Quasichemical equations for oxygen and sulphur in liquid binary alloys

An equation has been derived for predicting the activity coefficient of oxygen or sulphur in dilute solution in binary alloys, based on the quasichemical approach, where the metal atoms and the oxygen atoms are assigned different bond numbers. This equation is an advance on Alcock and Richardson's earlier treatment where all the three types of atoms were assigned the same coordination number. However, the activity coefficients predicted by this new equation appear to be very similar to those obtained through Alcock and Richardson's equation for a number of alloy systems, when the coordination number of oxygen in the new model is the same as the average coordination number used in the earlier equation. A second equation based on the formation of “molecular species” of the type XnO and YnO in solution is also derived, where X and Y atoms attached to oxygen are assumed not to make any other bonds. This equation does not fit experimental data in all the systems considered for a fixed value of n. Howover, if the strong oxygen-metal bonds are assumed to distort the electronic configuation around the metal atoms bonded to oxygen and thus reduce the strength of the bonds formed by these atoms with neighbouring metal atoms by approximately a factor of two, the resulting equation is found to predict the activity coefficients of oxygen that are in good agreement with experimental data in a number of binary alloys.

Interaction between oxygen and silver dissolved in liquid copper

The effect of silver on the activity of oxygen in solution in liquid copper has been measured at 1373 K. The results are compared with those of other authors who have studied the system; it is found that the results are in good agreement with Alcock and Richardson's quasichemical model when a coordination number of 2 is assigned to all atoms in the ternary solution.

Solubility and activity of oxygen in liquid gallium and gallium copper alloys

The solubility of oxygen in liquid gallium in the temperature range 775 –1125 °C and in liquid gallium-copper alloys at 1100 °C, in equilibrium with β-Ga2O3, has been measured by an isopiestic equilibrium technique. The solubility of oxygen in pure gallium is given by the equation log (at.% O) = −7380/T + 4.264 (±0.03) Using recently measured values for the standard free energy of formation of β-Ga2O3 and assuming that oxygen obeys Sievert's law up to the saturation limit, the standard free energy of solution of oxygen in liquid gallium may be calculated : View the MathML sourceΔ°298 = −52 680 + 6.53T (±200) cal where the standard state for dissolved oxygen is an infinitely dilute solution in which the activity is equal to atomic per cent. The effect of copper on the activity of oxygen dissolved in liquid gallium is found to be in good agreement with that predicted by a recent quasichemical model in which it was assumed that each oxygen is interstitially coordinated to four metal atoms and that the nearest neighbour metal atoms lose approximately half their metallic cohesive energies.

Solubility and activity of oxygen in liquid indium and copper indium alloys

The solubility of oxygen in liquid indium in the temperature range 650–820 °C and in liquid copper-indium alloys at 1100 °C in equilibrium with indium sesquioxide has been measured by a phase equilibration technique. The solubility of oxygen in pure indium is given by the relation log(at.% O) = −4726/T + 3.73 (±0.08) Using the recently measured values for the standard free energy of formation of In2O3 and assuming that oxygen obeys Sievert's law up to saturation, the standard free energy of solution of molecular oxygen in liquid indium is calculated as View the MathML sourceΔG°= −51 440 + 8.07 T (±500) cal where the standard state for dissolved oxygen is an infinitely dilute solution in which activity is equal to atomic per cent. The effect of indium additions on the activity coefficient of oxygen dissolved in liquid copper was measured by a solid oxide galvanic cell. The interaction parameter ϵ0In is given by View the MathML source The experimentally determined variation of the activity coefficient of oxygen in dilute solution in Cu-In alloys is in fair agreement with that predicted by a quasichemical model in which each oxygen atom is assumed to be interstitially coordinated to four metal atoms and the nearest neighbour metal atoms are assumed to lose approximately half their metallic cohesive energies.

Solubility and activity of oxygen in liquid germanium and germanium copper alloys

The solubility of oxygen in liquid germanium in the temperature range 1233 to 1397 K, and in liquid germanium-copper alloys at 1373 K, in equilibrium with GeO2 has been measured by the phase equilibration technique. The solubility of oxygen in pure germanium is given by the relation R470 log(at. pct 0)=-6470/T+4.24 (±0.07). The standard free energy of solution of oxygen in liquid germanium is calculated from the saturation solubility, and recently measured values for the free energy of formation of GeO2, assuming that oxygen obeys Sievert’s law up to the saturation limit. For the reaction, 1/2 O2(g)→ OGe ΔG° =-39,000 + 3.21T (±500) cal = -163,200 + 13.43T (±2100) J. where the standard state for dissolved oxygen is that which makes the value of activity equal to the concentration (in at. pct), in the limit, as concentration approaches zero. The effect of copper on the activity of oxygen dissolved in liquid germanium is found to be in good agreement with that predicted by a quasichemical model in which each oxygen was assumed to be bonded to four metal atoms and the nearest neighbor metal atoms to an oxygen atom are assumed to lose approximately half of their metallic bonds.

Vapor pressure of liquid metals and alloys

The Gibbs-Bogoliubov formalism in conjunction with the pseudopotential theory is applied to the calculation of the vapour pressure of eight liquid metals from Groups I to IV of the periodic table and of alloys (Na-K). The calculated vapour pressure of the elements and their temperature dependencies, the partial pressures, activities and boiling points of the alloys are all found to be in reasonable agreement with measured data.

Heat of Mixing and Activities in Liquid Al-Sn Alloys

The microscopic electron theory based on the pseudopotential formalism has been applied to the calculation of the heats of mixing and of activities in liquid Al·Sn alloys. The calculated values for both quantities were found to be in reasonable agreement with ,the experimental data.

Solubility and activity of oxygen in liquid antimony

The solubility limit of oxygen in liquid antimony has been measured by a novel isopiestic technique in the temperature range 995--1175 deg K. The results can be expressed by the equation log c = --5500/T + 3.754 ( plus/minus 0.04) with c in at.% O and T in deg K. The oxygen potential over Sb + O alloys equilibrium with Sb2O3 has been measured by a solid state cell using a fully stabilized CaO.ZrO2 electrolyte. The cell was designed to contain the Sb + Sb2O3 mixture in a closed volume, that the vaporization of the oxide can be minimized and true equilibrium attained. The Gibbs free energy of the reaction 2 Sb(s) + 3/2 O2 = Sb2O3(s) is Delta G deg = --719560 + 274.51 T( plus/minus 500) and Sb(l) + 3/2 O2 = Sb2O3(l), Delta G deg = --704711 + ( plus/minus 500) ( Delta G deg in J/mole, T in deg K). The combination of these results with Sieverts' law yields the standard free energy of solution of oxygen in liquid antimony according to the reaction 1/2 O2 = \O\Sb,at.% as Delta G deg = --129620 + 14.23 T ( plus/minus 950). The standard enthalopy and entropy of the solution of oxygen in Sb are compared with values for other metal- oyxgen systems, and with the standard enthalpies of formation of corresponding oxides. The resulting correlations permit the estimation of the standard free energy of solution of oxygen in pure metals for which experimental information is lacking. 24 ref.--AA

A comparison of the structure of liquid alloys derived from thermodynamic and diffraction studies

A significant amount of research on the thermodynamic properties of molten alloys is undertaken for obtaining insights into their structure . The partial and integral molar enthalpies, entropies and volumes of mixing provide some general information on the nature and strength of atomic bonds and the distribution of atoms. However, until recently it has been difficult to derive specific quantitative information because the excess entropy of mixing contains configurational , vibrational , electronic , and sometimes magnetic contributions which cannot be easily separated.

A derivation of thermodynamic quantities of liquid alloys from their structure factors

A method of deriving the thermodynamic properties of mixing in liquid alloys Delta G, Delta S and Delta H, from low-Q scattering data has been presented. As an example, the method has been demonstrated with liquid Na-Ga alloys for which both thermodynamic and diffraction data have recently been obtained by the authors.

Computation of thermodynamic properties of liquid ferrous alloys from structural measurements

Relation between X-ray scattering intensities, mean square thermal fluctuations and thermodynamic properties. High temperature X-ray diffraction study of liquid Fe-Ni and Fe-Si alloys using reflection and transmission geometries. Calculation of the structure factor as a function of wave vector. Extrapolation to zero wave vector. Calculation of the concentration-concentration correlation function defined by A. B. Bhatia and D. E. Thorton. Computation of thermodynamic quantities of mixing A G, LlH and LlS for the binary alloys. Comparison with direct thermodynamic measurements reported in the literature.

Mass spectrometric and electrochemical studies of thermodynamic properties of liquid and solid phases in the CaO Al2O3 system

The activities of CaO and Al2O3 in lime-alumina melts were studied by Knudsen cell-mass spectrometry at 2060 K. Emf of solid state cells, with CaF2 as the electrolyte, was measured from 923 to 1223 K to obtain the free energies of formation of the interoxide compounds. The results are critically evaluated in the light of data reported in the literature on phase equilibria, activities in melts, and stabilities of compounds. A coherent set of data is presented, including the previously unknown free energy of formation of CaO.6Al2O3 and the temperature dependence of activities in the liquid phase.

Solubility and activity of oxygen in liquid manganese

The oxygen concentration of liquid manganese in equilibrium with MnAl2+2xO4+3x and α−Al2O3 has been determined in the temperature range 1520 to 1875 K. The oxygen content of quenched samples, wrapped in oxygen-free nickel foil, was determined by an inert gas fusion technique. The results are combined with accurate data now available on the Gibbs energies of formation of MnO and Al2O3−saturated MnAl2+2xO4+3x to derive the oxygen content of liquid manganese in equilibrium with MnO and the Gibbs energy of solution of diatomic oxygen gas in liquid manganese. The enthalpy and entropy of solution of oxygen in manganese are compared with similar data on other metal-oxygen systems.