Partial Enthalpies Of Mixing Research Articles

Correct Expressions of Enthalpy of Mixing and Excess Entropy from MIVM and Their Simplified Forms

In this work, the author pointed out that empirically to compare the molecular interaction volume model (MIVM) with thermodynamic definition of excess Gibbs energy would result in the incorrect expressions of enthalpy of mixing and excess entropy. The correct expressions of molar and partial molar enthalpies of mixing and excess entropies from the MIVM are consistent thermodynamically and are suggested for replacing their past incorrect ones. The simplification of Zi = Z = 10 is verified to be feasible by the average errors of fitting in the binary liquid alloys M-P (M = Cr, Fe, and Mn) and of predicting in the ternary liquid alloys Fe-Cr-P and Fe-Mn-P by using two coordination numbers of phosphorus ZP = 3.04 and ZP = 8.96. Further, their simplified forms are proposed for predicting easily thermodynamic properties of a multicomponent liquid system and are preliminarily tested to be coordinated mutually in the binary liquid alloys Au-Cu, Cd-Zn, Ca-Zn, and Ni-Pb.

Mixing Enthalpies of Al–Co Melts

The partial mixing enthalpy of aluminum and the integral mixing enthalpies of liquid alloys in the binary Al–Co system are studied by high-temperature calorimetry at 1870 ± 5 K in the composition range 0 < x < 0.25. The energies of forming alloys of aluminum with metals in the second half of the 3d series are compared.

Thermodynamic properties of La–Ga–Al and U–Ga–Al alloys and the separation factor of U/La couple in the molten salt–liquid metal system

The electrochemical behaviour of lanthanum and uranium was studied in fused 3LiCl–2KCl eutectic and Ga–Al eutectic liquid metal alloy between 723 and 823 K. Electrode potentials were recorded vs. Cl−/Cl2 reference electrode and the temperature dependencies of the apparent standard potentials of La-(Ga–Al) and U-(Ga–Al) alloys were determined. Lanthanum and uranium activity coefficients and U/La couple separation factor were calculated. Partial excess free Gibbs energy, partial enthalpy of mixing and partial excess entropy of La-(Ga–Al) and U-(Ga–Al) alloys were estimated.

Enthalpy of Mixing of Liquid Cu-Fe-Zr Alloys at 1873 K (1600 °C)

The enthalpies of mixing of liquid Cu-Fe-Zr alloys were determined at 1873 K (1600 °C) by using a high-temperature isoperibolic calorimeter. The measurements were performed along sections xCu/xFe = 3/1, 1/1, 1/3 in the composition range xZr = 0 to 0.55. The limiting partial enthalpies of mixing of undercooled liquid zirconium in liquid Cu-Fe alloys are (–91.8 ± 8.4) kJ mol−1 (section xCu/xFe = 3/1), (–94.1 ± 12.8) kJ mol−1 (section xCu/xFe = 1/1), and (–107.3 ± 15.6) kJ mol−1 (section xCu/xFe = 1/3). The integral mixing enthalpies are sign changing over the investigated composition range. The Redlich–Kister–Muggianu polynomial was used for the least square fit of the experimental results in order to obtain an analytical expression for the integral mixing enthalpy.

Calorimetric investigation of mixing enthalpy of liquid (Co + Cu + Zr) alloys at T = 1873 K

The enthalpies of mixing of liquid (Co+Cu+Zr) alloys have been determined using the high-temperature isoperibolic calorimeter. The measurements have been performed along three sections (xCo/xCu=3/1, 1/1, 1/3) with xZr=0 to 0.55 at T=1873K. Over the investigated composition range, the partial mixing enthalpies of zirconium are negative. The limiting partial enthalpies of mixing of undercooled liquid zirconium in liquid (Co+Cu) alloys are (−138±18)kJ·mol−1 (the section xCo/xCu=3/1), (−155±10)kJ·mol−1 (the section xCo/xCu=1/1), and (−130±22)kJ·mol−1 (the section xCo/xCu=1/3). The integral mixing enthalpies are sign-changing. The isenthalpic curves have been plotted on the Gibbs triangle. The main features of the composition dependence of the integral mixing enthalpy of liquid ternary alloys are defined by the pair (Co+Zr) and (Cu+Zr) interactions.

Determinations of enthalpy and partial molar enthalpy in the alloys Bi–Cd–Ga–In–Zn, Bi–Cd–Ga–Zn and Au–Cu–Sn

In the present study, the relations of thermodynamic associated with Chou's general solution model (GSM), the models of Muggianu and Toop have been used in order to calculate the mixing enthalpy and partial molar mixing enthalpy of mixing of Bi–Cd–Ga–In–Zn, Bi–Cd–Ga–Zn with equimolar section at a temperature of 730 K and Au–Cu–Sn with the section xAu/xCu = 1/1 on the entire molar fraction range as a function of alloy composition at a temperature of 900 K. Some negativities are reported in the selected alloys mentioned above, particularly at high temperatures for the human health as well as difficulties in experimental measurement and high costs. Moreover, aim of us is to close the current article gap seen in the literature. In order to close the current gap seen in the literature, the article on the thermodynamic properties of the Bi–Cd–Ga–In–Zn alloys are presented in this study.

Determination of the thermodynamic parameters of ionic liquid 1-hexyl-3-methylimidazolium chloride by inverse gas chromatography

Some thermodynamic properties for the ionic liquid 1-hexyl-3-methylimidazolium chloride ([HMIM]Cl) were investigated by inverse gas chromatography (IGC) method at temperatures from 343.15K to 373.15K. The thermodynamic parameters, including weight fraction activity coefficient, Flory–Huggins interaction parameter, partial molar enthalpy of mixing, molar enthalpy of sorption, activity coefficient at infinite dilution and solubility parameter, were obtained to judge the interactions between [HMIM]Cl and the selected solvents at the studied temperatures. The results showed that dichloromethane, chloroform, carbon tetrachloride, ethanol, and carbinol were the favorite solvents for [HMIM]Cl, while n-C6 to n-C9, cyclohexane, benzene, toluene, m-xylene, acetone, ethyl acetate, tetrahydrofuran, ether, methyl, and acetate were bad solvents for [HMIM]Cl.

The calorimetric investigation of the mixing enthalpy of liquid Co–Ni–Zr alloys at 1873 K

The partial mixing enthalpies of zirconium in liquid Co–Ni–Zr alloys have been determined by means of high-temperature isoperibolic calorimeter. The measurements have been performed along the sections x Co/x Ni = 3/1, 1/1, 1/3 in the composition range x Zr = 0–0.50 at 1,873 K. The values of the partial function are negative over the investigated composition range. The limiting partial enthalpies of mixing of undercooled liquid zirconium in liquid Co–Ni alloys are (−140 ± 10) kJ mol−1 (the section x Co/x Ni = 3/1), (−199 ± 11) kJ mol−1 (the section x Co/x Ni = 1/1), and (−193 ± 16) kJ mol−1 (the section x Co/x Ni = 1/3). The integral mixing enthalpies have been calculated by Gibbs–Duhem integration. The calculated values are mainly negative. The obtained experimental results together with literature calorimetric data have been described by a least square fit using the Redlich–Kister–Muggianu polynomial. The integral mixing enthalpy has been calculated over the entire composition range.

Enthalpies of mixing of liquid ternary Co-Li-Sn alloys.

The partial and integral molar enthalpies of mixing of liquid Co–Li–Sn alloys were determined using drop calorimetry. The investigations were performed along six sections by the addition of lithium to mixtures with the compositions x_{text{Co}}/x_{text{Sn}} ≈ 2:98, x_{text{Co}}/x_{text{Sn}} ≈ 1:9, and x_{text{Co}}/x_{text{Sn}} ≈ 3:17 as well as by the addition of cobalt to mixtures with the compositions x_{text{Li}}/x_{text{Sn}} ≈ 3:17, x_{text{Li}}/x_{text{Sn}} ≈ 1:2, and x_{text{Li}}/x_{text{Sn}} ≈ 1:1 at a temperature of 1,173 K. The Co–Li–Sn system shows exothermic behavior of the integral molar enthalpy of mixing in the investigated concentration range. The integral molar enthalpy of mixing of liquid Co–Li system was calculated by Miedema’s model to fit our measured ternary data using an extended Redlich–Kister–Muggianu model for substitutional solutions.Graphical abstract

Partial and integral enthalpies of mixing in the liquid Ag–In–Sn–Zn quaternary alloys

The partial and integral enthalpies of mixing of liquid quaternary Ag–In–Sn–Zn alloys have been measured at 500 °C along seven ternary sections: In0.450Sn0.450Zn0.100, In0.375Sn0.375Zn0.250, In0.333Sn0.333Zn0.334, In0.225Sn0.550Zn0.225, In0.100Sn0.800Zn0.100, In0.550Sn0.225Zn0.225 and In0.800Sn0.100Zn0.100. The measurements were carried out using a Calvet-type microcalorimeter and drop calorimetric technique. Additionally, the enthalpies of mixing of the liquid Ag–In–Sn–Zn have been calculated using the traditional Kohler, Muggianu, Toop and Hillert geometric models and compared to the experimental one.

Thermochemical investigations in the system Cd–Gd

Vapour pressure measurements were performed in terms of a non-isothermal isopiestic method to determine vapour pressures of Cd in the system Cd–Gd between 693 and 1045K. From these results thermodynamic activities of Cd were derived as a function of temperature for the composition range 52–86at.% Cd. By employing an adapted Gibbs–Helmholtz equation, partial molar enthalpies of mixing of Cd were obtained for the corresponding composition range, which were used to convert the activity values of Cd to a common average sample temperature of 773K. The relatively large variation of the activity across the homogeneity ranges of the phases Cd2Gd and Cd45Gd11 indicates that they probably belong to the most stable intermetallic compounds in this system.An activity value of Gd for the two phase field Cd6Gd+L was available from literature and served as an integration constant for a Gibbs–Duhem integration. Integral Gibbs energies are presented between 51 and 100at.% Cd at 773K, referred to Cd(l) and α-Gd(s) as standard states. Gibbs energies of formation for the exact stoichiometric compositions of the phases Cd58Gd13, Cd45Gd11, Cd3Gd and Cd2Gd were obtained at 773K as about −19.9, −21.1, −24.8, and −30.0kJgatom−1, respectively.

The Enthalpies of Mixing of Liquid Ni-Sn-Zn Alloys.

The partial and integral enthalpies of mixing of liquid ternary Ni-Sn-Zn alloys were determined. The system was investigated along two sections x Ni/x Sn ≈ 1:9, x Ni/x Sn ≈ 1:6 at 1073 K and along two sections x Sn/x Zn ≈ 9:1, x Sn/x Zn ≈ 4:1 at 873 K. The integral enthalpy of mixing at each temperature is described using the Redlich-Kister-Muggianu model for substitutional ternary solutions. In addition, the experimental results were compared with data calculated according to the Toop extrapolation model. The minimum integral enthalpy of approx. −20000 J mol-1 corresponds to the minimum in the constituent binary Ni-Sn system, the maximum of approx. 3000 J mol-1 is equal to the maximum in the binary Sn-Zn system.

Thermodynamic properties of Eu-Pt and Al-Eu-Pt melts

The partial and integral enthalpies of mixing of Eu-Pt melts were determined by calorimetry at 1300 K in the composition range 0 < xPt < 0.36. The first partial enthalpy of mixing of Pt was found to be −171 ± 2 kJ/mol. The thermodynamic properties of the Eu-Pt melts were modeled in terms of ideal associated solution theory in wide composition and temperature ranges. The results indicate that the activities of the components have large negative deviations from Raoult’s law and that the integral Gibbs energy and enthalpy of mixing have a minimum near xPt = 0.7. The enthalpy and excess Gibbs energy of mixing of Al-Eu-Pt ternary melts were modeled using our and others’ data and Kohler’s equation.

Enthalpy of mixing of liquid Ag–Bi–Cu alloys at 1073 K

The Ag–Bi–Cu system is among those ternary systems which have not been fully studied yet, in particular the thermodynamic description of the liquid phase is missing. Partial and integral enthalpies of mixing of liquid ternary Ag–Bi–Cu alloys were determined over a broad composition range along six sections: x(Ag)/x(Bi)=0.25, 1, 4; x(Ag)/x(Cu)=1.5; x(Bi)/x(Cu)=1.86, 4. Measurements were carried out at 1073K using two Calvet type microcalorimeters and drop calorimetric technique. It was found that integral enthalpies of mixing are small and endothermic, similarly to limiting binary alloys. The ternary data were fitted on the basis of an extended Redlich–Kister–Muggianu model for substitutional solutions. There are no significant additional ternary interactions.

Thermodynamic Properties of Liquid Fe–Sc Alloys

The partial and integral mixing enthalpies of Fe–Sc melts are determined by calorimetry at 1873 K over the entire composition range. It is established that the minimum enthalpy of mixing is −12.4 ± 0.6 at x Sc = 0.46 and the first partial enthalpies of mixing are $ \Delta \overline{H}_{\mathrm{Sc}}^{\infty }=-43.8\pm 4.4 $ and $ \Delta \overline{H}_{\mathrm{Fe}}^{\infty }=-38.1\pm 3.8 $ (kJ/mol). Thermodynamic properties of the Fe–Sc melts are calculated with the model of ideal associated solutions. It is found that the activities of components have negative deviations from parameters of ideal solutions.

Thermochemical Investigations in the System Cadmium-Praseodymium Relevant for Pyrometallurgical Fuel Reprocessing

Vapor pressure measurements, in terms of a (non-)isothermal isopiestic method, were carried out in the system Cd-Pr between 749 K and 1067 K (476 °C and 794 °C). Thermodynamic activities of cadmium as a function of temperature were obtained directly for the composition ranging from 50.0 to 85.7 at. pct Cd. From these results, partial molar enthalpies of mixing of Cd were derived for the corresponding composition range. The activity values of Cd were converted to an average sample temperature of 823 K (550 °C) by applying an integrated form of the Gibbs–Helmholtz equation. These data indicate that Cd2Pr and Cd58Pr13 are probably the most stable intermetallic compounds in this system. Using an activity value of Pr from the literature as integration constant, Gibbs–Duhem integration was performed, and integral Gibbs energies are presented at 823 K (550 °C), referred to Cd(l) and α-Pr(s). Gibbs energies of formation at the stoichiometric compositions of the phases Cd6Pr, Cd58Pr13, Cd45Pr11, Cd3Pr, and Cd2Pr were determined to be about −18.8, −23.5, −24.8, −28.7, and −33.8 kJ g-atom−1 at 823 K (550 °C), respectively.

Enthalpies of mixing of Al-Ni-La ternary alloys

Partial (for nickel) and integral enthalpies of mixing of liquid alloys of the Al-Ni-La ternary system of three radial sections with a constant ratio of molar fractions of aluminum and lanthanum xAl/xLa = 0.3/0.7 at 1770 ± 5 K and 0.5/0.5 and 0.8/0.2 at 1870 ± 5 K up to molar fractions of nickel in ternary alloys of approximately 0.5–0.6 are studied by means of high-temperature calorimetry in isoperibolic mode. It is found that the enthalpies of mixing of the melts are essentially exothermic values. Based on the energetics of alloy formation of this ternary system, it is concluded that the main contribution is made by interaction between the components of melts of the boundary Ni-Al binary system.

Enthalpies of mixing of liquid Ag–Ga, Cu–Ga and Ag–Cu–Ga alloys

Abstract Using MHTC 96 Setaram high temperature drop calorimeter, partial and integral enthalpies of mixing of liquid alloys were determined in the Ag–Ga, Cu–Ga and in the ternary Ag–Cu–Ga system. The ternary alloys were investigated along two cross-sections at two different temperatures: 1128 K and 1273 K, respectively. Experimental data were used to find ternary interaction parameters by applying the Redlich–Kister–Muggianu model for substitutional solutions, and a full set of parameters describing the concentration dependence of the enthalpy of mixing was derived. The experimental data indicate that the heat of mixing in this system is slightly temperature dependent, at least in the measured temperature range.

Calorimetric studies of Cu–Li, Li–Sn, and Cu–Li–Sn

Integral molar enthalpies of mixing were determined by drop calorimetry for Cu–Li–Sn at 1073K along five sections xCu/xSn≈1:1, xCu/xSn≈2:3, xCu/xSn≈1:4, xLi/xSn≈1:1, and xLi/xSn≈1:4. The integral and partial molar mixing enthalpies of Cu–Li and Li–Sn were measured at the same temperature, for Li–Sn in addition at 773K. All binary data could be described by Redlich–Kister-polynomials. Cu–Li shows an endothermic mixing effect with a maximum in the integral molar mixing enthalpy of ∼5300J·mol−1 at xCu=0.5, Li–Sn an exothermic minimum of ∼ −37,000J·mol−1 at xSn∼0.2. For Li–Sn no significant temperature dependence between 773K and 1073K could be deduced. Our measured ternary data were fitted on the basis of an extended Redlich–Kister–Muggianu model for substitutional solutions. Additionally, a comparison of these results to the extrapolation model of Chou is given.

Thermodynamics of liquid Au–Sb–Sn

Abstract The thermodynamic properties of liquid Au–Sb–Sn are discussed with regard to the energetics of the system. The analysis in terms of the partial excess Gibbs energies and the partial enthalpies of mixing indicates that the presence of Sb in the alloys is energetically unfavourable. In addition, this is found also to be reflected by the concentration–concentration correlations in the long-wavelength limit, S cc ij , which are representative of the fluctuations in local composition occuring in the system. It is suggested that the analysis of the partial quantities in the system might give an extremely helpful contribution to understanding the energetics of multi-component systems.