The estimation of the thermodynamic properties of ternary alloys from binary data using the shortest distance composition path

A new composition path, Xi-Xj=constant, is suggested for the semi-empirical calculation of the thermodynamic properties of ternary ‘substitutional’ solutions from binary data, when the binary systems show deviations from the regular solution model. A comparison is made between the results obtained for integral and partial properties using this composition path and those calculated employing other composition paths suggested in literature. It appears that the best estimate of the ternary properties is obtained when binary data at compositions closest to the ternary composition are used.

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.

Potentiometric determination of the Gibbs free energy of formation of cadmium and magnesium chromites

The standard Gibbs free energy of formation of magnesium and cadmiumchromites have been determined by potentiometric measurements on reversiblesolid-state electrochemical cells [dformula (Au-5%Cd, , Au-5%Cd; Pt, + , CaO-ZrO[sub 2], + ,Pt; CdO, , CdCr[sub 2]O[sub 4] + Cr[sub 2]O[sub 3])] in the temperature range 500°–730°C, and [dformula Pt, Cr + Cr[sub 2]O[sub 3]/Y[sub 2]O[sub 3]-ThO[sub 2]/Cr + MgCr[sub 2]O[sub 4] + MgO, Pt] in the temperature range 800°–1200°C. The temperature dependence of the freeenergies of formation of the ternary compounds can be represented by theequations [dformula CdO(r.s.) + Cr[sub 2]O[sub 3](cor) --> CdCr[sub 2]O[sub 4](sp)] [dformula Delta G[sup 0] = - 42,260 + 7.53T ([plus-minus]400) J] and [dformula MgO(r.s.) + Cr[sub 2]O[sub 3](cor) --> MgCr[sub 2]O[sub 4](sp)] [dformula Delta G[sup 0] = - 45,200 + 5.36T ([plus-minus]400) J] The entropies of formation of these spinels are discussed in terms of cationdisorder and extent of reduction of Cr3+ ions to Cr2+ ions. Thermodynamicdata on the chromates of cadmium and magnesium are derived by combiningthe results obtained in this study with information available in the literatureon high temperature, high pressure phase equilibria in the systems CdO-Cr2O3-O2 and MgO-Cr2O3-O2.

Gibbs free energy of formation of magnesium stannate

he thermodynamic properties of the spinel Mg2SnO4 have been determined by emf measurements on the solid oxide galvanic cell,View the MathML source in the temperature range 600 to 1000°C. The Gibbs' free energy of formation of Mg2SnO4 from the component oxides can be expressed as View the MathML source,View the MathML source These values are in good agreement with the information obtained by Jackson et al. [Earth Planet. Sci. Lett.24, 203 (1974)] on the high pressure decomposition of magnesium stannate into component oxides at different temperatures. The thermodynamic data suggest that the spinel phase is entropy stabilized, and would be unstable below 207 (±25)°C at atmospheric pressure. Based on the information obtained in this study and trends in the stability of aluminate and chromite spinels, it can be deduced that the stannates of nickel and copper(II) are unstable.

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.

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.

Effect of rolling temperature and reduction in thickness on microstructure and mechanical properties of ZM21 magnesium alloy and its subsequent annealing treatment

In this present paper, the effects of non-isothermal rolling temperature and reduction in thickness followed by annealing on microstructure and mechanical properties of ZM21 magnesium alloy were investigated. The alloy rolled at four different temperatures 250 degrees C, 300 degrees C, 350 degrees C and 400 degrees C with reductions of 25%, 50% and 75%. Non-isothermal rolling resulted in grain refinement, introduction of shear bands and twins in the matrix alloy. Partial to full recrystallization was observed when the rolling temperature was above recrystallization temperature. Rolling and subsequent annealing resulted in strain-free equiaxed grains and complete disappearance of shear bands and twins. Maximum ultimate strength (345 MPa) with good ductility (14%) observed in the sample rolled at 250 degrees C with 75% reduction in thickness followed by short annealing. Recrystallization during warm/hot rolling was sluggish, but post-roll treatment gives distinct views about dynamic and static recrystallization. (C) 2011 Elsevier B.V. All rights reserved.