Showing papers in "Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science in 1991"

Behavior of metal alloys in the semisolid state

Abstract: During dendritic solidification of castings and ingots, a number of processes take place simultaneously within the semisolid region. These include crystallization, solute redistribution, ripening, interdendritic fluid flow, and solid movement. The dendritic structure which forms is greatly affected by convection during the early stages of solidification. In the limit of vigorous convection and slow cooling, grains become spheroidal. Alloys with this microstructure possess rheological properties in the semisolid state which are quite different from those of dendritic alloys. They behave thixotropically, and viscosity can be varied over a wide range, depending on processing conditions. The metal structure and its rheological properties are retained after solidification and partial remelting. The semisolid alloys can be formed in new ways, broadly termed «semisolid metal (SSM) forming processes». Some of these are now employed commercially to produce metal components and are also used to produce metal-matrix composites

A volume-averaged two-phase model for transport phenomena during solidification

Abstract: A basic model of the transport phenomena occurring during solidification of multicomponent mixtures is presented. The model is based on a two-phase approach, in which each phase is treated separately and interactions between the phases are considered explicitly. The macroscopic transport equations for each phase are derived using the technique of volumetric averaging. The basic forms of the constitutive relations are developed. These relations link the macroscopic transport phenomena to microscopic processes such as microstructure development, interfacial stresses, and interfacial heat and mass transfer. Thermodynamic relations are presented, and it is shown that nonequilibrium effects can be addressed within the framework of the present model. Various simplifications of the model are examined, and future modeling needs are discussed.

Mathematical modeling of the isothermal impingement of liquid droplets in spraying processes

Abstract: A mathematical representation has been developed and computed results are presented describing the spreading of droplets impacting onto a solid substrate. Problems of this type are of major practical interest in plasma spraying (PS) and in spray forming (SF) operations. While the present study was confined to the fluid flow aspects of the process, information has been generated on both the final splat dimensions and on the time required to complete the spreading process. Through this treatment, it is possible to relate these quantities (the splat size and the spreading time) to the operating conditions,i.e., droplet size and droplet velocity, and material properties. The theoretical predictions were found to be in good agreement with both Madejski’s asymptotic solution[17] and with available experimental results. For typical SF conditions (droplet sizes in the 100-µm range and droplet velocities in the 100 m/s range), the spreading times were of the order of microseconds,i.e., significantly shorter than the estimated solidification time.

Simulation of freckles during vertical solidification of binary alloys.

Abstract: A mathematical model of solidification that simulates the formation of channel segregates or freckles is presented. The model simulates the entire solidification process starting with the initial melt to the solidified cast, and the resulting segregation is predicted. Emphasis is given to the initial transient, when the dendritic zone begins to develop and the conditions for the possible nucleation of channels are established. The mechanisms that lead to the creation and eventual growth or termination of channels are explained in detail and illustrated by several numerical examples. Predictions of the pattern and location of channels in different cooling situations are in good agreement with experimental observations.

The energy and solute conservation equations for dendritic solidification

Abstract: The energy equation for solidifying dendritic alloys that includes the effects of heat of mixing in both the dendritic solid and the interdendritic liquid is derived. Calculations for Pb-Sn alloys show that this form of the energy equation should be used when the solidification rate is relatively high and/or the thermal gradients in the solidifying alloy are relatively low. Accurate predictions of transport phenomena in solidifying dendritic alloys also depend on the form of the solute conservation equation. Therefore, this conservation equation is derived with particular consideration to an accounting of the diffusion of solute in the dendritic solid. Calculations for Pb-Sn alloy show that the distribution of the volume fraction of interdendritic liquid (gL) in the mushy zone is sensitive to the extent of the diffusion in the solid. Good predictions ofgL are necessary, especially when convection in the mushy zone is calculated.

Slag foaming in bath smelting

Abstract: Slag foaming measurements in terms of the foaming index (∑) were conducted on bath smelting-type slags (CaO-SiO2-FeO, CaO-SiO2-MgO-Al2O3-FeO) at 1773 K. It was found that the slag foam stability decreases with increasing FeO (FeO > 2 pct) content and basicity. For the slag system (CaO-SiO2-FeO), no stable foam was observed at very low FeO content (<2 pct). As pct FeO increases, the slag foaming index goes through a maximum and then decreases; a similar phenomenon was observed for CaO-SiO2-NiO slags with respect to the NiO content. The foaming index determined from the normal small-scale experiments (3.8-cm ID diameter) were confirmed on a larger scale (9.2-cm ID diameter), indicating that the foaming index is independent of container size. Measurements were also made for the actual compositions for bath smelting slags. For these slags, the foaming index is higher than those of simple CaO-SiO2-FeO slags, because MgO and Al2O3 may increase their viscosities. The foam index is believed to be a function of the physical properties of the slag. Consequently, a dimensional analysis was performed, and a correlation was developed relating the foaming index to the viscosity, surface tension, and density of the slag. An estimation of slag foaming in actual pilot plant trials was also made from the results of the present study. Good agreement was observed between the predicted and observed foam heights and indicated coke in the slag can reduce the foam height by more than 50 pct.

Effect of evaporation and temperature-dependent material properties on weld pool development

Abstract: This paper evaluates the effect of weld pool evaporation and thermophysical properties on the development of the weld pool. An existing computational model was modified to include vaporization and temperature-dependent thermophysical properties. Transient, convective heat transfer during gas tungsten arc (GTA) welding with and without vaporization effects and variable properties was studied. The present analysis differs from earlier studies that assumed no vaporization and constant values for all of the physical properties throughout the range of temperature of interest. The results indicate that consideration of weld pool vaporization effects and variable physical properties produce significantly different weld model predictions. The calculated results are consistent with previously published experimental findings.

Mold behavior and its influence on quality in the continuous casting of steel slabs: Part II. Mold heat transfer, mold flux behavior, formation of oscillation marks, longitudinal off-corner depressions, and subsurface cracks

Abstract: Axial heat-flux profiles have been determined quantitatively from temperature measurements conducted on a slab mold under routine operating conditions. As in earlier studies, the heat flux was observed to have a maximum value at the meniscus and to decline with increasing distance down the mold. The mold heat flux increased with increasing casting speed and was greater with a mold powder having lower viscosity and melting point being applied as lubricant. The heat extraction was largest while casting 0.29 pet carbon steel and least for a 0.09 pet carbon grade; reducing the depth of the submerged entry nozzle increased the heat flux slightly in the upper region of the mold. Most significant was the higher heat flux observed at the meniscus of the outside-radius face, attributable to the locally greater copper plate thickness compared to that of the opposite broad face. All of the measurements can be explained straightforwardly by heat flow in the vicinity of the meniscus and the resulting behavior of the so-called slag rim adjacent to the mold wall. It is postulated that the difference in copper plate thickness between the two broad faces at the meniscus causes the slag rim to be smaller on the outside-radius face which gives rise to shallower oscillation marks, as observed, higher heat transfer, and a slightly thicker solid shell. The dissimilar behavior has implications for quality because the inside-radius shell, experiencing reduced heat extraction, cools and shrinks less than the outside-radius shell. Thus, for a given end-plate taper, the narrow face of the slab adjacent to the inside radius can push against the end plate, accelerating copper wear, and, owing to squeezing of the broad face, cause an off-corner depression and subsurface crack toward the mold exit. If this is correct, maintenance of the same copper plate thickness at the meniscus is fundamental to preventing such an occurrence. Moreover, adjustment of the heat extraction at the meniscus should be achievable by changing copper plate thickness, mold coating thickness/conductivity, cooling water velocity, cooling channel configuration, and mold flux composition for a given steel grade.

Heat flux transients at the casting/chill interface during solidification of aluminum base alloys

Abstract: Heat flow at the metal/chill interface of bar-type castings of aluminum base alloys was modeled as a function of thermophysical properties of the chill material and its thickness. Experimental setup for casting square bars of Al-13.2 pct Si eutectic and Al-3 pet Cu-4.5 pct Si long freezing range alloys with chill at one end exposed to ambient conditions was fabricated. Experiments were carried out for different metal/chill combinations with and without coatings. The thermal history at nodal locations in the chill obtained during the experiments was used to estimate the interface heat flux by solving a one-dimensional Fourier heat conduction equation inversely. Using the data on transient heat flux q, the heat flow at the casting/chill interface was modeled in two steps: (1) The peak in the heat flux curve qmax was modeled as a power function of the ratio of the chill thickness d to its thermal diffusivity a, and (2) the factor (q/qmax) X α0.05 was also modeled as a power function of the time after the solidification set in. The model was validated for Cu-10 pct Sn -2 pct Zn alloy chill and Al-13.2 pct Si and Al-3 pct Cu-4.5 pct Si as the casting alloys. The heat flux values estimated using the model were used as one of the boundary conditions for solidification simulation of the test casting. The experimental and simulated temperature distributions inside the casting were found to be in good agreement.

Magnetohydronamic and thermal behavior of electroslag remelting slags

Abstract: The paper is based on the development and use of a mathematical model that simulates the electroslag remelting (ESR) operation. The model assumes axisymmetrical geometry and steady state. Maxwell equations are first solved to determine the electromagnetic forces and Joule heating. Next, coupled fluid flow and heat transfer equations are written for the two liquids (slag and liquid metal). Thek-e model is used to represent turbulence. The system of coupled partial differential equations is then solved, using a control volume method. Using the operating parameters as inputs, the model calculates the current density, velocity, and temperature throughout the fluids. This paper is concerned with fluid flow and heat transfer in the slag phase. After being validated by comparing its results with experimental observation, the model is used to evaluate the influence of operating variables, such as the fill ratio, and the thermophysical properties of the slag.

Heat-flow simulation of laser remelting with experimenting validation

Abstract: A transient three-dimensional (3-D) conduction-based heat-flow model has been developed in order to simulate the experimental processing conditions during laser surface remelting. This study concentrates on the validation of the model by comparison with data obtained from laser remelting experiments made in the eutectic alloy Al-Cu 33 wt pct over a range of traverse speeds between 0.2 and 5.0 m/s. It is shown that the simulation not only requires thermophysical data, but also a good knowledge of the laser beam process parameters. When the steady state is reached, the fusion isotherm which outlines the liquid pool yields the trace cross section and the resulting microstructure. Good agreement with experimental data is found over the range of processing speeds for the maximum melt pool dimensions, the transverse profile of the laser trace, the melt surface shape, and the resolidified microstructural spacings.

Slag-metal reactions during welding: Part I. Evaluation and reassessment of existing theories

Abstract: A critical review of current thermodynamic theories of slag-metal reactions is presented. A series of preliminary experiments indicates that the previously proposed droplet theory is incorrect and the primary reactions controlling Mn, Si, and Cr content occur in the weld pool. In addition, these experiments show that the net transfer of oxygen is independent of the transfer of Mn and Si.

Slag-metal reactions during welding: Part II. Theory

Abstract: A kinetic model is developed to describe the transfer of alloying elements between the slag and the metal during flux-shielded welding. The model accounts for changes in alloy recovery based on the geometry of the resulting weld bead. It also distinguishes compositional differences between single-pass and multiple-pass weld beads. It is further shown that the final weld metal oxygen content is directly related to the weld solidification time as well as the type of flux used.

Phase transformations during heating of llmenite concentrates

Abstract: llmenite concentrates were heated in argon and oxygen in the temperature range 700 °C to 1000 °C to study the behavior of the pseudorutile phase and other changes which occur. Pseudorutile does not persist in argon or oxygen in the temperature range studied. In argon at 700 °C, pseudorutile decomposes into hematite and rutile, while at 1000 °C, it combines with ilmenite to form ferrous-ferritic pseudobrookite solid solution. A new phase “Fe2O3-2TiO2” was identified as an intermediate product during the heating of ilmenite or pseudorutile in oxygen. This compound decomposes into hematite and rutile below 800 °C and to pseudobrookite and rutile above 800 °C. The sequence of reactions during the heating of ilmenite and pseudorutile in oxygen is proposed.

Mold behavior and its influence on quality in the continuous casting of steel slabs: Part i. Industrial trials, mold temperature measurements, and mathematical modeling

Abstract: An extensive study has been conducted to elucidate mold behavior and its influence on quality during the continuous casting of slabs. The study combined industrial measurements, mathe matical modeling, and metallographic examination of cast slab samples. The industrial mea surements involved instrumenting an operating slab mold with 114 thermocouples in order to determine the axial mold wall temperature profiles for a wide range of casting conditions. A three-dimensional (3-D) heat-flow model of the mold wall was developed to characterize the heat fluxes in the mold quantitatively from the measured mold temperature data. Furthermore, heat-flow models were developed to examine steel solidification phenomena and mold flux behavior at the meniscus. Slab samples collected during the industrial trials were examined metallographically to evaluate the cast structure and defects. Owing to the length of the study, it is presented in two parts, the first of which describes the experimental techniques employed in the instrumentation of the mold together with the details of the industrial trials and mold temperature measurements. Also, the mathematical modeling technique applied to determine the axial heat-flux profiles from the measured mold temperature data is presented. It is shown that a fully 3-D model of the mold wall is needed to convert the measured temperatures to heat-flux profiles properly.

Computational modeling of stationary gastungsten-arc weld pools and comparison to stainless steel 304 experimental results

Abstract: A systematic study was carried out to verify the predictions of a transient multidimensional computational model by comparing the numerical results with the results of an experimental study. The welding parameters were chosen such that the predictions of the model could be correlated with the results of an earlier experimental investigation of the weld pool surface temperatures during spot gas-tungsten-arc (GTA) welding of Type 304 stainless steel (SS). This study represents the first time that such a comprehensive attempt has been made to experimentally verify the predictions of a numerical study of weld pool fluid flow and heat flow. The computational model considers buoyancy and electromagnetic and surface tension forces in the solution of convective heat transfer in the weld pool. In addition, the model treats the weld pool surface as a truly deformable surface. Theoretical predictions of the weld pool surface temperature distributions, the cross-sectional weld pool size and shape, and the weld pool surface topology were compared with corresponding experimental measurements. Comparison of the theoretically predicted and the experimentally obtained surface temperature profiles indicated agreement within ±8 pct for the best theoretical models. The predicted surface profiles were found to agree within ±20 pct on dome height and ±8 pct on weld pool diameter for the best theoretical models. The predicted weld cross-sectional profiles were overlaid on macrographs of the actual weld cross sections, and they were found to agree very well for the best theoretical models.

Slag-metal reactions during welding: Part III. Verification of the Theory

Abstract: A previously developed kinetic model of alloy transfer (Part II)[1] is tested experimentally for transfer of Mn, Si, Cr, P, S, Ni, Cu, and Mo. The results show very good agreement between theory and experiment. The transfer of carbon and oxygen is also discussed. It is shown that the transfer of oxygen into the weld metal occurs in the zone of droplet reactions, whereas oxygen is lost by formation and separation of inclusions in the solidifying weld pool. Methods of applying this analysis to multipass welds and active fluxes containing ferroalloy additions are also described.

Equilibrium phase relations and thermodynamics of the Cr-0 system in the temperature range of 1500 °C to 1825 °C

Abstract: Phase relations and thermodynamic properties of the Cr-O system were studied at temperatures from 1500 °C to 1825 °C. In addition to Cr and Cr2O2, a third crystalline phase was found to be stable in the temperature range from 1650 °C to 1705 °C. The atomic ratio of oxygen to chromium of this phase, which decomposes upon cooling to form Cr and Cr2O3, was determined as 1.33 + 0.02, in good agreement with the formula Cr3O4. Temperatures and phase assem blages for invariant equilibria of the Cr-O system were determined as follows: Cr2O3 + Cr + Cr3O4, 1650 °C ± 2 °C; Cr3O4 + Cr + liquid oxide, 1665 °C ± 2 °C; and Cr3O4 + Cr2O3 + liquid oxide, 1705 °C ± 3 °C. The composition of the liquid oxide phase at the eutectic temperature of 1665 °C was found to be close to CrO. Relations between oxygen pressure and temperature for the univariant equilibria of the Cr-O system were established by equilibrating Cr and/or Cr2O3 starting materials in H2-CO2 mixtures of known oxygen potentials at temper atures from 1500 ΔC to 1825 °C. From this information, the standard free-energy changes (ΔGΔ) for various reactions were calculated as follows: 2Cr (s) + 3/2O2 = Cr2O3 (s): ΔG ° = -1,092,442 + 237.94T Joules, 1773 to 1923 K; 3Cr (s) + 2O2 = Cr2O4 (s): ΔG ° =-1,355,198 + 264.64T Joules, 1923 to 1938 K; and Cr (s) + l/2O2 = CrO (1): ΔG ° =-334,218 + 63.81T Joules, 1938 to 2023 K.

In-situ technique for measuring the absorption during laser surface remelting

Abstract: The aim of this communication is to present a calorimetric method which has been used to determine the mean absorption during the dynamic process of remelting. Under specific processing conditions where most of the laser beam impinges on the liquid pool, this technique yields the absorption value in the liquid. It can also be extended to multitrack experiments or to other laser processes, such as laser surface alloying or cladding, which is not possible with stationary methods, such as ellipsometry

Numerical simulation of a solidifying Pb-Sn alloy: The effects of cooling rate on thermosolutal convection and macrosegregation

Abstract: Numerical simulations of a binary metal alloy (Pb-Sn) undergoing solidification phase change are performed using a continuum model for conservation of total mass, momentum, energy, and species. The system is contained in an axisymmetric, annular mold which is cooled along its outer vertical wall. Results show that thermosolutal convection in the melt and mushy zones is strongly coupled and that macrosegregation is reduced with increased cooling rate. For low cooling rates, solutally induced convection in the mushy zone favors the development of channels, which subsequently spawn macrosegregation in the form of A-segregates. With increasing solidification rate, however, thermosolutal interactions in the melt contribute to reducing the formation of channels and A-segregates.

The reduction mechanism of a natural chromite at 1416 °C

Abstract: The behavior of a natural chromite from the Bushveld Complex, Transvaal, South Africa, during reduction at 1416 °C by graphite was studied by means of thermogravimetric analysis, X-ray diffraction (XRD) analysis, energy-dispersive X-ray analysis (EDAX), and metallographic analysis. Experimental runs were allowed to proceed up to 120 minutes, resulting in 99 pct reduction. The specific objective of this study was to delineate the reduction mechanism of chromite by graphite. Zoning was observed in partially reduced chromites with degrees of reduction of up to about 70 pct. The inner cores were rich in iron, while the outer cores were depleted of iron. Energy-dispersive X-ray analysis revealed that Fe2+ and Cr3+ ions had diffused outward, whereas Cr2+, Al3+, and Mg2+ ions had diffused inward. The following mechanism of reduction, which is based on the assumption that the composition of the spinel phase remains stoichiometric with increasing degree of reduction, is proposed, (a) Initially, Fe3+ and Fe2+ ions at the surface of the chromite particle are reduced to the metallic state. This is followed immediately by the reduction of Cr3+ ions to the divalent state, (b) Cr2+ ions diffusing toward the center of the particle reduce the Fe3+ ions in the spinel under the surface of the particle to Fe2+ at the interface between the inner and outer cores. Fe2+ ions diffuse toward the surface, where they are reduced to metallic iron, (c) After the iron has been completely reduced, Cr3+ and any Cr2+ that is present are reduced to the metallic state, leaving an iron- and chromium-free spinel, MgAl2O4.

Kinetics of the reduction of bushveld complex chromite ore at 1416 °C

Abstract: The kinetics of the reduction of chromite ore from the LG-6 layer of the Bushveld Complex of the Transvaal in South Africa were studied at 1416 °C by the thermogravimetric analysis (TGA) technique. Spectroscopic graphite powder was employed as the reductant. The aim of this article is to present a kinetic model that satisfactorily describes the solid-state carbothermic reduction of chromite. A generalized rate model based on an ionic diffusion mechanism was developed. The model included the contribution of the interfacial area between partially reduced and unreduced zones in chromite particles and diffusion. The kinetic model described the process for degrees of reduction from 10 to 75 pet satisfactorily. It was observed that at a given particle size, the rate of reduction was controlled mainly by interfacial area up to about 40 pet reduction, after which the rate was dominated by diffusion. On the other hand, for a given degree of reduction, the contribution of the interfacial area to the rate increased, while that of diffusion decreased, with a decrease in the particle size. The value of the diffusion coefficient for the Fe2+ species at 1416 °C was calculated to be 2.63 x 10-2 cm2/s.

Mathematical modeling of sulfide flash smelting process: Part III. Volatilization of minor elements

Abstract: The mathematical model described in Part I[14] was extended to include the minor element behavior inside a flash-furnace shaft during flash smelting of copper concentrate. The volatilization of As, Sb, Bi, and Pb was computed, and experiments were carried out for Sb and Pb in a laboratory flash furnace. Satisfactory agreement between the predicted and measured results was obtained for antimony and lead. From the computational results, the behavior of each minor element was predicted for various target matte grades. The model predictions show that the elimination of As and Bi to the gas phase increases sharply at about 0.3 m from the burner; however, that of the Sb increases gradually along the flash-furnace shaft, and that of lead occurs suddenly at about 0.6 m from the burner. The predicted results also show that the elimination increases for Bi and Pb as the target matte grade increases; however, it is relatively independent of the target matte grade between 50 and 60 pet Cu for As and Sb. At higher target matte grades above 60 pet Cu, the elimination of As and Sb decreases as matte grade increases.

The electrochemical behavior of a semiconducting natural pyrite in the presence of bacteria

Abstract: The electrochemical oxidation of a natural pyrite electrode in sterile and inoculated sulfuric acid solutions has been studied using both linear-scan voltammetric and chronoamperometric techniques. The bacteria used consist of a pyrite-adapted mixed culture ofThiobacillus ferrooxidans. The influence of the iron concentration and the presence of bacteria have been studied at different pH values. The results from these electrochemical measurements are discussed in conjunction with surface characterization.

An improved mathematical model for electromagnetic casters and testing by a physical model

Abstract: The paper describes a physical model aimed at studying two important phenomena in electromagnetic (EM) casting of aluminum: the support of the molten metal pool and stirring caused by EM forces. The physical model is used both to test an improved mathematical model for EM casting and to provide insight into the effect of design changes on the two EM phenomena. Examples of design changes are changes in inductor current and position and screen position. The improved mathematical model, a two-dimensional (2-D) (axisymmetric) one, constrains the melt surface at the solidification line and neglects (with justification) buoyancy, surface tension, and the impact of flow on meniscus shape. The physical model was a cylindrical one where the solidified metal was simulated by a 248-mm-diameter aluminum bronze cylinder and the molten metal by Wood’s alloy. Measurements were made of electric field, magnetic field, meniscus deformation, and velocities for the two types of caster in commercial use. Generally, good agreement was obtained between the mathematical model and the experimental measurements.

Loss of current efficiency in aluminum electrolysis cells

Abstract: Consideration of the mechanism of loss of current efficiency (CE) leads to a form of equation which is simple, likely to give reasonable extrapolation beyond the range where experimental data are available, and convenient for responding to practical questions. With coefficients generated from plant experiments (performed by others), the equation is log (pct loss of efficiency) = 0.0095 (superheat) -−0.019 (pct A1F2) − 0.060 (pct LiF) + const where superheat is the difference (in °C) between cell temperature and the pseudo-binary eutectic temperature with A12O3, and pct A1F3 is excess A1F3. The coefficient for CaF2 is zero. The constant is characteristic of the cell design. The question of reconciling the values of the coefficients with literature data on the solubility of Al in cryolite melts and current theories of loss of efficiency is discussed.

A mathematical model of the nickel converter: Part I. Model development and verification

Abstract: A mathematical model of the nickel converter has been developed. The primary assumption of the model is that the three phases in the converter are in thermal and chemical equilibrium. All matte, slag, and gas in the converter is brought to equilibrium at the end of each of a series of short time steps throughout an entire charge. An empirical model of both the matte and slag is used to characterize the activity coefficients in each phase. Two nickel sulfide species were used to allow for the modeling of sulfur-deficient mattes. A heat balance is carried out over each time step, considering the major heat flows in the converter. The model was validated by a detailed comparison with measured data from six industrial charges. The overall predicted mass balance was shown to be close to that seen in actual practice, and the heat balance gave a good fit of converter temperature up to the last two or three blows of a charge. At this point, reactions in the converter begin to deviate strongly from “equilibrium,” probably due to the converter reactions coming under liquid-phase mass-transfer control. While the equilibrium assumption does work, it is not strictly valid, and the majority of the charge is probably under gas-phase mass-transfer control.

Thermodynamics of binary systems using interaction parameters

Abstract: A four-parameter equation for determining the excess integral property of a binary system is deduced based on the Maclaurin infinite series. The series is expressed separately in the neighborhood of each of the pure components of the system. The components are subjected to appropriate boundary conditions at the various stages of the treatment. The present form of the function is found to be capable of interpreting thermodynamic properties of several relatively weakly interacting binary systems based on the present equation. The infinite dilution parameters compare favorably with the values reported in the literature.

The mass transfer kinetics of niobium solution into liquid steel

Abstract: Niobium cylinders were immersed into liquid steel and their mass-transfer rates measured under dynamic conditions. The cylinders were suspended from a load cell, and the apparent weight of the cylinder as well as temperatures at various locations in the immersed specimens were measured continuously during immersion and recorded with a data acquisition system. From the weight measurements, the mass-transfer rate was deduced. A steel shell period and free dissolution period were identified. During the steel shell period, a shell of frozen steel wraps the cylinder following its initial immersion. When niobium cylinders were immersed into liquid steel with low superheat, a reaction was detected at the steel shell/niobium interface. This reaction took place during the later stages of the steel shell period. The intermetallic compounds Fe2Nb and Fe2Nb3 were identified as reaction products. The mass transfer which takes place during the free dissolution period was found to be exothermic, and the rate-controlling step was found to be liquid phase diffusion through a mass-boundary layer. The apparent activation energy was estimated to be 172 (±15) kJ/mol. This uncommonly high value of apparent activation energy is best explained on the basis of the macroexothermic reaction which takes place as niobium dissolves into liquid steel.