METALLURGICAL AND MATERIALS TRANSACTIONS B
	ABSTRACTS Volume 29B, No. 1, February 1998 This Month Featuring: The 1997 Howe Memorial Lecture; Composite Materials; Pyrometallurgy; Electrometallurgy; Transport Phenomena; Physical Chemistry; Solidification; Materials Processing; Mathematical Modeling; Environment. View February 1998 Contents.

THE 1997 HOWE MEMORIAL LECTURE

COMPOSITE MATERIALS

PYROMETALLURGY

Electrochemical Determination of Gibbs Energy of Formation of NiTiO₃ (Ilmenite)
G.M. KALE
Gibbs energy of formation of NiTiO₃ (ilmenite) relative to its component oxides, NiO (rock salt) and TiO₂ (rutile), has been measured employing the solid-state electrochemical cell,

between 994 and 1371 K. The open-circuit electromotive force (emf) of the preceding solid-state galvanic cell was found to be reversible and to vary linearly as a function of temperature in the range of measurement. The results obtained in this study give for the reaction

NiO (rs) + TiO₂ (rut) NiTiO₃ (ilm)

G°= -11,058 + 2.895T (±100) J mol^-1

Combining the Gibbs energy of formation of NiTiO₃ (ilm) from the component oxides with that for the formation of NiO (rs) from its elements gives for the reaction

Ni (s) + TiO₂ (rut) + 1/2O₂ (g) NiTiO₃ (ilm)

G°= -246,442 + 88.78T (±150) J mol^-1

Differential thermal analysis (DTA) of NiTiO₃ (ilm) between 373 and 1623 K indicated that NiTiO₃ (ilm) undergoes a reversible order-disorder phase transformation between 1540 and 1594 K. Based on the ideal mixing of cations on the cationic sublattice of NiTiO₃ (ilm) and a critical phase transformation of 1568 K obtained from the DTA, the Gibbs energy change for the order-disorder phase transformation in NiTiO₃ (ilm) is obtained as

G°_Tr = 18,073 - 11.526T (±1000) J mol^-1

Selective Oxidation of Copper from Liquid Copper-Silver Alloys
C.A. PICKLES
In this work, the oxygen refining of liquid copper-silver alloys with a borosilicate slag was studied. First, a comprehensive thermodynamic analysis was performed using the data available in the literature. The results indicate that since silver oxide is relatively unstable in silicate-based slags, then it should be thermodynamically feasible to oxidize copper from copper-silver alloys with a very low silver loss to the silicate slag. In actual practice, although relatively low copper levels can be achieved in the metal phase, the silver losses to the slag are excessive. Therefore, in the present work, both kinetic and equilibrium experiments were performed on a molten copper-silver alloy containing 12.68 mass pct silver in order to elucidate the mechanism of silver loss to the slag. The kinetic experimental results indicated that copper levels of less than 2 mass pct could be achieved with silver recoveries of about 95 pct after relatively short refining times of 15 minutes. In the equilibrium experiments, the copper contents of the metal were less than 1 mass pct, and these values were in good agreement with those which were calculated from the data of previous researchers. In order to explain the relatively high silver losses to the slag, a model was developed which is based on the transport of silver from the metal phase to the slag phase both in metallic form and as silver oxide in the copper oxide oxidation product. The copper and silver oxides and the metallic copper-silver alloy are all transported into the slag by the oxidizing gas bubbles. It is proposed that once in the slag, the silver oxide is unstable and decomposes into metallic silver which is not easily recovered in the metal phase. Also, the transfer of the copper-silver alloy into the slag, by the gas bubbles, promotes the slag-metal exchange reaction, which again results in the generation of silver particles in the slag.

ELECTROMETALLURGY

A Porous Titanium Diboride Composite Cathode Coating for Hall-Héroult Cells: Part I. Thin Coatings
J.A. SEKHAR, V. de NORA, and J. LIU
The mechanical, electrical, and electrochemical properties of a porous cathode coating, made by compositing titanium diboride powder and colloidal alumina, are described. Such coatings are expected to be used on the carbon cathodes employed in Hall-Héroult cells. The properties of the composite coating are compared with uncoated carbon cathode reference samples. The bonding properties of the coating with the carbon are also examined. The sodium trapping mechanisms of the coating are explored in this article.*
*An earlier version of this article appeared in TMS Light Metals 1996 Proc., edited by W. Hale. This previous article is cited herein in Ref. 28.

TRANSPORT PHENOMENA

Transport Phenomena in Electric Smelting of Nickel Matte: Part I. Electric Potential Distribution
Y.Y. SHENG, G.A. IRONS, and D.G. TISDALE
An electric potential probe was constructed so that simultaneous, multiple measurements of electric potential could be made in a six-in-line electric furnace for smelting nickel calcine having a maximum transformer capacity of 36 MVA. When the electric potential distributions were compared with those calculated from the solution of the Laplace equation, it was evident that there was significant electric potential drop at the electrode surface, 100 to 120 V for an applied potential of 180 to 230 V and currents of 20 to 30 kA. The Soderberg electrodes were continuously oxidized in the slag, likely creating carbon monoxide. The electric potential drop at the surface was attributed to arcing through the carbon monoxide. Thus, heat was released in the immediate vicinity of the electrode due to arcing, as well as in the bulk of the slag by Joule heating. The proper distribution of heat dissipation is required for the transport model, developed in Part II of this series.

Transport Phenomena in Electric Smelting of Nickel Matte: Part II. Mathematical Modeling
Y.Y. SHENG, G.A. IRONS, and D.G. TISDALE
A three-dimensional mathematical model was developed to simulate the distributions of electrical potential, heat release, temperature, and velocity in the slag and matte in a six-in-line 36 MVA capacity furnace for smelting nickel calcine. From Part I of this series, it was found that there was a substantial electrical potential drop at the electrode surface, likely due to arcing through evolved carbon monoxide. The incorporation of this phenomenon into the model permitted accurate calculation of the current, power, and temperature distributions in the slag and matte. The slag was found to be thermally homogenized due to the evolved gas, and to a lesser extent by natural convection. In contrast, the matte was thermally stratified; this finding was attributed to poor momentum transfer across the slag/matte interface. Ninety percent of the electrical energy was used in smelting reactions in the calcine; to simulate the heat transfer from the slag to the calcine, a heat transfer coefficient was deduced from plant data. The implications of these findings for stable furnace operation are discussed.

PHYSICAL CHEMISTRY

Computer Study of Structure, Thermodynamic, and Electrical Transport Properties of Na₃AlF₆-Al₂O₃ and CaF₂-Al₂O₃ Melts
D.K. BELASHCHENKO, O.I. OSTROVSKI, and S.YU. SAPOSZNIKOVA
Structure, thermodynamic, and electrical transport properties of Na₃AlF₆-Al₂O₃ and CaF₂-Al₂O₃ melts were examined by molecular dynamics. Ionic models were constructed for Na₃AlF₆-Al₂O₃ and CaF₂-Al₂O₃ melts at 1283 and 2000 K, respectively. It was found that in the Na₃AlF₆-Al₂O₃ melts, stable aluminum-fluorine-oxygen groups are formed. Although bonds between F^- and Al³⁺ ions in the first coordination shell are weaker than between 0^2- and Al³⁺ ions, very stable negatively charged AIF_6- groups are formed at low oxygen concentrations in the Na₃AlF₆-Al₂O₃. This results in migration of aluminum to the anode in an external electric field. In the CaF₂-Al₂O₃ melts, positively charged aluminum-oxygen groups dominate. This results in migration of aluminum to the cathode at almost all Al₂O₃ concentrations. Therefore, in Na₃AlF₆-Al₂O₃ melts, the Al³⁺ ion as a component of the complex anion has a negative partial conductivity and the 0^2- ion has positive partial conductivity; in CaF₂-Al₂O₃ melts, Al³⁺ has a positive transport number while 0^2- has a negative transport number.

The Kinetics of Dephosphorization of Carbon-Saturated Iron Using an Oxidizing Slag
B.J. MONAGHAN, R.J. POMFRET, and K.S. COLEY
The kinetics of dephosphorization of carbon-saturated iron by oxidizing slags were studied at 1330°C. Nine slag compositions were investigated in the systems CaO-Fe₂O₃-SiO₂-CaF₂ and CaO-Fe₂O₃-SiO₂-CaCl₂. Increasing Fe₂O₃ up to 50 pct was found to increase the rate and extent of dephosphorization, whereas further increases were found to decrease the rate and extent of dephosphorization. This was explained in terms of two competing effects on the driving force, where increased levels of iron oxide increase the oxygen potential for dephosphorization, hence the driving force, but simultaneously dilute the basic components in the slag, lowering the driving force for dephosphorization. CaF₂ and CaCl₂ were found to decrease the rate and extent of dephosphorization at levels higher than 12 pct. The rate of dephosphorization was found to be first order with respect to phosphorous in the metal and was controlled by mass transport in the slag. The oxygen potential at the slag/metal interface was controlled by the FeO activity in the slag. When the kinetic results were analyzed to take account of different driving forces, Fe₂O₃, CaF₂ and CaCl₂ were all found to increase the mass transfer coefficient of phosphorous in the slag, and a quantitative relationship has been demonstrated between these mass transfer coefficients and the slag viscosity for each system studied.

Activities of SiO₂ and Al₂O₃ and Activity Coefficients of Fe_tO and MnO in CaO-SiO₂-Al₂O₃-MgO Slags
HIROKI OHTA and HIDEAKI SUITO
The activities of SiO₂ and Al₂O₃ in CaO-SiO₂-Al₂O₃-MgO slags were determined at 1873 K along the liquidus lines saturated with 2CaO · SiO₂, 2(Mg,Ca)O · SiO₂, MgO, and MgO · Al₂O₃ phases using a slag-metal equilibration technique. Based on these and previous results obtained in ternary and quaternary slags, the isoactivity lines of SiO₂ and Al₂O₃ over the liquid region on the 0, 10, 20, 30, and 40 mass pct Al₂O₃ planes and those on the 10 and 20 mass pct MgO planes were determined. The activity coefficients of Fe_tO and MnO, the phase boundary, and the solubility of MgO were also determined.

Thermodynamics of Chromium Oxides in CaO-SiO₂-CaF₂ Slag
YASUSHI OKABE, ISAO TAJIMA, and KIMIHISA ITO
The distribution ratio of chromium between a CaO-SiO₂-CaF₂ slag and liquid silver under the oxygen partial pressure used in practical hot-metal dephosphorization treatment was measured at 1623 K. The distribution ratio was minimal when the basicity index of a slag, wt pct CaO/wt pct SiO₂, was about 2. The redox equilibrium between CrO (Cr²⁺) and CrO_1.5 (Cr³⁺) in the slag was also measured as a function of slag composition. The calculated activity coefficient of CrO had a maximum value at wt pct CaO/wt pct SiO₂ = 2, whereas that of CrO_1.5 decreased monotonously with the increase in slag basicity.

The Effect of Surfactants on the Interfacial Rates of Reaction of CO₂ and CO with Liquid Iron Oxide
S. SUN and G.R. BELTON
The ¹⁴CO₂-CO isotope exchange technique has been used to measure the rates of dissociation of CO₂ on liquid iron oxide containing the surface active components P₂O₅ or Na₂O, principally at 1673 K. The apparent first-order rate constant is found to decrease monotonically with small additions of P₂O₅ up to a factor of about 4 at 3.5 mol pct. Vaporization losses prevented detailed studies of the effect of Na₂O, but it is shown that there is probably a twofold increase in the rate constant at a concentration of about 0.2 wt pct and a fivefold increase at a concentration between 0.5 and 1.6 wt pct. A smoothed surface potential model, based upon the Vol'kenshtein model for catalysis by semiconductors, is developed, and it is shown that the required surface potential changes due to the segregation of P₂O₅ and Na₂O are physically reasonable.

Phosphorus Distribution Between Carbon-Saturated Iron at 1350°C and Lime-Based Slags Containing Na₂O and CaF₂
W.H. VAN NIEKERK and R.J. DIPPENAAR
The Corex process is capable of consistently producing hot metal with very low silicon contents (;lt0.1 pct), and as a consequence, its hot metal is ideally suited for the external removal of phosphorus. Various studies have shown that small additions of Na₂O significantly enhance the ability of lime-based slags to dephosphorize liquid iron. Additions of fluxes (such as CaF₂) may be required to ensure that the slags remain fluid during treatment. The aim of the present investigation was to study the dephosphorization capabilities of lime-based slags from the CaF₂-CaO-Na₂O-SiO₂ system. Phosphorus containing slag and carbon-saturated iron was equilibrated in carbon crucibles at 1350°C under a carbon monoxide atmosphere. It was confirmed that additions of Na₂O increase the phosphate capacity of silicate and lime-based slags considerably. Additions of CaF₂ to Na₂O containing lime-based slags increase the activity coefficient of P₂O₅ and, therefore, decrease the phosphate capacity thereof. These slags have high phosphate capacities and low melting points, yielding them suitable as effective reagents for dephosphorization, and even desulphurization, of hot metal at relatively low temperatures. However, CaF₂ additions to these slags should be limited.

Thermodynamic Properties of the Fe-Cr-P Liquid Solution
ALEXANDER I. ZAITSEV, NATALIYA E. SHELKOVA, and BORIS M. MOGUTNOV
A Knudsen-cell mass spectrometer was used to determine thermodynamic properties of the Fe-Cr-P alloys in the temperature range of 1403 to 1821 K. Concentration of the components varied within the mole-fraction ranges, as follows: Fe, 0.059 to 0.801; Cr, 0.054 to 0.789; and P, 0.048 to 0.318. The isoactivity lines of phosphorous are close to the secants connecting the Fe-P and Cr-P binary sides. Iron and chromium activities decrease regularly as the configuration point moves from the Fe-Cr liquid solution toward the Fe-P and Cr-P melts. The thermodynamic properties have been described, with the associated solution model assuming that binary and ternary complexes exist in the melt.

Thermodynamics of the Fe-Nb-C-N System and the Solubility of Niobium Carbonitrides in Austenite
S. ZAJAC and B. JANSSON
The solubility of niobium in microalloyed austenite has been analyzed using a thermodynamic description of the Fe-Nb-C-N system. The description of this system forms an important basis for calculations of precipitation of niobium carbonitrides in microalloyed steels. Previously presented thermodynamic descriptions are combined with a new description of the Fe-Nb-N system, and equilibria in the quaternary system are calculated. New experiments were performed on Nb, Nb-Ti, and Nb-Ti-V microalloyed steels to confirm the calculated results. The results of theoretical calculations show good agreement with the experimental data on dissolution/precipitation of Nb carbonitrides in microalloyed austenite.

Review and Modeling of Viscosity of Silicate Melts: Part I. Viscosity of Binary and Ternary Silicates Containing CaO, MgO, and MnO
LING ZHANG and SHARIF JAHANSHAHI
A structurally related model for the calculation of the viscosity of silicate melts is proposed based on the general behavior of the viscosity of binary silicate melts. It relates viscosity to the degree of polymerization, as represented by the three types of oxygen in the melts. The model parameters for binary systems were optimized to give best fit to the experimental values. For ternary systems, it was assumed as a first approximation that the model parameters were linear functions of the parameters of the two binary silicate systems. The model has been applied to the CaO-SiO₂, MgO-SiO₂, and MnO-SiO₂ binary systems and the CaO-MgO-SiO₂ and CaO-MnO-SiO₂ ternary systems. Good agreement was obtained between calculated values and experimental data over the composition and temperature ranges in which experimental data exist. Comparison was made between the present model and the Urbain model. The present model has the capability of representing changes in viscosity due to substitution of cation species in silicate melts.

Review and Modeling of Viscosity of Silicate Melts: Part II. Viscosity of Melts Containing Iron Oxide in the CaO-MgO-MnO-FeO-Fe₂O₃-SiO₂ System
LING ZHANG and SHARIF JAHANSHAHI
The viscosity of iron-containing silicate slags in the CaO-MgO-MnO-FeO-Fe₂O₃-SiO₂ system has been reviewed by analyzing the available experimental data and the results of modeling studies. The model proposed by the present authors for the calculation of viscosity of silicate melts has been found to provide a reasonably good description of the behavior of the viscosity of these melts with respect to both the change in silica content and the effect of different cations on viscosity. The results of the present model are compared with those of the Urbain model and that proposed by Utigard and Warczok (the UW model). The present model and the UW model gave a similar order of accuracy, while the results of the Urbain model tended to be higher than the experimental data for most systems examined. Although none of these models is capable of representing some peculiar behaviors, such as the peak observed around the fayalite composition in the FeO-SiO₂ binary system and the isoviscosity contours found in the MnO-FeO-SiO₂ system, they are considered to be very useful for representing the general behavior of viscosity in the systems studied.

Deoxidation Equilibria of Monten Nickel by Mg-Al and Mn-Al
YIHONG SHAO, KAZUKI MORITA, and NOBUO SANO
The deoxidtion equilibria of aluminum-magnesium and aluminum-manganese in liquid nickel equilibriated with Al₂O₃-saturated MgAl₂O₄, respectively, were investigated in the temperature range of 1773 to 1873 K. At 1773 K, the oxygen levels could be reduced to 5.8 to 6.6 ppm with 2.5 to 10 ppm magnesium and 0.05 to 0.9 mass pct aluminum in the Ni-Mg-Al-O system, and Al-O system. With the experimental results mainly obtained in the present work, the interaction parameters, , , , , and , and the equilibrium constants, log K_MgAl2O4(Ni), log K_MnAl2O4(Ni), log K_Mg(Ni), log K_Mn(Ni), and log K_Al(Ni), were estimated using a multiple regression analysis.

Communication: Distillation and Rectification of Osmium Tetraoxide Solution in Carbon Tetrachloride
A.B. MAIBORODA, I.D. TROSHKINA, and A.M. CHEKMAREV

Communication: The Effect of Sulfur on the Interfacial Rates of Reaction of CO₂ and CO with Liquid Copper
S. SUN and G.R. BELTON

Communication: Impact of Sulfur Loss on Activity Coefficient Measurements of Trace Elements in Matte
TOM ZHONG and DAVID C. LYNCH

SOLIDIFICATION

MATERIALS PROCESSING

MATHEMATICAL MODELING

Modeling of Multi Gas-Solid Reactions; Effect of Bulk Environment Parameters on Solid Conversion
M.A. HASTAOGLU and I.A. ABBA
A unified gas-solid reaction model that considers multi gas-solid components is developed for reactions in porous pellets with multiple reactants. The transient variables and properties of the reactants and transport parameters are continually updated in the simulation. Temperature, pressure, solid conversions, and concentration profiles are well predicted. Structural changes are also considered. Heat, mass, and reaction front tracking equations for all the components are solved simultaneously through a combination of solution techniques. Illustrative validation results for the model are presented for hematite/nickel oxide reduction at 608 K. The importance of bulk temperature and pressure on the overall and individual grain conversions is explored for a range of interest. The response of system parameters to dynamic changes in boundary conditions is studied.

A Kinetic Model of the Peirce-Smith Converter: Part I. Model Formulation and Validation
A.K. KYLLO and G.G. RICHARDS
A kinetics-based mathematical model of the Peirce-Smith converter has been developed. The model considers mass transfer, heat transfer, and reactions between each of the phases present in the converter. Model validation is carried out using industrial data obtained from both copper and nickel converters. The model is generally able to predict the temperature and compositional variations of the converters to within the errors of the industrial data. However, the interactions between the white metal and slag during the copper blow are not understood sufficiently to model well.

A Kinetic Model of the Peirce-Smith Converter: Part II. Model Application and Discussion
A.K. KYLLO and G.G. RICHARDS
A sensitivity analysis of a kinetics-based model of the Peirce-Smith converter has been carried out, and the model has then been applied to an analysis of copper converter operation. The results of the sensitivity analysis indicate that only factors relating to the mass-transfer rates have a significant effect on the model predictions. However, even with large changes in diffusivities, the model predictions remain within the error of the plant measurements. The converter analysis indicates that considerable improvements to converter productivity can be made, particularly through changes to gas injection practices.

Kinetic Modeling of Minor Element Behavior in Copper Converting
A.K. KYLLO and G.G. RICHARDS
The kinetics of minor element removal has been included in an overall model of the Peirce-Smith converter. Mass transfer between the condensed phases and to the gas has been considered. The model is able to predict the distribution of the minor elements fairly well but is limited by the scarcity of thermodynamic and kinetic data. It has been determined that the factors that increase oxygen efficiency, in particular gas velocity and tuyere submergence, tend to increase the proportion of the minor elements reporting to the dust. The reduction of the gas volume flow through the converter associated with oxygen enrichment does tend to reduce the minor element content in the dust. However, this effect may be offset by the increased temperature. Increasing temperature also increases the minor element content of the blister copper produced.

Alternative Approach to the Problem of Additivity
MICHAEL T. TODINOV
Conditions for additivity of nonisothermal reactions in a general sense and in a sense of Scheil are discussed. Scheil's additivity rule can be applied to a reaction additive in a general sense if, and only if, the time from the approximating isothermal reaction can be presented as a product of a function only of the temperature and fraction transformed. Thus, the reactions additive in the sense of Scheil are a subset of the reactions additive in a general sense. It is proved rigorously that Cahn's assumption for the reaction rate, as a function of the temperature and fraction transformed, is not sufficient for additivity in the sense of Scheil. It is sufficient for additivity in a general sense, but not necessary, which means that the class of the additive reactions in a general sense, is wider than that defined by the Cahn's condition. Alternative statements of the additivity rule and its application limits are discussed, on which basis methods are proposed that allow direct determination of the end temperature of the transformation. A method, to check geometrically whether a given isothermal function or a family of isothermal kinetics curves is consistent with the additivity rule, is also proposed.

Surface-Coupled Modeling of Magnetically Confined Liquid Metal in Three-Dimensional Geometry
CHARLES H. WINSTEAD, PETER C. GAZZERRO, and JAMES F. HOBURG
Alternating magnetic fields induce eddy currents within electrically conducting liquid metal that can be used to levitate and shape the liquid. If the frequency of the applied field is high enough, the electromechanical coupling can be reduced to the self-consistent relationship between the shape of the liquid metal and the distribution of the magnetic fields. This article describes a method of modeling this coupling for general three-dimensional geometries. The method is an extension of the free movement method previously used to describe two-dimensional magnetic levitation.

ENVIRONMENT