Partial Excess Gibbs Energy Research Articles

On the constitution and thermodynamics of Ni–La alloys

The thermodynamic properties of Ni–La alloys were determined between 923 and 1023 K by EMF measurements using CaF 2 single crystals as solid electrolytes. The results yield a complete set of thermodynamic functions for the intermetallic phases (Ni), Ni 5La, Ni 17La 4, Ni 7La 2, Ni 16La 7, Ni 3La 2, NiLa, Ni 3La 7, and NiLa 3 as well as information on the phase relations. The system is characterized by pronounced negative deviations from ideality. The relative partial excess Gibbs energy of La at infinite dilution, Δ G ̄ La E (x La →0) , was determined to be −(83±3) kJ/mol. This value is interpreted by taking electronic and elastic effects into account. The liquidus curve was fixed over the entire range of composition by differential thermal analysis. The present results were used as basis for a thermodynamic optimization of the system using a computer program based on the least squares method. Optimized and experimental data turned out to be in good agreement.

Thermodynamics of gold–erbium alloys

Galvanic cells with CaF 2 as solid electrolytes were used to obtain the thermodynamic properties of the gold–erbium system between 973 and 1073 K. A complete set of thermodynamic data was obtained for the gold-rich solid solution and for the intermetallic compounds Au 4Er, Au 3Er, Au 2Er, AuEr and AuEr 2. The relative partial excess Gibbs energy of erbium at infinite dilution was determined to be −257 kJ/mol at 1073 K. Electronic and elastic effects are discussed in order to account for the pronounced deviations from ideality.

Phase equilibria in aluminum-carbon system at high temperatures

The partial excess Gibbs energies of carbon and aluminum in liquid Al-C were used with the equilibrium vapor pressures of pure Al and pure C to obtain the phase diagrams (1) at I bar of total pressure, and (2) at pressures sufficient to suppress the gas phase. The first diagram contains [gas+graphite → liquid] tectoid-type reaction at 2900±20 K with the tectoid composition of 0.681 mol fraction of aluminum. The [gas/graphite] boundary is subject to large errors due to the large errors in the vapor pressure of pure graphite, but its general form is acceptable. The second diagram consists entirely of the condensed phases with peritectic reaction [liquid+graphite → Al 4 C 3 ] at 2429 K. The [liquid/graphite] phase boundary was obtained from the graphite solubility in liquid solutions at 2429-2800 K, yielding the partial excess Gibbs energy of carbon in solution. The resulting phase boundary is as reliable as the melting point of graphite, taken to be 4130 K.

III. Highly reactive and multicomponent systems: On the constitution and thermodynamics of Ni‐Gd alloys

AbstractThe thermodynamic properties of Ni‐Gd alloys were determined by electromotive force measurements between 873 and 1073 K on galvanic cells using CaF2 single crystals as solid electrolytes. Results yield a complete set of thermodynamic functions for the intermetallic phases (Ni), Ni17Gd2, Ni5Gd, Ni4Gd, Ni7Gd2, Ni3Gd, Ni2Gd, NiGd, Ni2Gd3, and NiGd3, as well as information on the phase relations. The system is characterized by pronounced negative deviations from ideality. The relative partial excess Gibbs energy of gadolinium at infinite dilution, ΔG (xGd→0), was determined to be ‐(104±5) kJ/mol. A comparison with analogous systems indicates the influence of the electronic structure of the components on thermodynamic properties of mixing. In order to fix the liquidus curve, differential thermal analysis was carried out over the entire range of composition.

Phase equilibria in aluminum‐carbon system at high temperatures

AbstractThe partial excess Gibbs energies of carbon and aluminum in liquid Al‐C were used with the equilibrium vapor pressures of pure Al and pure C to obtain the phase diagrams (1) at 1 bar of total pressure, and (2) at pressures sufficient to suppress the gas phase. The first diagram contains [gas+graphite → liquid] tectoid‐type reaction at 2900±20K with the tectoid composition of 0.681 mol fraction of aluminum. The [gas/graphite] boundary is subject to large errors due to the large errors in the vapor pressure of pure graphite, but its general form is acceptable. The second diagram consists entirely of the condensed phases with peritectic reaction [liquid+graphite → Al4C3] at 2429 K. The [liquid/graphite] phase boundary was obtained from the graphite solubility in liquid solutions at 2429‐2800 K, yielding the partial excess Gibbs energy of carbon in solution.The resulting phase boundary is as reliable as the melting point of graphite, taken to be 4130 K.

Thermodynamic Properties of Pd‐Nd Alloys

AbstractA complete set of thermodynamic functions was determined for the palladium‐rich solid solution and for the intermetallic compounds Pd5Nd, Pd3Nd, Pd2Nd, Pd4Nd3, and PdNd from electromotive force measurements between 700 and 800°C. A CaF2 single crystal was employed as the solid electrolyte. The activity of Nd in Pd‐rich alloys shows pronounced negative deviations from Raoult's law with a relative partial excess Gibbs energy of Nd at infinite dilution of −305 kJ/mol. Two effects are discussed to account for the non‐ideal properties of the solid solution: the transfer of the valence electrons of Nd to the electron gas of the alloy and the lattice distortion brought about by the size difference of the components. Remarkably exothermic values were obtained for the heats of formation of the intermetallic compounds. The results are compared with predictions of the Miedema model.

Wagner interaction coefficients and modified margules equations

The relationships between the Wagner interaction and Margules coefficients are derived to discuss their limitations and to clarify incorrect construction of the excess Gibbs energy from the partial excess Gibbs energies, expressed as linear functions of mole fractions. Margules-type equations with Henrian reference states are obtained, and their significance is discussed. An estimate for the Gibbs energy of melting of graphite is obtained, and the use of activity coefficients for deriving the Gibbs energy of melting of refractory elements is suggested. This research is part of the effort in materials properties at the U.S. Bureau of Mines.

Comments on the activity of carbon in liquid iron

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Thermodynamic Properties of Gold - Yttrium Alloys

Thermodynamic properties of mixing were determined for the binary Au-Y system between 700 and 800 o C by measurements of the electromotive force on galvanic cells using CaF 2 solid electrolytes. A complete set of thermodynamic functions was obtained for the gold-rich solid solution and for the intermetallic compounds Au 6 Y, Au 51 Y 14 , Au 3 Y, Au 2 Y, AuY, and AuY 2 . The system is observed to exhibit large negative deviations from ideality; the relative partial excess Gibbs energy of Y at infinite dilution was determined to be -255 kJ/mol at 800 o C. The strongly exothermic character of the system is attributed to a transfer of electrons from the Fermi level of Y to the Fermi level of the alloy

Estimation of partial excess Gibbs energy of solutes in infinitely dilute liquid iron base binary alloys

The partial excess Gibbs energy ΔḠBEx as well as the relationship between the partial enthalpy of mixing ΔH̄B and the partial excess entropy of solution ΔS̄BEx of various solute elements in liquid Fe, Al and Pb binary alloys were evaluated from a new solution model, in which ΔS̄BEx can be calculated from the values of ΔH̄B by Miedema's semi‐empirical method and some relevant physical properties of the components in the alloys. These calculated values of ΔḠBEx were found to be in reasonable agreement with the selected values presented so far. The present model gives the values of ΔḠBEx, for which the experimental data are not yet available.

Saturation vapour pressure and thermodynamic properties of potassium solutions in molten binary mixtures of its halides

The saturation vapour pressure of potassium solutions in molten binary mixtures of KF + KCl, KF + KBr, KF + KI, KCl + KI with molar ratios of their components being 3:1, 1:1, 1:3, and in equimolar mixtures of KCl + KBr and KBr + KI was measured as a function of temperature and the metal concentration by a statistical method. A device with a sylphon zero-manometer was used, the gas space of which was minimized to reduce changes in the composition of the melts caused by the evaporation of their components. Potassium partial pressure was determined. It deviates from additive quantities towards greater values. The deviations grow as the molar ratio of lighter and heavier halide anions replacing each other in the melts increases. The potassium activity coefficient calculated from experimental data as a function of temperature and the composition of the melts is much greater than unity. It diminishes as the metal concentration and the molar fraction of the heavier salt components are raised. Potassium partial excess Gibbs energy was computed for all the melts under study.

Thermodynamic properties of liquid Mg-ln-Cd ternary solutions

By means of concentration cells of the following type: Mg(s)∣MgCl2 in (LiCl-KCl)eut(l)∣Mg-In or Mg-ln-Cd(l), the partial thermodynamic data of Mg in Mg-ln and Mg-ln-Cd liquid solutions have been obtained in the composition range 0.1 ≤ XMg ≤ 0.7 for binary while for ternary alloys fort = 0.4, 0.6, and 0.8 (wheret = XIn/(XIn + XCd)) and at various mangesium concentrations 0.1≤ XMg ≤ 0.6. Both ternary and binary alloys were investigated at a temperature range 750 to 900 K. Experimental partial excess Gibbs energies of Mg were interpreted by the Pelton and Flengas method. Results for Mg-ln system show a slight difference in comparison with previously published data for the same system also from emf studies. Results of this study for Mg-ln system exhibit negative and positive excess entropies of magnesium and the same is observed in ternary system Mg-ln-Cd at the range of concentration close to Mg-ln.

On the thermodynamics in the NbRh and NbRhO systems

A section of the NbRhO system was investigated at 1273 K. The intermetallic phase NbRh 3 and the solid solution Rh(Nb) coexist with Nb 2O 5. E.m.f. measurements were made in the NbRh system using galvanic cells with oxygen-ion-conducting solid electrolytes for the purpose of determining the relative partial Gibbs energy of niobium in Nb x Rh 1− x ( x ≤ 0.13) and the Gibbs energies of formation of Nb x Rh 1− x and NbRh 3. The results can be expressed by the following relationships: f Δ°( Nb 0.13 Rh 0.87) = −29.7 + 0.0027 T (kJ mol −1) 1100–1300 K f Δ°( NbRh 3.55) = −223.0 + 0.0202 T (kJ mol −1) 1100–1300 K The relative partial excess Gibbs energy of niobium in rhodium at infinite dilution is xsΔ G ̄ Nb ∞ = −200 kJ mol −1 at 1200 K.