Integral Free Energy Of Mixing Research Articles

Electrochemical determination of free energy changes of allotropic transformation of ZnO

Partial and integral free energies of mixing of ZnO in single phase rock-salt solid solution of ZnO in NiO and CoO have been obtained in the temperature range 800 to 1000°C using electrochemical cells with calcia stabilized zirconia as solid electrolyte. The free energy of transformation of wurtzite ZnO to rock-salt ZnO, estimated from this thermodynamic data, is found to be 4,620 (±100) cal/mole at 900°C. Combining this value with the reported values for entropy changes, the enthalpy of transformation is estimated to be 4.150 (±335) cal/mole.

Thermodynamic properties of the binary molten salt systems, PbBr2-KBr, PbBr2-RbBr and PbBr2-CsBr, by measurement of the electromotive forces of galvanic cells

The electromotive forces of galvanic cells for the formation of PbBr2 in the molten binary salt systems, PbBr2-KBr, PbBr2,-RbBr and PbBr2-CsBr, have been measured. Activities, activity coefficients and partial molar free energies have been calculated for each component of the three systems. Integral free energies of mixing have also been calculated. Various models of mixing of molten salts have been applied to the results. The systems contain complex ions, probably mixtures of PbBr42-, PbBr64- with some PbBr3-.

Free energies of mixing in the liquid iron-cobalt orthosilicates at 1450°c

Measurements have been made of the equilibrium between liquid iron-cobalt orthosilicates and solid iron-cobalt alloys. It is shown that the integral free energies of mixing of the oxide components and the integral and partial molar free energies of mixing of the pseudobinary (orthosilicate) components can be derived from a knowledge of the metallic activities in such exchange equilibria. The thermodynamic properties are presented for 1450°C. It is found that the integral free energy of mixing shows a maximum deviation of −2.1 (±0.3) kJ per mole of MO • 1/2 SiO2 from ideal silicate mixing.

A thermodynamic study of the molten Pb-Sn-Ag system

Activity and partial free energy of mixing of tin in the molten Pb-Sn-Ag system were determined at 1073 K along three pseudobinary lines of fixedX Ag/X Pb ratios by the electromotive force method. The cell employed was Sn(l), SnO2(s)/Calcia stabilized zirconia/Sn(alloy), SnO2(s). Excess integral free energy of mixing (F ter E ) and the activities of lead and silver were calculated by the Darken’s method. The values when extrapolated toX Sn=0 agreed reasonably well with the literature data on the Pb-Ag binary. Error analysis revealed that the inconsistencies in the reported data arose as a result of the uncertainties inherently present in the integration and differentiation steps. A crosscheck onF ter E corroborated the above observation.F ter E were also calculated from the data on the bounding binaries by the method of Olson and Toop. Except in the silver-rich corner the predicted values were within 50 calories of those obtained from the experimental data.

A high-temperature thermodynamic investigation of the nb-mo system

The thermodynamic properties of solid Nb(Cb)-Mo alloys have been determined between 1050 and 1300 K using solid state galvanic cells with a thoria-based electrolyte. The activities of niobium and molybdenum exhibit negative deviations from Raoult’s law. The excess entropies of mixing are very small and negative, and the excess integral free energies of mixing are almost equal to the integral enthalpies of mixing. The negative entropies of mixing are attributed to a negative vibrational contribution and/or short-range ordering.

über den einfluss der Durchschnittlichen Zusammensetzung auf die Lage der Kohärenten Mischungslücke von Al-Zn Legierungen

The paper describes the thermodynamic calculation of the form of metastable coherent solubility gaps by which the separation of the solid solution into coherent zones in the Al-Zn system can be described. The integral free energy of mixing of the solid solution was approximated by the adapted Hillert relation and supplemented by the Cahn elastic energy term. The dependence of the Cahn energy term on the concentration and temperature was considered. The consequence of this concentration dependence is the appearance of a system of coherent solubility gaps lying near to one another instead of one curve in the case of concentration independent elastic term. The theoretically derived curves agree with the data obtained from resistometric measurements.

Dilute solutions in molten metals and alloys

Measurements have been made of the activity coefficients of sulphur in molten copper and in binary alloys of copper with gold, silicon, platinum, cobalt, iron and nickel at temperatures between 1100° and 1500°C. The results indicate that the thermodynamic properties of the dissolved sulphur either in elementary metals or in alloys, cannot be explained solely on the basis of the electron chemical potential of the metals or the corresponding electron: atom ratio. A chemical approach has therefore been developed and this leads to a qualitative relation between the activity coefficients of sulphur in elementary metals and the stabilities of the metal sulphides. It leads to a semi-quantitative relation between the effect of an alloying element at high dilution on the activity coefficient of sulphur at low concentrations. The effect is a function of the activity coefficients of sulphur in the two elementary metals and the activity coefficient of the alloying element. This relationship has been further developed to apply at high concentrations of an alloying element and tested with success on a variety of ternary systems. It follows, as previously suggested by Darken on purely thermodynamic grounds, that the integral free energy of mixing of a binary system can be determined within about 1 kcal by experiments of the type reported here.