Partial Enthalpies Of Mixing Research Articles

Mixing Enthalpies of Liquid Cu–Hf–Ti Alloys Studied by High-Temperature Calorimetry

The partial enthalpies of mixing of titanium and hafnium in liquid Cu–Hf–Ti alloys were investigated at 1873 K along the xCu/xHf = 3 (at xTi = 0–0.25) and xCu/xTi = 3 (at xHf = 0–0.5) sections by a hightemperature isoperibolic calorimeter. The limiting partial enthalpy of mixing of supercooled liquid titanium in liquid Cu–Hf alloy is 2.0 ± 1.5 kJ/mol. The limiting partial enthalpy of mixing of supercooled liquid hafnium in liquid Cu–Ti alloy is –43.0 ± 4.5 kJ/mol. The integral mixing enthalpies of components along the investigated sections are calculated by integrating the Gibbs–Duhem equation. The integral mixing enthalpy is negative in the investigated composition range. The comparison of our experimental results with the calculations according to Miedema’s model shows that this model’s prediction for the ΔmixH function should be treated with caution.

Enthalpy of mixing of liquid Ag-Li-Sb alloys

Ag-Li-Sb is a ternary system that has not yet been studied in terms of thermodynamic investigations. The partial and integral enthalpies of mixing of liquid Ag-Li-Sb alloys at 980 K were determined applying drop calorimetry. The investigations were performed along five sections by the addition of lithium to alloys with fixed Ag to Sb molar ratio of 1:1 and 1:4, by the addition of silver to alloys with fixed Li to Sb molar ratio equal to 1:9, 3:7 and 1:1. Experimental data were compared and discussed with Muggianu and Toop extrapolation models. From experimental ternary data the range of liquid at 980 K was deduced.

Enthalpy of Mixing of Ternary Li-Pb-Sb Alloys

Partial and integral enthalpies of mixing of ternary Li-Pb-Sb alloys were measured at 923 and 1023 K with drop calorimetry. In total 12 sections were studied of fixed molar ratios of Li to Pb equal to 1/9, 1/3, 2/3, 1, 3/2, 3, Pb to Sb equal to 3/1, 1, 1/3 and Li to Sb equal to 1/4, 2/3, 1. The measurements were performed by consecutive dropping solid metal samples (Li, Pb or Sb) from ambient temperature into calorimeter chamber. In the first step calibration was performed, in the second binary starting alloy was formed, and finally enthalpies of liquid ternary alloys were measured. Integral enthalpies of mixing are negative in the whole concentration range studied, and tend to a minimum associated with a minimum in Li-Sb system.

Calorimetric investigation of the mixing enthalpy of liquid Co–Cu–Ti alloys at 1873 K

ABSTRACTThe mixing enthalpies of liquid Co−Cu−Ti alloys were investigated at 1873 K using a high-temperature isoperibolic calorimeter. The experiments were performed along sections xCo/xCu = 3/1, 1/3 at xTi = 0 − 0.62 and along section xCo/xCu = 1/1 at xTi = 0 − 0.54. The limiting partial enthalpies of mixing of undercooled liquid titanium in liquid Co−Cu alloys, , are (–128 ± 21) kJ mol–1 (section xCo/xCu = 3/1), (–130 ± 12) kJ mol–1 (section xCo/xCu = 1/1) and (–107 ± 11) kJ mol–1 (section xCo/xCu = 1/3). The integral mixing enthalpies are predominantly negative in the investigated composition range. For the integral mixing enthalpy, an analytical expression was obtained by the least square fit of the experimental results using the Redlich–Kister–Muggianu polynomial.

Mixing enthalpies of liquid Bi–Ni and Ag–Bi–Ni alloys

Partial and integral enthalpies of mixing of liquid Bi-Ni alloys were determined at 1273K, while enthalpies of mixing of ternary Ag–Bi–Ni alloys were determined at 1173K over a broad composition range along six sections: x(Ag)/x(Bi)=3/2, 1, 2/3, 3/7, 1/4; x(Bi)/x(Ni)=4. Measurements were carried out using Calvet type microcalorimeters and drop calorimetric technique. It was found that integral enthalpies of mixing of binary Bi-Ni alloys are small exothermic, whereas integral mixing enthalpies of ternary Ag-Bi-Ni alloys change sign from negative to positive with decreasing Bi content. The ternary data were fitted on the basis of an extended Redlich–Kister–Muggianu model for substitutional solutions, and additional ternary interaction parameters were determined. From experimental ternary data the range of liquid at 1173K was deduced.

Interaction of Components in Cu–Fe Glass-Forming Melts with Titanium, Zirconium, and Hafnium. I. Calorimetric Study of Mixing Enthalpies

The partial mixing enthalpies of titanium, zirconium, and hafnium with liquid copper and iron alloys are studied by high-temperature calorimetry. The studies are carried out at a temperature of 1873 K along the sections with constant ratios x Cu/x Fe = 3, 1, and 1/3. Along all the studied sections, these functions are negative. The integral mixing enthalpies of components in the Cu–Fe–(Ti, Zr, Hf) systems along the studied sections are calculated by integrating the Gibbs–Duhem equation. The ΔH functions for ternary Cu–Fe–(Ti, Zr, Hf) melts are characterized by positive values in the vicinity of the binary Cu–Fe system and show negative values in a range of compositions with x Me > 0.1 (Me = = Ti, Zr, Hf).

Mixing enthalpy of liquid Cu–Hf–Ni alloys at 1873 K

The mixing enthalpies of liquid Cu–Hf–Ni alloys were determined at 1873 K by applying a high-temperature isoperibolic calorimeter. The investigation was performed along the sections xCu/xNi = 3/1, 1/3 at xHf = 0–0.45 and xCu/xNi = 1/1 at xHf = 0–0.40. The limiting partial mixing enthalpies of undercooled liquid hafnium in liquid Cu–Ni alloys are (–158 ± 13) kJ mol−1 (section xCu/xNi = 3/1), (–213 ± 11) kJ mol−1 (section xCu/xNi = 1/1), and (–229 ± 11) kJ mol−1 (section xCu/xNi = 1/3). The integral mixing enthalpies are negative in a wide composition range. The Redlich–Kister–Muggianu polynomial was used for the least square fit of the experimental results to obtain an analytical expression for the integral mixing enthalpy.

The Li-Sb phase diagram part II: Calorimetry and thermodynamic assessment

In this work, drop calorimetry measurements in the Li-Sb system were performed with different starting compositions to determine the enthalpies of mixing as well as liquidus compositions. By adding Sb into a Li bath at 979 K and 1080 K, the liquidus compositions were determined to lie between 0.5 at.% and 1.5 at.% at 979 K and between 1.5 at.% and 2.5 at.% at 1080 K. Furthermore, the limiting partial molar enthalpy of mixing of Li in Sb is −89.5 and −88 kJmol−1at 929 and 979 K, respectively. Likewise, the limiting partial enthalpy of mixing of Sb in Li is −238 kJmol−1at 1080 K. Based on our measurements, the enthalpy of formation for Li3Sb at 979 K was determined to be −76.5 kJmol−1 with respect to the pure solid components. Simultaneously, a thermodynamic description of the Li-Sb system was developed using the CALPHAD approach for the first time. Phase diagram information was taken from Part 1 of this publication, and all other phase diagram, thermochemical, and electrochemical data from the literature were taken into account. The thermodynamic calculations satisfactorily reproduced phase diagram data, enthalpy of mixing, enthalpy of formation and e.m.f. data.

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

A literature overview of Ag-Au-Ga system shows that the information about the liquid phase of this system does not exist. Therefore, using MHTC 96 Setaram high temperature drop calorimeter, partial and integral enthalpies of mixing of liquid alloys were determined at first in the binary systems Ag-Ga, Au-Ga and finally in ternary Ag-Au-Ga system. Next, the ternary alloys were investigated along two sections at two temperatures: 1223K and 1323K. Experimental results were used to find ternary interaction parameters by applying the Redlich–Kister–Muggianu model for substitutional solutions, and consequently a full set of parameters describing the concentration dependence of the enthalpy of mixing was derived. The experimental results indicate that the heat of mixing in this system is temperature independent, at least in the measured temperature range.

Enthalpy of mixing in the Ag-Cd-In ternary liquid phase

Most pressurized water reactor control rods are composed of the Ag-In-Cd neutron absorber alloy (80wt% Ag, 15wt% In, 5wt% Cd). Under accidental conditions such as a loss of coolant, vaporization of the metallic elements from the Ag–In–Cd alloy becomes important to consider in the evaluation of the fission product release to the environment. The enthalpy of mixing has been measured in the ternary Ag-Cd-In liquid for five isopleth sections by silver and cadmium drop dissolution calorimetry at 723K. The limits of the biphasic solid+liquid domain are derived from the slopes changes on the partial mixing enthalpy curves. A tentative partial isothermal section at 723K is proposed.

Enthalpy of mixing of liquid Cu–Fe–Hf alloys at 1 873 K

Abstract In the ternary Cu–Fe–Hf system, the mixing enthalpies of liquid alloys were investigated at 1873 K using a high-temperature isoperibolic calorimeter. The experiments were performed along the sections x Cu/x Fe = 3/1, 1/1 at x Hf = 0–0.47 and along the section x Cu/x Fe = 1/3 at x Hf = 0–0.13. The limiting partial enthalpies of mixing of undercooled liquid hafnium in liquid Cu–Fe alloys, Δ mix H ¯ Hf ∞ ${\Delta _{{\rm{mix}}}}\bar H_{{\rm{Hf}}}^\infty $ , are (−122 ± 9) kJ mol−1 (section x Cu/x Fe = 3/1), (−106 ± 9) kJ mol−1 (section x Cu/x Fe = 1/1), and (−105 ± 2) kJ mol−1 (section x Cu/x Fe = 1/3). In the investigated composition range, the integral mixing enthalpies are sign-changing. For the integral mixing enthalpy, an analytical expression was obtained by the least squares fit of the experimental results using the Redlich–Kister–Muggianu polynomial.

Enthalpy of mixing of liquid Ni–Ti–Zr alloys at 1873 K

The enthalpies of mixing of liquid Ni–Ti–Zr alloys were determined at 1873K by means of a high-temperature isoperibolic calorimeter. The investigations were performed along sections xNi/xTi=4/1 and xNi/xZr=4/1 in the corresponding composition ranges xZr=0–0.41 and xTi=0–0.48. The limiting partial enthalpy of mixing of undercooled liquid zirconium in liquid Ni–Ti alloy is (−192±8)kJmol−1. The limiting partial enthalpy of mixing of undercooled liquid titanium in liquid Ni–Zr alloy is (−130±12)kJmol−1. The integral mixing enthalpies are negative over the investigated composition range. An analytical expression for the representation of the integral mixing enthalpy was obtained and used for the calculation of the function in the whole composition range.

The effect of Al concentration on thermodynamic properties of Nd and U in Ga–Al-based alloys and the separation factor of Nd/U couple in a “molten salt-liquid metal system”

Electrochemical behavior of neodymium and uranium in a molten Nd(U)–(Ga–xAl)/3LiCl–2KCl system (x = 1.5; 5.0 and 20.0 wt% Al) between 723 and 823 K was studied. Temperature dependencies of apparent standard potentials of Nd–(Ga–Al) and U–(Ga–Al) alloys were determined versus Cl−/Cl2 reference electrode. Neodymium and uranium activity coefficients and Nd/U separation factor were calculated. Partial excess free Gibbs energy, partial enthalpy of mixing and partial excess entropy of Nd–(Ga–Al) and U–(Ga–Al) alloys were estimated.

Partial molar enthalpies of organic solutes in the ionic liquid [EMIM][EtSO4

Partial molar excess enthalpies of mixing of the organic liquids methanol, acetonitrile, acetone and propan-1-ol in 1-ethyl-3-methylimidazolium ethyl sulfate ([EMIM][EtSO4]) have been measured using a titration calorimeter. Data have been obtained at 298K, in the case of methanol also at 308K, in the mole fraction range of the organic liquid x2 from 0.005 to 0.05. The results have been extrapolated to infinite dilution for determining enthalpies of dilution at infinite concentrations H¯2,∞E (x2=0). Alternatively values of H¯2,∞E can be obtained from measurements of activity coefficients γ2∞ at different temperatures using the gas chromatographic or the dilutor technique. However, according to our error analysis calorimetric results of H¯2E,∞ are by a factor 2–3 more reliable than the results obtained by the indirect methods.

Thermodynamic properties of Ti in V-Ti-Ta alloys: Effect of Ta addition

The vaporization behaviour of Ti in V-4Ti-xTa (x = 0,1,3,7 wt%) alloys has been investigated in the temperature range 1960–2120 K by Knudsen effusion mass spectrometry (KEMS). The partial pressures and thermodynamic activities of Ti were evaluated directly from the measured ion intensities formed from the equilibrium vapor over the alloy. From the temperature dependence of the activity, the partial molar enthalpy of mixing, partial and excess free energy of mixing has been obtained. The following partial pressures could be obtained over the alloys:V-4Tilogp = −(2.15 ± 0.095) 104/T + (4.38 ± 0.46)1958–2065 KV-4Ti-1Talogp = −(2.64 ± 0.043) 104/T + (6.754 ± 0.21)1961–2070 KV-4Ti-3Talogp = −(2.41 ± 0.043) 104/T + (5.38 ± 0.21)1920–2052 KV-4Ti-7Talogp = −(3.00 ± 0.21) 104/T + (8.02 ± 1.0)2050–2119 KIt was observed that activity of Ti decreases from 0.036 to 0.010 as Ta content increases from 0 to 7 wt% in V-4Ti-xTa alloys.

Thermodynamic Properties of Liquid Silver-Antimony-Tin Alloys Determined from Electrochemical and Calorimetric Measurements

The thermodynamic properties of liquid Ag-Sb-Sn alloys were obtained through use of the drop solution calorimetric method and electromotive force (emf) measurements of galvanic cells with a yttria stabilized zirconia (YSZ) solid electrolyte. The experiments were carried out along Ag0.25Sb0.75, Ag0.5Sb0.5 and Ag0.75Sb0.25 sections of the ternary system in the temperature range from 973 K to 1223 K. From the measured emf, the tin activity in liquid solutions of Ag-Sb-Sn was determined for the first time. The partial and integral enthalpy of mixing were determined from calorimetric measurements at two temperatures. These measurements were performed along two cross-sections: Sb0.5Sn0.5 at 912 K and 1075 K, and Ag0.75Sb0.25 at 1075 K. Both experimental data sets were used to find ternary interaction parameters by applying the Redlich–Kister–Muggianu model of the substitutional solution. Consequently, the set of parameters describing the thermodynamic properties of the liquid phase was derived.

Composition dependences of thermodynamical properties associated with Pb-free ternary, quaternary, and quinary solder systems

In the present study, Chou’s General Solution Model (GSM) has been used to predict the enthalpy and partial enthalpies of mixing of the liquid Ag–In–Sn ternary, Ag–In–Sn–Zn quaternary, and Ag–Au–In–Sn–Zn quinary systems. These are of technical importance to optimize lead-free solder alloys, in selected cross-sections: xIn/xSn = 0.5/0.5 (ternary), Au–In0.1–Sn0.8–Zn0.1, Ag–In0.1–Sn0.8–Zn0.1 (quaternary), and t = xAu/xIn = 1, xIn = xSn = xZn (quinary) at 1173, 773, and 773 K, respectively. Moreover, the activity of In content in the ternary alloy system Ag–In–Sn has been calculated and its result is compared with that determined from the experiment, while the activities of Ag contents associated with the alloys mentioned above have been calculated. The other traditional models such as of Colinet, Kohler, Muggianu, Toop, and Hillert are also included in calculations. Comparing those calculated from the proposed GSM with those determined from experimental measurements, it is seen that this model becomes considerably realistic in computerization for estimating thermodynamic properties in multicomponent systems.

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.

Models for the thermodynamic properties of molten salt systems: Perspectives for ionic liquids

Over the past several years, the Modified Quasichemical Model for short-range ordering has been used successfully to obtain a quantitative thermodynamic description of various multicomponent high temperature inorganic molten salt systems. In the present paper, it was applied to the (LiN(FSO2)2 + KN(FSO2)2 + CsN(FSO2)2) ternary system and the ([C2mim]Cl + AlCl3) binary system (where [C2mim]Cl refers to 1-ethyl-3-methyl-imidazolium chloride), which both involve some ionic liquid compounds. Those two systems were selected as prototypes since experimental data were available for them in the literature. The (LiN(FSO2)2 + KN(FSO2)2 + CsN(FSO2)2) liquid displays relatively little short-range ordering, and the experimental ternary eutectic at T = 309 K or 312 K was satisfactorily reproduced by using solely the optimized binary parameters along with a standard symmetric interpolation method. The ([C2mim]Cl + AlCl3) liquid displays strong negative deviations from ideality, and two different compositions of maximum short-range ordering (near the [C2mim]AlCl4 and [C2mim]Al2Cl7 compositions) were introduced. All available experimental data (phase diagram, emf measurements, partial enthalpies of mixing) were satisfactorily reproduced by the model. The Volume-based Thermodynamics (VBT) from Glasser and Jenkins was used to assess the missing thermodynamic data for [C2mim]Cl, and it was also tested on several ionic liquid compounds of the methyl-imidazolium type.

Thermodynamic Properties of Alloys in the Binary Ca–Ge System

Mixing enthalpies of the liquid alloys in the binary Ca–Ge system were measured by isoperibolic solution calorimetry within the concentration ranges 0 < xGe < 0.08 at 1270–1300 K, and 0.54 < xGe < 1 at 1370–1520 K. The experimental data show great exothermic effects of alloy formation; the partial mixing enthalpies at infinite dilution of the components are \( \Delta \overline{H}_{\text{Ca}}^{\infty } \) = −138 to −140 kJ mol−1 and \( \Delta \overline{H}_{\text{Ge}}^{\infty } \) = −200 kJ mol−1 (at 1300 K). The Gibbs energies and entropies of mixing, activities of the components, and molar fractions of associates in the melts were calculated over a wide temperature range, using models of ideal and regular associated solutions, according to the data in literature for the thermodynamic properties of solid alloys and the phase diagram of the Ca–Ge system.