Estimation of the viscosities of binary metallic melts using Gibbs energies of mixing

In the present work, information on the integral molar Gibbs energies of mixing is employed to calculate the viscosities of binary substitutional metallic melts. A correlation has been established between the second derivative of the integral molar Gibbs energy of mixing with respect to composition and the corresponding function for the Gibbs energy of activation for viscosity. The viscosities predicted from available thermodynamic data in the case of a number of binary metallic systems using this correlation show satisfactory agreement with the values reported from experimental measurements. The value of this correlation in predicting the viscosities of complex metallic melts is also examined.     

Applicability of central atoms models to binary silicate and aluminate melts

A central atoms model is presented which reproduces the phase diagram and the activities in silicate and aluminate melts. A four energy parameter model is required for this purpose. An empirical relationship is proposed which reduces the number of energy parameters to three. P. Sastri, Formerly Research Student, Department of Metallurgy. Indian Institute of Science, Bangalore 560 012, India     

Activities of boron in the binary Ni-B and the ternary Co-Fe-B melts

Activities of boron in the binary Ni-B and the ternary Co-Fe-B melts have been directly determined by the electromotive force (emf) measurement. A boron crystal was mainly used as the reference electrode, and a ternary 29 wt pct B₂O₃-42 wt pct CaO-29 wt pct Al₂O₃ oxide melt was used as the electrolyte. Large negative deviations from Raoult’s law have been found in both the binary and the ternary systems. The activity of nickel has been calculated from the measured boron activity by means of the Gibbs-Duhem equation. Standard Gibbs energies of formation of Ni₃B (s), Fe₂B (s), and Co₃B (s) were estimated and compared with available data. Formerly Graduate Student, Department of Metallurgy, The University of Tokyo.     

Activities of boron in the binary Fe-B,Co-B,and Cu-B melts

Activities of boron in the binary Fe-B, Co-B, and Cu-B melts have been directly determined by the electromotive force (emf) measurement. Boron-saturated liquid Cu-B alloy was used as the reference electrode and a ternary 28 wt pct Al₂O₃-29 wt pct B₂O₃-43 wt pct CaO oxide melt was used as the electrolyte. Deviations of the boron activities from Raoult's law have been found largely negative for the Fe-B and Co-B systems but largely positive for the Cu-B system. Boron activities calculated from the literature data have not been in good agreement with the measured data. Activities of iron, cobalt, and copper have been calculated from the obtained boron activities by means of the Gibbs-Duhem equation. Some modifications to the liquidus curves on the Fe-B and Co-B phase diagrams have been presented. M. YUKINOBU, formerly Graduate Student, Department of Metallurgy, The University of Tokyo S. GOTO, Professor, formerly with the Department of Metallurgy, The University of Tokyo     

Estimation of viscosities of ternary silicate melts using the excess gibbs energy of mixing

A correlation to predict the viscosities of ternary silicates using the Gibbs energies of mixing of the silicate melts has been developed. This correlation has been employed to predict the viscosities of liquid slags in the systems FeO-MnO-SiO₂, FeO-MgO-SiO₂, CaO-FeO-SiO₂, CaO-MnO-SiO₂, and CaO-MgO-SiO₂. The good agreement between the calculated viscosities and the experimental data in the ternary silicate systems has indicated that this approach can be successfully employed to predict the viscosities of ternary silicate melts.     

The free energies of mixing of melts in the systems 2FeO-SiO2-2MnO-SiO2 and 2.33FeO-TiO2-2.33MnOTiO2

The free energies of mixing in melts in the system 2FeO · SiO₂-2MnO · SiO₂ at 1450°C and the system 2.33FeO · TiO₂-2.33MnO · TiO₂ at 1475°C have been obtained from measurement of the equilibrium Mn + FeO = Fe + MnO established between the melts and ironmanganese foils. Both systems exhibit ideal silicate mixing. The phase diagram for the system 2FeO-SiO₂-2MnO ·SiO₂ is calculated.     

Densities and molar volumes of silicate melts

Abstract

Expressions are derived for densities and molar volumes of binary and ternary silicate melts based on the interpretation that the constitution of the melts can be described in tern-IS of conventional polymer theory. For simplicity, the treatment is limited to the case in which only linear chains are considered to be present. The assumptions in this approach are that (a) the value of k_ln for the equilibrium constant of the polymerization process, as expressed in terms of the activities of the constituents, is independent of the chain length n of the reacting species, and (b) the enthalpy change for the mixing of the pure constituents is identical with the change in internal energy. It is readily shown that these are equivalent to the assumptions that there is a constant increment in standard free energy of formation and molar volume on passing from one member to the next along the homologous series of pure liquid silicates and that, for the molar volumes, this increment is equal to that on passing from the oxide to the pure liquid orthosilicate. Densities and molar volumes calculated on this basis are in good agreement with experiment for basic melts in the systems FeO-SiO₂, PbOSiO₂, FeO-CaO-SiO₂, FeO-MnO-SiO₂ and FeO-CoO-SiO₂. The treatment becomes inexact near the metasilicate composition due to the neglect of cyclic and network structures, not allowed in the theory. The increment in molar volume due to the MSiO₃ group, as calculated from the data, varies between 40 and 50 cm³ and increases with the ionic radius of the cation.

Résumé

Des expressions ont été dérivées pour calculer les densités et les volumes molaires des silicates binaires et ternaires fondus en supposant que la composition des silicates peut être représentée par la théorie conventionnelle de polymères. Pour cette analyse nous utilisons simplement Ie formalisme de chîines linéaires avec les hypothéses que: (a) la valeur de k_ln, la constante d'équilibre du procédé de polymérisation reliant les activités des constituants, est indépendante de la longueur de chaîne “n” des réactifs et (b) que l'enthalpie de mélange des composants purs est identique à l'énergie interne de mélange. On peut démontrer que ces hypothéses reviennent à supposer qu'il existe un acroissement constant dans l'enthalpie libre standard de formation et dans le volume molaire au cours de la progression entre les séries homologues de silicates purs fondus. Pour les volumes molaires, cet accroissenlent correspond à la différence entre l'oxyde et l'orthosilicate pur liquide. Sur cette base les valeurs calculées des densités et des volurnes molaires se comparent bien avec les valeurs expérimntales des silicates fondus dans les systèmes FeO-SiO₂, PbO-SiO₂, FeO-CaO-SiO₂, FeO-MnO-SiO₂ et FeO-CoO-SiO₂. La correspondance est moins bonne lorsqu'on tend vers la composition du métasilicate, à cause de la présence des structures cycliques et groupées, non incluses dans les hypothèses. L'accroissement du volume molaire dû au groupelnent MSiO₃, tel que calculé à partir des données, varie entre 40 et 50 cm³ et augmente avec le rayon ionique du cation.     

Solubilities of carbon dioxide in sodium silicate melts

Carbonate solubilities in Na₂O-SiO₂ melts were measured over the composition range X_{Na 2}O/ (X_{Na 2}O + X_{SiO 2}) = 0.5 to 1.0 and the temperature range 1100 to 1300 ‡C. The solubility increased with increasing X_Na2_O and decreased with increasing temperature. Carbonate capacities calculated from the experimental results compared favorably with values for sulfide and phosphate capacities obtained from the literature. In addition, an excellent correlation was obtained between carbonate capacity and the activity of sodium oxide. The carbonate capacity, which is an easier parameter to obtain, is a good measure of the basicity of sodium silicate melts. It would appear that carbonate capacity could be an excellent basicity index for iron and steelmaking slags as well as for fluxes used in other high temperature technologies. Formerly with University of Toronto. Formerly with the Department of Metallurgy, University of Tokyo.     

The thermodynamic activity of ZnO in silicate melts

The activity of ZnO in ZnO-SiO₂ and CaO-ZnO-SiO₂ melts has been measured at 1560 °C using a transpiration technique with CO-CO₂ mixtures as the carrier gas. The activities of ZnO in dilute solution in 42 wt pct SiO₂?38 wt pct CaO-20 wt pct A1₂O₃ in the range 1400° to 1550 °C and in 62 wt pct SiO₂?23.3 wt pct CaO?14.7 wt pct A1₂O₃ at 1550 °C have also been measured. The measured free energies of formation of ZnO-SiO₂ melts are significantly more negative than published estimated values and this, together with the behavior observed in the system CaO-Al₂O₃-SiO₂, indicate that ZnO is a relatively basic oxide. The results are discussed in terms of the polymerization model of binary silicate melts and ideal silicate mixing in ternary silicate melts. The behavior of ZnO in dilute solution in CaO-Al₂O₃-SiO₂ melts is discussed in terms of the possibility of the fluxing of ZnO by iron blast furnace slags.     

Modeling of sulfide capacities of silicate melts

An examination of the solution chemistry of sulfides in silicates leads to a method for the calculation of the sulfide capacities of silicate melts using the Flory model for polymeric silica chains. Calculations for the CaO−SiO₂, FeO−SiO₂, and MgO−SiO₂ binary systems at 1773 K and 1923 K are shown to be in good agreement with available experimental data and to be more reliable than calculations based on the empirical concept of basicity.     

Fuming of stannous oxide from silicate melts

The kinetics of vaporization of SnO from silicate melts was studied in helium, nitrogen, argon and argon-helium mixtures, and in inert gas—carbon monoxide mixtures. The rate of extraction of tin from the meltvia SnO vaporization was significantly higher in reducing gases than in inert gases. The enhanced vaporization phenomenon, commonly recognized in metallic systems, is demonstrated to occur in silicate melts. The vapor phase reduction of SnO (g) was studied experimentally, and the reduction was found to be very rapid. The addition of acidic or basic oxides to the binary SnO-SiO₂ melts decreased the vaporization rate.     

Montecarlo calculations of ionic structure in silicate and alumino-silicate melts

Results on structures of molten silicates and alumino-silicates calculated with the Montecarlo method are reported. The structure of the ions is in agreement with Masson’s hypotheses; in fact ions of the type Si_nO _(3n+1 ⁽²ⁿ⁺²⁾ with chains even 30 + 35 atoms long have been found. The spatial configurations of the polymer ions are dependent on the vacancy-silicon interaction energy and therefore on the nature of the cation. The linear chain configuration is more frequent as the interaction energy becomes stronger.     

Carbon solubility as carbide in calcium silicate melts

R.A. Berryman, Formerly Graduate Student, Department of Metallurgy and Materials Science, University of Toronto,     

Model experiments on mixing phenomena in gas-stirred melts

Mixing experiments were performed in a water model system of a gas-stirred ladle with both an optical decolourization method and conductivity measurements at different positions within the vessel. The experimental results show that the rate by which the concentration is homogenized depends on the location of the measuring probe as well as on the used stirring conditions. Using a centric nozzle at the bottom pronounced dead zones exist. The equalization is slowest between these dead zones and the remaining volume. The mixing process in the remaining volume is characterized by a circulating concentration cloud in which mixing takes place by random turbulent diffusion. With an eccentric nozzle arrangement dead zones can be avoided and thus, mixing times decrease and become more similar for different positions.     

Comparison between antigen-antibody binding energies and interfacial free energies

Antigen-antibody binding energies derived from equilibrium data are compared with the binding energies resulting from the interfacial free energies obtained from contact angle measurements of antigens and antibodies. From these interfacial free energies two sorts of theoretical antigen-antibody binding energies can be derived, as well as the Hamaker constants for most antigen-antibody systems. For interaction in vacuo the Hamaker constants obtained are between 4 and 6 X 10(-13) ergs, while these constants for hydrated antigen antibody interactions are less than 10(-14) ergs. For interactions in vacuo, interfacial free energies yield binding energies (delta Fa) that lie between -120 and -140 ergs/cm2. For interactions in the aqueous phase (with interstitial water still present), much lower binding energies (delta Fb) are derived, of the order of -.01 and -1 ergs/cm2. In comparison, dextran-anti-dextran interactions show a binding energy derived from equilibrium data (delta Feq) of the order of -10 ergs/cm2. In general the equilibrium binding energies delta Feq of most antigen-antibody systems would vary between -1 and -20 ergs/cm2. The implications of this comparison are discussed in the light of the influence of residual water between antigenic determinant and antibody-active site, as well as in the light of the degree of perfection of fit between these sites.     

Activities of carbon and nitrogen in Fe-Cr and Fe-Cr-Ni melts

Carbon and nitrogen in steel are the original sources of carbides, nitrides and carbonitrides which exert a strong effect on the production process and the service properties of steel. The knowledge of the activities and contents of carbon and nitrogen in Fe-Cr and Fe-Cr-Ni melts under atmospheric and vacuum conditions is indispensable to optimize existing processes and to create new ones. With the help of computer based modelling and simulation programs, the thermodynamic behaviour of carbon and nitrogen was analyzed. The calculated results are supported by the available experimental ones. They provide a basis to better understand metallurgical reactions occurring in steelmaking and enable an improved control of the steelmaking process.