Excess Gibbs Energies Of Mixing Research Articles

Ab initio calculations of lattice stability of sigma-phase and phase diagram in the Cr–Fe system

Total energy of pure metals in the sigma-phase structure and in the standard element reference (SER) structure were calculated by full-potential linear augmented plane waves method in the general gradient approximation at the equilibrium volume of all phases. Relaxation of lattice parameters of sigma-phase and SER structure were performed. The difference of total energy of sigma-phase and of standard element phase for pure constituents ( Δ 0E i σ– SER ) was used in a new two-sublattice model of sigma-phase, which was subsequently employed for calculation of phase diagram. Entropy term of Gibbs energy of elements in sigma-phase structure and excess Gibbs energy of mixing of sigma-phase have still to be adjusted to the experimental phase equilibrium data. This procedure was tested on the Fe–Cr system.

Thermodynamic Properties of the Ternary System Potassium Bromide + Lithium Bromide + Water at 25°C

Activity coefficients of potassium bromide in aqueous mixtures of potassium bromide and lithium bromide were determined by emf measurement at 25°C and at six ionic strengths from 0.1 to 2.5 mol·kg-1. The experimental data were fitted using the Scatchard–Rush–Johnson and Pitzer models. The osmotic coefficients, excess Gibbs energies of mixing, and activity coefficients of lithium bromide in aqueous mixtures were calculated using Pitzer mixing parameters obtained in this work.

Evaluation of Excess Gibbs Energy of Mixing in Binary Mixtures of Di-Isobutyl Ketone (Dibk) and Nonpolar Solvents

Excess Gibbs energy of mixing in binary mixture of Di-isobutyl ketone (DIBK) in nonpolar solvents namely n-heptane, p-xylene, cyclohexane, dioxane, benzene and tetra-chloromethane have been evaluated at 303°K. The results indicate that (ΔGAB)maxima is in the order, n-heptane > p-xylene > cyclohexane > benzene > dioxane > tetra-chloromethane.

Tie-lines and mixing properties of solid solutions in the system CaO-SrO-PbO-O at 1100 K

Phase relations in the system CaO-SrO-PbO-O2 at 1100 K have been determined by equilibrating samples with different compositions in air, oxygen, or evacuated ampoules for 7 days and characterizing quenched specimens by optical and scanning electron microscopy, energy-dispersive analysis of x-rays (EDX), and x-ray diffraction (XRD). There is a solid-state miscibility gap in the pseudo-binary system CaO-SrO, and continuous solid solubility between Ca2PbO4 and Sr2PbO4 at 1100 K. Substitution of Ca for Sr occurs only to a limited extent (∼2 mol.%) in SrPbO3. The calcium-rich solid solutions (Ca1−y Sr y )2PbO4 characterized by y≤0.255 are in equilibrium with PbO in air; compositions with y≥0.255 coexist with (Ca1−z Sr z )PbO3. There is a three-phase region involving the two monoxide solid solutions (Ca1−x Sr x )O on either side of the miscibility gap with x=0.24 and 0.71 and (Ca1−y Sr y )2PbO4 with y=0.96. Accurately determined are the locations of tie-lines between the solid solutions. Attainment of equilibrium was checked by the conventional tie-line rotation technique. The excess Gibbs energy of mixing of the solid solution with orthorhombic structure is obtained by an analysis of tie-line data; for the mixing of one mole of Ca and Sr represented by (Ca1−y Sr y )Pb0.5O2, ΔG E=y(1−y) [15,840−2950 y] J/mol. The thermodynamic properties suggest the onset of immiscibility in this solid solution below 884 (±5) K. The miscibility gap is asymmetric with a critical composition at y=0.43 (±0.02). Inside the triangle (Ca1−y Sr y )Pb0.5O2−(Ca1−z Sr z )PbO3−PbO, a small liquid-phase region is present close to the PbO corner, surrounded by three two-phase fields. Each corner of the approximately triangular liquid-phase region is associated with a three-phase field.

Estimation of viscosities of ternary silicate melts using the excess gibbs energy of mixing

A correlation to predict the viscosities of ternary silicates using the Gibbs energies of mixing of the silicate melts has been developed. This correlation has been employed to predict the viscosities of liquid slags in the systems FeO-MnO-SiO2, FeO-MgO-SiO2, CaO-FeO-SiO2, CaO-MnO-SiO2, and CaO-MgO-SiO2. The good agreement between the calculated viscosities and the experimental data in the ternary silicate systems has indicated that this approach can be successfully employed to predict the viscosities of ternary silicate melts.

Interactions of mono- and di-sialogangliosides with phospholipids in mixed monolayers at air-water interface

The interactions among five different gangliosides (three monosialogangliosides GM1, GM2. GM3 and two disialogangliosides GDla and GDlb) in mixed monolayers with dipalmitoylphosphatidylcholine [DPPC] were investigated at the air-water interface by means of surface pressure measurements. The surface pressure-area isotherms have been obtained on aqueous substrates at an ionic strength 0.145 M NaCl, pH=7.2, at a temperature of 20°C. Excess Gibbs energies of mixing in the monolayers have been calculated as a function of composition and surface pressure. Deviation from ideality denotes a different molecular organization of monosialogangliosides and disialogangliosides, indicating changes in their molecular arrangement in phospholipid monolayers due to different polar head group interactions. The possible significance of these observations is discussed in relation to ganglioside organization in biological cell membranes.

Measurement of activity of gallium in liquid Ga‐Sb‐Ge alloys by EMF method with zirconia as solid electrolyte

AbstractThe emf of galvanic cells with zirconia solid electrolytes was measured from 975 to 1242 K on binary Ga‐Ge alloys and from 1058 to 1236 K on ternary Ga‐Sb‐Ge alloys by use of Ga‐Ga2O3 as a reference electrode. From the emf values the activity of gallium in the liquid alloys is determined. At 1073 K the activity of gallium in the Ga‐Ge alloys and in the three pseudobinary alloys Ga‐(SbyGe1‐y) where y=0.25, 0.50 and 0.75 shows small negative deviations from ideality. Isoactivity curves in the ternary Ga‐Sb‐Ge alloys were derived by combining the activity data of Ga‐Sb, Ga‐Ge and the ternary alloys. The shape of the curves at 1073 K is simple in the Ga‐poor region, but shows a very small wavy form with increasing Ga concentration. Isovalues curves in the excess Gibbs energies of mixing in the ternary alloys are derived from Darken's method, and the results are compared with the model calculation proposed by Chou based on the experimental data in three binary systems. The shape of isovalue curves in ΔGxs is similar to those obtained from Chou's method, but the agreement between them in the values is not good.

Solid‐State Immiscibility and Thermodynamics of the Calcium Oxide‐Strontium Oxide System

Solid‐state miscibility gap in the pseudo‐binary calcium oxide‐strontium oxide (CaO‐SrO) system is delineated by X‐ray diffractometry studies on samples equilibrated either under vacuum or in a flowing inert‐gas atmosphere at temperatures of 973‐1273 K. For the CaxSr1−xO solid solution, an asymmetric phase boundary that is characterized by a critical temperature of 1173 (±3) K and a composition of x= 0.53 (±0.01) is obtained. The excess Gibbs energy of mixing of the solid solution, which is derived from the experimental phase‐boundary compositions and temperatures, can be represented by the expression ΔGE=x (1−x)[(27040 − 5.82 T) x+ (24915 − 5.34 T)(1 −x)] (in units of J/mol). It is necessary to include excess entropy terms to obtain a good fit to the experimental data. The chemical spinodal curve is computed from the thermodynamic parameters. The results obtained in this study are compared with phase‐diagram and calorimetric information that is available in the literature.

Evaluation of Excess Gibbs Energy of Mixing in Extremely Dilute in Nonpolar Solvents Solutions of TRI-N-Butyl Phosphate

The excess gibbs energy of mixing in binary mixtures of TBP in nonpolar solvents viz. bcnzene, carbon disulphide, cyclohexane, n-heptane, n–hexane, p–xylene, tetrachloromethane at temperature 303°K is studied. The excess free energy of mixing (AGA8) is in the order, n–hexane < n–heptane < benzene < cyclohexane < p–xylene < CCI4 < CS2. The results corroborate the findings obtained through evaluation of the excess correlation Factor.

Construction of a quasi-ternary phase diagram in the NdO 1.5BaOCuO system in the air atmosphere Part II. Phase equilibria of the neodymium-rich Nd 1+ xBa 2− xCu 3O z solid solution

In the present work phase relations in a copper-rich corner of the NdO 1.5BaOCuO system were studied at 970–1060°C in air by DTA, quenching experiments, EPMA, XRD, ICP AES and finally confirmed by growth of several test single crystals. It was found that in the analyzed region the Nd 1+ x Ba 2− x Cu 3O z solid solution (Nd123ss) with maximum x values co-exists at 970–1060°C with Cu-rich melt and different solid phases: CuO (970–990°C), Nd 2CuO 4 (990…995–1045°C) or Nd 4Ba 2Cu 2O 10 (1060°C). The decomposition temperature of Nd123ss decreases with increasing the neodymium content, and the limit composition of Nd123ss extends up to Nd 2BaCu 3O z at 990–995°C. The Nd123ss unit cell volume deviations from the ideal solution of the Nd123 and Nd213 phases were found positive by XRD, as well as their excess Gibbs energy of mixing, estimated thermodynamically using the experimental phase diagram. This provides a probability of a spinodal decomposition phenomena of such a solution.

Thermodynamics and phase diagram of the binary system Bi 2O 3-B 2O 3

We analyzed the thermodynamic data of the binary system Bi 2O 3-B 2O 3. The phase diagram contains five compounds, of which four melt congruently, and a miscibility gap, close to pure B 2O 3. The three sets of transformation data of Bi 2O 3, the enthalpy of mixing data in the liquid, and the critical point of the miscibility gap gave five equations for the excess Gibbs energy of mixing and five sets of values for the enthalpies of formation of the binary compounds. The critical point data yielded another set of transformation data for Bi 2O 3. Using the monotectic composition and the enthalpy of mixing data also yielded a set of transformation data for Bi 2O 3. The values obtained using the enthalpy of mixing data are the most reliable values.

Thermodynamic properties and phase equilibria in the Fe–P system

Differential scanning calorimetry (DSC) has been used to measure the heat capacities of iron phosphides Fe3P, Fe2P and FeP in the temperature range 113–873 K. Simultaneously a Knudsen effusion method with mass-spectrometric analysis of the gaseous phase has been applied to investigate the thermodynamic properties of iron phosphides (1041–1549 K), bcc solid solutions Fe–P (1384–1619 K) and Fe–P liquid alloys (1349–1811 K). ΔfS of the iron phosphides calculated according to the second and third laws of thermodynamics agree within the limits of experimental error. ΔfG of the phosphides produced from γ-Fe and P2 gas have been approximated with the following equations (in J mol–1): ΔfGFe3 P=–(239 076 ± 2269)+(80.44 ± 1.70)T, ΔfGFe2 P=–(231 728 ± 1110)+(79.95 ± 0.81)T, ΔfGFeP=–(193 892 ± 2700)+(82.10 ± 2.30)T. The thermodynamic behaviour of P diluted in α-Fe obeys Henry's law, the non-magnetic part of the excess Gibbs energy of mixing of the bcc solid solution being equal to (standard states: α-Fe and white P)ΔfGex(nm)=(–280.4T+ 0.195T2–3.70 × 10–5T3)XPXFe J mol–1. The thermodynamic properties of liquid solutions have been described with the ideal associated-solution model assuming that Fe3P, Fe2P and FeP complexes exist in the melt. The phase diagram computed with the help of the thermodynamic data agrees with the published information.

Comment on thermodynamics of binary phase diagrams with a miscibility gap and a

The Gibbs energy of mixing and the excess Gibbs energy of mixing in the binary systems treated in an earlier study are calculated. In these types of systems, these functions cannot be described by an equation extending between the two end components and also represent the partial quantities correctly.

Rules for predicting vapor-liquid equilibria of amorphous polymer solutions using a modified Flory-Huggins equation

A method is proposed to predict solvent activities in amorphous polymer solutions. The method relies on two main assumptions: (i) the configurational entropie term of the excess Gibbs energy of mixing is adequately represented by the classical Flory-Huggins relation; (ii) the enthalpic term arising from the attractive interactions between the solvent molecules and the segments which constitute the polymer can be described by using the NRTL equation. To calculate the binary interaction parameters of the NRTL equation, the same strategy as previously adopted is followed to predict vapor-liquid equilibria of non-polymeric mixtures. Accordingly, literature experimental data are subdivided into the following classes of mixtures: — non-polar polymers in non-polar solvents — non-polar polymers in polar solvents — polar polymers in non-polar solvents — polar polymers in polar solvents For each of the above classes, simple rules are proposed which link the binary energy parameters of the NRTL equations to the difference between the Hildebrand solubility parameters of the polymer and the solvent. The proposed method is applied to over forty binary mixtures for which reliable data are found in the literature. A new procedure to calculate the Hildebrand solubility parameter of the polymer is also reported.

A New Model of the Excess Gibbs Energy of Mixing for a Regular Solution.

The excess Gibbs energy of mixing for a regular solution can be derived systematically by defining the interaction energy for particle groups composed of closest neighbors at equivalent site. The internal energy of a system is regarded as the sum of the interaction energy for particle groups and the excess function is derived from the sum of the interaction energy change caused by the formations of particle groups. In the present paper, we have derived the excess Gibbs energy of mixing for ternary and quaternary regular solutions with a closest packing. For a ternary regular solution, the molar excess Gibbs energy of mixing is given as follows, Gex=XAXB(XAWAAB+XBWABB)+XBXC (XBWBBC+XCWBCC) +XCXA(XCWCCA+XAWCAA)+2XAXBXCWABC, where Xi is a mole fraction of the component i and Wijk is an interaction parameter of [ijk] triplet. The following expressions for n-component systems are derived by the similar method by supposing interaction energy among r particles. Some previously proposed models can be derived from our model. n=2, r=2: Gex=XAXBWAB (symmetric binary regular solution model) n=2, r=3: Gex=XAXB(XAWAAB+XBWABB)(asymmetvie binary regular solution model) n=3, r=2: Gex=XAXBWAB+XBXCWBC+XCXAWCA (symmetric ternary regular solution model) n=3, r=3: Gex=XAXB(XAWAAB+XBWABB)+XBXC(XBWBBC+XCWBCC) +XCXA(XCWCCA+XAWCAA)+2XAXBXCWABC (new ternary model: stated above) n=4, r=4: Gex=XA3XBWAAAB+XB3XAWBBBA+XA3XCWAAAC+XC3XAWCCCA +XA3XDWAAAD+XD3XAWDDDA+XB3XCWBBBC+XC3XBWCCCB +XB3XDWBBBD+XD3XBWDDDB+XC3XDWCCCD+XD3XCWDDDC +3/2XA2XB2WAABB+3/2XA2XC2WAACC+3/2XA2XD2WAADD +3/2XB2XC2WBBCC+3/2XB2XD2WBBDD+3/2XC2XD2WCCDD +3XA2XBXCWAABC+3XA2XBXDWAABD+3XA2XCXDWAACD +3XB2XAXCWBBAC+3XB2XAXDWBBAD+3XB2XCXDWBBCD +3XC2XAXBWCCAB+3XC2XAXDWCCAD+3XC2XBXDWCCBD +3XD2XAXB⊗WDDAB+3XD2XAXCWDDAC+3XD2XBXCWDDBC +6XAXBXCXDWABCD.

Thermodynamic Study of Mixed Anionic Solid Solutions Using Gradient Solid Electrolytes: System

The thermodynamic properties of solid solutions with hexagonal structure have been measured using a solid‐state cell, incorporating a composite solid electrolyte with step‐changes in composition. The cell with the onfigurationX=1 X=X was investigated in the temperature range of 925 to 1165 K. The composite gradient solid electrolyte consisted of pure at one extremity and the solid solution under study at the other. The Nernstian response of the cell to changes in partial pressures of and at the electrodes and temperature was demonstrated. The activity of in the solid solution was measured by three techniques. All three methods gave identical results, indicating unit transport number for K+ ions and negligible diffusion potential due to concentration gradients of carbonate and sulfate ions. The activity of exhibits positive deviation from Raoult's law. The excess Gibbs energy of mixing of the solid solution can be represented using a subregular solution modelBy combining this information with the phase diagram, mixing properties of the liquid phase were obtained.

Activity coefficients of sodium bromide in alkaline earth bromides plus water systems at 298 K

The activity coefficients of sodium bromide in MgBr 2, CaBr 2, SrBr 2 and BaBr2 were determined at 298 K and constant total ionic strengths of 0.1, 0.5, 0.75, 1.0, 1.5 and 2.0 mol kg −1 at 298 K using emf techniques. The experimental activity coefficients were analyzed using the Harned, Scatchard, Reilly et al. and Pitzer equations. Using the values of mixing parameters obtained from the above equations, the excess Gibbs energies of mixing were calculated. Trace activity coefficients were also calculated and discussed in the light of modern theories of electrolyte solutions.

鉄還元揮発法による亜鉛製錬の基礎研究 （第１０報） Ｆｅ３Ｏ４‐ＺｎＦｅ２Ｏ４‐Ｆｅ２Ｏ３系の相平衡およびＦｅ３Ｏ４‐ＺｎＦｅ２Ｏ４スピネル固溶体の活量と格子定数

Phase relations in the Fe3O4-ZnFe2O4-Fe2O3 system at 1, 100 K have been determined by the X-ray microanalysis and X-ray diffraction studies of the quenched samples. The results show that in the Fe304-ZnFe2O4 system magnetite (Fe304) and zinc ferrite (ZnFe2O4) form a complete series of solid solutions which is in equilibrium with the Fe2O3 that is practically pure.The activities were measured by an e. m. f. method using the stabilized zirconia solid electrolytes. Both the activities of magnetite and zinc ferrite in the Fe3O4-ZnFe2O4 solid solutions coexisting with the Fe2O3 exhibit slightly positive deviations from Raoult's law at 1, 100 K. The activity coefficient at infinite dilution, γ0ZnFe2O4 at 1, 100 K was estimated at 2.2.Lattice constants for the Fe3O4-ZnFe2O4 spinel solid solutions in equilibrium with the Fe2O3 obey Vegard's law. It was also found that the excess Gibbs energy of mixing in the Fe3O4-ZnFe2O4 solid solutions coexisting with the Fe203 at 1, 100 K showed small values. These two results are interrelated in the similar behavior, which suggest that activities are closely connected with crystal structures.

Solid-solute phase equilibria in aqueous solution. V: The system CdCO3-CaCO3-CO2-H2O

The system CdCO3-CaCO3-CO2-H2O was investigated potentiometrically at 25 °C and 1 atm total pressure. Cd(1−x)CaxCO3 solid solutions were prepared over the entire compositional range. Aqueous solutions were kept at constant ionic strength I=3 mol (Na)ClO4kg H2O. Experimental results were depicted in Lippmann (x−xaq−log ∑∗Kps0) diagrams. The solutus was investigated by pH and Cd2+ sensitive electrodes and it turned out that the solid solutions neither dissolved congruently nor attained stable equilibrium with aqueous solutions within one week of observation. Consequently, the excess Gibbs energy of mixing of otavite and calcite was determined by a method of successive approximations. Aqueous solutions were presaturated to the supposed equilibrium composition prior to equilibration with solid solutions, and constant pH values, corresponding to constant log ∑∗Kps0 values, indicated stable equilibrium. A recently proposed technique of sequential Bayesian excess parameter estimation was employed for data evaluation which led to the conclusion that the otavite-calcite solid solution series has ideal mixing properties.

Evaluation of the Excess Gibbs Energy of Mixing in Binary Alcohol‐Water Mixtures from the Liquid‐Liquid Partition Data in Electrolyte‐Water‐Alcohol Systems

AbstractThe excess Gibbs energies of mixing at 298.15 K in fully or partially miscible water‐alcohol mixtures (1‐propanol, 2‐propanol, 1‐butanol, 2‐butanol, 2‐methyl‐1‐propanol (isobutanol), 2‐methyl‐2‐propanol (tert. butanol), 1‐pentanol, 2‐pentanol, 1‐hexanol, 1‐heptanol, 1‐octanol, 2‐octanol and cyclohexanol) are reported. They were calculated from the solubility and partition data by applying the Gibbs‐Duhem relationship and changing the standard state of water from water saturated with alcohols to pure water. In the 1‐propanol‐water, 2‐propanol‐water, 1‐butanol‐water, 2‐butanol‐water, 1‐pentanol‐water and 2‐pentanol‐water systems the excess entropies of mixing were also determined.