Integral Molar Enthalpies Of Mixing Research Articles

Calorimetric study of the enthalpy of mixing in the liquid systems Li-Zn and Li-Sn-Zn

Partial and integral molar enthalpies of mixing of binary liquid Li-Zn alloys and ternary liquid Li-Sn-Zn alloys were determined by drop calorimetry at 823 K. The binary system was investigated up to xZn = 0.85 and the integral mixing enthalpy was described with a Redlich-Kister-polynomial. Li-Zn shows an exothermic behavior and a minimum molar mixing enthalpy of about ΔHmix = -11.7 kJ⋅mol−1 at xZn = 0.6. The mixing enthalpy along nine ternary sections of Li-Sn-Zn (A: xLi/xSn ≈ 9:11, B: xLi/xSn ≈ 1:4, C: xSn/xZn ≈ 9:1, D: xSn/xZn ≈ 7:3, E: xSn/xZn ≈ 1:1, F: xLi/xZn ≈ 1:3, G: xLi/xZn ≈ 1:1, H: xLi/xZn ≈ 3:2, I: xLi/xZn ≈ 7:3) was investigated. Solid pieces of Li, Sn, and Zn respectively were dropped to the liquid binary starting alloys in the calorimeter at 823 K. The integral values at the crossing points of the various sections show excellent agreement. The course of the partial and integral enthalpy values along the sections A, D, E, F, G, H, and I indicate multiple-phase regions. The occurrence of such partially liquid and de-mixed liquid regions is discussed and compared with a calculated version of the isothermal section at 823 K which exhibits a large ternary liquid miscibility gap. The experimental ternary data allocated to the fully liquid monophasic regions was numerically fitted based on a Redlich-Kister-Muggianu polynomial for substitutional solutions including ternary interactions. In addition, a comparison with enthalpy values from the extrapolation methods based on binary data according to the Muggianu and Toop model, respectively, is shown. Both models fail to accurately reproduce the experimental values. Iso-enthalpy plots of calculated integral mixing enthalpy for stable and metastable fully homogeneous liquid alloys for the entire ternary system are shown.

Calorimetric studies and thermodynamic calculations of the Ag-Mg system

The experimentally determined integral enthalpy of mixing of liquid Ag-Mg alloys has been presented. Three separate measurements have been made at 991, 1141, and 1272 K with the use of an MHTC 96 Line Evo line drop calorimeter. The values of integral molar mixing enthalpy are characterized by negative deviations from the ideal solutions in the entire concentration range. Based on the obtained calorimetric results and other thermodynamic data available in the literature, the Ag-Mg system has been re-optimized. Additionally, the mechanical properties of the Ag-Mg intermetallic phases have been calculated based on the ab initio calculations.

Calorimetric studies and thermodynamic properties of Li-Pb-Pd liquid alloys

The first ever calorimetric results of integral enthalpies of mixing of liquid Li-Pb-Pd alloys were investigated with the use of an MHTC 96 drop calorimeter. Five separate measurements were performed for such liquid alloys as (Li0.5Pb0.50)1−xPdx, (Li0.25Pb0.75)1−xPdx at 926 K, (Pb0.90Pd0.10)1−xLix at 1005 K, as well as (Li0.75Pb0.25)1−xPdx, and (Pb0.60Pd0.40)1−xLix at 1026 K. Based on the authors' own equations describing the excess Gibbs energy of binary Li-Pb, Li-Pd, and Pb-Pd liquid solutions, and the experimental values of integral molar enthalpy of mixing of liquid Li-Pb-Pd alloys presented in this work, the ternary interaction parameters were calculated. Finally, the values of molar thermodynamic functions of liquid Li-Pb-Pd alloys were calculated and presented in the form of tables and figures.

On the Mg-Pb system. Calorimetric studies and thermodynamic calculations

In this paper, the experimentally determined integral and partial molar enthalpy of mixing of liquid Mg-Pb alloys is presented. Five separate measurements were performed at 1012 and 1014 K with the use of MHTC 96 Line Evo line drop calorimeter. The values of integral molar mixing enthalpy are characterized by negative deviations from the ideal solutions in the entire concentration range. Based on obtained results and other thermodynamic quantities available in the literature the Mg-Pb phase diagram was optimized. The calculated and experimentally obtained values of the integral molar mixing enthalpy are also compared with the Miedema model prediction of the integral molar mixing enthalpy. The formation enthalpy for the Mg2Pb phase is computed by ab initio calculations and equals −5978 J/mol of atoms at 0 K. For the Mg2Pb intermetallic phase, the calculated bulk isothermal and adiabatic modulus, as well as a variation of primitive cell volume and thermal expansion coefficient with the temperature, are presented. Moreover, the heat content of the Mg2Pb intermetallic phase is shown and compared with experimental data for temperatures from 0 K to its melting temperature.

Calorimetric investigation of the Li[sbnd]Pt system

The paper presents the first worldwide, original, thermodynamic measurements for LiPt system. The partial and integral molar enthalpy of mixing of liquid LiPt alloys was determined with the use of MHTC 96 drop calorimeter. The measurements for this binary system were carried out at four different temperatures (622 K, 722 K, 824 K, 926 K), up to a maximum platinum content equalled xPt = 0.34. The values of the integral molar enthalpies of mixing were negative in the entire studied concentration range. The experimental data of liquid LiPt solutions were elaborated by the Redlich-Kister equation. This study has begun the experimental measurements of the LiPt system.

Thermodynamic assessment of the Ga-Sn-Zn system

The integral molar mixing enthalpy of liquid ternary Ga-Sn-Zn alloys has been investigated using drop calorimetry method along five intersections as follows: XGa/XZn = 3/1 at 720 K, xGa/xZn = 1/1 at 718 K and 720 K, xGa/xZn = 1/3 at 718 K, xGa/xSn = 3/17 at 718 K and for xGa/xSn = 1/3 at 720 K. Based on obtained thermodynamic results and those available in the literature the thermodynamic optimization was done using Thermo-Calc software. Next, the phase equilibria in the binary and ternary systems were calculated and the results were compared with those obtained using different experimental techniques.

Enthalpy of mixing of liquid Li-Sb-Sn alloys

The partial and integral molar enthalpies of mixing of liquid Li-Sb-Sn alloys were determined by drop calorimetry at 879 K along ten sections xLi:xSb ≈ 2:3, xLi:xSb ≈ 3:7, xLi:xSn ≈ 1:1, xLi:xSn ≈ 3:5, xLi:xSn ≈ 1:3, xSb:xSn ≈ 4:1, xSb:xSn ≈ 13:7, xSb:xSn ≈ 1:1, xSb:xSn ≈ 1:3 and xSb:xSn ≈ 3:17. A check of enthalpy values at the crossing points of the ten sections proved high accuracy of the measurements. The behavior of the partial and integral enthalpy of mixing along these sections can be grouped into three types, depending on the starting binary systems. For the description of the integral enthalpy over the entire concentration range our experimental 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 models of Muggianu and Toop is given. The entire system shows a strong exothermic behavior with a minimum of ΔmixH ≈ −65,000 J mol−1 in the binary LiSb near to Li3Sb. From experimental ternary data the phase boundary of the liquid at 879 K was derived. It showed that high melting Li3Sb dominates the solidification behavior of the Li-Sb-Sn system.

Thermodynamic description of the Ge-In-Li liquid alloys

The integral molar mixing enthalpy of liquid ternary Ge-In-Li alloys was investigated using drop calorimetry method. Five separate measurements of (In0.75Li0.25)1-xGex, (In0.50Li0.50)1-xGex, and (In0.25Li0.75)1-xGex, (Ge0.50Li0.50)1-xInx and (Ge0.50In0.50)1-xLix liquid alloys at 1076K were studied. Next, the ternary interaction parameters were calculated based on available in literature equations describing the excess Gibbs energy of binary Ge-Li, Ge-In and In-Li liquid solutions (the Redlich-Kister relation), and presented in this work experimental values of mixing enthalpy of liquid Ge-In-Li alloys. Finally, the values of partial and molar thermodynamic functions of liquid ternary Ge-In-Li alloys for the fixed temperature of 1076K and for the constant rations of In/Li, Ge/Li and Ge/In as mentioned above were calculated and presented in the form of tables and figures.

Thermodynamic description of the Ge-Li liquid alloys

This paper presents the calorimetric results of the integral molar mixing enthalpy of liquid Ge-Li alloys, measured at two temperatures: at 1076K and 1176K for the mole fractions of Ge: XGe=0.02–0.69, and XGe=0.71–0.81, respectively. The obtained calorimetric results indicate that the integral molar enthalpy of liquid alloys from this binary system is independent of temperature. The available experimental data of partial or molar Gibbs free energies, together with the enthalpy of mixing, were used for the elaboration of the equation in the form proposed by Redlich and Kister, which describes the dependence of the excess Gibbs energy on the concentration and temperature. The experimental thermodynamic values of the excess free energy, mixing enthalpy change and activity were compared with those calculated with the use of the elaborated Redlich-Kister equation. Moreover, the partial structure factors and the short-range order parameter were calculated and discussed in relation to the thermodynamic properties and the phase diagram of the Ge-Li system.

Thermodynamic description of the Ga-Li-Zn system

The integral molar mixing enthalpy of liquid ternary Ga-Li-Zn alloys has been investigated using drop calorimetry method at different temperatures and along four intersections as follows: XLi/XZn=9/1 at 1006K, XGa/XZn=1/9 at 813K, XGa/XZn=1/1 at 1018K XGa/XZn=9/1 at 1017K. The available in the literature equations describing the excess Gibbs energy of binary Ga-Li, Ga-Zn and Li-Zn systems in the form of the Redlich-Kister relation, and presented in this work experimental values of mixing enthalpy of liquid Ga-Li-Zn alloys were used for the calculation of ternary interaction parameters. Next, the partial and molar thermodynamic function of liquid ternary alloys for the fixed temperature and intersections, and the values were presented in the form of tables and figures.

Calorimetric study and thermodynamic description of liquid In-Li alloys

This paper presents the results of the integral molar mixing enthalpy of liquid In-Li alloys, measured calorimetrically at three temperatures: at 653K for the concentration range of In lower than 0.12at.%, at 940K for the concentration range of In lower than 0.27at.%, and at 994K in the entire concentration range. The obtained experimental values in these ranges of temperatures indicate that the integral molar enthalpy of liquid alloys from this binary system is independent of temperature. The available experimental data of partial or molar Gibbs free energies, together with the enthalpy of mixing, were used for the elaboration of the equation in the form proposed by Redlich and Kister, which describes the dependence of the excess Gibbs energy on the concentration and temperature. The experimental thermodynamic values of the excess free energy, mixing enthalpy change and activity were compared with those calculated with the use of the elaborated Redlich-Kister equation. Moreover, the partial structure factors and short-range order parameter were calculated and discussed in relation to the thermodynamic properties and the phase diagram of the In-Li system.

Thermodynamic properties of Ga-Zn system. Experiment vs model

This paper contains the results of the integral molar mixing enthalpy of Ga-Zn liquid alloys, measured calorimetrically at two temperatures: 722K over the entire concentration range and 923K for the concentration range of Zn lower than 0.5at.%. Experimental values obtained in this range of temperatures indicate that the integral molar enthalpy of liquid alloys of this binary system is temperature independent. The available experimental values of the partial or molar Gibbs energies, together with the enthalpy of mixing, were used for the elaboration of the equation in the form proposed by Redlich and Kister, which describes the dependence of the excess Gibbs energy on the concentration and temperature. The experimental thermodynamic values of the excess Gibbs energy, mixing enthalpy change and activity were compared with those calculated with the use of the elaborated Redlich-Kister equation. Moreover, the partial structure factors and short-range order parameter were calculated and discussed in relation to the thermodynamic properties and the phase diagram of the Ga-Zn system.

Calorimetric Measurements of Liquid Al-Zn Alloys

The integral molar enthalpies of mixing were determined by the drop calorimetric method for binary AL-Zn liquid solutions and compared with the Miedema model as well as the earlier experimental data. The measurements were conducted at two temperatures: 957 K and 1001 K (684 °C and 728 °C), in the entire concentration range. Based on the experimental calorimetric data of this study as well as those available in the literature and the results of the activity studies, the interaction parameters of the Redlich-Kister equation for the liquid Al-Zn phase were worked out with the use of the least square method. The partial and integral Gibbs energies, entropies and enthalpies were calculated and presented in tables and figures. Additionally, the concentration-concentration partial structure factors for the ideal and real Al-Zn solutions were calculated and graphically presented.

Enthalpy of formation of Li2Sb and Li3Sb and mixing enthalpy of liquid Li–Sb alloys

The enthalpies of formation of Li3Sb and Li2Sb intermetallics and mixing enthalpy of liquid Li–Sb alloys were measured with the use of two calorimetric techniques. The direct reaction calorimetric method was used to measure the formation enthalpy of Li3Sb at 942 K (four separate measurements) and Li2Sb at 820 K (three separate measurements). The enthalpies of formation of Li3Sb and Li2Sb were equal to −70.3 ± 0.3 kJ/mol at. and −66.7 ± 0.5 kJ/mol at., respectively. The partial and integral mixing enthalpies were measured in the Li–Sb system by using the drop calorimetry in three separate series starting from the lithium side at 820 K, 942 K, 1024 K and one series starting from the antimony side at 922 K. The integral molar mixing enthalpy has negative values in the whole concentration range. Partial enthalpies of Li agree with available data from electrochemical measurements. Partial enthalpies of Sb are generally constant, which indicates they were measured in the liquid–solid range.

Thermodynamic properties of liquid Ga–Li alloys: Experiment vs. modeling

The integral molar enthalpy of mixing was determined by the drop calorimetric method for binary Ga–Li liquid alloys. The measurements were conducted at three temperatures, i.e. 873K, 992K and 1039K, and in the following concentration ranges: XLi=0.7030 to 0.9801, 0.0908 to 0.3748 and 0.4284 to 0.8282, respectively. A strong negative deviation from the ideal solution was observed, with the minimum value equal to −21.2kJ/mol for XLi=0.5421. The analysis of the experimental data suggests that the integral mixing enthalpy of the Ga–Li liquid solutions is independent of temperature. The values calculated from the Miedema’s model are more positive in comparison to the measured ones, and the maximum difference of about 12.5kJ/mol is observed for the 0.5mol fraction of Li. By way of applying the calorimetric data from this work and the electromotive force measurements of Wen and Huggins and Yatsenko et al., the Redlich–Kister relation was worked out for the excess Gibbs energy of the liquid Ga–Li liquid solutions. The calculated Scc(0) partial structure factor points to the GaLi associates in liquids.

Calorimetric measurements of liquid (Al + Li + Zn) alloys

The integral molar enthalpies of mixing are described by drop calorimetry for liquid alloys based on the (Al+Li) and (Al+Li+Zn) system, with the use of the Setaram MHTC 96 Line Evo calorimeter.The measurements for the (Al+Li) system were carried out at two temperatures, 1023K and 1027K, and compared with the literature data. The integral molar enthalpies of mixing of the liquid binary system over the entire concentration range have negative values. Moreover, for the mole fraction of lithium (XLi=0.5053), the minimum value of the integral enthalpy of mixing of the (Al+Li) system is equal to ΔmixHm=−12.1kJ·mol−1.The experimental studies for the (Al+Li+Zn) system involved measurements at three different temperatures: 942K for the (Al0.90Li0.10)1−xZnx alloy composition; 978K for the (Al0.35Li0.65)1−xZnx and (Al0.65Li0.35)1−xZnx alloy composition and finally, 1014K for the (Al0.50Li0.50)1−xZnx alloy composition.This work presents a complete study of mixing enthalpies in (Al+Li) and (Al+Li+Zn) systems and may therefore provide reference for earlier attempts on calorimetric measurements of the (Al+Li+Zn) system.

Calorimetric measurements and first principles to study the (Ag-Li) liquid system

Integral molar enthalpies of mixing were determined by drop calorimetry for (Ag-Li) liquid alloys at two temperatures (1253 and 873)K. The integral molar enthalpies of mixing are negative in the entire range of concentrations. For the mole fraction of lithium XLi=0.5664, minimum value of the integral enthalpy of mixing of at ΔHm=−11.679kJ/mol was observed. For (Ag-Li) liquid alloys, between T=(873 and 1253)K no temperature dependence was observed. Ab initio molecular dynamics was used to simulate liquid phase structures at T=873K (Li-rich side) and at T=1250K (Ag-rich phase) for subsequent calculation of the vibrational energy, respectively. Our measured and calculated data were compared with literature data.

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

Calorimetric studies and thermodynamic properties of liquid Ag–Ca alloys

Integral molar enthalpies of mixing were determined by drop calorimetric method for Ag–Ca liquid alloys at temperatures (1254 and 1131)K using a Setaram MHTC 96 Line evo calorimeter. Measurements were conducted for alloys of concentrations between 0.0642⩽XCa⩽0.9396 at T=1254K and at 1131K between 0.7564⩽XCa⩽0.9647. The obtained values are negative in the entire range of concentrations and the minimum of the integral enthalpy of mixing equal –24609 J/mol of atoms was observed for 0.4634mol fraction of calcium at T=1254K. The analysis of experimental data showed that most probably ΔHm of Ag–Ca liquid alloys is independent of temperature and that they are almost twice less exothermic than those ones by the partial pressure measurements. Based on the data of this study and that available in the literature, the interaction parameters of Redlich–Kister equation for the liquid Ag–Ca phase were evaluated. The concentration fluctuation structure factor Scc(0) calculated using drawn up in this study equation showed the swallow minimum between Ca concentrations appropriate for Ag9Ca2 and AgCa intermetallic phases what can suggest at two kind of associates in liquid solutions.

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.