nucleation of the L ₂ droplets, diffusion-controlled growth, interphase interactions such as Marangoni force at the L ₁-L ₂ interface, Stokes force, solute partitioning, and heat release of decomposition were taken into account by corresponding source and exchange terms in the conservation equations. The monotectic reaction was modeled by adding the latent heat on the L ₁ phase during monotectic reaction, and applying an enlarged viscosity to the solidified monotectic matrix. A two-dimensional (2-D) square casting with hypermonotectic composition (Al-10 wt pct Bi) was simulated. This paper focused on Marangoni motion, hence gravity was not included. Results with nucleation, droplet evolution, Marangoni-induced droplet motion, solute transport, and macrosegregation formation were obtained and discussed.     

Advanced Solute Conservation Equations for Dendritic Solidification Processes Part II: Numerical Simulations and Comparisons

The mathematical model of derived solute equations in part I for equiaxed dendritic solidification with melt convection streams and interdendritic thermo‐metallurgical strain is applied numerically to predict macrosegregation distributions with different diffusing mechanisms in dendritic solid. Numerical and experimental results are present for solidification of a Al–4.5% Cu alloy inside horizontal rectangular cavity at different superheats. The numerical simulations were performed by using simpler method developed by Patanker. The experiments were conducted to measure the cooling curves via thermocouples and the metallurgical examinations to measure the grain size and macrosegregation distributions in Part I. Preliminary validity of the model is demonstrated by the qualitative and quantitative agreements between the measurements and predications of cooling curves and predicted macrosegregation distributions including mushy permeability and interdendritic strain. In addition, several important features of macrosegregation in equiaxed dendritic solidification are identified through this combined experimental and numerical study. Also, quantitative agreements between the numerical simulations and experiments reveal several areas for future research work. The differences and errors between predicted macrosegregation results under different diffusing mechanisms have been discussed.     

Vacuum distillation of copper matte to remove lead,arsenic, bismuth,and antimony

Vacuum-refining experiments were carried out on copper matte melts, containing 35 to 73 pct Cu, to measure the removal rates of lead, bismuth, arsenic, and antimony over the temperature range of 1373 to 1523 K under pressures in the range of 50 to 130 Pa. High rates of refining, controlled by mass transport in the liquid phase, were achieved for all impurities in melts containing up to 65 pct Cu and for chamber pressures less than 100 Pa. After 40 to 60 minutes of treatment, lead elimination was between 70 and 96 pct, bismuth elimination was between 88 and 98 pct, arsenic, elimination was between 60 and 93 pct, and antimony elimination was between 40 and 92 pct. The overall mass transfer coefficients for vacuum refining for the impurities considered fell in the range of 5×10⁻⁵ to 2×10⁻⁴ m s⁻¹. The values were insensitive to small changes in melt temperature but decreased with increasing pressure above 250 Pa. Also, the rates of refining were seen to be influenced by the sulfur and oxygen activity in the melt. The evaporation and subsequent elimination of the impurities were mathematically modeled by extending previously published models beyond consideration only of evaporation of monomers to consideration of the evaporation of monomers and dimer compounds. The model showed that due to the contributions to the refining by evaporation of each of the metallic, oxide, or sulfide vapor species, arsenic and antimony exhibited a maximum in refining rates atP _{o 2} andP _{s 2} potentials corresponding to matte grades of about 55 pct copper, whereas lead showed a minimum at about the same matte grade, and bismuth showed a continuously decreasing rate of refining with increasing matte grade. The model was also used to simulate the refining behavior of copper matte melts. An example of a commercial-scale operation is given.     

Computational modelling of heat⧹mass transfer near the LIQUID–SOLID interface during rapid solidification of binary metal alloys under laser treatment

This paper presents the results of an investigation into the problem of planar solid–liquid interface stability during rapid solidification of binary metal alloys under laser treatment. A new quantitative model is proposed. This model describes the self-organized development of stable spatially-periodic vortices in the melt near the solid–liquid interface due to concentration- (or thermal) capillary effectsfn2 together with effects due to the influence of normal concentration or temperature gradients directed from the interface towards the melt. These vortices give rise to a cellular structure at the solid–liquid interface of rapidly frozen melts.A computer code was developed to solve the set of second-order linear differential equations which describe heat and mass transfer at the liquid–solid interface. This model allows calculation of the liquid phase velocity field, the second component concentration field in the melt, as well as the temperature field in the liquid and solid phases near the solid–liquid interface at a given solidification rate.     

Effect of permanent magnet stirring on internal quality of steel

Permanent magnet stirring (PMS) featuring low power dissipation and high-intensity magnetic field was investigated as a means of decreasing internal solidification defects. In this study, the magnetic Taylor number (Ta) was used to quantify the melt ?ow. Initial research of PMS involved a laboratory study of the solidification of Sn–20 wt-% Pb alloy. An industrial plant trial with continuously cast tire cord steel confirmed that PMS, in accord with the laboratory findings, produced an improvement in central cavities in the cast product. Moreover, it was established that PMS is an alternative method for reducing carbon macrosegregation in tire cord steel billets with different section sizes. It was also found that PMS (Ta?=?8.97?×?10⁷) was more effective for improving central carbon macrosegregation of tire cord steel than electromagnetic stirring (Ta?=?6.33?×?10⁷) due to the larger Ta related to the driven-flow intensity of the residual melt.     

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.