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.

Prediction of activities of oxygen in dilute quaternary solutions using binary data

Equations are developed for predicting the activity coefficients of oxygen dissolved in ternary liquid alloys. These are extensions of earlier treatments, and are based on a model in which each oxygen atom is assumed to make four bonds with neighboring metal atoms. It is also postulated that the strong oxygen-metal bonds distort the electronic configuration around the metal atoms bonded to oxygen, and that the quantitative reduction of the strength of bonds made by these atoms with all of the adjacent metal atoms is equivalent to a factor of approximately two. The predictions of the quasichemical equation which is derived agree satisfactorily with the partial molar free energies of oxygen in Ag-Cu-Sn solutions at 1200°C reported in literature. An extension of this treatment to multicomponent solutions is also indicated.

An improved method for calculating activities from distribution equilibria

The method of Gibbs-Duhem integration suggested by Speiser et al. has been modified to derive activities from distribution equilibria. It is shown that, in general, the activities of components in melts with a common anion can be calculated, without using their standard Gibbs energies of formation, from eqUilibrium ratios and the knowledge of activities in the metal phase. Moreover, if systems are so chosen that the concentration of one element in the metal phase lies in the Henry's law region (less than 1 %), information on activities in the metal phase is not required. Conversely, activities of elements in an alloy can be readily calculated from equilibrium distribution ratios alone, if the salt phase in equilibrium contains very small amounts of one element. Application of the method is illustrated using distribution ratios from the literature on AgCI-CuCI, AgBr-CuBr, and CuDo.5 -PbD systems. The results indicate that covalent bonding and van der Waals repulsive interactions in certain types of fused salt melts can significantly affect the thermodynamic properties of mixing.

Solubilities of Pb+2, Bi+3, Sb+3 and Cu+1 sulphides in (NaCl KCl Na2S) melts

Solubilities of common metal sulfides have been determined in the (NaCl+KCl) eutectic melt with and without Na2S. A novel gas-phase equilibrium technique has been used for PbS, Bi2S3, and So2S3, and an improved liquid phase equilibrium technique for Cu2S, which eliminates the errors due to physical entrapment of the sulfide phase and segregation on quenching, enabling precise measurements to be made. Solubilities in the (NaCl+KCl) eutectic melt were determined as a function of temperature in the rante 700° to 950°C, and were found to be small. The partial molar heats of mixing of the sulfides in the eutectic melt have been calculated from the solubility measurements, to be 13.3, 31.4, 37.1, and 49.0 kcal for PbSs), Sb2S2(l), and Cu2S(s), respectively. Sodium sulfide addition was observed to enhance these solubilities, the effect being largest for Cu2S followed by Sb2S3, Bi2S3, and PbS. This effect is explained qualitatively. It was observed that PbS and Sb2S3 obey Henry's law up to saturation in (NaCl+KCl+Na2S) melts.

Thermodynamics of solid solutions of silver with indium and tin

A solid oxide galvanic cell and a gas-solid (View the MathML source) equilibration technique have been used to measure the activities of the solutes in the α-solid solutions of silver with indium and tin. The results are consistent with the information now available for the corresponding liquid alloys, the phase diagram and the heats of mixing of the solid alloy. When the results of this study are taken together with published data for the α-solid solutions in Ag + Cd system, it is found that the variation of the excess partial free energy of the solute with mole fraction can be correlated to the electron/atom ratio. The significant thennodynamic parameter that explains the Hume-Rothery findings in these alloys appears to be the rate of change of the excess partial free energy with composition near the phase boundary, and this in turn reflects the value of the solute-solute interaction energy.

Activities of indium in solid solutions of Cu+In, Au+In and Cu+Au+In alloys

Thin foils of Cu, Au and Cu + Au alloys embedded in indium sesquioxide were equilibrated with controlled streams of CO-CO2 mixtures. The equilibrium concentrations of indium in the foils were determined by neutron activation analysis. The corresponding chemical potentials of indium were calculated from the standard free energies of formation of carbon monoxide, carbon dioxide, and indium oxide. It was found that the size difference between the solute and the solvent does not make significant contributions to the solute—solute interaction energy in the α-phase. The chemical potential of indium at one at.% concentration is 8.6 Kcals more negative in gold than in copper at 900°K. The variation of this chemical potential with alloy composition in Cu + Au system was in good agreement with Alcock and Richardson's quasichemical equation. The agreement is strengthened by the accurate knowledge of the co-ordination number in these substitutional solid solutions from X-ray diffraction studies.

Electrochemical measurement of the oxygen potential of the system iron+alumina+ hercynite in the temperature range 750 to 1600oC

Solid oxide galvanic cells using CaO-ZrO2 and CaO-ZrO2 in combination with YO1.5-ThO2 as electrolyte were used to determine the free energy of formation of hercynite from 750–1600°C. The formation reaction is 2Fe(s,1) + O2(g) + Al2O3(α) = 2FeO.Al2O3(s)for which ΔG° = − 139,790 + 32.83T (±300) cals. (750–1536°C) ΔG° = − 146,390 + 36.48T (±300) cals. (1536–1700°C)These measurements can be used to resolve the discrepancies that exist in published thermochemical data, and provide an accurate oxygen potential standard for calibrating and assessing the performance of oxygen probes under steelmaking conditions.

Chemical potential of germanium in its solid solutions with Cu, Ag and Au

Thin foils of copper, silver and gold were equilibrated with tetragonal GeO2 under controlled View the MathML source gas streams at 1000 K. The equilibrium concentration of germanium in the foils was determined by the X-ray fluorescence technique. The standard free energy of formation of tetragonal GeO2 was measured by a solid oxide galvanic cell. The chemical potential of germanium calculated from the experimental data and the free energies of formation of carbon monoxide and carbon dioxide was found to decrease in the sequence Ag + Ge > Au + Ge > Cu + Ge. The more negative value for the chemical potential of germanium in solid copper, compared to that in solid gold, cannot be explained in terms of the strain energy factor, electro-negativity differences or the vaporization energies of the solvent, and suggests that the d band and its hybridization with s electrons are an important factor in determining the absolute values for the chemical potential in dilute solutions. However, the variation of the chemical potential with solute concentration can be correlated to the concentration of s and p electrons in the outer shell.

Solute solute and solvent solute interactions in solid solutions of Cu+Sn, Au+Sn and Cu+Au+Sn alloys

The chemical potentials of tin in its α-solid solutions with Cu, Au and Cu + Au alloys have been measured using a gas-solid equilibration technique. The variation of the excess chemical potential of tin with its composition in the alloy is related to the solute-solute repulsive interaction, while the excess chemical potential at infinite dilution of the solute is a measure of solvent-solute interaction energies. It is shown that solute-solute interaction is primarily determined by the concentration of (s + p) electrons in the conduction band, although the interaction energies are smaller than those predicted by either the rigid band model or calculation based on Friedel oscillations in the potential function. Finally, the variation of the solvent-solute interaction with solvent composition in the ternary system can be accounted for in terms of a quasi-chemical treatment which takes into account the clustering of the solvent atoms around the solute.

Electrochemical Determination of the Stability of Mono- and Dicalcium Stannates

he thermodynamic properties of mono- and dicalcium stannates have been determined in the temperature range 973–-1423°K from the electromotive force measurements on solid oxide galvanic cells[dformula Pt, Ni + NiO//CaO - ZrO[sub 2]/Y[sub 2]0[sub 3] - ThO[sub 2]//SnO[sub 2] + Sn, W, Pt][dformula Pt, Ni + NiO//CaO - ZrO[sub 2]/Y[sub 2]O[sub 3] - ThO[sub 2]//CaSnO[sub 3] + SnO[sub 2] + Sn, W, Pt][dformula Pt, Ni + NiO//CaO - ZrO[sub 2]/Y[sub 2]O[sub 3] - ThO[sub 2]/Ca[sub 2]SnO[sub 4] + CaSnO[sub 3] + Sn, W, Pt]and [dformula Pt, Ni + NiO//CaO - ZrO[sub 2]sol;Y[sub 2]O[sub 3] - ThO[sub 2]//Ca[sub 2]SnO[sub 4] + CaO, W, Pt] The Gibbs free energy changes accompanying the formation of the stannates from component oxides may be represented by the equations[dformula 2CaO + SnO[sub 2] --> Ca[sub 2]SnO[sub 4]][dformula Delta G[degree] = - 17,040 + 0.85T ([plus-minus]300) cal][dformula CaO + SnO[sub 2] --> CaSnO[sub 3]][dformula Delta G[degree] = - 17,390 + 2.0T ([plus-minus]300) cal]The partial pressures of the tin bearing oxide species resulting from the decomposition of the stannates have been calculated as a function of the oxygen partial pressure by combining the results of this study with published information on the partial pressures and composition of oxide species over stannic oxide.

The oxygen potential of the systems Fe+FeCr2O4+ Cr2O3 and Fe+FeV2O4+ V2O3 in the temperature range 750 1600o C

From electromotive force (emf) measurements using solid oxide galvanic cells incorporating ZrOz-CaO and ThOz-YO~.s electrolytes, the chemical potentials of oxygen over the systems Fe + FeCrzO 4 + Cr20 ~ and Fe + FeV204 + V203 were calculated. The values may be represented by the equations: 2Fe(s, I) + Oz(g) + 2Cr2Oa(s) -- 2FeCr204 (s)Akto2 = - 151,400 + 34.7T (• cal= -633,400 + 145.5T(• J (750 to 1536~ A~tO2 = -158,000 + 38.4T(• cal= -661,000 + 160.5T(*1250) J (1536 to 1700~2Fe (s, I) + O2 (g) + 2V203 (s) -- 2FeV204 (s) A/~Oz = - 138,000 + 29.8T(+300) cal= - 577,500 + 124.7T (• J (750 to 1536~A/IO2 = -144,600 + 33.45T(-300) cal = -605,100 + 140.0T(~-1250) J (1536 to 1700~At the oxygen potentials corresponding to Fe + FeCrzO a + Cr203 equilibria, the electronic contribution to the conductivity of ZrO2-CaO electrolyte was found to affect the measured emf. Application of a small 60 cycle A.C. voltage with an amplitude of 50 mv across the cell terminals reduced the time required to attain equilibrium at temperatures between 750 to 9500C by approximately a factor of two. The second law entropy of iron chromite obtained in this study is in good agreement with that calculated from thermal data. The entropies of formation of these spinel phases from the component oxides can be correlated to cation distribution and crystal field theory.