METALLURGICAL AND MATERIALS TRANSACTIONS B
ABSTRACTS
Volume 26B, No. 5, October 1995

This Month Featuring: Hydrometallurgy; Pyrometallurgy; Transport Phenomena; Process Control; Physical Chemistry; Mechanical Working; Welding and Joining; Mathematical Modeling. View October 1995 Table of Contents.

HYDROMETALLURGY

The Role of Migration in Shrinking-Core Leaching Reactions Controlled by Pore Transport
MARK D. PRITZER
The conventional shrinking-core model for pore diffusion through product layers formed during leaching reactions has been generalized to include electrical migration as well. This has involved solving the steady-state diffusion-migration transport equations for all soluble reacting and nonreacting species in the system in conjunction with the electroneutrality requirement and the appropriate boundary condition for a given rate-controlling regime. The resulting expression for transport-limiting conditions has the identical form 1-2/3-(1-)2/3=kdt as the conventional one, except that kd is now a function of the valences and bulk concentrations of all species and the effective diffusion coefficients of all reacting species. The analysis shows that as long as the diffusion coefficients differ, migrational transport will occur and that the greater this difference the greater is its importance. For conditions, typical of some practical leaching systems, it is estimated that migrational flux can be considerable, reaching as high as 80 pct of the diffusional flux. Other comparisons of the generalized and standard models are made and the resulting errors in neglecting migration are discussed.

PYROMETALLURGY

Oxidation Kinetics of Zinc Vapor in CO:CO2 Mixtures: Part II. Application of Plug Flow Concepts
L.A. LEWIS AND A.M. CAMERON
The methods employed and the results obtained during a recent investigation of the oxidation of gaseous zinc by CO:CO2 mixtures are described. The kinetic data are tested against the predictive models derived and employed by previous investigators of this reaction. Although the experimentally determined reaction rates are highly reproducible, no consistent agreement can be found with the models presented in the prior literature. Efforts to account for the kinetics on the basis of the oxygen potential of the gas mixture are also unsuccessful. It is concluded that previous attempts to understand the kinetics in terms of the reaction Zn(g)+CO2(g)=>ZnO(s)+CO(g) are oversimplistic. A novel interpretation which appears to resolve the discrepancies of the literature is detailed in the second of two articles on the subject.

Oxidation Kinetics of Zinc Vapor in CO:CO2 Mixtures: Part II. Application of Plug Flow Concepts
L.A. LEWIS AND A.M. CAMERON
In the first of two articles on the subject, it was shown that the oxidation kinetics of Zn vapor in CO:CO2 mixtures cannot be understood on the basis of previously proposed rate expressions. In this second article, an alternative interpretation, which appears capable of reconciling the apparent discrepancies of the past literature, is proposed. Evidence is provided to the effect that competing reactions occur in the system Zn-CO-CO2 under the majority of conditions investigated. Analysis on the basis of simple "plug flow" model reveals that oxidation by CO2 can take place indirectly by a combination of the reactions


and

Zinc is also oxidized by direct reaction with both CO and CO2. It is proposed that the distinctive morphologies observed (coarse, intermediate, and fine) can be related to the degree of direct and/or indirect oxidation occurring in the system.

Sulfide Capacities of Na2O-SiO2 Melts
R.G. REDDY and W. ZHAO
Sulfide capacities of Na2O-SiO2 melts at 1473, 1573, 1623, and 1673 K were calculated a priori using the revised Reddy-Blander model. An expression for Cs in the composition range of 0 ¾ XSiO2 < 1.0 was derived. Our predictions of Cs values are in very good agreement with the experimental data available in the range of 0 < XSiO2 < 0.8. The sulfide capacities of slags are found to be directly related to two independent quantities: the equilibrium constant K and the activity of the base oxide.

Two Wavelength Pyrometry Study of the Combustion of Sulfide Minerals: Part I. Apparatus and General Observations
N.E. TUFFREY, G.G. RICHARDS, AND J.K. BRIMACOMBE
The temperatures of individual sulfide particles combusting in air have been measured with a two-wavelength radiation pyrometer. The pyrometer design allowed the temperature of the combusting particles to be measured for 15 to 30 ms; and the response of the system was sufficient to determine the heating rates of particles during reaction. The combustion of galena, pyrite and pyrrhite, in air, at 1130 K was investigated. The different minerals produced distinct combustion pulses which were recorded repeatedly. Galena particles reacted in air at a relatively constant apparent temperature of between 1400 and 1700 K. Reaction product fume was observed trailing behind the combusting particles. The pyrometer pulses recorded during the combustion of pyrite and pyrrhotite particles were similar; however, pyrite tended to ignite more rapidly than pyrrhotite. During combustion in air, the temperature of the iron sulfide particles increased at a constant rate up to a maximum of 2200 to 2600 K, after which rapid cooling occurred; a sudden rise in combustion energy at peak temperature was likely due to an increase in the particle size resulting from the formation of censospheres.

Two Wavelength Pyrometry Study of the Combustion of Sulfide Minerals: Part II. Galena and Commercial Lead Concentrates
N.E. TUFFREY, G.G. RICHARDS, and J.K. BRIMACOMBE
The combustion of galena and two commercial lead concentrates has been investigated using a specially constructed fast-response, two wavelength pyrometer. The changes in the particle morphology and in the chemical composition of the individual particles during combustion were also investigated through scanning electron microscopy and energy dispersive X-ray/wavelength dispersive X-ray (EDX/WDX) studies of quenched reaction products. The effects of oxygen concentration and particle size on combustion were studied, together with the influence of chemical and morphological difference between the different lead concentrates. Increasing gas oxygen content from 10 to 100 pct elevated the particle combustion temperature from about 1600 to over 2000 K. The higher oxygen content also resulted in a change of mechanism from relatively constant combustion temperatures in air to much more rapid transient combustion pulses in pure oxygen. Thus, it is suggested may also be important, because both sulfide and metallic lead phases were identified in the quenched partially reacted particles. It is thought that the metallic lead in the particles is produced through reaction between surface sulfates and untreated lead sulfides. The commercial concentrate feeds were found to consist mainly agglomerates of many smaller particles, with the chemical and mineral composition of the individual particles dictating their combustion behavior. Increasing quantities of galena in the agglomerates enhance the vaporization reactions and limit reaction temperatures, whereas increasing quantities of iron sulfides raise the intensity of reaction and combustion temperatures. Zinc sulfides act as a thermal load. Reaction mechanisms for both galena and commercial concentrate particles are proposed.

Two Wavelength Pyrometry Study of the Combustion of Sulfide Minerals: Part III. Galena and Commercial Lead Concentrates
C. SOMSIRI and D.R. GASKELL
The strong influence of oxygen concentration on the combustion of pyrite at a furnace temperature of 1130K has been investigated by pyrometer measurements of the temperature of individual particles and by morphological examination of the reaction products. Three distinct types of behavior were identified depending on the oxygen concentration. With oxygen levels between 10 and 40 pct, the maximum temperature of the pyrite particles increased linearly from about 2000 to over 3000K while heating rates also climbed. The characteristics of the combustion pulses from the pyrometer revealed that cenosphere inflation occurred at the maximum particle temperature was independent of oxygen concentration, remaining constant at 3000 to 3400K; however, heating rates were somewhat variable. The combustion pulse characteristics again suggested that particles inflate into cenospheres but there was an increased tendency for them to rupture. At oxygen concentrations of 80 pct and greater, higher heating rates were measured bu the maximum particle temperatures were limited to 3200 to 3500K. The combustion pulse characteristics in oxygen suggested that the termination of reactions is consistent with material ejection or particle disintegration as opposed to cenosphere inflation. The results generally were consistent with the reaction rate being governed by oxygen transport in the gas phase, although at higher oxygen concentrations, evaporation of the iron species and other physical phenomena limited the particle temperature.

Communication: Application of the Radioisotope Excited X-Ray Fluorescence Technique in Change Optimization during Thermite Smelting of Fe-Ni, Fe-Cr, and Fe-Ti Alloys
I.G. SHARMA, D. JOSEPH, MADAN LAL, and D.K. BOSE

TRANSPORT PHENOMENA

The Effect of Surface Movements on Nitrogen Mass Transfer in Liquid Iron
N. HIRASHIMA, R.T.C. CHOO, J.M. TOGURI, and K. MUKAI
Marangoni convection due to surface tension gradients set up in a nitrogen-liquid iron system at 1873 K has been mathematically simulated and experimentally confirmed by measuring the rate of nitrogen absorption into liquid iron and by observing the free surface motion of liquid iron via zirconium oxide particles using X-ray radiography. This surface flow was created by blowing nitrogen gas through a small lance over the free surface of the liquid iron contained in an alumina boat under resistance heating. Absorption measurements indicated that the mass-transfer coefficient of nitrogen in liquid iron due to Marangoni convection (k'm=1.5X10-4m/s) is slightly less than that due to induction stirring (k'm=2.1X10-4 to 1.5X10-4m/s). The free surface velocity induced by the surface tension gradient with an initial composition difference of 425 to 10 ppm, was found to be of the order of 0.05 to 0.11 m/s. Mathematical modeling was also carried out to determine the velocity and nitrogen concentration profiles in the alumina boat. It was found that Marangoni convection creates mildly turbulent flows in liquid iron. Good agreements between the experimentally obtained data (nitrogen concentration and surface velocity) and the computed results were attained when a constant eddy viscosity which was five times the molecular value was assumed. This prescription allows both the predicted apparent mass-transfer coefficient and the predicted surface velocity to match the experimental results simultanesouly. Note that the transport coefficients in the momentum and the convective-diffusive equations are correlated by the turbulent Schmidt number. The dimensionless mass-transfer correlation obtained for the present N-Fe system at 1873K under resistance heating was found to be Sh=0.104 Re0.7·Sc0.7 with Sc=79.5 (3500 < Re < 7700).

Settling and Clustering of Silicon Carbide Particles in Aluminum Metal Matrix Composites
G.A. IRONS and K. OWUSU-BOAHEN
The settling of 14-µm silicon carbide particles in an aluminum-silicon alloy was monitored with an electrical resistance probe to measure the in situ particle volume fraction. The rate of settling was much greater than expected from hindered settling of single 14-µm particles. From the observed settling rate, an equivalent hydrodynamic diameter and density of clusters of particles were deduced, settling rate, an equivalent hydrodynamic diameter and density of clusters of particles were deduced, 38-µm and 2740 kg/m3, respectively. Other work was analyzed with the same procedure; it was concluded that if the stirring prior to settling were intense, then the clusters would be smaller than with weaker stirring. The implications for foundry practice and mechanical properties were discussed.

PROCESS CONTROL

Communication: Effect of Temperature on Slag Foaming
BAHRI OZTURK and R.J. FRUEHAN

PHYSICAL CHEMISTRY

Effects of Ti, Zr, V, and Cr on the Rate of Nitrogen Dissolution into Molten Iron
HIDEKI ONO, KAZUKI MORITA, and NOBUO SANO
The rate of nitrogen dissolution into molten iron-M (M: Ti, Zr, V, and Cr) alloys at temperatures from 1873 to 2023 K has been measured using an isotope exchange reaction. The rate of nitrogen dissolution into molten iron is shown to increase by adding an element with a stronger affinity for nitrogen than Fe, such as Ti, Zr, V, and Cr. Of these, Ti increased the reaction rate most and the rate constant for an Fe-0.08 mass pct Ti alloy was 1.5 times larger as that for pure iron at 1873 K. The correlation of rate constant with thermodynamic interaction parameter with nitrogen was observed. This effect is discussed in terms of the change in the activity of the vacant site on the surface of the molten alloy.

Kinetics for Reaction of Low-Carbon Steel Melts with CO-CO2 Gas Mixtures using Nonlinear Rate Equations
MASAHIRO SUSA and KAZUHIRO NAGATA
The transfer reactions of carbon and oxygen from or to molten steel have been analyzed using nonlinear rate equations. The nonlinear rate equations successfully reproduced the change of carbon and oxygen concentrations in molten steel. It was shown that the coupling of chemical reaction and diffusion of carbon and oxygen should be taken into account within the diffusion layer in molten steel in order to explain the change of the concentrations in molten steel.

Preparation and Characterization of Polycrystalline Lead-Exchanged Sodium Beta"-Alumina and Its Use as a Pb2+ Ion-Conducting Electrolyte for Galvanic Cells
X.Y. YAN, D.E. LANGBERG, and W.J. RANKIN
Sodium in Na+"-alumina was partially exchanged with lead by ion exchange between polycrystalline Na+"-alumina and a molten salt mixture containing lead cations. Examination of the exchanged material showed that it was free of cracks and porosity and that the lead was uniformly distributed. The bulk conductivity of the exchanged material was measured using molten lead electrodes and a two-prove alternating current technique. The electrochemical behavior of lead ions in the material was investigated using a concentration cell of the type

W, Pb(1)| Pb-partially-exchanged Na+"-alumina | Pb-Bi(1), W

It was found that the lead ion behaved as Pb2+, and its mobility was high in the exchanged Na+"-alumina over the range 723 to 1098K. It is concluded that the prepared Pb2+-"-alumina could be used as Pb2+ ion-conducting solid electrolytes in galvanic cells for thermodynamic measurements on Pb-containing and Na-free metallic melts or Pb2+-containing and Na+-free slags or mattes.

Thermodynamic Properties of the MgAl2O4-MnAl2O4 Spinel Solid Solution
YIHONG ZHAO, KAZUKI MORITA, and NOBUO SANO
The thermodynamic properties of the MgAl2O4-MnAl2O4 system are required for calculating the deoxidation equilibrium of molten iron and nickel containing magnesium, manganese, and aluminum. The thermodynamic properties of the MgAl2O4-MnAl2O4 spinel solid solution have been determined by equilibrating it with silver at known oxygen partial pressures. The free energy of formation of MnAl2O4 from its oxide components at 1673 and 1823K was found to be -30.6 and -28.3kJ/mol, respectively. It was observed that the MgAl2O4-MnAl2O4 spinel solid solution exhibited small negative deviations from ideal behavior at 1673 and 1823K. The excess partial free energies of MgAl2O4, and MnAl2O4 at 1673 and 1823K are expressed as


Communication: Effects of Gas Type and Pressure on Slag Foaming
Y. ZHANG and R.J. FRUEHAN

MECHANICAL WORKING

Heat Transfer in the Hot Rolling of Metals
C.O. HLADY, J.K. BRIMACOMBE, I.V. SAMARASEKERA, and E.B. HAWBOLT
The heat-transfer coefficient (HTC) in the roll gap during the hot rolling of AA5XXX-series (aluminum-magnesium) alloys has been measured in a laboratory mill with the aid of thermocouples attached to the surface and embedded in the interior of test samples. The heat-transfer coefficient was calculated from the sample temperature response using an implicit finite-difference model over a range of temperatures, strain rates, and pressures. Values of 200 to 450 kW/m2°C were obtained by back calculation. A comparison of the results from this study with those measured in a previous investigation on two steel alloys has led to the development of an equation which characterizes the THC as a function of the ratio of the rolling pressure to the flow stress at the surface of the workpiece. This relationship has been employed to explain the apparent differences in the heat-transfer behavior of different metals at similar rolling pressures.

WELDING AND JOINING

Temperatures in the Keyhole
E.A. METZBOWER
The size and temperatures of the keyhole have been calculated through the thickness of the plate being welded. The temperature calculations are based on a critical intensity and the power loss resulting from vaporization. The evaporative power loss is set equal to the Gaussian power density, which is used to represent the laser beam. The result is a temperature distribution across the surface of the plate. The temperatures through the thickness of the plate are calculated on the basis of a minimum intensity at the bottom of a drilled hole. The intensity at the bottom of the plate is assumed to exceed this minimum intensity. This permits an absorption coefficient to be calculated. Thus, the intensity through the thickness can be calculated and temperatures corresponding to this intensity can also be evaluated. The results are used to explain the "nail head" appearance of the fusion zone, which is quite common in laser beam welds. The results also explain some visual observations of laser beam welds.

MATHEMATICAL MODELING

Mathematical Modeling of the Zinc Pressure Leach Process
SUSAN A. BALDWIN, GEORGE P. DEMOPOULOS, and VLADIMIROS G. PAPANGELAKIS
A comprehensive mathematical model is described for the zinc pressures leaching process. Generic kinetic expressions were derived from experimental data found in the literature for the following reaction events: (1) dissolution of marmatite, (Zn, Fe)S, (2) oxidation of ferrous to ferric, and (3) precipitation of lead jarosite. Aqueous solution properties, oxygen solubility, density, enthalpy, and vapor pressure, were correlated with solution composition and temperature. Subsequently, a kinetics-based model for simultaneous sulfide dissolution and iron precipitation in a multistage, three-phase reactor was developed. The population balance method was used for sulfide mineral material balances, and apparent equilibrium was assumed for iron precipitation. A gas-phase material balance was included, which allows for prediction of oxygen utilization. The model was solved for a particular operation of the Cominco Ltd. (trail, BC) autoclave, and prediction results were shown to be in very good comparison with actual plant performance.

Permeability for Cross Flow Through Columnar-Dendritic Alloys
M.S. BHAT, D.R. POIRIER, and J.C. HEINRICH
Experiments for measuring permeability in columnar-dendritic microstructures have provided data only up to volume fraction of liquid of 0.66. Hence, the permeability for flow perpendicular to the primary dendrite arms in columnar-dendritic microstructures was calculated, extending our data base for permeability to volume fractions of liquid as high as 0.98. Analyses of the dendritic microstructures were undertaken first by detecting the solid-liquid interfaces with a special computer program and then be generating a mesh for a finite-element fluid flow simulation. Using a Navier-Stokes solver, the velocity and pressure at the nodes were calculated at the microstructural level. In turn, the average pressure gradient was used to calculate the Darcy permeability. Permeabilities calculated by this versatile technique provided data at high volume fractions of liquid that merged with the empirical data at the lower volume fractions.

Modeling of Fluid Flow and Heat Transfer in the Plasma Region of the dc Electric Arc Furnace
F. QIAN, B. FAROUK, and R. MUTHARASAN
A mathematical model describing the transport process in the plasma arc in dc electric arc furnaces has been developed. The equations of conservation of mass, momentum, and energy are solved numerically in conjunction with Maxwell's equations of the electromagnetic field to calculate the velocity and temperature distribution in the plasma region. The heat transfer from the arc to a rigid anode surface is calculated. The model is applied to obtain quantitative results on the relative importance of the various modes of heat transfer from electric are to the anode surface. Computational results were obtained for varying arc current magnitudes and anode-cathode distances. The model predicts higher arc jet velocity and a broader arc core at higher are current. The shorter arc length is more efficient for transferring heat to the anode.

Mathematical Modeling of Macrosegregation of Iron Carbon Binary Alloy: Role of Double Diffusive Convection
A.K. SINGH and B. BASU
During alloy solidification, macrosegregation results from long range transport of solute under the influence of convective flow and leads to nonuniform quality of 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 solidification 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 formation, the governing equations were solved using the finite volume method. The numerical model was validated by simulating experiments on an ammonium chloride water 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 and vice versa, are shown at various stages of solidification. Under the given set of parameters, it was found that the thermal buoyancy affects the macrosegreation field globally, whereas the solutal buoyancy has a localized effect.

Communication: A Permeability Length Scale for Cross Flow Through Model Structures
M.S. BHAT, D.R. POIRIER, and J.C. HEINRICH

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