The diffusivity of oxygen in liquid copper-lead alloys

The oxygen diffusivity in liquid copper-lead alloys at 1403 K (1130° C) was measured using the electrochemical cell: Ni−NiO/ZrO₂(+CaO)/O in liquid Cu−Pb alloy(I)/ZrO₂(+CaO)/O in liquid Cu−Pb alloy (II). Oxygen in liquid Cu−Pb alloy (I) was transferred to the right by applying a preselected voltage between the two liquid Cu−Pb alloys. The oxygen diffusivity in liquid Cu−Pb alloy(I) was calculated from the emf change with time between the Ni−NiO and liquid Cu−Pb alloy (I) electrodes. The results were: It was found that the oxygen diffusivity in liquid copper-lead alloys did not change drastically over the entire composition range, in contrast with that reported by other investigators for liquid copper-nickel alloys. The oxygen diffusivity in pure liquid lead agreed with the results of our previous work using an FeO−Fe₃O₄ mixture as a sink for oxygen.     

Thermodynamic properties of liquid copper-lead alloys

Activities of lead in liquid copper-lead alloys were measured in the temperature range 1000 to 1200 °C at intervals of 50 °C by the dew-point technique. Various partial and integral molar properties of the liquid alloys were evaluated from the data, and the boundaries of liquid immiscibility in the Cu-Pb phase diagram were calculated. The activity coefficients of lead and copper in dilute solutions are represented by: In γ^o _Pb = (346/T@#@) + 0.181, and In γ^o _cu = (3852/T) − 0.945. The temperature dependence of Gibbs energy self-interaction coefficients for lead and copper are given by: ε^Pb _Pb = − (7828/T) − 3.506, and ε^Cu _Cu = − (8804/T) + 3.140. Various coefficients have the following values at 1200 °C: γ^o _Pb = 12.58,ε^Pb _Pb = − 8.85.η^Pb _Pb = − 52,197 J/gfw, σ^Pb _Pb = 38.15 J/gfw-K, γ^o _Cu = 5.31, ε^Cu _Cu = −2.92,η^Cu _Cu = − 63,970 J/gfw, and σ^Cu _Cu = 19.19 J/gfw-K.     

The diffusivity and solubility of oxygen in liquid tin and solid silver and the diffusivity

The diffusivity and solubility of oxygen in liquid tin and solid silver in the temperature range of about 750° to 950°C (1023 to 1223 K) and the diffusivity of oxygen in solid nickel at 1393°C (1666 K) were determined using the electrochemical cell arrangement of cylindrical geometry: Liquid or Solid Metal + O (dissolved) | ZrO₂ + (3 to 4%)CaO | Pt, air The diffusivity and solubility of oxygen in liquid tin are given by:D _O(Sn) = 9.9 × 10⁻⁴ exp(−6300/RT) cm²/s (9.9 × 10⁻⁸ exp − 6300/RT m²/s) andN _O ^S (Sn) = 1.3 × 10⁵ exp(−30,000/RT) at. pct The diffusivity and solubility of oxygen in solid silver follow the relations:D _O(Ag) = 4.9 × 10⁻³ exp (−11,600/RT) cm²/s ( 4.9 × 10⁻⁷ exp − 11,600/RT m²/s) andN _O ^S (Ag) = 7.2 exp (−11,500/RT) at. pct The experimental value for the preexponential in the expression forD _O(Ag) is lower than the value calculated according to Zener’s theory of interstitial diffusion by a factor of 11. The diffusivity of oxygen in solid nickel at 1393°C (1666 K) was found to be 1.3 × 10⁻⁶ cm²/s (1.3 × 10⁻¹⁰ m²/s). Formerly Graduate Student, Department Formerly Graduate Student, Department Formerly Graduate Student, Department This paper is based upon a This paper is based upon a This paper is based upon a This paper is based upon a     

Oxygen solubility in liquid indium and oxygen diffusivity in liquid indium and tin

The solubility of oxygen in liquid indium, C_o, at 973 and 1073 K in equilibrium with its oxide was determined by an isopiestic equilibration technique in order to resolve discrepancies reported in the literature. The present results, C_o = 0.0092 at. pet at 973 K and 0.0377 at. pet at 1073 K, agree with those obtained by Otsuka, Sano, and Kozuka using a modified coulometric titration method. Oxygen diffusivity in liquid indium from 873 to 1073 K and in liquid tin from 973 to 1273 K was measured utilizing a combined potentiostatic and emf method using the following double electrochemical cells: Fe,FeO/ZrO₂(+CaO)/O in Me(I)/ZrO₂(+CaO)/O in Me(II). The present results are D_O(In) = 6.6 ( _-1.6 ^+2.0 ) x 10⁻³ exp[(-3-600 ± 5600)/RT]873 K ≤T ≤ 1073 K and D_O(Sn), = 8.7( _-5.7 ^+13.5 ) x 10⁻⁴ exp[(-18800 ± 6700)/RT]973 K ≤T ≤ 1273 K. The present results are of the same order of magnitude with the self-diffusivity of the liquid metals, and are about two orders of magnitude greater than the oxygen diffusivity reported by Stevenson and co-workers. The ratio of oxygen diffusivity to self-diffusivity of the solvent was found to be correlated to the enthalpy of formation per mole of oxygen of the respective oxide at 298 K.     

Activity of oxygen in liquid In-Sb alloys

In order to provide fundamental insights into the role of the ratio of the solvent metallic valences (V _b/V_a) on the compositional dependence of In γo, the activity coefficients of oxygen, γo, in liquid In-Sb alloys at 1073 K have been measured by modified coulometric titrations on the galvanic cell:O in liquid In-Sb alloys/ZrO₂( + CaO)/Air, Pt. Present results indicated the Henrian behavior of oxygen in liquid In-Sb alloys. The dependence of the activity coefficient of oxygen on alloy composition is represented as follows: N_IN 0 0.07 0.15 0.30 0.45 0.60 0.80 0.90 1 −lnγo 8.24 8.96 9.64 10.80 11.71 12.59 13.35 13.57 13.64 These results differ significantly from those predicted by Jacob and Alcock's equation and by Wagner's equation combined with Chang et al's correlation of the energy parameter, h. However, by modifying Chang et al's definition of ( V_b/ V_a), the Wagner's equation has been found to be capable of approximately describing the compositional dependence of the activity coefficient of oxygen in liquid In-Sb alloys.     

The chemical diffusivity of oxygen in liquid iron oxide and a calcium ferrite

Measurements have been made of the chemical diffusion coefficient of oxygen in liquid iron oxide at temperatures from 1673 to 1888 K and in a calcium ferrite (Fe/Ca = 2.57) at temperatures from 1573 to 1873 K. A gravimetric method was used to measure the oxygen uptake during the oxidation of the melts by oxygen or CO₂-CO mixtures. The rate was shown to be controlled by mass transfer in the liquid melt. The chemical diffusivity of oxygen in liquid iron oxide at oxygen potential between air and oxygen was found to be 4.2±0.3 × 10⁻³ cm²/s at 1888 K. That in iron oxide at oxidation state close to iron saturation was established to be given by the empirical expression log D=−6220/T + 1.12 for temperatures between 1673 and 1773 K. For the calcium ferrite (Fe/Ca=2.57) at oxygen potential between air and oxygen, the diffusivity of oxygen was found to be given by log D=−1760/T−1.31 for temperatures between 1673 and 1873 K. This article is based on a presentation made in the “Geoffrey Belton Memorial Symposium,” held in January 2000, in Sydney, Australia, under the joint sponsorship of ISS and TMS.     

The activity coefficient of oxygen in binary liquid metal alloys

The Wagner model with one energy parameter,h, for describing the effect of alloying elements on the activity coefficients of nonmetallic solutes in liquid metals is extended to have two energy parameters,h ₁andh ₂. The validity of both the Wagner one-parameter equation and the newly derived two-parameter equation is tested using data available in the literature for twelve ternary metal-oxygen systems. In order to have consistent thermodynamic data, all the relevant binary, as well as the twelve ternary metal-oxygen systems are evaluated using the same thermodynamic values for the reference materials which were used in carrying out the experimental measurements. It is found that the twoparameter equation is capable of quantitatively accounting for the compositional dependences of the activity coefficients of oxygen in all twelve ternary systems while the Wagner one-parameter equation is not. A correlation between the Wagner parameter,h, and the thermodynamic properties of the respective binary metal-oxygen and binary metals systems is found, from which the value of this parameter may be predicted without referring to any ternary data. Accordingly, the two-parameter equation is more useful in evaluating ternary experimental data while the Wagner one-parameter equation in connection with the correlation betweenh and binary data is capable of predicting ternary data without any experimental investigation in the ternary region. Based on the one-parameter and the two-parameter equations, theoretical equations for the first-order and second-order free energy interaction parameters,(∈ ₀ ^j )_sand(ρ ₀ ^j )_s, are derived in terms of the model parameters. The values of(∈ ₀ ^j )_s and(ρ ₀ ^j )_s for all the systems are derived and are found to vary linearly with the reciprocal of temperature. Furthermore, linear relationships between these two interaction parameters and their slopes with 1/T are found, from which the temperature dependence of the interaction parameters may be estimated in the absence of experimental data.     

The detection of solutal convection during electrochemical measurement of the oxygen diffusivity in liquid tin

Electrochemical titration was used as a means to determine the mass diffusivity of oxygen in liquid tin at various temperatures. Solutal convection was present depending on the conditions, and this was inferred from an enhancement in the effective diffusivity. The experiments were conducted in two different modes of operation, and in each case, we attempted to align the oxygen concentration gradient such that it was parallel to the gravitational field. In the first mode, the concentration gradient was such that the fluid was heavy at the bottom and lighter at the top, and in the second, the reverse was true. The second mode was potentially unstable and sometimes gave rise to substantial convection for large values of the oxygen concentration gradient. The measured effective diffusivities were then higher than the corresponding measurements in the first mode of operation. Activation energies in two different temperature ranges were obtained by using an Arrhenius relationship. Formerly Graduate Student, Chemical Engineering Department, University of Florida     

Permeability,diffusivity, and solubility of oxygen gas in liquid slag

An experimental procedure for measurement of the permeability of dissolved oxygen gas in liquid slag has been developed using an oxygen concentration cell. The small amount of oxygen gas which penetrated through the liquid oxide from a pure oxygen compartment to a pure argon compartment was determined by the galvanic cell. The permeabilities of oxygen through liquid PbO-SiO₂ and FeO-PbO-SiO₂ were found to be in the range 3 x 10^-8 to 3 x 1O^-7 moles/cm s. The permeabilities were little influenced by temperature but more influenced by the composition. In separate experiments, the oxygen pressure change at the bottom of a column of slag was detected by another galvanic cell. By this method, it is not necessary to quench the specimen to determine the concentration profile of dissolved oxygen and to determine its diffusivity. Liquid oxides in the PbO-SiO₂, CaO-SiO₂-Al₂O₃and FeO-PbO-SiO₂ systems were studied. The oxygen diffusion coefficients (5 x 10^-5 to 3 x 10^-3 cm²/s) were found to increase with temperature for a fixed composition of slag, and with an increase of network-modifier oxide content at constant temperature. The solubility of oxygen gas in PbO-SiO₂ melts was estimated to be 2 x 10^-4 to 2 x 10^-5 moles/cm³ from the determined diffusivities and permeabilities. The solubilities decreased with increasing temperature in the composition range studied. Physical solubilities of gases and metals in slags determined by other investigators are compared with the present results.     

Activities of oxygen in liquid Cu-Sb and Cu-Ge alloys

In order to determine the activity coefficients of oxygen, γΩ in liquid Cu-Sb and Cu-Ge alloys at 1373 K as a function of alloy composition, the modified coulometric titrations, described previously, have been performed by using the galvanic cell: O in liquid Cu-Sb or Cu-Ge alloys/ZrO₂ (+CaO)/Air, Pt. A pronounced point of inflection in the In γΩvs alloy composition curve has been observed both for Cu-Sb and Cu-Ge alloys, as predicted by Jacob and Alcock’s quasichemical equation. The measured data itself, however, are significantly different from those predicted by their equation. The validity of Wagner’s solution model with one or two energy parameters has been also tested. YOSHIHIRO MATSUMURA, formerly a Graduate Student, Osaka University.     

Activities of oxygen in liquid Bi-Pb and Bi-Sb alloys

The activity coefficient of oxygen, γ_o, in liquid Bi-Pb and Bi-Sb alloys at 1073 K has been measured over the entire composition range utilizing a modified coulometric titration method with the electrochemical cell: O in liquid Bi-Pb or Bi-Sb alloys/ZrO₂(+CaO)/Air, Pt. The measured In y0 values for both systems, plotted in terms of alloy composition, lie on upwardly concave curves. This behavior is significantly different from what is predicted by the quasi-chemical equations. The models of Wagner and of Blanderet al., which involve one adjustable parameter,h, give a satisfactory representation of the data. YOSHIKAZU KUROSE, formerly a Graduate Student, Osaka University, Osaka, 565, Japan