Integral Gibbs Free Energy Research Articles

Theoretical Investigation of the Thermodynamic Properties of Lead-free Ternary Alloys Sn-Sb-Bi and their Subsystems

The concentration-dependent properties, like the constituents’ activities for the binary liquid alloys like Sb-Sn at 905 K, Bi-Sn at 600 K, and Bi-Sb at 1200 K, and the integral Gibbs free energy of mixing, ΔGXS, of the correspondent alloys were computed using the molecular interaction volume model (MIVM). Further, the model has been used to compute the activities of the component Sn in the ternary Sn-Sb-Bi system at 900K at the three cross-sections, i.e., Sb:Bi = 1:3, 1:1, and 3:1. The theoretical data have been analyzed with the corresponding experimental data accessible in the literature. An acceptable concurrence has been obtained, with some inconsistencies. The activities of the ternary alloys along the three cross-sections, i.e., Sb:Bi = 1:3, 1:1, and 3:1, show that the deviations change from positive to negative with increasing Sb content. The results confirm that MIVM is a good model for estimating the thermodynamic properties of binary and ternary systems.

Thermodynamic properties of liquid Cu–In–Zn alloys

Abstract The partial Gibbs energies of zinc in the liquid Cu– In–Zn system as a function of temperature and concentration were measured in the temperature range between the melting points of the alloys and 1073 K using an EMF method with a liquid electrolyte. The thermodynamic properties were determined for 30 alloys at three different constant ratios of Cu : In of 1 : 2, 1 : 1, and 2 : 1 with zinc added in the concentration range between 5 and 90 at.%. The integral Gibbs free energy and the integral enthalpy of mixing of the ternary system were calculated with the Gibbs Duhem equation.

Analysis of water sorption isotherms of amorphous food materials by solution thermodynamics with relevance to glass transition: evaluation of plasticizing effect of water by the thermodynamic parameters.

Relation between the thermodynamic parameters obtained from water sorption isotherms and the degree of reduction in the glass transition temperature (Tg), accompanied by water sorption, was quantitatively studied. Two well-known glassy food materials namely, wheat gluten and maltodextrin were used as samples. The difference between the chemical potential of water in a solution and that of pure water ([Formula: see text]), the difference between the chemical potential of solid in a solution and that of a pure solid ([Formula: see text]), and the change in the integral Gibbs free energy ([Formula: see text]) were obtained by analyzing the water sorption isotherms using solution thermodynamics. The parameter [Formula: see text] correlated well with ΔTg (≡Tg-Tg0; where Tg0 is the glass transition temperature of dry material), which had been taken to be an index of plasticizing effect. This indicates that plasticizing effect of water on foods can be evaluated through the parameter [Formula: see text].

Thermodynamic properties of liquid Au–Bi–Sn alloys

The thermodynamic properties of the liquid ternary Au–Bi–Sn alloys were determined using an electromotive force (EMF) method with an eutectic mixture of (KCl+LiCl) as liquid electrolyte. The cell arrangement was:W,Sn(l)/KCl–LiCl–SnCl2/Au–Bi–Sn(l),W.The measurements were carried out over the temperature range from 723K to 973K. The compositions investigated were situated on three different cross-sections with a constant ratio of Au:Bi=2:1, 1:1, and 1:2. The partial Gibbs free energies of Sn in liquid Au–Bi–Sn alloys were determined as a function of concentration and temperature. The integral Gibbs free energy and the integral enthalpy at T=800K were calculated by the Gibbs–Duhem integration. The ternary interaction parameters were evaluated using the Redlich–Kister–Muggianu polynomial.

Thermodynamic properties of liquid Au–Cu–Sn alloys determined from electromotive force measurements

The thermodynamic properties of the ternary Au–Cu–Sn system were determined with the electromotive force (EMF) method using a liquid electrolyte. Three different cross-sections with constant Au:Cu ratios of 3:1, 1:1, and 1:3 were applied to measure the thermodynamic properties of the ternary system in the temperature range between the liquidus temperature of the alloys and 1023K. The partial free energies of Sn in liquid Au–Cu–Sn alloys were obtained from EMF data. The integral Gibbs free energy and the integral enthalpy at 900K were calculated by Gibbs–Duhem integration. The ternary interaction parameters were evaluated using the Redlich–Kister–Muggianu polynomial.

Electromotive Force Measurements in the Ternary System Bi-In-Zn

The thermodynamic properties of the ternary Bi-In-Zn system were determined with the electromotive force (EMF) method using a liquid electrolyte. Four different cross sections with constant In/Bi ratios of 1:2, 1:1, 2:1, and 9:1 were applied to measure the thermodynamic properties of the ternary system in the temperature range between the liquidus temperature of the alloys and 973 K (700 °C). Zinc was added in steps of 5 at. pct from 5 to 90 pct. The partial free energies of Zn in liquid Bi-In-Zn alloys were determined as a function of concentration and temperature. The integral Gibbs free energy and the integral enthalpy of the ternary system at 873 K (600 °C) were calculated by Gibbs–Duhem integration. The ternary interaction parameters were evaluated using the Redlich–Kister–Muggianu polynomials.

Study of the Thermodynamic Properties of the Al-Mg Binary System Between 973-1073 K by the EMF Method

The thermodynamic properties of an Al-Mg binary system with 0.07 to 12.10 at% Mg were determined at temperatures between 973-1073 K. The following Mg concentration cell was used: Mg (pure), MgCl2-CaCl2 (eutectic), Al-Mg (melt). In this system, Mg shows negative deviation from Raoult's law. Alloys between 0 to 6 at% Mg obey Henry's law. The Henrian coefficient of Mg was 0.47, 0.52 and 0.53 at 973, 1023 and 1073 K, respectively. The EMF values were used for calculating the partial and integral Gibbs free energies, enthalpies, entropies, excess Gibbs free energies and Wagner's first order interaction coefficient.

Thermodynamic description of the ternary Pd–Sn–Zn system

Abstract The thermodynamic properties of the liquid Pd–Sn–Zn ternary system were investigated, because the Sn–Zn alloy is a promising lead-free solder and Pd can be used as a substrate material. Using an appropriate galvanic cell, the partial free energies of Zn in liquid Pd–Sn–Zn alloys were determined as a function of concentration and temperature. Thermodynamic properties were obtained for 18 alloys. Their composition was situated on two cross-sections with the constant molar ratios of Pd: Sn = 1:3 and 1:9. The integral Gibbs free energy and the integral enthalpy for the ternary system at 1000 K were calculated by Gibbs–Duhem integration. For the liquid binary Pd–Sn system, some inconsistencies were found in previous CALPHAD results. Considering the latest experimental information, the interaction parameters of the liquid phase were reevaluated. The liquidus temperatures were also determined from EMF measurements.

Thermodynamic properties of liquid Cu–In–Zn alloys

Abstract The partial Gibbs energies of zinc in the liquid Cu–In–Zn system as a function of temperature and concentration were measured in the temperature range between the melting points of the alloys and 1073K using an EMF method with a liquid electrolyte. The thermodynamic properties were determined for 30 alloys at three different constant ratios of Cu:In of 1:2, 1:1, and 2:1 with zinc added in the concentration range between 5 and 90at.%. The integral Gibbs free energy and the integral enthalpy of mixing of the ternary system were calculated with the Gibbs Duhem equation.

Thermodynamics of Formation of Double Salts and Mixed Crystals from Aqueous Solutions

AbstractFor Abstract see ChemInform Abstract in Full Text.

Thermodynamics of formation of double salts and mixed crystals from aqueous solutions

This paper describes a chemical model that calculates (solid + liquid) equilibria in the ( m 1CuCl 2 + m 2NiCl 2)(aq), ( m 1MgCl 2 + m 2CrCl 3)(aq), ( m 1(NH 4) 2SO 4 + m 2CuSO 4)(aq), and ( m 1(NH 4) 2SO 4 + m 2MgSO 4)(aq) systems, where m denotes molality at T = 298.15 K. The Pitzer ion-interaction model has been used for thermodynamic analysis of the experimental mixing solutions solubility data, presented in the literature. The thermodynamic functions needed have been calculated and the theoretical solubility isotherms have been plotted. The mixed solution model parameters { θ(MN) and ψ(MNX)} have been chosen on the basis of the compositions of saturated ternary solutions and data on the pure water solubility of the (NH 4) 2SO 4 · CuSO 4 · 6H 2O and (NH 4) 2SO 4 · MgSO 4 · 6H 2O double salts. The results of Pitzer ion interaction model-based thermodynamic studies at T = 298.15 K on 62 binary, 82 ternary and eight multicomponent (water + salt) systems where solid phases with a constant stoichiometric composition (simple and double salts) crystallize have been summarized. The values of the pure electrolyte and mixing ion-interaction parameters, which give the best fit of the activity data in binary solutions and of the ternary solutions solubility data are tabulated. Important thermodynamic characteristics (thermodynamic solubility products K sp ∘ ; standard molar Gibbs free energy of reaction Δ r G m ∘ of the synthesis of the double salts from the corresponding simple salts, components of the ternary solutions; and the standard molar Gibbs free energy of formation Δ f G m ∘ ) of the solids crystallizing from the saturated binary and ternary solutions are given. The Δ f G m ∘ values obtained are compared with those available in the literature. The results of thermodynamic simulation of binary and ternary systems at temperatures differing from the standard (273.15 K and 348.15 K) are presented. The model parameterization is tested by comparison of the predicted and the experimental composition of the invariant points in multicomponent solutions (not used in parameterization process). The component activities of the saturated ( m 1(NH 4) 2SO 4 · CuSO 4 + m 2(NH 4) 2SO 4 · MgSO 4)(aq) and in the mixed crystalline phase were determined and the change of the molar Gibbs free energy of mixing Δ mix G m ∘ ( s ) of crystals was determined as a function of the solid phase composition. It is established that at T = 298.15 K the mixed (NH 4) 2SO 4 · (Cu,Mg)SO 4 · 6H 2O crystals show positive deviations from the ideal mixed crystals. Values for the integral Gibbs free energy of mixing Δ mix G m ∘ ( s ) and excess Gibbs free energy of mixing Δ G m E ( s ) in crystals calculated by different methods for the 23 ternary systems with co-crystallization of the salt components have been summarized.

Thermodynamics of formation of aluminum–iron–germanium amorphous alloys

Thermodynamic properties of ternary liquid Al–Fe–Ge alloys were studied by electromotive force method at 1050–1250 K and by high-temperature isobasic calorimetry at 1740 ± 5 K. The heat capacity change at ternary alloy formation (Δ mix C p) was estimated using the temperature dependence of integral enthalpy of mixing. Thermodynamics of the formation of Al–Fe–Ge amorphous alloys was evaluated by extrapolation of thermodynamic functions of mixing to the temperature of amorphization. The process of glass forming is preferable by both enthalpy and entropy for compositions of (0.1< x Fe<0.6, x Ge<0.5). The area with most negative integral Gibbs free energy and enthalpy of amorphous alloy formation corresponds well to the area of amorphization estimated by a glass-forming tendency (GFT) criterion.

Thermodynamics of liquid aluminium–copper–germanium alloys

Partial for aluminium and integral enthalpies of mixing of liquid Al–Cu–Ge alloys have been measured by high-temperature isoperibolic calorimetry at T=(1380±5) K. Thermodynamic activities, partial for aluminium and integral Gibbs free energies of mixing have been determined by the electromotive force method (emf) over the range 1050⩽ T/K⩽1250. Integral excess entropies of mixing have been calculated from calorimetric enthalpies and emf measured Gibbs free energies of mixing. The integral enthalpies of mixing and the integral excess Gibbs free energies of mixing have been also evaluated based on the literature data for boundaries using the Bonnier geometric model. Differences between experimental and calculated thermodynamic functions of mixing are positive. These facts as well as negative excess integral entropies of mixing reveal information about microsegregation in the melt. Therefore, the existence of ternary eutectic has been forecasted for Al–Cu–Ge phase diagram.

Analysis of Water Sorption Isotherms of Superabsorbent Polymers by Solution Thermodynamics

Water sorption isotherms of superabsorbent polymers were measured, and their affinity for water was evaluated by solution thermodynamics. The results provide basic data for the functional packaging of food to control the water content of food during its transportation or storage. Water activity above 0.9 was measured by adding a specific amount of water to the samples, while that below 0.9 was measured with apparatus for evaluating water sorption isotherms. Thus, water sorption isotherms for superabsorbent polymers were obtained up to a water activity of approximately 0.98. The amount of water sorbed by the superabsorbent polymers was influenced by the type of functional groups in the polymers, and not by the degree of cross-linking in the polymers. The integral Gibbs free energy, which is the most suitable parameter for evaluating the affinity of a material for water, was evaluated from the water sorption isotherms by using solution thermodynamics.

Thermodynamic Properties of Liquid Au-sSb-Zn Alloys

The change of the thermodynamic properties of liquid Sb-Zn alloys with the addition of gold as third component was determined. The thermodynamic properties of 30 liquid Au-Sb-Zn alloys at three cross-sections with constants Au-to-Sb ratios of 3:1, 1:1 and 1:3 were measured applying the emf method with a liquid electrolyte. By Gibbs-Duhem integration the integral Gibbs free energy and the integral enthalpy of mixing for the ternary system at 973 K were calculated