METALLURGICAL AND MATERIALS TRANSACTIONS B
	ABSTRACTS Volume 29B, No. 5, October 1998 This Month Featuring: Hydrometallurgy; Pyrometallurgy; Transport Phenomena; Process Control; Physical Chemistry; Solidification; Materials Processing; Mathematical Modeling. View October 1998 contents.

HYDROMETALLURGY

Model for the Ferric Chloride Leaching of Galena
MARK PRITZKER
A shrinking core model for the FeCl₃ leaching of galena (PbS), which accounts for the microstructure previously observed during this process, is presented. The microstructure is characterized by two distinct product layers-PbCl₂ in direct contact with the PbS core and S° above the PbCl₂ layer. Rate equations for the evolution of the three solid phases and the PbS leaching conversion are derived for the case of flat plate geometry appropriate for the reaction of massive galena fragments. In the case of rate control by diffusion of the lead chloride reaction products through the S° layer, the system is shown to exhibit parabolic behavior as long as the S° layer is built up primarily at the PbCl₂-S° interface. For the mechanism considered in this study, negative deviation from parabolic behavior is observed to increase as the amount of S° forming at the external S°-solution interface rises. When the system is controlled by surface reaction kinetics, the model predicts linear rates under all circumstances.

Leaching Kinetics of Digenite Concentrate in Oxygenated Chloride Media at Ambient Pressure
M.C. RUIZ, S. HONORES, and R. PADILLA
The leaching of digenite concentrate in CuCl₂-HCl-NaCl oxygenated solutions is very rapid. From the effect of variables on the leaching rate and measurements of the concentrations of cuprous and cupric species in the solution as a function of time, it was concluded that the leaching in O₂ atmosphere proceeds by the attack of cupric ions on the copper sulfides to produce cuprous ions which are subsequently oxidized to cupric by the O₂ present in the system. The kinetic study showed that the leaching proceeds in two sequential stages. In the first stage, the digenite is transformed to covellite, and in the second stage, the covellite is dissolved to copper and elemental sulfur. In the first stage, the fraction of copper extracted varied linearly with time according to = k_lt, whereas in the second stage, the dissolution of covellite was well represented by a shrinking core model controlled by diffusion through a porous product layer kinetic equation: 1 - 2/3_cv - (1 - _cv)^2/3 = k_cvt. The calculated activation energies were 15.8 and 80.0 kJ/mol for the first and second stages, respectively. These results were explained by an electrochemical mechanism of digenite dissolution.

PYROMETALLURGY

Chlorine Fluxing for Removal of Magnesium from Molten Aluminum: Part II. Mathematical Model
QIAN FU and JAMES W. EVANS
This second part of a two-part article presents a mathematical model for the "chlorine fluxing" of aluminum alloys, in particular, for the "demagging" of Al-Mg alloys such as those resulting from the recycling of used beverage cans. The model is based on the experimental results described in Part I and, in conformity with those results, assumes that neither the reaction kinetics at the melt-bubble interface, nor mass transfer on the gas side of that interface, are rate determining. With the introduction of one correction factor (applied to the surface renewal model for mass transfer on the melt side of the melt-gas interface), the model fitted the experimental data well, once measured values for the bubble size and rise velocity were introduced. The model was then used to predict the progress of demagging operations on an industrial scale. Computed results for these larger melts suggest that gross emissions of chlorine/chlorides are avoidable in bringing the magnesium content down to a critical value (which depends on operating characteristics such as bubble size). A multiple-step strategy is suggested when a batch of alloy is to be brought to yet-lower magnesium levels. In that strategy, the chlorine content of the injected gas is reduced as the processing of the batch proceeds. The predicted effects of other operating changes (deeper nozzle submergence, broad bubble size distribution, etc.) are reported.

Communication: Estimation of Isothermal Values of Activation Energy for Aluminothermic Reduction
B. SARANGI, H.S. RAY, AND R.R. DASH

TRANSPORT PHENOMENA

Re (Ma)^2/3

The Marangini convection flow was quantitatively evaluated by using an order-of-magnitude evaluation, and a general correlation of the Marangoni convection flow was derived. The calculated correlation is in good agreement with experimental results.

Experimental and Mathematical Investigation of the Fluid Flow inside and below a 1/4 Scale Air Model of a Flash Smelting Burner
I.D. SUTALO, F.R.A. JORGENSEN, and N.B. GRAY
Single-phase turbulent fluid flow inside and below a burner model was studied to better understand the fluid flow processes occurring inside and below flash smelting burners. The effect of Reynolds number and temperature on the axial velocity profiles in a 1/4 scale experimental air model of a jet flow burner and shaft were investigated. Laser Doppler anemometry (LDA) was used to determine the mean and fluctuating axial velocity components within and below this burner. Also experimentally determined were the pressure profiles along the length of the burner and shaft and the inlet air and wall temperature profiles. In the experiments, the Reynolds number range was approximately 60,600 to 76,100, which was in the turbulent flow regime. A mathematical model was used to simulate axisymmetric two-dimensional air flow through a jet flow burner and shaft for Reynolds numbers of 60,000 to 304,000. The axial velocity predictions of the high axial velocity region and surrounding region in the shaft were in reasonable agreement with the axial velocity experimental results. Recommendations are made for the improvement of the design of flash smelting burners.

PROCESS CONTROL

PHYSICAL CHEMISTRY

Surface Tension Measurements on Liquid Metals in Microgravity
IVAN EGRY, ELLIOT SCHWARTZ, JULIAN SZEKELY, GERD JACOBS, GEORG LOHOEFER, and PETRA NEUHAUS
The results of surface tension measurements on liquid metals and alloys, performed in microgravity, are presented. Using electromagnetic levitation and the oscillating drop technique, the surface tension of gold, gold-copper, and zirconium-nickel was measured. We find excellent agreement with available results obtained on earth by the same technique, but only if the latter are corrected to account for gravity effects. This not only shows the necessity for the correction of surface tension data derived from earthbound oscillating drop experiments but also proves its correctness.

Thermodynamics of Yttrium and Oxygen in Molten Ti, Ti₃Al, and TiAl
YOSHINAO KOBAYASHI and FUMITAKA TSUKIHASHI
The solubility of yttrium and oxygen in molten Ti, Ti₃Al, and TiAl equilibrated with solid Y₂O₃ has been measured from 1793 to 2093 K. The equilibrium constant of reaction Y₂O₃ (s) = 2Y (mass pct) + 3O (mass pct) and the interaction parameter between yttrium and oxygen in molten metals were determined. The standard Gibbs energy of reaction was also obtained as a function of temperature. The deoxidation of Ti, Ti₃Al, and TiAl by using yttrium-based fluxes is discussed and the deoxidation ability of yttrium is compared with that of calcium.

Thermodynamic Properties of Aluminum, Magnesium, and Calcium in Molten Silicon
TAKAHIRO MIKI, KAZUKI MORITA, and NOBUO SANO
The thermodynamic properties of aluminum, magnesium, and calcium in molten silicon were investigated using a chemical equilibration technique at 1723 to 1848 K, 1698 to 1798 K, and 1723 to 1823 K, respectively. The activity coefficient of aluminum in molten silicon was determined by equilibrating molten silicon-aluminum alloys with solid Al₂O₃ and Al;i6Si₂O₁₃, that of magnesium was determined by equilibrating molten silicon-magnesium alloys and MgO-SiO₂-Al₂O₃ melts doubly saturated with MgSiO₃ and SiO₂, and that of calcium was determined by equilibrating molten silicon-calcium alloys with SiO₂-saturated CaO-SiO₂ melts. The activity coefficients at infinite dilution relative to the pure liquid state were determined as follows:

log °_{Al(l)in Si}= -+0.236 (1723 to 1848 K)

log °_{Mg(l)in Si}= -+1.96 (1698 to 1798 K)

log °_{Ca(l)in Si}= -+1.53 (1723 to 1823 K)

Communication: Reduction of FeWO₄-NiWO₄ Solid Solutions by Hydrogen Gas
J.A. BUSTNES, DU SICHEN, AND S. SEETHARAMAN

SOLIDIFICATION

Stress Formation in Solidifying Bodies. Solidification in a Round Continuous Casting Mold
KLAUS SCHWERDTFEGER, MITSURU SATO, and KARL-HERMANN TACKE
In solidifying bodies, there is no stress-free reference state for the displacements as in normal bodies with fixed dimensions, which are stress free, in all their volume elements, in the isothermal state prior to cooling or prior to heating. This difficulty has been solved in the present work by using displacement rates, rather than displacements, and all the other relevant quantities also in time differentiated form. The equations obtained for the time differentiated quantities are integrated with respect to time to obtain the quantities themselves. Different assumptions on the material behavior have been used, viz. viscoplastic-elastic or purely elastic behavior. The concept was applied to bodies with cylindrical symmetry and, for the sake of simplicity and clarity, to the state of plane strain. The computational examples refer to the solidification of steel with 0.6 pct carbon in a round continuous casting mold. The calculated stress distributions show compressive circumferential stress at the surface of the strand and tensile stress in the interior of the solid shell. Shrinkage profiles depend mainly on the temperature profile and on the thermal strain data used, and can be approximated by the free shrinkage of the strand surface.

MATERIALS PROCESSING

Formation of TiN/TiC-Fe Composites from Ilmenite (FeTiO₃) Concentrate
N.J. WELHAM and P.E. WILLIS
The production of a ceramic hard material-metal composite directly from a mineral concentrate has great potential application. An homogenizing pretreatment of a mixture of ilmenite (FeTiO₃) and graphite, followed by annealing under an argon ambient, showed the formation of titanium carbide and elemental iron. Annealing of the same powder in nitrogen resulted in the formation of a composite of elemental iron and titanium nitride. The nitride was formed at a lower temperature than the carbide with almost complete conversion after 1 hour at 1000°C. The rate of carbide formation was controlled by carbon diffusion, whereas the nitridation reaction was controlled by either oxygen or nitrogen diffusion. The TiC was found to form via TiC_0.5, which slowly increased its carbon content until near stoichiometric TiC was formed; stoichiometric TiN formed directly with no intermediate phases. Titanium carbide showed the presence of a second phase with a slightly smaller unit cell size; this was due to interdiffusion between the iron and TiC. The titanium carbide composite was found to be composed of 3 to 4 µm anhedral iron grains dispersed in the titanium-rich matrix. There was no segregation in the iron/titanium nitride composite with apparently submicron distribution.

MATHEMATICAL MODELING

Modeling of Porosity during Spray Forming: Part II. Effects of Atomization Gas Chemistry and Alloy Compositions
WEIDONG CAI and ENRIQUE J. LAVERNIA
In this article, the effects of gas chemistry and alloy composition on the level of porosity in deposited materials are investigated by using a porosity model established in Part I of this article. The calculated results reveal that atomization gas chemistry has a significant influence on the level of porosity during spray forming, which can be rationalized on the basis of the influence of gas properties such as gas density, viscosity, and gas constant on the melt flow rate. The alloy properties that predominantly affect the variation of porosity with melt flow rate include melt viscosity, density, surface tension, solvent melting point, liquidus temperature, and equilibrium partition coefficient. A material property factor, µ_mm/²_m, plays an important role in determining the processing conditions required to attain a minimum amount of porosity in deposited materials.

Mathematical Modeling of the Reduction Process of Iron Ore Particles in Two Stages of Twin-Fluidized Beds Connected in Series
Y.B. HAHN and K.S. CHANG
A mathematical model is presented to describe the reduction process of iron ore particles in two stages of twin-fluidized beds (TFBs) connected in series: prereduction and final reduction stages. Main features of the model are the inclusion of particle degradation phenomenon to account for its effect on reduction of iron oxides and reduction kinetics for multiparticles having a wide size distribution. It was found that about 90 pct of overall particle degradation occurs in the prereduction stage mainly due to thermal stress and volume expansion. The reduction degree of particles larger than 1 mm decreased fast with increasing particle size in both the prereduction and final reduction stages. However, the particles sized between 0.2 and 1 mm showed mild increase in reduction degree, and steep increase for the fines smaller than 0.2 mm. The reduction degree was also gradually decreased with increasing the gas oxidation degree of feed gas in both the prereduction and final reduction stages. It was found that to obtain a desired reduction degree, it is of great importance to control the bed temperature in stage I rather than in stage II. The optimum range of residence time was 15 to 20 minutes in the prereduction stage and 30 to 35 minutes in the final reduction stage.

Numerical Investigation of the Free Surface in a Continuous Steel Casting Mold Model
G.A. PANARAS, A. THEODORAKAKOS, and G. BERGELES
This article presents a numerical investigation of the turbulent flow in a water model, simulating a continuous steel casting mold. Special attention is given to the free-surface oscillations. The governing differential equations are discretized in a curvilinear coordinate system moving with the free surface by the Finite Volume Methodology (FVM). The results indicate that the free-surface wave has a predominant length and frequency and the wave amplitude scales with the flow dynamic head. Wave instability, which may be associated with emulsification, is predicted at a critical casting speed.

The Free-Surface Shape and Temperature Distribution Produced in Liquid Metal Droplets by Heating Coil Pulses in the TEMPUS Electromagnetic Levitation Facility
ELLIOT SCHWARTZ and JULIAN SZEKELY
We present the results of analytical and numerical calculations of the free-surface shape and temperature distribution produced in liquid metal droplets processed in the TEMPUS electromagnetic levitation facility. The mathematical models were developed to predict the behavior of liquid metal droplets in containerless experiments used to measure thermophysical properties aboard the Space Shuttle Columbia during the IML-2 mission in July 1994. A normal stress balance model was used to numerically calculate the equilibrium free-surface shapes for various samples produced by a number of induction coil voltages. Analytical and numerical calculations were performed to model the heat transfer in the liquid metal droplets during and following the heating coil pulses. The work illustrates the use of mathematical modeling in the design of microgravity experiments and is applicable to industrial processes such as casting and skull melting.